Method and system for solving heteromating combinatorial optimization problem based on graph neural network

Abstract

The invention relates to the technical field of artificial intelligence, and particularly discloses a method and a system for solving a heterogeneity combinatorial optimization problem based on a graph neural network, and the method comprises the steps: constructing a heterogeneity graph encoder; carrying out pre-training on the disparity graph encoder to obtain a pre-trained graph encoder; sequentially connecting the pre-trained graph encoder, the linear layer and the softmax layer, and constructing a solution model; and freezing the pre-trained graph encoder, carrying out fine tuning on the linear layer to obtain a heterogeneity combinatorial optimization problem solving model, and solving the heterogeneity combinatorial optimization problem by using the heterogeneity combinatorial optimization problem solving model. According to the method, by designing a disparity graph encoder and utilizing a mechanism of separating nodes from neighbors, disparity features are accurately captured, and meanwhile, a double-layer optimization strategy of node-level contrast learning and graph-level structure entropy optimization is fused, so that the discrimination capability and the globality of the model are improved.

Description

Technical Field

[0001] The present invention relates to the field of artificial intelligence technology, and in particular to a method and system for solving heterogeneous combination optimization problems based on graph neural networks. Background Art

[0002] Combinatorial optimization problems are widely present in modern science and engineering. These problems require finding optimal solutions under specific constraints and resource limitations. Due to the unique advantages of graphs in representing entity relationships, many combinatorial optimization problems can be transformed into graph optimization problems. However, traditional algorithms often face high computational complexity and unsatisfactory performance when dealing with such problems, especially for large-scale instances of NP-hard problems.

[0003] With the development of deep learning technology, especially the outstanding performance of neural networks in various tasks, more and more studies have begun to try to apply it to solve NP-hard combinatorial optimization problems. In such problems, some have the characteristics of homogeneity, that is, adjacent nodes tend to have the same labels or similar features, such as graph partitioning problems. Using the message passing mechanism of graph neural networks, embedding vectors are generated by aggregating node information to guide subsequent optimization tasks. This makes GNN show great potential in solving homogeneous combinatorial optimization problems.

[0004] However, many combinatorial optimization problems exhibit heterogeneity characteristics, that is, adjacent nodes are more likely to have different labels or features. For example, the graph coloring problem requires assigning colors to the nodes of the graph so that adjacent nodes do not have the same color. This type of problem is widely used in practice, but because traditional GNNs are based on the assortativity assumption, they perform poorly in solving heterogeneity problems. Summary of the invention

[0005] The present invention aims to solve the problem that existing graph neural networks have poor performance when dealing with heterogeneous combinatorial optimization problems. To this end, the present invention provides a method and system for solving heterogeneous combinatorial optimization problems based on graph neural networks. By designing a heterogeneous graph encoder and utilizing a mechanism to separate nodes from their neighbors, the heterogeneous characteristics are accurately captured. At the same time, a two-layer optimization strategy of node-level contrast learning and graph-level structural entropy optimization is integrated to improve the discrimination ability and globality of the model. The present invention significantly improves the accuracy, generalization ability and computational efficiency in graph coloring and maximum k-cut problems, and has obvious advantages over a variety of baseline algorithms.

[0006] The present invention provides a method for solving heterogeneous combination optimization problems based on graph neural networks, and the technical solution adopted is as follows: comprising: Constructing a heterogametic graph encoder; Pre-training the heteroassociative graph encoder to obtain a pre-trained graph encoder; Connect the pre-trained graph encoder, linear layer, and softmax layer in sequence to build a solution model; Freeze the pre-trained graph encoder and fine-tune the linear layer to obtain a model for solving heterogeneous combinatorial optimization problems. The heteroassociative combinatorial optimization problem solving model is used to solve the heteroassociative combinatorial optimization problem.

[0007] Furthermore, the working process of the heterogeneity graph encoder is: The initial representation of the node is obtained according to the original graph, and the calculation formula is: in, For Node The initial representation of For Node The features in the original image, is the learnable weight matrix, is a nonlinear activation function; The initial representation of the node extracts the information of 1-hop, 2-hop, 3-hop and 4-hop neighbors through two layers of GNN, and the calculation formula is: in, For Node The initial representation of For Node The first-order neighbor set of excluding itself, For Node The set of second-order neighbors of excluding itself, For Node The information of the 1-hop neighbor, For Node The information of the 2-hop neighbors, For Node The 3-hop neighbor information, For Node The information of the 4-hop neighbors, AGGR() is the aggregation function; Update the node representation by concatenating the initial representation of the node with the information of its 1-hop, 2-hop, 3-hop, and 4-hop neighbors to generate the initial embedding of the node. The calculation formula for updating the representation of a node is: in, For the updated node The expression, For connection operation.

[0008] Furthermore, the aggregation function adopts GraphSAGE.

[0009] Furthermore, in the pre-training stage, node-level optimization and graph-level optimization are performed alternately. In each alternating optimization, multiple node-level optimizations are performed first, and then multiple graph-level optimizations are performed.

[0010] Furthermore, the node-level optimization adopts a contrastive learning strategy. For node u, it takes itself as a positive sample and its L 1-hop neighbor nodes as negative samples. The node-level optimization loss function is The calculation formula is: in, is the representation of node u, is the representation of the i-th negative sample, sim() is the dot product similarity between node pairs, is the temperature parameter.

[0011] Furthermore, the process of graph-level optimization is as follows: Construct the original graph The 2-hop neighbor graph ,based on Construct a 2-layer coding tree and use the structural entropy of the 2-layer coding tree as the loss function for graph-level optimization. Loss Function for Graph-Level Optimization The calculation formula is: in, Represents a 2-hop neighbor graph The sum of the degrees of all vertices in , express Midpoint and The sum of the edge weights between external nodes, express The sum of the degrees of the midpoints, express The sum of the degrees of the midpoints, Represents the coding tree Midpoint The parent node of Represents the coding tree The root node of Represents a 2-hop neighbor graph A node subset, including all nodes in the coding tree T As the leaf point of the ancestor.

[0012] Furthermore, in step 4, during the fine-tuning process, the comprehensive objective function is minimized : in, represents the hyperparameter, represents the utility-based objective function, represents the row vector corresponding to node u in the assignment matrix C, T represents the transpose, E represents the edge set, represents the objective function based on information entropy, and N represents the total number of nodes.

[0013] Furthermore, the process of solving the heterogeneous combination optimization problem using the heterogeneous combination optimization problem solving model is as follows: The original graph is fed into the pre-trained graph encoder to generate the initial node embedding. The initial node embedding passes through two linear layers and a softmax layer to generate a distribution matrix. According to the assignment matrix, the class label is determined for each node using a greedy rounding method.

[0014] The present invention also provides a system for solving heterogeneous combination optimization problems based on graph neural network, and the technical scheme adopted is as follows: comprising: a heterogeneous graph encoder construction module, a pre-training module, a solution model construction module and a fine-tuning module connected in sequence, The heterogametic graph encoder construction module is used to construct a heterogametic graph encoder; The pre-training module is used to pre-train the heterogeneous graph encoder to obtain a pre-trained graph encoder; The solution model construction module is used to connect the pre-trained graph encoder, linear layer, and softmax layer in sequence to construct a solution model; The fine-tuning module is used to freeze the pre-trained graph encoder and fine-tune the linear layer to obtain a model for solving the heterogeneous combinatorial optimization problem; The heteroassociative combination optimization problem solving model is used to solve the heteroassociative combination optimization problem.

[0015] The above one or more technical solutions in the embodiments of the present invention have at least one of the following technical effects: The present invention adopts a network architecture and a two-level optimization strategy for heterogeneity: in network design, a heterogeneity graph encoder is proposed, which improves the traditional message passing mechanism by separating nodes from their neighbors and fusing the information of 1-hop, 2-hop, 3-hop, and 4-hop neighbors. At the node level, an optimization strategy based on contrastive learning is adopted to enhance the distinguishability of adjacent node representations; at the graph level, an optimization strategy based on structural entropy is introduced to optimize the clustering structure from a global perspective, thereby significantly improving the model performance.

[0016] The pre-trained and fine-tuned heterogeneous combinatorial optimization problem-solving model of the present invention has been verified to be superior in a large number of experiments on graph coloring problems and maximum K-cut problems. Compared with a variety of baseline algorithms, it has shown significant improvements in accuracy, computational efficiency, and generalization ability.

[0017] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the technical solutions in the present invention or 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 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.

[0019] Figure 1 It is a flow chart of the method provided by the present invention.

[0020] Figure 2 It is a flow chart of the heterogametic graph encoder provided by the present invention. DETAILED DESCRIPTION

[0021] In order to make the purpose, technical scheme and advantages of the present invention clearer, the technical scheme of the present invention will be clearly and completely described below in conjunction with the drawings in the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in the field without creative work are within the scope of protection of the present invention. The following embodiments are used to illustrate the present invention, but cannot be used to limit the scope of the present invention.

[0022] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the embodiment of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0023] Combine the following Figure 1 to Figure 2 The present invention is further described in detail, and a method and system for solving heterogeneous combination optimization problems based on graph neural network are described as follows: In this embodiment, Figure 1 As shown, a method for solving heterogeneous combination optimization problems based on graph neural networks is provided, comprising the following steps: Step 1: Construct a heterogametic graph encoder.

[0024] This method designs a heterogeneous graph encoder to solve the problem that traditional graph neural networks perform poorly in heterogeneous scenarios. Figure 2 As shown, the working process of the heterogeneity graph encoder is: Original image As the input of the heterogamous graph encoder, according to the original graph Get the initial representation of the node, the calculation formula is: in, For Node The initial representation of For Node The features in the original image, is the learnable weight matrix, is a non-linear activation function.

[0025] This method uses a separation mechanism to update the node's own representation and the representation of its neighbors independently, so that they evolve separately in multiple rounds of propagation.

[0026] In heterogeneous scenarios, the information of 1-hop and multi-hop neighbors has different characteristics. This method extracts the information of 1-hop, 2-hop, 3-hop and 4-hop neighbors from the initial representation of the node through two layers of GNN, and the calculation formula is: in, For Node The initial representation of For Node The first-order neighbor set of excluding itself, For Node The set of second-order neighbors of excluding itself, For Node The information of the 1-hop neighbor, For Node The information of the 2-hop neighbors, For Node The 3-hop neighbor information, For Node The information of the 4-hop neighbors is obtained, and AGGR() is an aggregation function. In this embodiment, the aggregation function adopts GraphSAGE.

[0027] Finally, the initial representation of the node is concatenated with the information of the 1-hop, 2-hop, 3-hop, and 4-hop neighbors to update the representation of the node and generate the initial embedding of the node. .

[0028] The calculation formula for updating the representation of a node is: in, For the updated node The expression, For connection operation.

[0029] Step 2: Pre-train the heterogeneous graph encoder to obtain a pre-trained graph encoder.

[0030] In this step, the heterogeneous graph encoder constructed in step 1 is pre-trained. In the pre-training stage, node-level optimization and graph-level optimization are performed alternately. In each alternating optimization, multiple node-level optimizations are performed first, and then multiple graph-level optimizations are performed. That is, in each alternating optimization, a random original graph G is first generated, and its adjacency matrix is ​​used as the feature matrix. The initial node embedding is generated by the heterogeneous graph encoder, and the node-level optimization loss function is calculated. The parameters of the heterogeneous graph encoder are updated using gradient descent. This node-level optimization is performed for multiple rounds; next, the original graph is constructed. The 2-hop neighbor graph The 2-layer encoding tree T is constructed, and the loss function of the graph-level optimization is used to update the parameters of the heterogeneous graph encoder using gradient descent. The graph-level optimization is performed for multiple rounds. After multiple rounds of alternating optimization, a pre-trained graph encoder with excellent performance is obtained at the end of the pre-training process.

[0031] Node-level optimization uses a contrastive learning strategy to optimize the discrimination of node representation in heterogeneous scenarios. Contrastive learning enhances the discrimination of node representation by bringing positive samples closer and negative samples farther apart in feature space. For node u, take itself as the positive sample and its L one-hop neighbor nodes as negative samples. If the number of one-hop neighbors is less than L, then randomly add negative samples from non-neighbor nodes.

[0032] Node-level optimization loss function The calculation formula is: in, is the representation of node u, is the representation of the i-th negative sample, sim() is the dot product similarity between node pairs, calculated using the inner product, is a temperature parameter used to control the sensitivity of sample distribution in contrastive learning. , the model is able to learn the ability to separate adjacent node representations in the feature space.

[0033] This method introduces a graph-level optimization strategy based on structural entropy to enhance the model's ability to capture global structural features. By minimizing structural entropy, the model can better extract and utilize global information in heterogeneous scenarios, thereby overcoming the local defects of graph neural networks and improving the ability to solve heterogeneous combinatorial optimization problems.

[0034] The process of graph-level optimization is as follows: Construct the original graph The 2-hop neighbor graph .exist In G, nodes only establish edges with their 2-hop neighbors in G to enrich the global information expression of the graph.

[0035] based on Constructing a 2-layer coding tree aims to extract the hierarchical structure of the whole graph through hierarchical clustering. Weight It is defined by the Pearson Correlation Coefficient (PCC) of its embedding representation: in, Indicates the calculation of the Pearson correlation coefficient. Representation Node The value of express The mean of express The standard deviation of Representation Node The value of express The mean of express The standard deviation of .

[0036] The structural entropy of the 2-layer coding tree As the loss function for graph-level optimization.

[0037] Loss Function for Graph-Level Optimization The calculation formula is: in, Represents a 2-hop neighbor graph The sum of the degrees of all vertices in , express Midpoint and The sum of the edge weights between external nodes, express The sum of the degrees of the midpoints, express The sum of the degrees of the midpoints, Represents the coding tree Midpoint The parent node of Represents the coding tree The root node of Represents a 2-hop neighbor graph A node subset of , which includes all leaf nodes in the coding tree T that have node α as their ancestor.

[0038] The global structural information extraction capability of the graph encoder is optimized by minimizing the structural entropy. The lower the structural entropy, the clearer the hierarchical division of the encoding tree, so that the global structural features of the graph can be better captured. By iteratively optimizing the structural entropy, the graph-level optimization strategy of this method can improve the model's ability to learn heterogeneity features globally.

[0039] A coding tree is a tool for representing graph hierarchical structures. It organizes the nodes in a graph hierarchically in the form of a tree. When the height of a leaf node is restricted to K, the tree is called a K-layer coding tree.

[0040] The 2-layer coding tree T is constructed by a greedy algorithm. The specific process is as follows: Initially, All nodes are connected to the root node of the encoding tree as leaf nodes Then, select The two child nodes , perform the merge operation, that is, and Insert a new node between , and ensure that the coding tree after the operation reduces the structural entropy to the greatest extent. Iterate the merging operation until the coding tree becomes a binary tree. If the height of the coding tree exceeds 2 at this time, perform the lifting operation again until the height of the coding tree does not exceed 2. The lifting operation is to select two nodes ,in yes The child nodes of and its subtrees are directly connected to The parent node of the vector is used to ensure that the coding tree after the operation reduces the structural entropy to the greatest extent.

[0041] Step 3: Connect the pre-trained graph encoder, linear layer, and softmax layer in sequence to build a solution model.

[0042] In this embodiment, two linear layers are used, namely a first linear layer and a second linear layer.

[0043] Node initial embedding Through two linear layers and a softmax layer, the distribution matrix is ​​generated , and its calculation formula is as follows: in, represents the learnable weights of the first linear layer, represents the learnable bias of the first linear layer, represents the learnable weights of the second linear layer, represents the learnable bias of the second linear layer, represents the output of the first linear layer, represents the output of the first linear layer, represents the ReLU activation function, express Operation. Assignment Matrix Elements in Indicates that the node The probability of being assigned to the jth class.

[0044] Step 4: Freeze the pre-trained graph encoder and fine-tune the linear layer to obtain a model for solving heterogeneous combinatorial optimization problems.

[0045] In this step, the solution model is fine-tuned. In the fine-tuning stage, the pre-trained graph encoder is frozen and only the linear layer is fine-tuned. An unsupervised objective function based on utility and information entropy is adopted to better adapt to the heterogeneous combinatorial optimization problem.

[0046] This embodiment uses a utility-based objective function to measure the similarity between adjacent nodes, and the calculation formula is: in, represents the utility-based objective function, represents the row vector corresponding to node u in the assignment matrix C, T represents the transpose, E represents the edge set, represents the row vector corresponding to node v in the assignment matrix C. This formula measures the similarity between adjacent nodes by inner product. By minimizing , which can reduce the similarity of adjacent node pairs, thereby effectively capturing heterogametic characteristics.

[0047] In order to improve the uncertainty of node category assignment and avoid falling into a local optimal solution, this embodiment introduces information entropy as the objective function, and the calculation formula is: in, represents the objective function based on information entropy, N represents the total number of nodes, Represents the row vector corresponding to node i in the assignment matrix C. When the probability of a node being assigned to a category is close to 1, the category transfer difficulty of the node is greater, which may lead to falling into a local optimum. By maximizing the information entropy, the uncertainty of node category assignment can be increased, thereby improving the performance of the model.

[0048] Combining the above two objective functions, the comprehensive objective function of this embodiment is as follows: in, represents the hyperparameter, 0, used to balance the two types of objective functions. In the fine-tuning stage, the pre-trained graph encoder is frozen and only the parameters of the linear layer are adjusted to minimize the comprehensive objective function.

[0049] This unified pre-trained-fine-tuned model significantly reduces the time and resources required to train from scratch for different heteroscedastic combinatorial optimization problems and different datasets.

[0050] Step 5: Use the heteroassociative combinatorial optimization problem solving model (HOCO) to solve the heteroassociative combinatorial optimization problem.

[0051] The process of solving the heterogeneous combination optimization problem using the heterogeneous combination optimization problem solving model is as follows: The original graph is fed into the pre-trained graph encoder to generate the initial node embedding. The initial node embedding passes through two linear layers and a softmax layer to generate a distribution matrix. According to the assignment matrix, the category label is determined for each node using a greedy rounding method to obtain a segmentation graph.

[0052] The class label is determined for each node v by the following greedy rounding , that is, assigning the node to the category with the highest probability: in, Indicates the category corresponding to the maximum value.

[0053] The present invention firstly separates the representation of nodes from their neighbors through a heterogeneous graph encoder, and updates the node embedding in combination with multi-hop neighbor features. Secondly, at the node level, the discrimination of adjacent node representations is improved through contrastive learning; at the graph level, the global structural expression capability of the graph is enhanced by structural entropy optimization. Finally, in the fine-tuning stage, the linear layer is optimized based on the objective functions of utility and information entropy to further improve the accuracy of node category assignment and the generalization ability of the model. This method is applicable to a variety of heterogeneous combinatorial optimization problems, and outperforms existing baseline algorithms in graph coloring problems and maximum K-cut problems, with higher performance and efficiency. The present invention effectively extracts heterogeneous features through a pre-trained model, significantly improving the solution efficiency and generalization ability of downstream optimization tasks.

[0054] The following uses an existing graph to verify the solution results of the heterogeneous combinatorial optimization problem solving model (HOCO) obtained in this embodiment on the graph coloring problem, and compares it with other existing baseline algorithms. The test results are shown in Table 1.

[0055] Table 1 Results of this method and the baseline algorithm on the graph coloring problem In Table 1, 1-Insertions_4, myciel5, queen5-5, le450_5a, etc. are existing graphs. Nodes, Edges, Density and Respectively represent the number of nodes, number of edges, edge density and true color number of the graph. Greedy, Tabucol, Run-CSP, PI-SAGE and RelCol represent the baseline algorithms for comparison, HOCO represents the model corresponding to this embodiment, and the values ​​in the table are the minimum number of colors for conflict-free coloring output by each model (the smaller the value, the better).

[0056] This example also verifies the results of HOCO and other baseline algorithms on the maximum K-cut problem (K=3, 4, 5), as shown in Table 2.

[0057] Table 2 Results of this method and the baseline algorithm on the maximum K-cut problem In Table 2, G14, G15, G22, G49, G50, and G55 are existing graphs. Greedy, DSDP, Run-CSP, and PI-GNN represent the baseline algorithms for comparison. The values ​​in the table are the total number of edges between the parts in the optimal partition output by each model (the larger the value, the better). Among them, DSDP takes more than 36 hours to run on graph G55, which is marked as "-".

[0058] This embodiment also conducts ablation experiments on the graph coloring problem and the maximum cut problem, and the results are shown in Tables 3 and 4. In Tables 3 and 4, w / o CL represents that the node-level optimization is removed from the model, w / o SE represents that the graph-level optimization is removed from the model, w / homo represents that the model is changed to a homogeneous network architecture, that is, the classic GNN, w / o PT represents that the node-level optimization and graph-level optimization are removed from the model, and HOCO represents a complete model, that is, no part is removed from the model. The values ​​in Table 3 are the minimum number of colors for conflict-free coloring output by each algorithm (the smaller the value, the better). The values ​​in Table 4 are the total number of edges between the parts in the optimal partition output by each algorithm (the larger the value, the better).

[0059] Table 3 Ablation experiment results of graph coloring problem Table 4 Ablation experiment results of the maximum cut problem The present invention also provides a system for solving heterogeneous combination optimization problems based on graph neural networks, and the technical solution adopted is as follows: it includes: a heterogeneous graph encoder construction module, a pre-training module, a solution model construction module and a fine-tuning module connected in sequence.

[0060] The heterogametic graph encoder construction module is used to construct a heterogametic graph encoder; The pre-training module is used to pre-train the heterogeneous graph encoder to obtain a pre-trained graph encoder; The solution model construction module is used to connect the pre-trained graph encoder, linear layer, and softmax layer in sequence to construct a solution model; The fine-tuning module is used to freeze the pre-trained graph encoder and fine-tune the linear layer to obtain a model for solving the heterogeneous combinatorial optimization problem; The heteroassociative combination optimization problem solving model is used to solve the heteroassociative combination optimization problem.

[0061] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for solving heterogeneous combination optimization problems based on graph neural networks, characterized in that: include: Constructing heterogametic graph encoders; Pre-training the heteroassociative graph encoder to obtain a pre-trained graph encoder; Connect the pre-trained graph encoder, linear layer, and softmax layer in sequence to build a solution model; Freeze the pre-trained graph encoder and fine-tune the linear layer to obtain a model for solving heterogeneous combinatorial optimization problems. The heteroassociative combinatorial optimization problem solving model is used to solve the heteroassociative combinatorial optimization problem.

2. A method for solving heterogeneous combination optimization problems based on graph neural networks according to claim 1, characterized in that: The working process of the heterogeneity graph encoder is: The initial representation of the node is obtained according to the original graph, and the calculation formula is: in, For Node The initial representation of For Node The features in the original image, is the learnable weight matrix, is a nonlinear activation function; The initial representation of the node extracts the information of 1-hop, 2-hop, 3-hop and 4-hop neighbors through two layers of GNN, and the calculation formula is: in, For Node The initial representation of For Node The first-order neighbor set of excluding itself, For Node The set of second-order neighbors of excluding itself, For Node The information of the 1-hop neighbor, For Node The information of the 2-hop neighbors, For Node The 3-hop neighbor information, For Node The information of the 4-hop neighbors, AGGR() is the aggregation function; Update the node representation by concatenating the initial representation of the node with the information of its 1-hop, 2-hop, 3-hop, and 4-hop neighbors to generate the initial embedding of the node. The calculation formula for updating the representation of a node is: in, For the updated node The expression, For connection operation.

3. A method for solving heterogeneous combination optimization problems based on graph neural network as claimed in claim 2, characterized in that: The aggregation function uses GraphSAGE.

4. A method for solving heterogeneous combination optimization problems based on graph neural network according to claim 1, characterized in that: During the pre-training phase, node-level optimization and graph-level optimization are performed alternately. In each alternating optimization, multiple node-level optimizations are performed first, and then multiple graph-level optimizations are performed.

5. A method for solving heterogeneous combination optimization problems based on graph neural network as claimed in claim 4, characterized in that: The node-level optimization adopts a contrastive learning strategy. For node u, it takes itself as a positive sample and its L one-hop neighbor nodes as negative samples. The node-level optimization loss function is The calculation formula is: in, is the representation of node u, is the representation of the i-th negative sample, sim() is the dot product similarity between node pairs, is the temperature parameter.

6. A method for solving heterogeneous combination optimization problems based on graph neural network according to claim 4, characterized in that: The process of graph-level optimization is as follows: Construct the original graph The 2-hop neighbor graph ,based on Construct a 2-layer coding tree and use the structural entropy of the 2-layer coding tree as the loss function for graph-level optimization. Loss Function for Graph-Level Optimization The calculation formula is: in, Represents a 2-hop neighbor graph The sum of the degrees of all vertices in , express Midpoint and The sum of the edge weights between external nodes, express The sum of the degrees of the midpoints, express The sum of the degrees of the midpoints, Represents the coding tree Midpoint The parent node of Represents the coding tree The root node of Represents a 2-hop neighbor graph A node subset, including all nodes in the coding tree T As the leaf point of the ancestor.

7. A method for solving heterogeneous combination optimization problems based on graph neural network according to claim 1, characterized in that: In step 4, during the fine-tuning process, minimize the comprehensive objective function : in, represents the hyperparameter, represents the utility-based objective function, represents the row vector corresponding to node u in the assignment matrix C, T represents the transpose, E represents the edge set, represents the objective function based on information entropy, and N represents the total number of nodes.

8. The method for solving heterogeneous combination optimization problems based on graph neural network according to claim 1, characterized in that: The process of solving the heterogeneous combination optimization problem using the heterogeneous combination optimization problem solving model is as follows: The original graph is fed into the pre-trained graph encoder to generate the initial node embedding. The initial node embedding passes through two linear layers and a softmax layer to generate a distribution matrix. According to the assignment matrix, the class label is determined for each node using a greedy rounding method.

9. A system for solving heterogeneous combination optimization problems based on graph neural networks, characterized in that: The method for solving heteroassociative combinatorial optimization problems based on graph neural networks according to any one of claims 1 to 8 comprises: a heteroassociative graph encoder construction module, a pre-training module, a solution model construction module and a fine-tuning module connected in sequence, The heterogametic graph encoder construction module is used to construct a heterogametic graph encoder; The pre-training module is used to pre-train the heterogeneous graph encoder to obtain a pre-trained graph encoder; The solution model construction module is used to connect the pre-trained graph encoder, linear layer, and softmax layer in sequence to construct a solution model; The fine-tuning module is used to freeze the pre-trained graph encoder and fine-tune the linear layer to obtain a model for solving the heterogeneous combinatorial optimization problem; The heteroassociative combination optimization problem solving model is used to solve the heteroassociative combination optimization problem.

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