Job-shop scheduling method and system based on principal component heterogeneous graph neural network

Abstract

The invention relates to the technical field of intelligent workshop scheduling, and provides a job shop scheduling method and system based on a principal component heterogeneous graph neural network, and the method comprises the following steps: determining a constraint condition of a distributed flexible workshop, taking the minimization of the maximum completion time as a control target, and building a problem model according to the constraint condition; obtaining a current state of workshop operation, performing embedding based on a graph attention network to obtain an embedded representation of the state, and extracting an embedded representation of a key state based on principal component analysis after fusion; the obtained embedded representation of the current key state serves as input, the problem model is solved through a strategy network, and probability distribution, distributed to a specific machine tool, of each working procedure serves as an initial solution; and based on the obtained initial solution, performing iterative optimization by adopting an enhanced local search heuristic algorithm to obtain an optimal solution. According to the method, the high efficiency and accuracy of the final solution can be ensured, the defects of a traditional GNN-based method in a subsequent optimization mechanism are overcome, and the method is suitable for the scheduling problem of various types of distributed flexible workshops and has high expansibility and adaptability.

Description

Technical Field

[0001] The present disclosure relates to the technical field related to smart workshop scheduling, and specifically, to a job shop scheduling method and system based on principal component heterogeneous graph neural network. Background Art

[0002] The statements in this section merely provide background information related to the present disclosure and do not necessarily constitute prior art.

[0003] In modern manufacturing, the Job Shop Scheduling Problem (JSSP) is a classic optimization problem that is widely found in many industries such as aviation, automobiles, and electronics. Its goal is to optimize production plans, improve resource utilization, and shorten production cycles by rationally allocating workpieces, processes, and machine tools. However, in a distributed flexible workshop, it is necessary not only to allocate workpieces to different factories, but also to select specific machine tools for each process and determine the order and time of process processing. Multiple constraints such as process priority, machine tool availability, and workpiece group switching time further increase the complexity of the problem. In a multi-factory environment, it is also necessary to ensure that all processes for the same workpiece must be completed in the same factory, which increases the complexity of the scheduling algorithm.

[0004] The inventors found in their research that although conventional optimization algorithms (such as heuristic methods and meta-heuristic algorithms) can achieve good performance on small-scale instances, it is often difficult to obtain high-quality solutions within a reasonable time for large-scale, highly complex distributed scheduling problems. Traditional algorithms have poor adaptability to multi-constraint and multi-objective optimization and cannot fully utilize the characteristic relationships in complex systems.

[0005] In order to solve the above problems, scheduling methods based on deep learning and reinforcement learning have gradually become a research hotspot in recent years. In particular, Graph Neural Network (GNN) performs well in modeling complex relationships and high-dimensional data. However, existing GNN-based scheduling methods still have the following shortcomings: lack of specialized processing for the characteristics of heterogeneous nodes (such as machine tools, workpieces, and factories), resulting in poor feature fusion effects. The importance of feature dimensionality reduction and noise filtering is ignored, and the expressive power of embedded features is limited. The quality of the generated solution is not optimized enough, and there is a lack of effective subsequent optimization mechanisms. Summary of the invention

[0006] In order to solve the above problems, the present invention proposes a job shop scheduling method and system based on principal component heterogeneous graph neural network, which can ensure the efficiency and accuracy of the final solution, overcome the shortcomings of traditional GNN-based methods in subsequent optimization mechanism, and is suitable for various types of distributed flexible shop scheduling problems, with high scalability and adaptability.

[0007] In order to achieve the above objectives, the present disclosure adopts the following technical solutions:

[0008] One or more embodiments provide a job shop scheduling method based on a principal component heterogeneous graph neural network, comprising the following steps:

[0009] Determine the constraints of the distributed flexible workshop, take minimizing the maximum completion time as the control objective, and establish the problem model based on the constraints;

[0010] Obtain the current status of the workshop operation, embed it based on the graph attention network to obtain the embedded representation of the status, and extract the embedded representation of the key status based on principal component analysis after fusion;

[0011] The obtained embedding representation of the current key state is used as input, and the problem model is solved through the policy network to obtain the probability distribution of each process being assigned to a specific machine tool as the initial solution;

[0012] Based on the initial solution obtained, an enhanced local search heuristic algorithm is used to perform iterative optimization to obtain the optimal solution.

[0013] One or more embodiments provide a job shop scheduling system based on a principal component heterogeneous graph neural network, including:

[0014] Model building module: configured to determine the constraints of the distributed flexible workshop, take minimizing the maximum completion time as the control objective, and establish a problem model according to the constraints;

[0015] Embedding module: It is configured to obtain the current status of the workshop operation, embed the status based on the graph attention network to obtain the embedded representation, and extract the embedded representation of the key status based on principal component analysis after fusion;

[0016] Policy network module: configured to take the obtained embedding representation of the current key state as input, solve the problem model through the policy network, and obtain the probability distribution of each process being assigned to a specific machine tool as an initial solution;

[0017] Optimization module: is configured to use an enhanced local search heuristic algorithm based on the obtained initial solution to perform iterative optimization to obtain the optimal solution.

[0018] An electronic device includes a memory and a processor, and computer instructions stored in the memory and executed on the processor. When the computer instructions are executed by the processor, the steps of the job shop scheduling method based on principal component isomorphic graph neural network described in the claim are completed.

[0019] A computer-readable storage medium is used to store computer instructions. When the computer instructions are executed by a processor, the steps in the above-mentioned job shop scheduling method based on principal component heterogeneous graph neural network are completed.

[0020] Compared with the prior art, the present invention has the following beneficial effects:

[0021] The present invention uses a graph attention network to embed the workshop operation status, which can capture the complex node relationships in the workshop (such as the relationship between machine tools, workpieces, and processes), and effectively highlight the characteristics of heterogeneous nodes. The graph neural network is used to model complex system relationships, which effectively improves the feature fusion capabilities under multi-objective and multi-constraint conditions, and enables the scheduling model to have higher performance in large-scale complex instances. Principal component analysis is used for dimensionality reduction and noise filtering to extract the most representative embedded information from high-dimensional features, thereby improving the expressive power of embedded features. The policy network generates a probability distribution of solutions based on these key states, thereby using deep reinforcement learning to quickly generate feasible solutions in complex scheduling problems. Finally, combined with an enhanced local search heuristic algorithm, the quality of the initial solution is further optimized to ensure the efficiency and accuracy of the final solution, overcoming the shortcomings of traditional GNN-based methods in subsequent optimization mechanisms. This method is suitable for various types of distributed flexible workshop scheduling problems and has high scalability and adaptability.

[0022] The advantages of the present disclosure and the advantages of additional aspects will be described in detail in the following specific embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] The accompanying drawings constituting a part of the present disclosure are used to provide a further understanding of the present disclosure. The exemplary embodiments of the present disclosure and the description thereof are used to explain the present disclosure but do not constitute a limitation of the present disclosure.

[0024] Figure 1 is a flow chart of a job shop scheduling method according to Embodiment 1 of the present disclosure;

[0025] Figure 2 is a complete solution representation diagram of an example state of Embodiment 1 of the present disclosure;

[0026] Figure 3 is a training curve diagram of an experimental instance in the experiment of Example 1 of the present disclosure;

[0027] Figure 4 is a comparison result diagram of enhanced local search capability in the experiment of Example 1 of the present disclosure;

[0028] FIG5( a ) is a comparison diagram of variance analysis results of all instances using HGNN and HGNP in the experiment of Example 1 of the present disclosure;

[0029] FIG5( b ) is a comparison chart of variance analysis results of 20×5 instances using HGNN and HGNP in the experiment of Example 1 of the present disclosure;

[0030] FIG5( c ) is a comparison chart of variance analysis results of 30×10 instances using HGNN and HGNP in the experiment of Example 1 of the present disclosure;

[0031] FIG5( d ) is a comparison chart of variance analysis results of 40×10 instances using HGNN and HGNP in the experiment of Example 1 of the present disclosure;

[0032] Figure 6 is a variance analysis comparison chart of the maximum completion time values ​​obtained by nine algorithms in the experiment of Example 1 of the present disclosure;

[0033] Figure 7 It is a Gantt chart of a solution of a specific example in the experiment of Example 1 of the present disclosure. DETAILED DESCRIPTION

[0034] The present disclosure is further described below in conjunction with the accompanying drawings and embodiments.

[0035] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present disclosure. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present disclosure belongs.

[0036] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit exemplary embodiments according to the present disclosure. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof. It should be noted that, in the absence of conflict, the various embodiments in the present disclosure and the features in the embodiments can be combined with each other. The embodiments will be described in detail below in conjunction with the accompanying drawings.

[0037] In view of the problems in the background technology, this paper proposes a distributed flexible job shop scheduling method based on HGNPL of principal component heterogeneous graph neural network (PCA-enhancedHeterogeneous Graph Neural Network, HGNP) combined with local search process. This method can efficiently handle multi-objective and multi-constraint scheduling problems by combining graph attention network (GAT), principal component analysis (PCA) and reinforcement learning strategy, and further significantly improve the scheduling efficiency and effect by enhancing the quality of the local search optimization solution.

[0038] Example 1

[0039] In the technical solutions disclosed in one or more embodiments, Figures 1 to 7 As shown in FIG, the job shop scheduling method based on principal component heterogeneous graph neural network includes the following steps:

[0040] Step 1: Determine the constraints of the distributed flexible workshop, take minimizing the maximum completion time as the control objective, and establish a problem model based on the constraints;

[0041] Step 2: Get the current status of the workshop operation, embed it based on the graph attention network to get the embedded representation of the status, and extract the embedded representation of the key status, i.e. the main features, based on principal component analysis (PCA) after fusion;

[0042] Step 3: Take the obtained embedding representation of the current key state as input, solve the problem model through the policy network, and obtain the probability distribution of each process assigned to a specific machine tool as the initial solution;

[0043] Step 4: Based on the initial solution, an enhanced local search heuristic algorithm is used to perform iterative optimization to obtain the optimal solution.

[0044] In this embodiment, the workshop operation status is embedded and represented through the graph attention network, which can capture the complex node relationships in the workshop (such as the relationship between machine tools, workpieces, and processes), and effectively highlight the characteristics of heterogeneous nodes. The graph neural network is used to model complex system relationships, which effectively improves the feature fusion ability under multi-objective and multi-constraint conditions, so that the scheduling model has higher performance in large-scale complex instances. Principal component analysis is used for dimensionality reduction and noise filtering to extract the most representative embedded information from high-dimensional features, thereby improving the expressive power of embedded features. The policy network generates the probability distribution of solutions based on these key states, thereby using deep reinforcement learning to quickly generate feasible solutions in complex scheduling problems. Finally, combined with the enhanced local search heuristic algorithm, the quality of the initial solution is further optimized to ensure the efficiency and accuracy of the final solution, overcoming the shortcomings of the traditional GNN-based method in the subsequent optimization mechanism. This method is suitable for various types of distributed flexible workshop scheduling problems and has high scalability and adaptability.

[0045] The following is a detailed description of the above steps:

[0046] Step 1: Build a problem model;

[0047] Problem description of distributed flexible workshop operations;

[0048] The distributed flexible workshop is a typical scheduling problem with the following characteristics: First, the scheduling problem involves h factories, each factory has m machine tools, and n workpieces need to be processed. Each workpiece has a certain number of processes, and the processing paths of the workpieces are independent of each other. Each process of each workpiece has multiple parallel available machine tools.

[0049] Based on this, distributed flexible job shop scheduling needs to solve the following three tasks, namely:

[0050] Task 1 is to assign each workpiece to a unique factory;

[0051] Task 2 is to select a unique processing machine tool for each process;

[0052] Task 3 is to sort the workpieces assigned to each machine tool to determine the start and completion time of each process.

[0053] In this embodiment, constraints of the distributed flexible job shop scheduling problem are set, including: at the same time, each process needs to be assigned to a uniquely designated machine tool; each machine tool can only process one process at the same time; all processes of the same workpiece need to be assigned to the same factory for processing; all parallel factories have the same processing capacity and number of parallel machine tools; processing overlap is not allowed; no emergencies, such as machine tool failure, order insertion / cancellation, etc., are considered; only the switching time or preparation time between workpieces in different groups is considered; resources are unlimited, and there is enough buffer space between machine tools; the transportation time of the workpiece is not considered, or it is assumed that the transportation time is included in the processing time of the workpiece; the processing time of each process is pre-determined and fixed.

[0054] Define the symbols of the various parameters involved in the problem description as follows:

[0055] n represents the total number of workpieces, m represents the total number of machine tools, h represents the total number of factories, θ j represents the total number of processes of workpiece j; θ represents the total number of processes θ=∑ j θ j ; j, j' represents the workpiece index, i, k represents the machine tool index, f represents the factory index, r represents the processing position index, O j,q represents the qth process of workpiece j, S j,q,f Indicates process O j,q At the start time of factory f, C j,q,f Indicates process O j,q The completion time at factory f, S k,r,f represents the start time of machining position r of machine tool k in factory f, C k,r,f represents the completion time of machining position r of machine tool k in factory f, P j,q,i Indicates process O j,qMachining time on machine tool i, M j,q Indicates process O j,q The collection of available machines, ST j,j' represents the switching time between workpieces j and j', G j represents the group to which workpiece j belongs, and L represents a very large number;

[0056] Decision variables:

[0057] Y i,j,q,r,f is a 0 / 1 variable. If process O j,q Assigned to machine tool i in factory f for processing at position r, then Y i,j,q,r,f =1; otherwise Y i,j,q,r,f =0;

[0058] Z j,q,f is a 0 / 1 variable. If process O j,q Assigned to factory f for processing, then Z j,q,f =1; otherwise, Z j,q,f =0;

[0059] In this embodiment, the optimization goal of the distributed flexible workshop operation problem is to minimize the maximum completion time. The objective function of the problem model is as follows:

[0060] min C max (1)

[0061]

[0062] Optionally, the constraints include start time and completion time constraints, machine tool and factory allocation related constraints, processing location related constraints, and group switching time related constraints;

[0063] Start time and completion time constraints:

[0064] 1) The start and finish times of machining position r on machine tool k in factory f are not zero, and the start time is less than the finish time:

[0065]

[0066] The start and finish time are key results of scheduling. This embodiment takes into account the switching time between consecutive processes on the same machine tool and defines the start and finish time for each processing position on each machine tool.

[0067] 2) The start and finish time of each process are positive values:

[0068]

[0069] 3) The start time of the subsequent process of the same workpiece should be less than the completion time of the previous process:

[0070]

[0071] 4) Two consecutive processes on the same machine tool do not overlap:

[0072]

[0073] 5) The completion time of processing position r on machine tool k in factory f is equal to the start time plus the processing time of the corresponding process:

[0074]

[0075] 6) The time of two consecutive processes of the same workpiece does not overlap:

[0076]

[0077] Machine tool and factory allocation related constraints:

[0078] 7) Each process can only be performed at one location on one machine tool in one factory, as shown in formula (11);

[0079] 8) Only one factory can be selected for each process, as shown in formula (12);

[0080] 9) All processes belonging to the same factory should select the same factory, as shown in formula (13);

[0081]

[0082] Processing position related constraints:

[0083] 10) Each position on each machine tool shall not process more than one process at a time;

[0084]

[0085] 11) The position of each machine tool should be assigned to the process one by one from left to right, and no blank position is allowed between two processing positions;

[0086]

[0087] 12) The processing location corresponds to the start and completion time between the corresponding operations processed thereon;

[0088]

[0089] 13) If the process is assigned to a plant, it should be assigned to a unique processing location in the plant;

[0090]

[0091] Group switching time related constraints: The group setup time constraint shown in formula (19) ensures that the setup time between two workpieces should be considered if the following conditions are met: (a) the two workpieces are machined at consecutive positions on the same machine tool; (b) the workpieces are not in the same group;

[0092]

[0093] In step 2, obtain the current status s of the workshop operation t , where the current state of the shop floor operations includes the characteristics describing the machine tools, processes, and factories; the characteristics of the OM arc and the characteristics of the JF arc;

[0094] Process characteristics include: processing time, workpiece status, number of unscheduled processes, etc.

[0095] Machine tool characteristics include: available time, utilization rate, etc.;

[0096] Factory characteristics include: number of workpieces allocated, factory utilization, etc.;

[0097] Specifically, the characteristics of the process include:

[0098] (1.1) The status of the current workpiece, indicating whether the current workpiece has been scheduled;

[0099] (1.2) The number of adjacent machines gives the number of candidate machines for the current workpiece |N t (O ij )|;

[0100] (1.3) Processing time ij , if the workpiece has been scheduled, its value is equal to the actual processing time p ijk ;otherwise, in, It represents the average processing time of the workpiece on all candidate machines.

[0101] (1.4) Start time, if O ij If it has already started, Equal to the actual start time of the workpiece, otherwise set to the expected start time.

[0102] (1.5) The number of unscheduled processes in the same workpiece;

[0103] (1.6) The process completion time is equal to the sum of the start time, processing time, changeover time and transportation time;

[0104] Specifically, the characteristics of the machine tool include:

[0105] (2.1) The number of adjacent processes, which indicates the number of processes that the current machine tool can handle;

[0106] (2.2) Machine availability time;

[0107] (2.3) Machine tool utilization, which is used to calculate the ratio between the total processing time of the current machine tool and the current time t;

[0108] (2.4) The current processing step is used to calculate the switching time between two steps processed on the same machine tool;

[0109] Specifically, the factory features include:

[0110] (3.1) The number of workpieces currently allocated by the factory;

[0111] (3.2) Factory utilization is used to calculate the ratio between the total processing time of the current factory and the current time t.

[0112] Characteristics of OM arc: It represents the relationship between the process and the machine tool, which contains only one part, namely Indicates the processing time of the operation on the machine tool.

[0113] Characteristics of JF arcs: They represent the relationship between artifacts and factories. These relationships contain only one part, namely: Indicates that if the artifact is assigned to the corresponding factory, then Set to "1".

[0114] Workshop operation status t , as follows:

[0115]

[0116] like Figure 2 As shown, a complete solution of 6 states is marked. In the figure, factory represents the factory, M1 to M6 represent the machine tools, s1 to s6 represent the states, and the number 5-1 represents the first process of workpiece 5. Similar numbers in the figure are used in the same way;

[0117] In this embodiment, the policy network receives the current state, which is used to predict the action distribution and select the corresponding action according to the state; wherein the action is to allocate the process to the machine tool;

[0118] Actions are used to interact with the environment in certain states; at time t, an appropriate action a is selected t ∈A, take out a pair of processes and machines, and assign the process to the selected machine. The selected process becomes the scheduled process.

[0119] Based on this, the action workspace A is defined as follows:

[0120] A={ <op 1 ,ma 1 >,..., <op n ,ma n >}(22)

[0121] Furthermore, it also includes the determination of a reward function, which provides an optimization direction for strategy learning by quantifying the quality of the scheduling solution (such as the maximum completion time difference). In this embodiment, the reward function is the maximum completion time difference between the current state and the next state. The reward is calculated by the maximum completion time difference between the current state and the next state to promote the optimization of the scheduling strategy.

[0122] Specifically, calculate two states s t and t+1 The difference in the maximum completion time between the two is used as a reward, and the calculation formula is:

[0123] r(s t ,a t ,s t+1 )=C max (s t )-C max (s t+1 )(twenty three)

[0124] In step 2, the current state of the workshop operation is obtained, and the embedded representation of the state is obtained based on the graph attention network. After fusion, the main features are extracted based on principal component analysis (PCA);

[0125] The present invention adopts the Graph Attention Networks (GAT) method to implement machine tool node embedding. This strategy can effectively use the attention mechanism to capture the importance between adjacent nodes. Optionally, the embedding operation includes machine tool node word embedding, process node word embedding, and factory node word embedding;

[0126] The achievable,machine tool node word embedding method includes the embedding steps:

[0127] Step 21.1: Construct the relationship between process nodes and machine tools based on the graph attention network;

[0128] Specifically, given a machine tool M k , for machine tool Mk All adjacent process nodes O ij ∈N t (M k );

[0129] Step 21.2: Concatenate the original features of the process and the original OM arc features processed by the process on the machine tool to construct the feature vector μ ijk ;

[0130]

[0131] in, For process O ij The original characteristics of For process O ij In machine tool M k The original OM arc feature machined on.

[0132] Step 21.3: Based on the constructed feature vector, calculate the tool M k and process O ij The attention coefficient of the connection edge between them. And normalized;

[0133] Machine Tool k and process O ij The calculation formula of the attention coefficient of the connection edge between is:

[0134]

[0135] in,

[0136] The normalized attention coefficient is calculated as follows:

[0137] α ijk =σ(Norm([e ijk ||e kk ])) 1:N

[0138] α kk =σ(Norm([e ijk ||e kk ])) N+1

[0139] Among them, σ(.) is the softmax function, Norm(.) is the normalization function, (.) 1:N Used to get the first N rows, (.) N+1 Used to get the (N+1)th row.

[0140] Step 21.4: Perform weighted fusion on the feature vector of the machine tool itself and the feature vector of its adjacent process nodes to generate the embedding vector ν of the machine tool k; Machine tool M k Embedded k The calculation is as follows:

[0141]

[0142] In this step, the attention coefficient α kk and α ijk The weighting of captures the correlation between the machine tool node and the adjacent process node, and strengthens the representation ability of the overall graph structure.

[0143] A feasible word embedding method for process nodes. In this embodiment, a multilayer perceptron (MLP) mechanism is used to embed the word of process nodes. i,j ;

[0144] Each process node has a d-dimensional output, 2 dh-dimensional hidden layers and an ELU activation function.

[0145] Four MLP layers are used to process the four feature information of the process, namely: O i,j , and O i,j+1 ; The following formula is used to combine these four features to construct the word embedding of the process node:

[0146]

[0147] The feasible method of word embedding of plant nodes uses Graph Attention Networks (GAT) to calculate the word embedding of plant nodes, including the following steps:

[0148] Step 23.1: Based on the relationship characteristics between artifacts and factories The attention coefficient between the factory node and the process node is calculated through the attention mechanism;

[0149] Calculate the plant's characteristic F g and relationship characteristics Edge attention coefficient:

[0150]

[0151] in, Represents the characteristic value of process Oij processed in factory f;

[0152] Step 23.2, normalize the attention coefficients between the factory node and the process node;

[0153] Specifically, using α ig =σ(Norm(eig ))Calculate the normalized attention coefficient;

[0154] Step 23.3: Use normalized weights to normalize adjacent features Weighted summation is performed to generate the embedded representation of the factory node; the calculation formula is:

[0155]

[0156] Furthermore, the HGNN layer stacking method is used to fuse the machine tool node word embedding, process node word embedding, and factory node word embedding;

[0157] In this embodiment, the three embeddings of machine tools, processes, and factories are one HGNN (heterogeneous graph neural network) layer. In order to enhance the fusion of features, this embodiment adopts a stacking method of H HGNN layers with the same structure and different parameters to obtain a better embedding result.

[0158] Most of the current literature uses a pooling strategy to reduce the dimension or aggregate features of the embedding after stacking the HGNN layer, thereby extracting the main features;

[0159] Different from the current literature, this embodiment proposes a PCA-based transformation mechanism to improve the ability to capture and fuse embeddings, so that features can be effectively utilized. Based on the PCA-based transformation mechanism, these embeddings are reduced in dimension or fused, thereby further improving the quality of the embedding results; PCA optimizes the capture and utilization of embedded features to avoid feature loss that may be caused by direct pooling;

[0160] The detailed steps of the transformation process based on PCA are given below, where QR(·) represents QR decomposition and SVD(.) represents singular value decomposition. By combining QR decomposition and singular value decomposition (SVD), the fused embedded features are transformed to extract the main features, that is, the embedded representation of the current key state, including the following steps:

[0161] Step 24.1: Three input word embeddings ν for machine tools, processes, and factories k , μ i,j , g , calculate the average embedding and get Calculating the average embedding provides a reference center value for subsequent dimensionality reduction and optimization of the embedded features;

[0162] Step 24.2, generate a random matrix R n×q , where q = min{n,6};

[0163] The generation of random matrices is used to randomly project the input embedding, providing a data basis for subsequent PCA and singular value decomposition (SVD).

[0164] Step 24.3, based on the random matrix, extract the main direction of the embedded feature through multiple iterations of QR decomposition;

[0165] In this step, the input embedding is mapped into the orthogonal subspace through QR decomposition, which lays the foundation for improving numerical stability and computational efficiency. Through multiple iterations of QR decomposition, the projection results of the subspace are gradually optimized to further extract the main features. The QR decomposition formula is:

[0166]

[0167] The iterative update formula is:

[0168]

[0169] In this step, the main directions of the embedded features are extracted through random projection and orthogonal decomposition;

[0170] Step 24.4, based on the result of QR decomposition, extract the principal component information through SVD decomposition, project the high-dimensional data into low-dimensional space, and retain the main features;

[0171] The SVD decomposition formula is:

[0172]

[0173] Step 24.5: Update the word embedding based on the principal components after SVD decomposition, calculate the row mean of the updated embedding, and obtain the main features after extraction;

[0174] The word embedding update formula is:

[0175] ν' k =v k .V m , μ i,j =μ' i,j .V j ,υ' g =υ g .V g ;

[0176] The updated embedded row mean is:

[0177] ν" k =mean(ν' k ,line)

[0178] μ” i,j =mean(μ i,j ,line)

[0179] υ" g =mean(υ' g ,line)

[0180] In step 3, the embedding of the current problem state is used as input, and the problem model is solved through the policy network to obtain the probability distribution of each process assigned to a specific machine tool as the initial solution;

[0181] Optionally, the policy network adopts a neural network, including an action network (Actor network) and a comment network (Critic network); the network structure and parameters of the Actor network and the Critic network can be the same;

[0182] (1) Action network;

[0183] Optionally, the Actor network includes a two-dimensional hidden layer and a tanh-activated MLP; through the Actor network, the current state s t The activation probability under is calculated as follows:

[0184]

[0185] Then, softmax is applied to all P(at|st) to obtain the following selection probability:

[0186]

[0187] (2) Comment Network

[0188] In this embodiment, the Critic network is also designed as an MLP, and its structure is similar to that of the Actor. The input of the Critic network is different from that of the Actor network. The input of the Critic network has only three parts. The calculation of the Critic network is as follows:

[0189] ψ(s t )=MLP φ [ν" k ||μ” ij ||υ” g ]

[0190] Among them, MLP ω 、MLP φ Represents the Actor network and Critic network MLP operations respectively; It represents the combination of the three eigenvalues ​​of machine tool, process and factory at the l+1th level;

[0191] Furthermore, we adopt proximal policy optimization (PPO) as the policy learning method, where the policy π θ (at |s t ) is achieved by using s t As the neural network input to learn, action a t The probability distribution of is taken as output; the learning parameter χ of the policy network is updated by maximizing L(χ) as follows:

[0192] Step 31: Get the current strategy and use the current strategy π χ Generate trajectories as training samples:

[0193] Generate N trajectories expressed as: (s 1 ,a 1 ,r 1 ),…,(s N ,a N ,r N ), update π χold =π χ .

[0194] Step 32: Calculate the advantage estimate under each trajectory state to provide an evaluation index for strategy optimization;

[0195] For each trajectory t, the formula Calculate odds estimates.

[0196] Among them, V χ (s t ) is the result value calculated by the Critic network, and γ is the discount parameter (set to 0.99 in the present invention).

[0197] Step 33: Based on the advantage estimate and the objective function, update the policy parameters so that the policy achieves a balance between diversity, stability and value function accuracy, and obtain a trained policy network;

[0198] According to (s 1 ,a 1 ,r 1 ,A 1 ),…,(s N ,a N ,r N ,A N ) maximizes the objective function L(χ) and updates the parameter χ using the following formula:

[0199]

[0200] χ 1 =π χ (a t |s t )

[0201] χ 2 =πχold (a t |s t )

[0202]

[0203] Among them, R t represents the reward value obtained in step t, c 1 c 2 are two learning rates;

[0204] The above loss function consists of three parts: the first part ensures that the higher the A t The higher the probability of being selected, the higher the probability of being selected. This embodiment adopts a novel clip function to set the ratio between the new and old probabilities between [1-ε, 1+ε], where ε = 0.2. The second part ensures that the improved V χ (s t ) effect. The third part ensures the randomness of the strategy learning method, which can balance the development and exploration capabilities. The two parameters c1 and c2 are set to 0.50 and 0.01 respectively.

[0205] Step 4: Based on the initial solution, an enhanced local search heuristic algorithm is used to perform iterative optimization to obtain an optimal solution;

[0206] Furthermore, the enhanced local search heuristic algorithm combines the local search heuristic algorithm with the genetic algorithm, combines the matching crossover operator of the genetic algorithm with the local exchange, insertion and reversal operators of the local search heuristic algorithm, performs iterative optimization, and improves the quality of the solution during the optimization process;

[0207] In this step, the global search capability of the genetic algorithm (PMX operator) and the local optimization capability of the local search heuristic algorithm (including exchange, insertion, and reversal) are combined to continuously improve the quality of the solution during the iteration process while avoiding falling into the local optimum, and finally output the optimization result;

[0208] Enhanced local search heuristic algorithm: the input is the initial solution s i ; Output is the updated solution

[0209] Furthermore, an enhanced local search heuristic algorithm is used to perform an iterative optimization process, including:

[0210] Step 41: Randomly generate P s solutions, using the initial solution s i Replace one of the random solutions as the current population;

[0211] In this step, P is randomly generated sA solution can be used to replace the poor solutions in the population, which can enrich the diversity of solutions and provide more potential optimal solutions for subsequent iterative optimization;

[0212] Step 42, using a partially-matched crossover (PMX) operator to optimize the current solution to the solutions in the current population;

[0213] Specifically, the local matching crossover operator exchanges the partial structures of the two parent solutions to generate two child solutions.

[0214] Step 43: Use a local search operator to further optimize the current solution;

[0215] Specifically, local search operators include:

[0216] Exchange operation: Randomly select elements at two positions in the solution and exchange their positions.

[0217] Insertion operation: insert an element at a certain position in the solution to another position;

[0218] Reverse operation: Reverse the order of elements in the solution.

[0219] In this step, fine-grained adjustments to the solution through local search can help correct the suboptimal solution generated by the PMX operator and further improve the performance of the solution;

[0220] Step 44: Compare the quality of the currently generated solution and select the optimal solution based on the set reward function value.

[0221] Step 45, iteratively execute the above steps 42 to 44, reach the set number of iterations, and output the optimal solution.

[0222] In order to illustrate the effect of the method of this embodiment, an experimental analysis was carried out, which is specifically described as follows:

[0223] 3.1 Experimental Environment

[0224] (1) Test example

[0225] This embodiment selects three types of examples to test the performance of the proposed algorithm. The first type of examples are training examples, which are randomly generated during the training process, and 100 examples are selected for each problem size. The training data set contains six different problem sizes, namely (10 workpieces, 5 machine tools), (20 workpieces, 5-machine tools), and (15 workpieces, 10 machine tools). For the problem with 5 machine tools, the number of processes is sampled from U(4,6), and for the example with 10 machine tools, the number of processes is sampled from U(8,12). For the problem with 5 machine tools, the number of candidate machine tools for each process is sampled from U(1,5), and for the example with 10 machine tools, it is sampled from U(1,10). The processing time of each process is sampled from U(1,20). All examples of the present invention have two parallel factories with the same machine tool layout and processing capabilities. The number of groups is set to Table 1 lists the detailed information of the first type of examples.

[0226] The second type of examples is used for comparison with modeling software such as CPLEX. A set of small-scale examples is tested based on the above generation method, including seven different problem sizes, namely (4,2), (4,3), (4,4), (6,2), (6,3), (6,4) and (6,5), where the two numbers represent the number of workpieces and machine tools, respectively.

[0227] The third category of examples is extended from two well-known flexible job shop scheduling benchmark examples, including 10 mk examples (mk01-mk10); three groups of la examples (rdata, edata and vdata), each with 40 examples.

[0228] Table 1 Problem scale

[0229]

[0230] In the table, represents the number of processes for each workpiece j; |M j,q | 2 Indicates the number of optional machine tools for each process; P j,q 3 Indicates the processing time of each process; ST j,j' 4 Indicates the switching time between workpieces; F 5 Indicates the number of groups.

[0231] (2) Experimental configuration

[0232] All training and testing in this example are performed on a 2.60GHz 16-vCPU Intel(R) Xeon(R) Platinum 8350C CPU, an RTX 3090 (24GB) graphics card, and an Ubuntu 20.04 system. The code is implemented in Pytorch. Detailed parameters are shown in Table 2.

[0233] Table 2 System parameters

[0234]

[0235]

[0236] (3) Comparison Algorithms

[0237] The algorithms compared in this invention include three types: the first type is heuristic methods, such as FIFO (First-in-first-out), MOR (Most operations remaining), SPT (Shortest processing time), MWKR (Most work remaining), LPT (Longest processing time). The second type is the deep learning method HGNN. The third type is the meta-heuristic method, such as HGA, HGA-VNS. The comparison index gap is calculated as follows:

[0238] gap=(C max -C B ) / C B ×100%

[0239] Among them, C B is the best objective value obtained by all compared algorithms.

[0240] A detailed description of the comparison algorithm and the control parameters are given below.

[0241] Hybrid genetic algorithm (HGA) was used with the following parameters: population size: 100, crossover probability: 0.7, mutation probability: 0.05, and 500 iterations as the stopping criterion. In order to apply the HGA algorithm to solve the scheduling problem with group switching time, the following modifications were made: (1) the solution representation was modified from a two-dimensional matrix to a three-dimensional matrix, where plant assignments were added; (2) the following components, namely, elite selection, single-point crossover, job-based crossover, exchange, and inversion mutation operators, were used directly.

[0242] A hybrid genetic algorithm with variable neighborhood search (HGA-VNS) was developed with the following parameters: mutation probability: 0.3, elite individual proportion: 0.1, crossover probability: 0.3, combined crossover probability: 0.3%, combined mutation probability: 0.5, population size: 200, and the number of iterations was set to 500 as the stopping criterion. The following components are described as follows: (1) the decoding scheme was modified from a two-dimensional matrix to a three-dimensional matrix; (2) the initialization scheme was directly used as in the literature, except that the plant assignment was generated in a random manner; (3) the elite retention strategy was directly embedded; (4) a hybrid selection operator including tournament selection and elite retention was used; (5) crossover: 0-1 crossover, fixed position crossover (FPX), and improved priority order crossover (IPOX); mutation operators: exchange mutation and swap mutation; and (6) a key order-based VNS operator.

[0243] Random heuristics generate a series of operations in a random manner and select machines and factories to perform the operations in a random manner.

[0244] FIFO heuristic, randomly generates a sequence of operations and selects the first available plant and machine tool for each operation.

[0245] The MOR heuristic first sorts all jobs in non-increasing order according to the number of remaining operations and selects the first job. The above steps are repeated until all operations have been scheduled.

[0246] The SPT heuristic sorts all operations in non-decreasing order according to their average processing time and selects the first available plant and machine tool for each operation.

[0247] The LPT heuristic is different from the SPT heuristic in that the LPT sorts all the processes in non-increasing order based on their average processing time.

[0248] The MWKR heuristic algorithm is different from MOR in that MWKR sorts all jobs in non-increasing order according to the amount of work remaining.

[0249] 3.2 Comparative analysis with CPLEX;

[0250] The method HGNP of this embodiment is compared with the CPLEX software to solve the problem model. The stopping criterion for each instance is set to 5400 seconds. The collected makespan values ​​are compared, as shown in Table 3. It can be concluded that: (1) for a given small-scale instance, the proposed algorithm obtains 12 optimal values ​​in the given 20 instances, while CPLEX obtains 14 better results; (2) the average gap value in the last row shows that the proposed algorithm better considers the average performance; (3) the algorithm finds 7 better results than CPLEX in 5 minutes, which is significantly faster than CPLEX's 1.5 hours.

[0251] Table 3 Comparison results with CPLEX

[0252]

[0253] 3.3 Analysis of Algorithm Generalization Ability

[0254] Figure 3 The training curves of the examples are shown, which shows that the proposed algorithm can learn high-quality strategies based on its own solution experience.

[0255] In order to test the generalization performance of the proposed HGNP algorithm on large problem scale instances, the algorithm was trained on small scale examples and the obtained model was applied to the large scale instance test. To test the generalization performance, two types of results were collected: (1) results using the model trained on small scale examples; and (2) results directly using the model trained on randomly generated large instances.

[0256] The generalization process is divided into four steps, namely: (1) applying the 10-5-2 model to directly solve 15-10, 20-5, 20-10, 30-10 and 40-10; (2) applying the 15-10-2 model to directly solve 20-5, 20-10, 30-10 and 40-10; (3) applying the 20-5 model to directly solve 20-10, 30-10 and 40-10; and (4) applying the 20-10 model to solve 30-10 and 40-10. The number of bars indicates the scale of the example, for example, 10-5-2 means 10 workpieces, 5 machine tools, and 2 factories;

[0257] From the comparison results, we can see that: (1) When the 10-5-2 model is applied to solve the other five medium and large instances, the proposed algorithm can obtain two better results compared with HGNN; (2) When the 15-10-2 model is applied to the other four large instances, HGNP obtains better results. (3) Compared with HGNN, the 20-5 model is also effective for 30-10 and 40-10; (4) The 20-10 model can be directly used for large instances, which represents the knowledge transfer ability of the proposed algorithm; (5) On average, the value of HGNP is 0.76, which is lower than that of HGNN. The gap value shown further verifies the efficiency of the generalization ability of the proposed algorithm.

[0258] 3.4 Analysis of algorithm-enhanced local search capabilities;

[0259] In order to verify the efficiency of the enhanced local search heuristic algorithm, two types of HGNPs are implemented, namely HGNP without local search method and HGNPL with local search process.

[0260] Table 4 shows the comparison results, indicating that: (1) HGNL obtains better results, significantly outperforming HGNP; (2) For small-scale instances such as 10-5, 15-10, and 20-5, the enhanced local search heuristic algorithm significantly improves the network performance, which contributes more to the gap value; (3) For relatively large instances, the two methods are slightly different, which shows that the enhanced local search heuristic does not contribute much to large instances. The main reason is that the stopping criterion is set within a limited time to adapt to realistic production requirements; The average values ​​listed in the last row show that the enhanced local search heuristic algorithm significantly improves the average performance.

[0261] Analysis of Variance (ANOVA) was used to verify whether there were significant differences between the two compared algorithms. Figure 4 ANOVA comparisons with HGNP and HGNPL are presented, showing that the differences between the two algorithms are significant.

[0262] Table 4 Comparison results of enhanced local search capabilities

[0263]

[0264] 3.5 Analysis of the effectiveness of conversion strategy based on principal components

[0265] In order to test the efficiency of the proposed PCA-based transformation mechanism, two methods were encoded, namely, HGNN with an average pooling method; and the HGNP method of the present embodiment in which the pooling method is replaced by a PCA-based mechanism.

[0266] Table 5 shows the results and gap values ​​obtained by the two compared algorithms. It can be seen from the table that: (1) for instances with different problem sizes, the proposed algorithm obtains five better values ​​in the given six instances of different sizes; (2) the average performance shown in the last row verifies that the proposed HGNP algorithm obtains a value of 0.43, which is about 0.06 lower than the HGNN algorithm.

[0267] Table 5 Comparison results of principal component analysis conversion mechanisms

[0268]

[0269] ANOVA Comparison of HGNN and HGNP,Figure 5(a) shows the ANOVA comparison of the two algorithms,instances at all six different scales. Figure 5(b)-5(d) ANOVA comparisons of three different types of instances are shown, namely 20-5, 30-10, and 40-10 instances. Figure 4 It can be concluded that the proposed algorithm is significantly better than HGNN. Therefore, the PCA-based transformation mechanism is an effective way to improve the algorithm.

[0270] 3.6 Comparative Analysis with Heuristic and Metaheuristic Methods

[0271] This embodiment compares some common heuristic and metaheuristic methods. Table 6 shows the maximum completion time values ​​obtained by the nine compared algorithms (i.e., HGA, HGA-VNS, RANDOM, LPT, SPT, MOR, MWKR, FIFO, and HGNP). Table 7 gives the comparison results of the gap value. It can be seen from the two tables that: (1) the proposed HGNP algorithm can obtain four better values ​​in the given six instances of different sizes, especially for relatively large instances, i.e., 20-10, 30-10, and 40-10 instances; (2) HGA is a suboptimal algorithm, obtaining better results in 105 and 205 instances. However, HGA becomes worse in solving large instances. Therefore, HGA is suitable for small instances; (3) For the solution of large instances, MOR is an effective heuristic method for solving 40 10 instances, and MWKR is suitable for 30 10 instances; (4) In short, among the nine algorithms, HGNP is the most effective algorithm, followed by HGA and HGA-VNS. Then, the performance of heuristic methods such as MOR, MWKR, LPT, FIFO, and SPT is worse than these metaheuristic methods, but better than the RANDOM method.

[0272] Figure 6 The ANOVA comparison of the maximum completion time values ​​obtained by the nine algorithms is shown. As can be seen from the figure, the performance of the proposed HGNP algorithm is significantly better than the other eight algorithms, which further verifies the efficiency of the proposed algorithm.

[0273] Table 6 Comparison with heuristic and metaheuristic methods

[0274]

[0275] Table 7 Comparison with heuristic and metaheuristic methods

[0276]

[0277] 3.7 Run time comparison

[0278] In order to make a detailed comparison of the computation time, four algorithms, namely HGA, HGA-VNS, HGNP and HGNPL, are selected. Table 8 collects the comparison results, and it can be concluded that: (1) For all instances of different sizes, HGNP consumes the least computation time, which is about 10% of the other algorithms. Therefore, HGNP can generate relatively satisfactory solutions for instances of different sizes. For example, for a given 100 instances of 40 jobs-10 machine tools, HGNP takes 1.18E+3 seconds, which can generate a near-optimal solution in 11.8 seconds, which is lower than HGA and suitable for realistic production systems; (2) After embedding local search, the time consumed increases slightly for small and medium-sized instances, but the time consumed increases significantly for large instances. Table V shows that the enhanced local search slightly improves the performance. Therefore, embedding the enhanced local search heuristic algorithm to solve small and medium-sized instances is effective, but it is not suitable to add an enhanced local search mechanism for large instances;

[0279] Table 8 Comparison of running time (seconds)

[0280]

[0281] 3.8 Comparison of Classic Examples

[0282] The classic examples selected in this embodiment include four categories, namely mk, rdata, edata and vdata, ranging from 10 jobs to 30 jobs, and 5 machine tools to 15 machine tools. Table 9 shows the comparison results of two factories in eight methods (i.e., HGA, HGA-VNS) and six different models applicable to the classic examples. For example, the "105" method means directly applying the 105 model to solve the corresponding instance.

[0283] From the table, we can conclude that: (1) For 10 mk instances, the “20-10” model achieved the best performance, and the “40-10” model was the second-best method. Compared with the policy network, the results of HGA and HGA-VNS were relatively poor, with gap values ​​of 5.12% and 5.94%, respectively. Note that the computation time consumed by the proposed algorithm is about 20 times lower than that of the metaheuristic algorithm; (2) For 40 rdata instances, the HGA method is the best one; (3) For 40 edata instances, the “40-10” model performed the best, significantly outperforming the two metaheuristic algorithms at 1.68 seconds per instance, which is more suitable for realistic production systems; (4) For 40 vdata instances, the “40-10” model also achieved better results, especially in terms of the minimum computation time. For vdata instances, all models achieved better results than HGA and HGA-VNS, and the policy network consumed about 20 times less time than the metaheuristic algorithm; (5) Overall, the policy network proposed in this study showed efficiency in both solution performance and time consumption.

[0284] Table 9 Comparative analysis of classic examples

[0285]

[0286] Figure 7 The Gantt chart shows a solution for the "e_la11" example, which has 2 plants, 10 jobs, and 5 machines. Each job is represented by a different color, and each operation is represented by a rectangle labeled with the job number and the operation number. It can be clearly seen that all operations are scheduled without violating the constraints.

[0287] Example 2

[0288] Based on Example 1, this embodiment provides a job shop scheduling system based on a principal component heterogeneous graph neural network, including:

[0289] Model building module: configured to determine the constraints of the distributed flexible workshop, take minimizing the maximum completion time as the control objective, and establish a problem model according to the constraints;

[0290] Embedding module: It is configured to obtain the current status of the workshop operation, embed the status based on the graph attention network to obtain the embedded representation, and extract the embedded representation of the key status based on principal component analysis after fusion;

[0291] Policy network module: configured to take the obtained embedding representation of the current key state as input, solve the problem model through the policy network, and obtain the probability distribution of each process being assigned to a specific machine tool as an initial solution;

[0292] Optimization module: is configured to use an enhanced local search heuristic algorithm based on the obtained initial solution to perform iterative optimization to obtain the optimal solution.

[0293] It should be noted here that the various modules in this embodiment correspond one-to-one to the various steps in Example 1, and the specific implementation process is the same, which will not be repeated here.

[0294] Example 3

[0295] Based on Example 1, this embodiment provides an electronic device, including a memory and a processor, and computer instructions stored in the memory and running on the processor. When the computer instructions are executed by the processor, the steps in the job shop scheduling method based on principal component isomorphic graph neural network described in claim Example 1 are completed.

[0296] Example 4

[0297] Based on Example 1, this embodiment provides a computer-readable storage medium for storing computer instructions. When the computer instructions are executed by a processor, the steps in the job shop scheduling method based on principal component isomorphic graph neural network described in Example 1 are completed.

[0298] The above description is only a preferred embodiment of the present disclosure and is not intended to limit the present disclosure. For those skilled in the art, the present disclosure may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present disclosure shall be included in the protection scope of the present disclosure.

[0299] Although the above describes the specific implementation methods of the present disclosure in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present disclosure. Technical personnel in the relevant field should understand that on the basis of the technical solution of the present disclosure, various modifications or variations that can be made by those skilled in the art without creative work are still within the scope of protection of the present disclosure.

Claims

1. A job shop scheduling method based on principal component heterogeneous graph neural network, characterized in that: The steps include: Determine the constraints of the distributed flexible workshop, take minimizing the maximum completion time as the control objective, and establish the problem model based on the constraints; Obtain the current status of the workshop operation, embed it based on the graph attention network to obtain the embedded representation of the status, and extract the embedded representation of the key status based on principal component analysis after fusion; The obtained embedding representation of the current key state is used as input, and the problem model is solved through the policy network to obtain the probability distribution of each process being assigned to a specific machine tool as the initial solution; Based on the initial solution obtained, an enhanced local search heuristic algorithm is used to perform iterative optimization to obtain the optimal solution.

2. The job shop scheduling method based on principal component heterogeneous graph neural network according to claim 1, characterized in that: The embedding operations include machine tool node word embedding, process node word embedding, and factory node word embedding; The machine tool node word embedding method includes the following embedding steps: Construct the relationship between process nodes and machine tools based on graph attention network; The original features of the process and the original OM arc features processed by the process on the machine tool are spliced ​​to construct a feature vector; Based on the constructed feature vector, the attention coefficient of the connection edge between the tool and the process is calculated and normalized; The feature vector of the machine tool itself is weightedly fused with the feature vectors of its adjacent process nodes to generate the embedding vector of the machine tool.

3. The job shop scheduling method based on principal component heterogeneous graph neural network according to claim 2, characterized in that: A multi-layer perceptron mechanism is used to embed the words of process nodes; Alternatively, the plant node word embedding method uses a graph attention network to calculate the word embedding of the plant node, including the following steps: Based on the relationship characteristics between the workpiece and the factory, the attention coefficient between the factory node and the process node is calculated through the attention mechanism; Normalize the attention coefficients between factory nodes and process nodes; The normalized weights are used to perform weighted summation of adjacent features to generate the embedding representation of the plant node.

4. The job shop scheduling method based on principal component heterogeneous graph neural network according to claim 2, characterized in that: The HGNN layer stacking method is used to fuse the machine tool node word embedding, process node word embedding and factory node word embedding.

5. The job shop scheduling method based on principal component heterogeneous graph neural network according to claim 1, characterized in that: Transform the fused embedded features to obtain the embedded representation of the current key state, including the following steps: For the three input word embeddings of machine tool, process and factory, calculate the average embedding; Generate a random matrix; Based on the random matrix, the main direction of the embedded features is extracted through multiple iterations of QR decomposition; Based on the results of QR decomposition, the principal component information is extracted through SVD decomposition, and the high-dimensional data is projected into a low-dimensional space; The word embedding is updated based on the principal components after SVD decomposition, and the row means of the updated embedding are calculated respectively to obtain the embedded representation of the main features after extraction, that is, the current key state.

6. The job shop scheduling method based on principal component heterogeneous graph neural network according to claim 1, characterized in that: The policy network uses a neural network, including an Actor network and a Critic network. The Actor network includes a two-dimensional hidden layer and a tanh-activated MLP. The network structure and parameters of the Actor network and the Critic network are the same. The proximal policy optimization is used to train and learn the policy network, including the following steps: Get the current strategy and use the current strategy π θ Generate trajectories as training samples; Calculate the advantage estimate for each trajectory state to provide an evaluation metric for strategy optimization; Based on the advantage estimate and the objective function, update the policy parameters.

7. The job shop scheduling method based on principal component heterogeneous graph neural network according to claim 1, characterized in that: The enhanced local search heuristic algorithm is used to perform iterative optimization, including: Step 41, randomly generate multiple solutions, and replace one of the random solutions with the initial solution as the current population; Step 42: Use a local matching crossover operator to optimize the current solution for the solutions in the current population; Step 43: Use a local search operator to further optimize the current solution; Step 44: compare the quality of the currently generated solution and select the optimal solution based on the set reward function value; The above steps 42 to 44 are iteratively executed until the set number of iterations is reached and the optimal solution is output.

8. A job shop scheduling system based on principal component heterogeneous graph neural network, characterized in that: include: Model building module: configured to determine the constraints of the distributed flexible workshop, take minimizing the maximum completion time as the control objective, and establish a problem model according to the constraints; Embedding module: It is configured to obtain the current status of the workshop operation, embed the status based on the graph attention network to obtain the embedded representation, and extract the embedded representation of the key status based on principal component analysis after fusion; Policy network module: configured to take the obtained embedding representation of the current key state as input, solve the problem model through the policy network, and obtain the probability distribution of each process being assigned to a specific machine tool as an initial solution; Optimization module: is configured to use an enhanced local search heuristic algorithm based on the obtained initial solution to perform iterative optimization to obtain the optimal solution.

9. An electronic device, characterized in that: It includes a memory and a processor, and computer instructions stored in the memory and running on the processor. When the computer instructions are run by the processor, the steps in the job shop scheduling method based on principal component isomorphic graph neural network described in any one of claims 1 to 7 are completed.

10. A computer-readable storage medium, characterized in that: Used to store computer instructions, which, when executed by a processor, complete the steps of the job shop scheduling method based on principal component isomorphic graph neural network described in any one of claims 1 to 7.

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