A dynamic difference flow hypergraph neural network scheduling method for production order insertion

Abstract

The present application belongs to the field of information technology and intelligent manufacturing technology, and particularly relates to a dynamic difference flow hypergraph neural network scheduling method for production order insertion. The present application firstly acquires order data, equipment data, process constraint data and current scheduling state data within a production cycle; secondly, uniformly represents discrete attributes and continuous attributes of orders; thirdly, constructs a dynamic hypergraph model based on order nodes and equipment nodes, inputs the dynamic hypergraph into a hypergraph neural network for feature propagation, and obtains high-order embedding representation of order nodes and equipment nodes; further, constructs a production scheduling network flow model based on the high-order embedding representation; finally, comprehensively scores candidate positions, determines optimal insertion equipment and insertion time period, and executes updating according to a local rearrangement strategy to output a final scheduling scheme after order insertion. The present application realizes integrated processing of order feature representation, high-order relationship modeling and dynamic disturbance quantification in the production order insertion scenario.

Description

Technical Field

[0001] This invention belongs to the field of information technology and intelligent manufacturing technology, specifically relating to a dynamic differential flow hypergraph neural network scheduling method for production order insertion. Background Technology

[0002] In discrete manufacturing, especially in production scenarios characterized by high variety, small batches, multiple specifications, and strong process constraints, Advanced Planning and Scheduling (APS) systems are key tools for achieving efficient production coordination. APS aims to improve production efficiency and resource utilization through the meticulous arrangement of production elements such as orders, equipment, processes, and time. However, frequent disruptions during actual production execution, such as last-minute order insertions, delivery date changes, and equipment status fluctuations, pose a significant challenge to the stability of existing production schedules. In particular, order insertions, due to their suddenness and uncertainty, can easily disrupt established production rhythms, leading to a series of problems such as localized equipment load imbalances, a surge in mold changeovers, order batch delays, and a decline in the overall stability of the production schedule.

[0003] To address the aforementioned order insertion scheduling problem, existing technical solutions can be mainly categorized as follows:

[0004] The first category is scheduling methods based on human experience or fixed rules. These methods typically determine the insertion position based on simple criteria such as order priority, delivery date, or equipment idle status. While simple to operate and fast to calculate, they rely excessively on expert knowledge, lack the ability to quantitatively analyze the global coupling relationships of the system, and are difficult to adapt to dynamic and ever-changing production environments.

[0005] The second category comprises optimization scheduling methods based on mathematical programming, heuristic algorithms, or network flow models. These methods mathematically optimize order allocation and equipment load by establishing objective functions (such as minimizing delay costs or maximizing equipment utilization) and constraints. Although theoretically, relatively optimal solutions can be obtained, when facing large-scale, highly dynamic order insertion scenarios, the model recalculation time is long, the real-time response capability is insufficient, and local disturbances are often amplified into global reordering, resulting in huge computational overhead.

[0006] The third category is scheduling methods based on intelligent algorithms. For example, graph neural networks and other models are used to learn the correlation features between orders and equipment to assist in production scheduling decisions. However, these methods can only capture binary relationships between pairs of nodes and are insufficient in expressing the multi-dimensional, high-order coupling relationships that naturally exist between orders, processes, and equipment. In addition, these methods have difficulty effectively quantifying the propagation effects of changes in task allocation before and after order insertion, as well as fluctuations in equipment capacity, in the production chain, resulting in limited ability of the model to perceive and adapt to dynamic disturbances.

[0007] In addition to the limitations shared by the aforementioned methods, existing technologies also have significant shortcomings in processing order attributes. Order data typically includes discrete attributes (such as order type and specifications) and continuous attributes (such as quantity, delivery date, and process time). Traditional feature construction methods often treat these two attributes separately or perform simple encoding, which easily leads to sparse feature representations and loss of key correlation information. This results in poor generalization ability of the scheduling model, rigid local reordering strategies, and difficulty in accurately supporting the rapid identification and dynamic optimization scheduling of production order insertions in discrete manufacturing scenarios.

[0008] Patent CN114186791A proposes a dynamic scheduling method for the assembly and production of complex equipment products with multiple models and small batches. Although it considers various disturbance factors, its core relies on a hybrid variable neighborhood solution algorithm and particle swarm optimization, essentially remaining a mathematical heuristic framework. It does not provide new solutions for high-order relationship modeling and dynamic disturbance quantification. Similarly, patent CN115239199A discloses a distributed scheduling method for flexible mixed-line production in the automotive industry. It determines the production schedule through reinforcement learning, but focuses on distributed architecture and communication mechanisms, failing to explicitly express the complex coupling relationships between orders, processes, and equipment. It lacks effective modeling methods for the local differential flow evolution and disturbance propagation caused by order insertion.

[0009] In summary, existing production order insertion scheduling technologies generally suffer from the following shortcomings: insufficient expression of high-order coupling relationships, making it difficult to uniformly represent the multi-faceted relationships between orders, processes, and equipment; difficulty in quantifying dynamic disturbance processes, lacking quantitative descriptions of changes in task allocation, equipment capacity, and disturbance propagation before and after order insertion; high rescheduling costs, with local disturbances easily triggering large-scale rescheduling; and the hybrid feature construction method of order discrete and continuous attributes leading to information sparsity and weak model generalization ability. Therefore, there is an urgent need for an intelligent scheduling method that can achieve high-order relationship modeling, dynamic differential flow quantification, and fast local rescheduling to meet the real-time, accuracy, and stability requirements of production order insertion processing in discrete manufacturing scenarios. Summary of the Invention

[0010] The technical problem to be solved by this invention is to provide a dynamic differential flow hypergraph neural network scheduling method for production order insertion. By using a unified feature representation of the discrete and continuous attributes of orders, a dynamic hypergraph composed of order nodes and equipment nodes is constructed. Combined with the changes in task allocation and equipment capacity before and after order insertion, a dynamic differential flow representation is formed, which realizes rapid identification, local rearrangement and dynamic optimization scheduling of new orders, thereby improving the real-time performance, accuracy and stability of production order insertion processing in discrete manufacturing scenarios.

[0011] The technical solution adopted is as follows:

[0012] A dynamic differential flow hypergraph neural network scheduling method for production order insertion includes the following steps:

[0013] Step S1: Obtain order attributes, equipment parameters, process constraint data, and current production scheduling status data within the production cycle;

[0014] Step S2: Perform unified feature representation on discrete and continuous attributes of orders: normalize the continuous attributes of order quantity and priority; tokenize and embed the discrete attributes of brand, specifications, pattern, level and size; fuse the above processed attribute features according to preset weights to generate order feature vectors; stack all order feature vectors to form an order node feature matrix.

[0015] Step S3: Construct a dynamic hypergraph model based on order nodes and equipment nodes; the node set consists of the order node set and the equipment node set; construct similar order clustering hyperedges based on order cosine similarity and threshold, construct process matching hyperedges based on process matching indicators, and represent the membership relationship between nodes and hyperedges through an association matrix;

[0016] Step S4: Input the dynamic hypergraph model into the hypergraph neural network for feature propagation to obtain the high-order embedding representation Z of the order node and the device node;

[0017] A production scheduling network flow model is constructed based on the higher-order embedded representation Z; the allocation flow of orders on the equipment set of the forming stage, the equipment set of the vulcanization stage, and the discrete time set is defined; process continuity constraints, flow conservation constraints, equipment capacity constraints, and process feasibility constraints are set; the initial remaining capacity before the equipment order is inserted and the updated remaining capacity after the order is inserted are calculated, and a dynamic differential flow model is constructed based on the difference between the two to quantify the local disturbance caused by the new order to the original scheduling resource structure;

[0018] Step S5: Construct a set of candidate insertion positions based on process feasibility, time feasibility, remaining capacity, and dynamic differential flow disturbance; use a multi-objective evaluation function to comprehensively score the candidate positions, determine the optimal insertion equipment and insertion time period; then execute the scheduling update according to the local rearrangement strategy of direct assignment of idle equipment, order priority adjustment, merging or delaying similar orders, and output the final scheduling scheme after order insertion.

[0019] The multi-objective evaluation function includes: maximum completion time, delivery deviation, delay penalty, task completion rate, mold change loss, and order insertion disturbance cost.

[0020] Preferably, in step S1, the order data includes at least brand, specifications, pattern, level, size, quantity, priority, and delivery date; the equipment data includes at least equipment brand, minimum processing size, maximum processing size, fixed size, rated capacity, mold change loss, and equipment operating status; the process constraint data includes at least order-equipment process matching relationship, process continuity constraints, process feasibility markers, mold change rules and mold change loss, similar order continuous processing rules, equipment access set for each process stage, and processing time and resource usage parameters related to process execution; the production scheduling status data includes at least the current process of each order, allocated equipment, estimated completion time, remaining unscheduled output, and current remaining capacity of each piece of equipment.

[0021] Preferably, in step S2, the Order2Ten order feature extraction method is used to uniformly map the multidimensional heterogeneous attributes of orders into a low-dimensional dense representation suitable for subsequent modeling.

[0022] Preferably, before constructing the Order2Ten model, the numerical and discrete attributes of the order are preprocessed. For continuous or quantifiable attributes such as quantity, delivery date, guaranteed production quantity, and priority, the Min-Max normalization method is used to map them to a uniform scale. The calculation formula is as follows:

[0023] ;

[0024] In the formula, The original data value; These are the minimum and maximum values ​​of the data, respectively. The value is the normalized value;

[0025] Secondly, order attributes are divided into three categories: indexed attributes, discrete attributes, and continuous attributes. A weighted input representation of order attributes is established, the expression of which is:

[0026] ;

[0027] in, Indicates order priority. These represent the brand, specifications, pattern, grade, size, and order quantity, respectively. These are the weight coefficients for each attribute. This is a mapping matrix (which enables unified input of attributes for different types of orders).

[0028] Then, the discrete attributes are tokenized and embedded, and feature learning is performed by combining the internal attribute context of the order and the cross-order sequence context to obtain the low-dimensional semantic vector of each discrete attribute.

[0029] Furthermore, the discrete attribute embedding vectors are weighted and aggregated according to their attribute weights to obtain the discrete attribute aggregated vector of the order:

[0030] ;

[0031] in, For discrete attribute sets, For orders The embedding vector on the j-th discrete attribute, For the corresponding attribute weights;

[0032] Based on the discrete attribute embeddings, the normalization result of the continuous attributes is shown in the following equation:

[0033] ;

[0034] In the formula, C i It is a continuous attribute aggregation vector of the order. Indicates order The quantity normalization result;

[0035] After obtaining the discrete attribute aggregate vector, it is concatenated with the continuous attribute vector, and then the final order feature vector is generated through order-level mapping. The expression is as follows:

[0036] ;

[0037] In the formula, This represents the final low-dimensional feature vector of order i. This represents a vector concatenation operation. Represents the order-level mapping matrix. Indicates the bias term. Represents a non-linear activation function;

[0038] Finally, the feature vectors of all orders are stacked row-wise to form the order node feature matrix:

[0039] ;

[0040] in, The order node feature matrix serves as the input for subsequent dynamic hypergraph construction and dynamic differential hypergraph neural network scheduling models; I represents the order set. This represents the total number of order nodes. The dimension of the order node features.

[0041] Preferably, in step S3, the process of constructing the dynamic hypergraph model is as follows:

[0042] Construct a dynamic hypergraph model at time t:

[0043] ;

[0044] in, For a set of nodes, For a set of superedges, Let be the correlation matrix between the hyperedges and the nodes; The node feature matrix;

[0045] Furthermore, the node set is composed of both the order node set and the device node set:

[0046] ;

[0047] In the formula, Represents the set of order nodes. This represents a set of equipment nodes; among them, the order node features are generated by the Order2Ten method, and the equipment node features include at least the equipment brand, the range of compatible sizes, the fixed size, the rated capacity, and the operating status; for the continuous attributes of the equipment, a normalization method is also used to process them, so as to realize the representation of order nodes and equipment nodes in a unified feature space.

[0048] Preferably, the scheduling method further establishes order similarity relationships and order-device matching relationships, constructing two types of hyperedges;

[0049] The first category consists of hyperedges for clustering similar orders, which connect order nodes that are similar in brand, specifications, patterns, hierarchy, and size attributes. Their similarity is represented by cosine similarity:

[0050] ;

[0051] in, and These represent orders. and orders eigenvectors;

[0052] When the order similarity is greater than a preset threshold When this happens, they are grouped into the same similar order cluster superedge:

[0053] ;

[0054] in, Let the superedge of the clustering of the q-th similar order be represented. This represents the i-th order node. Indicates time The set of order nodes Indicates order node Similarity to reference order q;

[0055] The second type is the process matching hyperedge, which can connect order nodes with a set of equipment nodes that meet its processing constraints. When the equipment... In the process The order is satisfied When defining machining constraints, the process matching indicator is defined as follows:

[0056] ;

[0057] Then build orders In the corresponding process The process matching the super edge:

[0058] ;

[0059] in, This indicates that order i is in the process... The process on the upper edge matches the super edge. This represents the i-th order node. This represents the k-th device node. This represents the set of equipment nodes corresponding to process m at time t.

[0060] Preferably, the membership relationship between nodes and hyperedges is represented by an incidence matrix, the elements of which are defined as:

[0061] ;

[0062] When a new order arrives or the equipment status changes, the node feature matrix and hyperedge relationships are dynamically updated. The update format is as follows:

[0063] ;

[0064] in, Indicates the current scheduling status information. This indicates information about new orders and changes in equipment status. and Let these represent the node feature matrices at time t and time t+1, respectively. and Let these represent the hyperedge incidence matrices at time t and time t+1, respectively. This represents the node feature update function. This represents the function for updating hyperedge association relationships.

[0065] Preferably, in step S4, after the dynamic hypergraph is constructed, feature updates are performed using a "node-hyperedge-node" propagation method. The basic propagation formula can be expressed as:

[0066] ;

[0067] in, Let the node degree matrix be... It is the hypermarginality matrix. For the first Layer weight matrix, For activation functions; The node feature matrix is ​​the input of the l-th layer;

[0068] By introducing a hypergraph attention mechanism to weight the contributions of hyperedges, a higher-order embedding representation of the order node and the device node is finally obtained:

[0069] ;

[0070] The higher-order embedding representation Z serves as the input for subsequent dynamic differential flow modeling and single-insertion discrimination decision-making. i Let V be the high-order embedding vector of the i-th node, and V be the set of nodes. The total number of nodes. For higher-order embedding feature dimensions, Represents the real number field.

[0071] Preferably, a spatiotemporal network flow model is constructed:

[0072]

[0073] In the formula, It is a set of spatiotemporal state nodes; For the set of arcs;

[0074] Define the spatiotemporal state node as This represents the processing state of equipment k on process m during discrete time interval d;

[0075] The equipment status nodes for the molding and vulcanization processes are defined as follows:

[0076] ;

[0077] In the formula, This represents the state node of device k during the discrete time period t in the forming stage; This represents the state node of device k during the vulcanization stage in the discrete time period t; Indicates the molding stage. Indicates the vulcanization stage;

[0078] Furthermore, the actual traffic allocation for order i on device k and time period t is defined as follows:

[0079] ;

[0080] and These represent the flow rates of order i allocated to molding machine k and vulcanizing machine k during time period t, respectively.

[0081] And define binary allocation variables:

[0082] ;

[0083] in, and Let represent the binary decision variables for whether order i is assigned to the k-th molding machine and the k-th vulcanizing machine in time period t, respectively;

[0084] The process continuity constraint is as follows:

[0085] ;

[0086] In the formula, For orders The completion time of the molding process; For orders The start time of the vulcanization process is determined to ensure that the vulcanization process can only begin after the molding process of each order is completed;

[0087] Secondly, the order flow conservation constraint is:

[0088] ;

[0089] In the formula, Indicates order Demand;

[0090] Secondly, the equipment capacity constraint is:

[0091] ;

[0092] in, and These represent orders. Resource utilization coefficient per unit on the corresponding device and These represent the maximum available capacity of the corresponding equipment during time period t;

[0093] Finally, the process feasibility constraints are:

[0094] ;

[0095] In the formula, and This is a process matching indicator parameter. When its value is 1, it means that the equipment meets the order process requirements; if its value is 0, it means that the infeasible constraint of the allocation can effectively reduce the search space for subsequent order insertions.

[0096] The initial remaining capacity calculation before equipment order placement is defined as follows: for the molding stage and the vulcanization stage, respectively:

[0097] ;

[0098] In the formula, and These represent the initial remaining capacity of the molding machine and the vulcanizing machine k in time period t, respectively. and These represent the maximum available capacity of the equipment. and This indicates the capacity load that the equipment has already occupied under the original schedule.

[0099] Once a new order arrives and participates in scheduling, the remaining capacity is updated based on the traffic distribution of the new order across different devices and time periods. The updated remaining capacity is represented as follows:

[0100] ;

[0101] In the formula, This represents the set of newly arrived orders. and These represent the flow rates allocated to the order during the molding and vulcanization stages, respectively. and This indicates the unit processing time or unit capacity utilization coefficient of an order on the corresponding equipment;

[0102] After a new order is inserted, the remaining capacity of the equipment will be reduced based on the processing volume and resource utilization coefficient of the corresponding order.

[0103] A dynamic differential flow model is constructed based on the difference between the initial remaining capacity before the equipment order placement and the updated remaining capacity after the order placement, namely:

[0104] ;

[0105] In the formula, and These represent the changes in the remaining capacity of the molding machine and the vulcanizing machine during time period t, respectively.

[0106] Preferably, in step S5, the maximum completion time is:

[0107] ;

[0108] The formula for calculating delivery time deviation is:

[0109] ;

[0110] The formula for calculating delay penalty is:

[0111] ;

[0112] The formula for calculating task completion rate is:

[0113] ;

[0114] In the formula, This indicates the completion time of order o in process h; Delivery date; This represents the percentage of orders completed within the current scheduling period, used to measure scheduling efficiency.

[0115] The formula for calculating task mode change loss is:

[0116] ;

[0117] In the formula, This is a mold change indicator. 1 indicates that the specifications of the previous and subsequent orders are different and a mold change is required, while 0 indicates that the specifications are the same and a mold change is not required. For mold changing losses;

[0118] The formula for calculating the cost of single-entry disturbance is:

[0119] ;

[0120] The objective function for minimizing variable costs is as follows:

[0121] ;

[0122] In the formula, , , , , , These are the weighting coefficients for each objective item, and their values ​​are adjusted according to the company's actual management preferences;

[0123] The sets of insertable candidate positions for order i in the molding and vulcanization stages are as follows:

[0124] ;

[0125] in, For order demand, and These are the unit resource occupancy coefficients for the order on the molding machine and vulcanizing machine, respectively. This refers to the completion time of the order in the molding process; and Let i represent the set of insertable candidate positions for order i in the molding stage and the vulcanization stage, respectively. and These represent orders. Whether the indicator variable can be assigned to the molding machine and the vulcanizing machine; and These represent the initial remaining available capacity of the molding machine and the vulcanizing machine during time period t, respectively.

[0126] A quantitative comparison of different devices and time periods is performed, and the comprehensive scoring function can be expressed as follows:

[0127] ;

[0128] In the formula, This represents the normalized matching score between the order and the equipment at the corresponding stage. This indicator mainly reflects the degree to which the equipment is adapted to the order's processing requirements. Prioritize orders; This represents the normalized percentage of remaining capacity of device k at stage g and time t. This represents the revenue from continuous processing of similar orders at this candidate position for order i; This represents the inventory support coefficient for order i in stage g;

[0129] This represents the normalized mold-changing cost incurred by order i when it is inserted into machine k at stage g and time t;

[0130] This represents the normalized differential current disturbance caused by stage g at the time t when order i is inserted into machine k.

[0131] This represents the normalized processing time penalty term for order i occupying machine k at stage g and time t.

[0132] The higher the score, the more favorable the insertion position is for a smooth insertion of new orders while meeting the constraints.

[0133] The final insertion position of an interim order can be represented as:

[0134] ;

[0135] That is, select the device and time period with the highest comprehensive score from the set of feasible candidate locations as the optimal insertion location for new orders.

[0136] After determining the candidate insertion positions, perform a local rearrangement update according to the following strategy:

[0137] The first strategy is to directly assign idle equipment. When the equipment has sufficient spare capacity in stage g and time period t, the order is directly assigned to that equipment. The judgment condition is expressed as follows:

[0138] ;

[0139] in, The initial remaining capacity of the equipment before the order is inserted. When this condition is met, the system will prioritize the direct insertion method to reduce additional rearrangement overhead.

[0140] The second strategy is to adjust order priorities. When current resources are insufficient but the urgency of order insertion is high, the order priorities are recalculated, and higher-priority orders are inserted first. The updated priorities are represented as follows:

[0141] ;

[0142] in, This indicates a suppression item related to inventory or business buffers. Indicates order The overall business score, This represents the maximum overall score. For smoothing coefficients;

[0143] The third strategy is to merge similar orders for processing. When a new order has a high similarity to a currently scheduled order in the embedding space, continuous processing is prioritized to reduce mold change losses. The benefit of merging processing is expressed as follows:

[0144] ;

[0145] In the formula, This represents the revenue generated from processing order i and order j together during the vulcanization stage; and These represent mold change losses when two orders are processed independently. This indicates the combined mold-changing loss after the two are merged;

[0146] The fourth strategy is to prioritize inventory support and short processing time. When a rush order has an inventory buffer advantage or a short processing time, it is prioritized to enter a local gap to reduce the disruption to the main plan.

[0147] Compared with the prior art, the significant advantages of the present invention are as follows:

[0148] (1) This invention achieves unified modeling of high-order coupling relationships between orders and equipment, significantly improving the expressive power of complex constraints. This invention innovatively constructs a dynamic hypergraph model, which upgrades the originally scattered binary relationships into high-order semantic associations shared by multiple nodes within the hyperedge through similar order clustering hyperedges and process matching hyperedges. Combined with feature propagation using a hypergraph neural network, it can fully capture the complex high-order coupling information in the production system, thereby providing a more accurate and complete state representation for subsequent scheduling decisions.

[0149] (2) This invention improves the quality of order feature expression by unifying the feature representation of discrete and continuous attributes of orders, and reduces the problems of information sparsity and missing key information in traditional feature construction methods; by constructing a dynamic hypergraph composed of order nodes and equipment nodes, and introducing similar order clustering hyperedges and process matching hyperedges, it realizes the effective representation of high-order coupling relationships between orders, processes and equipment, and improves the modeling capability in complex order insertion scenarios; by constructing a dynamic differential flow model, it quantifies the changes in task allocation and equipment capacity before and after order insertion, and can more accurately identify the range of local disturbances and reduce the cost of global reordering; by combining dynamic differential flow with hypergraph neural network, it realizes the rapid identification, local reordering and dynamic optimization scheduling of new orders, which is conducive to improving the real-time performance, accuracy and stability of production order insertion processing and equipment resource utilization.

[0150] (3) In the order insertion discrimination stage, this invention constructs a multi-objective evaluation function that includes maximum completion time, delivery deviation, delay penalty, task completion rate, mold change loss and order insertion disturbance cost, thereby realizing a comprehensive quantitative evaluation of candidate insertion positions. At the same time, it designs hierarchical local reordering strategies such as direct assignment of idle equipment, priority adjustment, similar order merging, and delayed processing, and proposes an order insertion scheduling algorithm that combines dynamic differential flow with hypergraph neural network. Through candidate position screening, comprehensive scoring and local reordering decision-making, it realizes rapid discrimination and dynamic optimization scheduling in production order insertion scenarios.

[0151] (4) This invention fully considers the typical discrete manufacturing characteristics of multi-variety, small-batch, and strong process constraints (such as equipment matching and mold change losses in the molding and vulcanization stages). All modeling elements (such as process matching indicators, equipment capacity constraints, and two-stage network flow models) are highly consistent with the actual production process. It can quickly respond to order insertion events, reduce the number of mold changes, alleviate uneven equipment load, reduce order delays, and significantly improve the robustness and resource utilization of the production system. It has good engineering implementation value and cross-industry promotion potential. Attached Figure Description

[0152] Figure 1 This is a flowchart illustrating the order feature representation of the present invention.

[0153] Figure 2 This is a schematic diagram comparing the ordinary graph and the supergraph structure of the present invention.

[0154] Figure 3 This is a schematic diagram of the similar order clustering hyperedge and process matching hyperedge of the present invention.

[0155] Figure 4 This is a schematic diagram of the dynamic hypergraph construction and feature propagation of the present invention.

[0156] Figure 5This is a flowchart illustrating the process from order features to scheduling solution in this invention.

[0157] Figure 6 This is a schematic diagram of the production scheduling network flow model of the present invention.

[0158] Figure 7 This is a schematic diagram of the network flow difference before and after the insertion of a single element in this invention.

[0159] Figure 8 This is a schematic diagram of the single-entry local update strategy of the present invention.

[0160] Figure 9 This is the overall framework diagram of the dynamic differential hypergraph neural network of the present invention. Detailed Implementation

[0161] The accompanying drawings are for illustrative purposes only. To make the objectives, technical solutions, and beneficial effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only for explaining this invention and are not intended to limit the scope of protection of this invention.

[0162] Example 1.

[0163] A dynamic differential flow hypergraph neural network scheduling method for production order insertion is presented, taking the discrete tire manufacturing production scenario as an example to illustrate the dynamic differential flow hypergraph neural network scheduling method for production order insertion.

[0164] Step S1: Obtain order attributes, equipment parameters, process constraint data, and current production scheduling status data within the production cycle. Order attributes include brand, specifications, pattern, level, size, quantity, priority, and delivery date. Equipment parameters include equipment brand, minimum processing size, maximum processing size, fixed size, rated capacity, mold change loss, and equipment operating status. Process constraint data mainly includes order-equipment process matching relationships, process continuity constraints, process feasibility markers, mold change rules and mold change losses, similar order continuous processing rules, equipment access sets for each process stage, and processing time and resource usage parameters related to process execution. Production scheduling status data includes at least the current process for each order, allocated equipment, estimated completion time, remaining unscheduled output, and current remaining capacity of each piece of equipment. After cleaning, field unification, and normalization, the above data serves as input for subsequent feature construction and scheduling solutions. This process can be combined with... Figure 5 This corresponds to the "processing flow from order features to scheduling solution" shown.

[0165] Step S2: Perform unified feature representation on discrete and continuous attributes of orders: normalize the continuous attributes of order quantity and priority; tokenize and embed the discrete attributes of brand, specifications, pattern, level and size; fuse the above processed attribute features according to preset weights to generate order feature vectors; stack all order feature vectors to form an order node feature matrix.

[0166] like Figure 1 As shown, an Order2Ten method for order feature extraction is proposed, which maps the multidimensional heterogeneous attributes of orders into a low-dimensional dense representation suitable for subsequent modeling. Before constructing the Order2Ten model, the numerical and discrete attributes of orders are preprocessed. For continuous or quantifiable attributes such as quantity, delivery date, guaranteed production quantity, and priority, the Min-Max normalization method is used to map them to a uniform scale to avoid interference from different units of measurement during embedding training. The calculation formula is as follows:

[0167] ;

[0168] In the formula, The original data value; These are the minimum and maximum values ​​of the data, respectively. This is the normalized value.

[0169] Secondly, order attributes are divided into three categories: indexed attributes, discrete attributes, and continuous attributes. A weighted input representation of order attributes is established, the expression of which is:

[0170] ;

[0171] in, Indicates order priority. These represent the brand, specifications, pattern, grade, size, and order quantity, respectively. These are the weight coefficients for each attribute. This is a mapping matrix. This method enables unified input of attributes for different order types.

[0172] Then, the discrete attributes are tokenized and embedded, and feature learning is performed by combining the internal attribute context of the order and the cross-order sequence context to obtain low-dimensional semantic vectors for each discrete attribute.

[0173] Furthermore, the discrete attribute embedding vectors are weighted and aggregated according to their attribute weights to obtain the discrete attribute aggregated vector of the order:

[0174] ;

[0175] in, For discrete attribute sets, For orders The embedding vector on the j-th discrete attribute, This represents the weight of the corresponding attribute.

[0176] Based on the discrete attribute embeddings, the normalization result of the continuous attributes is shown in the following equation:

[0177] ;

[0178] In the formula, C i It is a continuous attribute aggregation vector of the order. Indicates order The normalized result of the quantity.

[0179] After obtaining the discrete attribute aggregate vector, it is concatenated with the continuous attribute vector, and then the final order feature vector is generated through order-level mapping. The expression is as follows:

[0180] ;

[0181] In the formula, Indicates order The final low-dimensional feature vector, This represents a vector concatenation operation. Represents the order-level mapping matrix. Indicates the bias term. This represents a non-linear activation function.

[0182] Finally, the feature vectors of all orders are stacked row-wise to form the order node feature matrix:

[0183] ;

[0184] in, The order node feature matrix serves as the input for subsequent dynamic hypergraph construction and dynamic differential hypergraph neural network scheduling model.

[0185] Step S3: As Figure 2 As shown, a dynamic hypergraph model is constructed based on order nodes and equipment nodes; the node set consists of the order node set and the equipment node set; similar order clustering hyperedges are constructed based on order cosine similarity and threshold, process matching hyperedges are constructed based on process matching indicators, and the membership relationship between nodes and hyperedges is represented by an association matrix.

[0186] The process of constructing a dynamic hypergraph model is as follows:

[0187] Construct a dynamic hypergraph model at time t:

[0188] ;

[0189] in, For a set of nodes, For a set of superedges, Let be the correlation matrix between the hyperedges and the nodes; This is the node feature matrix.

[0190] Furthermore, the node set is composed of both the order node set and the device node set:

[0191] ;

[0192] In the formula, Represents the set of order nodes. This represents a set of equipment nodes; among them, the order node features are generated by the Order2Ten method, and the equipment node features include at least the equipment brand, the range of compatible sizes, the fixed size, the rated capacity, and the operating status; for the continuous attributes of the equipment, a normalization method is also used to process them, so as to realize the representation of order nodes and equipment nodes in a unified feature space.

[0193] like Figure 3 As shown, in order to characterize the order similarity relationship and the order-device matching relationship, this invention also establishes the order similarity relationship and the order-device matching relationship, and constructs two types of hyperedges.

[0194] The first category consists of hyperedges for clustering similar orders, which connect order nodes that are similar in brand, specifications, patterns, hierarchy, and size attributes. Their similarity is represented by cosine similarity:

[0195] ;

[0196] in, and These represent orders. and orders eigenvectors.

[0197] When the order similarity is greater than a preset threshold When this happens, they are grouped into the same similar order cluster superedge:

[0198] ;

[0199] in, Let the superedge of the clustering of the q-th similar order be represented. This represents the i-th order node. Indicates time The set of order nodes Indicates order node Similarity to the reference order q.

[0200] The second type is the process matching hyperedge, which can connect order nodes with a set of equipment nodes that meet its processing constraints. When the equipment... In the process The order is satisfied When defining machining constraints, the process matching indicator is defined as follows:

[0201] ;

[0202] Then build orders In the corresponding process The process matching the super edge:

[0203] ;

[0204] in, This indicates that order i is in the process... The process on the upper edge matches the super edge. This represents the i-th order node. This represents the k-th device node. This represents the set of equipment nodes corresponding to process m at time t.

[0205] Through the two types of hyperedges mentioned above, the present invention can simultaneously characterize the similar processing relationships between orders and the feasible processing relationships between orders and equipment in a unified hypergraph structure.

[0206] Furthermore, the membership relationship between nodes and hyperedges is represented by an incidence matrix, the elements of which are defined as follows:

[0207] ;

[0208] When new orders arrive or equipment status changes, such as Figure 4 As shown, the node feature matrix and hyperedge relationships are dynamically updated, and the update form is as follows:

[0209] ;

[0210] in, Indicates the current scheduling status information. This indicates information on new orders and changes in equipment status; and Let these represent the node feature matrices at time t and time t+1, respectively. and Let these represent the hyperedge incidence matrices at time t and time t+1, respectively. This represents the node feature update function. This represents the function for updating hyperedge association relationships.

[0211] Step S4: Input the dynamic hypergraph model into the hypergraph neural network for feature propagation to obtain the high-order embedding representation Z of the order node and the device node;

[0212] A production scheduling network flow model is constructed based on the higher-order embedded representation Z; the allocation flow of orders on the equipment set in the forming stage, the equipment set in the vulcanization stage, and the discrete time set is defined; process continuity constraints, flow conservation constraints, equipment capacity constraints, and process feasibility constraints are set; the initial remaining capacity before the equipment order is inserted and the updated remaining capacity after the order is inserted are calculated, and a dynamic differential flow model is constructed based on the difference between the two to quantify the local disturbance caused by the new order to the original scheduling resource structure.

[0213] After completing the construction of the dynamic hypergraph, as shown in the attached figure Figure 4 As shown, feature updates are performed using a "node-hyperedge-node" propagation method, and its basic propagation formula can be expressed as:

[0214] ;

[0215] in, Let the node degree matrix be... It is the hypermarginality matrix. For the first Layer weight matrix, This is the activation function.

[0216] By introducing a hypergraph attention mechanism to weight the contributions of hyperedges, a higher-order embedding representation of the order node and the device node is finally obtained:

[0217] ;

[0218] The higher-order embedding representation Z serves as the input for subsequent dynamic differential flow modeling and single-insertion discrimination decision-making. i Let V be the high-order embedding vector of the i-th node, and V be the set of nodes. The total number of nodes. For higher-order embedding feature dimensions, Represents the real number field.

[0219] like Figure 5 , Figure 6 and Figure 7 As shown, after obtaining the high-order embedding representation of nodes in the dynamic hypergraph after multi-layer feature propagation, this invention further maps the high-order association between order nodes and equipment nodes into a spatiotemporal network flow model, thereby transforming the production order insertion scheduling problem into a constrained flow optimization problem in the three-dimensional space of "process-equipment-time". (The appendix...) Figure 5 The processing flow from corresponding order characteristics to scheduling solution. Figure 6 Corresponding to the production scheduling network flow model, Figure 7This corresponds to the network flow difference update process before and after inserting the order.

[0220] Constructing a spatiotemporal network flow model:

[0221] ;

[0222] In the formula, It is a set of spatiotemporal state nodes; It is a set of arcs.

[0223] Define the spatiotemporal state node as This represents the processing state of equipment k on process m during discrete time interval d.

[0224] The equipment status nodes for the molding and vulcanization processes are defined as follows:

[0225] ;

[0226] In the formula, This represents the state node of device k during the discrete time period t in the forming stage; This represents the state segment of device k during the vulcanization stage in discrete time interval t.

[0227] Furthermore, the actual traffic allocation for order i on device k and time period t is defined as follows:

[0228] ;

[0229] And define binary allocation variables:

[0230] ;

[0231] This enables the representation of the processing status of orders at different processes, on different equipment, and at different times.

[0232] Based on this, to ensure that the network flow model meets actual production constraints, this invention further sets the following key constraints. First, the process continuity constraint is:

[0233] ;

[0234] In the formula, For orders The completion time of the molding process; For orders The start time of the vulcanization process is determined to ensure that the vulcanization process can only begin after the molding process of each order is completed.

[0235] Secondly, the order flow conservation constraint is:

[0236] ;

[0237] In the formula, Indicates order The demand.

[0238] Secondly, the equipment capacity constraint is:

[0239] ;

[0240] in, and These represent orders. Resource utilization coefficient per unit on the corresponding device and These represent the maximum available capacity of the corresponding equipment during time period t.

[0241] Finally, the process feasibility constraints are:

[0242] ;

[0243] In the formula, and This is a process matching indicator parameter. When its value is 1, it means that the equipment meets the order process requirements; if its value is 0, it means that the allocation infeasible constraint can effectively reduce the search space for subsequent order insertions.

[0244] After completing the network flow modeling described above, this invention introduces a dynamic differential flow mechanism to quantify the local disturbances to the original schedule resource structure caused by the insertion of new orders. Specifically, the initial remaining capacity of the equipment before the insertion of orders under the original schedule is first calculated. For the molding stage and the vulcanization stage, the following definitions apply:

[0245] ;

[0246] In the formula, and These represent the initial remaining capacity of the molding machine and the vulcanizing machine k in time period t, respectively. and These represent the maximum available capacity of the equipment. and This indicates the capacity load already occupied by the equipment under the original schedule; this step corresponds to the attached... Figure 7 The original scheduling status on the left.

[0247] Once a new order arrives and participates in scheduling, the remaining capacity is updated based on the traffic distribution of the new order across different devices and time periods. The updated remaining capacity is represented as follows:

[0248] ;

[0249] In the formula, This represents the set of newly arrived orders. and These represent the flow rates allocated to the order during the molding and vulcanization stages, respectively. and This represents the unit processing time or unit capacity utilization factor of the order on the corresponding equipment. This formula indicates that after a new order is inserted, the remaining capacity of the equipment will be deducted based on the processing volume and resource utilization factor of the corresponding order, thus forming a new resource status after the order insertion. This process corresponds to... Figure 7 The local network stream update status is displayed after the right-side insertion.

[0250] After a new order is inserted, the remaining capacity of the equipment will be reduced based on the processing volume and resource occupancy coefficient of the corresponding order.

[0251] To further characterize the degree of change in resource structure before and after order placement, a dynamic differential flow model is constructed using the difference between the initial remaining capacity before order placement and the updated remaining capacity after order placement.

[0252] ;

[0253] In the formula, and These represent the changes in the remaining capacity of the molding machine and the vulcanizing machine during time period t, respectively.

[0254] If the differential flow value is small, it means that the insertion of new orders has a weak impact on the original scheduling resource structure, and the direct insertion strategy can be used first; if the differential flow value is large, it means that the insertion position is close to the local bottleneck, and further strategies such as delayed insertion, priority adjustment or local rearrangement need to be adopted.

[0255] Through the above steps, this invention combines the high-order embedded representation of dynamic hypergraph output with the production scheduling network flow model, and explicitly models the resource changes before and after order insertion through dynamic differential flow. This enables subsequent order insertion judgment to no longer rely solely on static feasibility judgment, but to comprehensively consider the original schedule load structure, equipment remaining capacity, and local disturbance intensity, thereby providing a unified quantitative input for subsequent order insertion judgment criteria and local rearrangement optimization.

[0256] Step S5: As Figure 8 , 9 As shown, a set of candidate insertion positions is constructed based on process feasibility, time feasibility, remaining capacity, and dynamic differential flow disturbance. A multi-objective evaluation function is used to comprehensively score the candidate positions to determine the optimal insertion equipment and insertion time. Then, the scheduling is updated according to the local rearrangement strategy of direct assignment of idle equipment, order priority adjustment, and merging or delaying similar orders, and the final scheduling scheme after order insertion is output.

[0257] The dynamic hypergraph construction module outputs the state update results, which, after order feature encoding and differential flow feedback, enter the hierarchical decision criterion module. This module then performs order insertion discrimination and local updates based on order insertion priority evaluation, similar order clustering, order-equipment matching, and dynamic differential flow optimization results. For example... Figure 8 Four typical local update scenarios are given, including direct assignment of idle equipment, delayed order processing, immediate insertion, and merging of similar orders.

[0258] First, to balance production efficiency, delivery performance, schedule stability, and the cost of order insertion disruptions, this invention employs a variable cost minimization criterion to uniformly evaluate candidate order insertion schemes. Specifically, the objective terms in the multi-objective evaluation function are defined as follows.

[0259] The maximum completion time is:

[0260] ;

[0261] Delivery time deviation reflects the level of customer service, and its calculation formula is as follows:

[0262] ;

[0263] Delay penalty: This penalty is applied to orders that exceed the delivery date to encourage early or on-time completion. The calculation formula is as follows:

[0264]

[0265] Task completion rate, a measure of scheduling execution effectiveness, is calculated using the following formula:

[0266] ;

[0267] In the formula, This indicates the completion time of order o in process h; Delivery date; This represents the percentage of orders completed within the current scheduling period, used to measure scheduling efficiency.

[0268] The formula for calculating task mode change loss is:

[0269] ;

[0270] In the formula, This is a mold change indicator. 1 indicates that the specifications of the previous and subsequent orders are different and a mold change is required, while 0 indicates that the specifications are the same and a mold change is not required. This is for mold changing losses.

[0271] To explicitly reflect the impact of order insertion on the original scheduling resource structure, the following formula is introduced to calculate the disturbance cost of order insertion:

[0272] .

[0273] Multi-objective scheduling optimization is achieved by minimizing variable costs. This optimization criterion provides a quantitative basis for subsequent dynamic production scheduling and order insertion scheduling, enabling the production plan to achieve optimal overall efficiency while meeting equipment capacity, order priority, and process constraints. It also provides a clear objective for solving the intelligent scheduling model. The objective function of the variable cost minimization criterion is as follows:

[0274] ;

[0275] In the formula, , , , , , These are the weighting coefficients for each objective item, and their values ​​are adjusted according to the company's actual management preferences.

[0276] After constructing the objective function, this invention further filters the feasible insertion positions of the order. Preferably, the order insertion is divided into a candidate position set for the molding stage and a candidate position set for the vulcanization stage. The candidate insertion position sets for order i in the molding stage and the vulcanization stage are defined as follows:

[0277] ;

[0278] in, For order demand, and These are the unit resource occupancy coefficients for the order on the molding machine and vulcanizing machine, respectively. This represents the completion time of the order in the molding process. By constructing the above candidate position set, insertion positions that do not meet the requirements of process feasibility, time feasibility, and resource feasibility can be eliminated, thereby narrowing the search space.

[0279] Building upon the candidate location screening, this invention further constructs a comprehensive scoring function to quantitatively compare the locations of different devices and time periods. The comprehensive scoring function can be expressed as:

[0280] ;

[0281] In the formula, This represents the normalized matching score between the order and the equipment at the corresponding stage. This indicator mainly reflects the degree to which the equipment is adapted to the order's processing requirements. Prioritize orders; This represents the normalized percentage of remaining capacity of device k at stage g and time t. This represents the revenue from continuous processing of similar orders at this candidate position for order i; This represents the inventory support coefficient for order i in stage g;

[0282] This represents the normalized mold-changing cost incurred by order i when it is inserted into machine k at stage g and time t;

[0283] This represents the normalized differential current disturbance caused by stage g at the time t when order i is inserted into machine k.

[0284] This represents the normalized processing time penalty term for order i occupying machine k at stage g and time t.

[0285] The higher the score, the more favorable the insertion position is for a smooth insertion of new orders while meeting the constraints.

[0286] Therefore, the final insertion position of the supplementary order can be represented as:

[0287] ;

[0288] That is, select the device and time period with the highest comprehensive score from the set of feasible candidate locations as the optimal insertion location for new orders.

[0289] After determining the candidate insertion positions, perform a local rearrangement update according to the following strategy:

[0290] The first strategy is to directly assign idle equipment. When the equipment has sufficient spare capacity in stage g and time period t, the order is directly assigned to that equipment. The judgment condition is expressed as follows:

[0291] ;

[0292] in, This refers to the initial remaining capacity of the equipment before order insertion. When this condition is met, the system prioritizes direct insertion to reduce additional rearrangement overhead.

[0293] The second strategy is to adjust order priorities. When current resources are insufficient but the urgency of order insertion is high, the order priorities are recalculated, and higher-priority orders are inserted first. The updated priorities are represented as follows:

[0294] ;

[0295] in, This indicates a suppression item related to inventory or business buffers. Indicates order The overall business score, This represents the maximum overall score. This is the smoothing coefficient.

[0296] The third strategy is to merge similar orders for processing. When a new order has a high similarity to a currently scheduled order in the embedding space, continuous processing is prioritized to reduce mold change losses. The benefit of merging processing is expressed as follows:

[0297] ;

[0298] In the formula, This represents the revenue generated from processing order i and order j together during the vulcanization stage; and These represent mold change losses when two orders are processed independently. This represents the combined mold-changing loss after the two are merged.

[0299] The fourth strategy is to prioritize inventory support and short processing time. When a rush order has an inventory buffer advantage or a short processing time, it is prioritized to enter a local gap to reduce the disruption to the main plan.

[0300] In summary, this invention achieves rapid identification and local rearrangement updates for production order insertion scenarios through a hierarchical decision-making mechanism of "multi-objective variable cost minimization criterion—candidate position screening—comprehensive scoring and optimization—local update strategy execution." Combined with... Figure 9 As can be seen from the overall framework shown, this step does not rely solely on static rule judgment, but takes upstream dynamic hypergraph modeling, feature encoding and dynamic differential feedback as input to form a closed-loop decision-making process from state update, candidate evaluation to execution feedback, thereby improving the real-time performance, accuracy and stability of order insertion processing.

[0301] Of course, the above description is not intended to limit the present invention, and the present invention is not limited to the examples given above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A dynamic differential flow hypergraph neural network scheduling method for production order insertion, characterized in that, Includes the following steps: Step S1: Obtain order data, equipment data, process constraint data, and current production scheduling status data within the production cycle; Step S2: Perform unified feature representation on discrete and continuous attributes of the order: normalize the continuous attributes of order quantity and priority; tokenize and embed the discrete attributes of brand, specifications, pattern, level and size; fuse the above processed attribute features according to preset weights to generate the order feature vector. Stack all order feature vectors to form an order node feature matrix; Step S3: Construct a dynamic hypergraph model based on order nodes and equipment nodes; the node set consists of the order node set and the equipment node set; construct similar order clustering hyperedges based on order cosine similarity and threshold, construct process matching hyperedges based on process matching indicators, and represent the membership relationship between nodes and hyperedges through an association matrix; Step S4: Input the dynamic hypergraph model into the hypergraph neural network for feature propagation to obtain the high-order embedding representation Z of the order node and the device node; A production scheduling network flow model is constructed based on the higher-order embedded representation Z; the allocation flow of orders on the equipment set of the forming stage, the equipment set of the vulcanization stage, and the discrete time set is defined; process continuity constraints, flow conservation constraints, equipment capacity constraints, and process feasibility constraints are set; the initial remaining capacity before the equipment order is inserted and the updated remaining capacity after the order is inserted are calculated, and a dynamic differential flow model is constructed based on the difference between the two to quantify the local disturbance caused by the new order to the original scheduling resource structure; Step S5: Construct a set of candidate insertion positions based on process feasibility, time feasibility, remaining capacity, and dynamic differential flow disturbance; use a multi-objective evaluation function to comprehensively score the candidate positions, determine the optimal insertion equipment and insertion time period; then execute the scheduling update according to the local rearrangement strategy of direct assignment of idle equipment, order priority adjustment, merging or delaying similar orders, and output the final scheduling scheme after order insertion. The multi-objective evaluation function includes: maximum completion time, delivery deviation, delay penalty, task completion rate, mold change loss, and order insertion disturbance cost.

2. The dynamic differential flow hypergraph neural network scheduling method for production order insertion according to claim 1, characterized in that, In step S1, the order data should include at least the brand, specifications, pattern, level, size, quantity, priority, and delivery date; the equipment data should include at least the equipment brand, minimum processing size, maximum processing size, fixed size, rated capacity, mold change loss, and equipment operating status; the process constraint data should include at least the order-equipment process matching relationship, process continuity constraints, process feasibility markers, mold change rules and mold change loss, similar order continuous processing rules, equipment access set for each process stage, and processing time and resource usage parameters related to process execution; the production scheduling status data should include at least the current process of each order, allocated equipment, estimated completion time, remaining unscheduled output, and current remaining capacity of each piece of equipment.

3. The dynamic differential flow hypergraph neural network scheduling method for production order insertion according to claim 1, characterized in that, In step S2, the Order2Ten order feature extraction method is used to uniformly map the multidimensional heterogeneous attributes of orders into a low-dimensional dense representation suitable for subsequent modeling.

4. The dynamic differential flow hypergraph neural network scheduling method for production order insertion according to claim 3, characterized in that, Before constructing the Order2Ten model, the numerical and discrete attributes of orders are preprocessed. For continuous or quantifiable attributes such as quantity, delivery date, guaranteed production quantity, and priority, the Min-Max normalization method is used to map them to a uniform scale. The calculation formula is as follows: ； In the formula, x is the original data value; These are the minimum and maximum values ​​of the data, respectively. The value is the normalized value; Secondly, order attributes are divided into three categories: indexed attributes, discrete attributes, and continuous attributes. A weighted input representation of order attributes is established, the expression of which is: ； in, Indicates order priority. These represent the brand, specifications, pattern, grade, size, and order quantity, respectively. These are the weight coefficients for each attribute. It is a mapping matrix; Then, the discrete attributes are tokenized and embedded, and feature learning is performed by combining the internal attribute context of the order and the cross-order sequence context to obtain the low-dimensional semantic vector of each discrete attribute. Furthermore, the discrete attribute embedding vectors are weighted and aggregated according to their attribute weights to obtain the discrete attribute aggregated vector of the order: ； in, For discrete attribute sets, For orders The embedding vector on the j-th discrete attribute, For the corresponding attribute weights; Based on the discrete attribute embeddings, the normalization result of the continuous attributes is shown in the following equation: ； In the formula, C i It is a continuous attribute aggregation vector of the order. Indicates order The quantity normalization result; After obtaining the discrete attribute aggregate vector, it is concatenated with the continuous attribute vector, and then the final order feature vector is generated through order-level mapping. The expression is as follows: ； In the formula, This represents the final low-dimensional feature vector of order i. This represents a vector concatenation operation. Represents the order-level mapping matrix. Indicates the bias term. Represents a non-linear activation function; Finally, the feature vectors of all orders are stacked row-wise to form the order node feature matrix: ； in, The order node feature matrix serves as the input for subsequent dynamic hypergraph construction and dynamic differential hypergraph neural network scheduling models; I represents the order set. This represents the total number of order nodes. The dimension of the order node features.

5. The dynamic differential flow hypergraph neural network scheduling method for production order insertion according to claim 1, characterized in that, In step S3, the process of constructing the dynamic hypergraph model is as follows: Construct a dynamic hypergraph model at time t: ； in, For a set of nodes, For a set of superedges, Let be the correlation matrix between the hyperedges and the nodes; The node feature matrix; Furthermore, the node set is composed of both the order node set and the device node set: ； In the formula, Represents the set of order nodes. This represents a set of equipment nodes; among them, the order node features are generated by the Order2Ten method, and the equipment node features include at least the equipment brand, the range of compatible sizes, the fixed size, the rated capacity, and the operating status; for the continuous attributes of the equipment, a normalization method is also used to process them, so as to realize the representation of order nodes and equipment nodes in a unified feature space.

6. The dynamic differential flow hypergraph neural network scheduling method for production order insertion according to claim 1, characterized in that, The scheduling method also establishes order similarity relationships and order-device matching relationships, and constructs two types of hyperedges; The first category consists of hyperedges for clustering similar orders, which connect order nodes that are similar in brand, specifications, patterns, hierarchy, and size attributes. Their similarity is represented by cosine similarity: ； in, and These represent orders. and orders eigenvectors; When the order similarity is greater than a preset threshold When this happens, they are grouped into the same similar order cluster superedge: ； in, Let the superedge of the clustering of the q-th similar order be represented. This represents the i-th order node. Indicates time The set of order nodes Indicates order node Similarity to reference order q; The second type is the process matching hyperedge, which can connect order nodes with a set of equipment nodes that meet its processing constraints. When the equipment... In the process The order is satisfied When defining machining constraints, the process matching indicator is defined as follows: ； Then build orders In the corresponding process The process matching the super edge: ； in, This indicates that order i is in the process... The process on the upper edge matches the super edge. This represents the i-th order node. This represents the k-th device node. This represents the set of equipment nodes corresponding to process m at time t.

7. A dynamic differential flow hypergraph neural network scheduling method for production order insertion according to claim 6, characterized in that, The membership relationship between nodes and hyperedges is represented by an incidence matrix, whose elements are defined as: ； When a new order arrives or the equipment status changes, the node feature matrix and hyperedge relationships are dynamically updated. The update format is as follows: ； in, Indicates the current scheduling status information. This indicates information on new orders and changes in equipment status; and Let these represent the node feature matrices at time t and time t+1, respectively. and Let these represent the hyperedge incidence matrices at time t and time t+1, respectively. This represents the node feature update function. This represents the function for updating hyperedge association relationships.

8. The dynamic differential flow hypergraph neural network scheduling method for production order insertion according to claim 7, characterized in that, In step S4, after the dynamic hypergraph is constructed, feature updates are performed using a "node-hyperedge-node" propagation method. The basic propagation formula can be expressed as: ； in, Let the node degree matrix be... It is the hypermarginality matrix. For the first Layer weight matrix, For activation functions; The node feature matrix is ​​the input of the l-th layer; By introducing a hypergraph attention mechanism to weight the contributions of hyperedges, a higher-order embedding representation of the order node and the device node is finally obtained: ； The higher-order embedding representation Z serves as the input for subsequent dynamic differential flow modeling and single-insertion discrimination decision-making. i Let V be the high-order embedding vector of the i-th node, and V be the set of nodes. The total number of nodes. For higher-order embedding feature dimensions, Represents the real number field.

9. A dynamic differential flow hypergraph neural network scheduling method for production order insertion according to claim 8, characterized in that, Constructing a spatiotemporal network flow model: ； In the formula, A is the set of spatiotemporal state nodes; A is the set of arcs; Define the spatiotemporal state node as This represents the processing state of equipment k on process m during discrete time interval d; The equipment status nodes for the molding and vulcanization processes are defined as follows: ； In the formula, This represents the state node of device k during the discrete time period t in the forming stage; This represents the state node of device k during the vulcanization stage in the discrete time period t; Indicates the molding stage. Indicates the vulcanization stage; Furthermore, the actual traffic allocation for order i on device k and time period t is defined as follows: ； and These represent the flow rates of order i allocated to molding machine k and vulcanizing machine k during time period t, respectively. And define binary allocation variables: ； in, and Let represent the binary decision variables for whether order i is assigned to the k-th molding machine and the k-th vulcanizing machine in time period t, respectively; The process continuity constraint is as follows: ； In the formula, For orders The completion time of the molding process; For orders The start time of the vulcanization process is determined to ensure that the vulcanization process can only begin after the molding process of each order is completed; Secondly, the order flow conservation constraint is: ； In the formula, Indicates order Demand; Secondly, the equipment capacity constraint is: ； in, and These represent orders. Resource utilization coefficient per unit on the corresponding device and These represent the maximum available capacity of the corresponding equipment during time period t; Finally, the process feasibility constraints are: ； In the formula, and This is a process matching indicator parameter. When its value is 1, it means that the equipment meets the order process requirements; if its value is 0, it means that the infeasible constraint of the allocation can effectively reduce the search space for subsequent order insertions. The initial remaining capacity calculation before equipment order placement is defined as follows: for the molding stage and the vulcanization stage, respectively: ； In the formula, and These represent the initial remaining capacity of the molding machine and the vulcanizing machine k in time period t, respectively. and These represent the maximum available capacity of the equipment. and This indicates the capacity load that the equipment has already occupied under the original schedule; Once a new order arrives and participates in scheduling, the remaining capacity is updated based on the traffic distribution of the new order across different devices and time periods. The updated remaining capacity is represented as follows: ； In the formula, This represents the set of newly arrived orders. and These represent the flow rates allocated to the order during the molding and vulcanization stages, respectively. and This indicates the unit processing time or unit capacity utilization coefficient of an order on the corresponding equipment; After a new order is inserted, the remaining capacity of the equipment will be reduced based on the processing volume and resource utilization coefficient of the corresponding order. A dynamic differential flow model is constructed based on the difference between the initial remaining capacity before the equipment order placement and the updated remaining capacity after the order placement, namely: ； In the formula, and These represent the changes in the remaining capacity of the molding machine and the vulcanizing machine during time period t, respectively.

10. A dynamic differential flow hypergraph neural network scheduling method for production order insertion according to claim 9, characterized in that, In step S5, the maximum completion time is: ； The formula for calculating delivery time deviation is: ； The formula for calculating delay penalty is: ； The formula for calculating task completion rate is: ； In the formula, This indicates the completion time of order o in process h; Delivery date; This represents the percentage of orders completed within the current scheduling period, used to measure scheduling efficiency. The formula for calculating task mode change loss is: ； In the formula, This is a mold change indicator. 1 indicates that the specifications of the previous and subsequent orders are different and a mold change is required, while 0 indicates that the specifications are the same and a mold change is not required. For mold changing losses; The formula for calculating the cost of single-entry disturbance is: ； The objective function for minimizing variable costs is as follows: ； In the formula, , , , , , These are the weighting coefficients for each objective item, and their values ​​are adjusted according to the company's actual management preferences; The sets of insertable candidate positions for order i in the molding and vulcanization stages are as follows: ； in, For order demand, and These are the unit resource occupancy coefficients for the order on the molding machine and vulcanizing machine, respectively. This refers to the completion time of the order in the molding process; and Let i represent the set of insertable candidate positions for order i in the molding stage and the vulcanization stage, respectively. and These represent orders. Whether the indicator variable can be assigned to the molding machine and the vulcanizing machine; and These represent the initial remaining available capacity of the molding machine and the vulcanizing machine in time period t, respectively. A quantitative comparison of different devices and time periods is performed, and the comprehensive scoring function can be expressed as follows: ； In the formula, This represents the normalized matching score between the order and the equipment at the corresponding stage. This indicator mainly reflects the degree to which the equipment is adapted to the order's processing requirements. Prioritize orders; This represents the normalized percentage of remaining capacity of device k at stage g and time t. This represents the revenue from continuous processing of similar orders at this candidate position for order i; This represents the inventory support coefficient for order i in stage g; This represents the normalized mold-changing cost incurred by order i when it is inserted into machine k at stage g and time t; This represents the normalized differential current disturbance caused by stage g at the time t when order i is inserted into machine k. This represents the normalized processing time penalty term for order i occupying machine k at stage g and time t; The higher the score, the more favorable the insertion position is for a smooth insertion of new orders while satisfying the constraints; The final insertion position of an interim order can be represented as: ； That is, select the device and time period with the highest comprehensive score from the set of feasible candidate locations as the optimal insertion location for the new order; After determining the candidate insertion positions, perform a local rearrangement update according to the following strategy: The first strategy is to directly assign idle equipment. When the equipment has sufficient spare capacity in stage g and time period t, the order is directly assigned to that equipment. The judgment condition is expressed as follows: ； in, The initial remaining capacity of the equipment before the order is inserted. When this condition is met, the system will prioritize the direct insertion method to reduce additional rearrangement overhead. The second strategy is to adjust order priorities. When current resources are insufficient but the urgency of order insertion is high, the order priorities are recalculated, and higher-priority orders are inserted first. The updated priorities are represented as follows: ； in, This indicates a suppression item related to inventory or business buffers. Indicates order The overall business score, This represents the maximum overall score. For smoothing coefficients; The third strategy is to merge similar orders for processing. When a new order has a high similarity to a currently scheduled order in the embedding space, continuous processing is prioritized to reduce mold change losses. The benefit of merging processing is expressed as follows: ； In the formula, This represents the revenue generated from processing order i and order j together during the vulcanization stage; and These represent mold change losses when two orders are processed independently. This indicates the combined mold-changing loss after the two are merged; The fourth strategy is to prioritize inventory support and short processing time. When a rush order has an inventory buffer advantage or a short processing time, it is prioritized to enter a local gap to reduce the disruption to the main plan.

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