A special steel forging production scheduling method for sparse data

Abstract

The application discloses a special steel forging production scheduling method for sparse data, belongs to the technical field of intelligent manufacturing and production scheduling, and solves the problems that forging time prediction is inaccurate due to sparse data in the prior art, and a scheduling scheme is difficult to be globally optimized due to complex coupling of processes and resources. The method comprises the following steps: based on historical forging order data, a forging time prediction model is constructed, and the model is used to predict standard processing time of a new order to be scheduled on a fast forging machine and a radial forging machine; based on the predicted fast forging standard processing time and the radial forging standard processing time, a special steel forging scheduling optimization model is defined; the special steel forging scheduling optimization model is solved, and a scheduling scheme is output. Through the construction of the integrated solving framework of "prediction-optimization", the scheduling precision and efficiency under the sparse data are effectively improved, the equipment utilization is significantly improved, the manufacturing cycle is shortened, and the production energy consumption is reduced.

Description

Technical Field

[0001] This invention relates to the field of intelligent manufacturing and production scheduling technology, and in particular to a special steel forging production scheduling method for sparse data. Background Technology

[0002] Special steel forging, as a fundamental link in high-end equipment manufacturing, is a core process in high-end manufacturing industries such as aero-engines and nuclear power equipment. The quality of its production scheduling directly affects the manufacturing cycle of major equipment, the efficiency of production resource utilization, the company's ability to fulfill contracts and delivery costs. Special steel forging typically involves multiple processes such as fast forging and radial forging, and orders are characterized by "multiple varieties, small batches, and heterogeneous process paths".

[0003] Existing scheduling methods typically separate time forecasting from scheduling optimization. Regarding time forecasting, traditional methods (such as linear regression and time series analysis) struggle to depict the complex nonlinear relationships between steel grade, billet, and finished product, and their accuracy drops sharply when historical data is sparse. As for scheduling optimization, existing research often employs heuristic rules or simplified models, which can quickly generate feasible solutions, but they struggle to accurately address multiple objectives while ensuring global optimality, such as the dependence between rapid forging and radial forging processes, the dual-layer resource allocation between the radial forging mill and the hammer, and the collaborative optimization of total project duration and equipment stability (e.g., hammer replacement frequency).

[0004] In recent years, although some studies have attempted to apply machine learning methods for time prediction or introduce metaheuristic algorithms for scheduling search, these improvements have not fundamentally solved the inherent problems caused by data sparsity and model complexity. Specifically, machine learning models exhibit large prediction variance and weak generalization ability when there are insufficient samples; while metaheuristic algorithms suffer from slow convergence speed and unstable solution quality when solving large-scale, strongly constrained scheduling problems. Crucially, because the prediction and optimization stages are treated separately, errors in the prediction stage are directly propagated and amplified in subsequent optimization stages, creating a vicious cycle of "garbage in, garbage out," resulting in the actual performance of the final scheduling scheme falling far short of theoretical expectations. Therefore, how to construct an integrated optimization framework that can effectively overcome data sparsity and accurately characterize the complex constraints of the entire special steel forging process, thereby breaking down the barrier between prediction and optimization, has always been a key technical bottleneck that urgently needs to be overcome in this field. Summary of the Invention

[0005] Based on the above analysis, the present invention aims to provide a special steel forging production scheduling method for sparse data, in order to solve the problems in the prior art where inaccurate forging time prediction is caused by data sparsity and the scheduling scheme is difficult to optimize globally due to the complex coupling of processes and resources.

[0006] The objective of this invention is mainly achieved through the following technical solutions:

[0007] This invention provides a special steel forging production scheduling method for sparse data, comprising the following steps: S1: Based on historical forging order data, construct a forging time prediction model, and use the model to predict the standard processing time of new orders to be scheduled on the high-speed forging mill and the radial forging mill; S2: Based on the predicted standard processing time for fast forging and standard processing time for radial forging, a special steel forging scheduling optimization model is defined; S3: Solve the special steel forging scheduling optimization model and output the scheduling scheme; The historical forging order data includes the steel type of the order, the specifications of the billet before forging, and the specifications of the finished product after forging.

[0008] Further, step S1 includes: S11: Based on historical forging order data, construct dimensionally aligned fast forging time tensors respectively. With radial forging time tensor Structured storage of historical forging times under different process combinations; S12: Construct specification relationship diagrams for both rapid forging and radial forging processes, and calculate the corresponding Laplace matrices. and This allows domain knowledge of forging processes to be transformed into computable spatial smoothness constraints. S13: Based on the normalized multivariate decomposition framework, design objective functions with spatial regularization terms for the rapid forging time tensor and the radial forging time tensor, respectively. and ; S14: Use the stochastic gradient descent algorithm to evaluate the objective function. and Parallel optimization is performed to obtain the optimal factor matrix; S15: Reconstruct the complete fast forging and radial forging time tensors using the optimal fast forging factor matrix and the optimal radial forging factor matrix obtained from the solution, respectively, so as to provide a new order query to predict the processing time; In step S11, the dimensions include: dimension A represents the steel type classification of the order, dimension B represents the pre-forging billet specification classification, and dimension C represents the post-forging finished product specification classification.

[0009] Further, step S2 includes: S21: Define the core elements of the special steel forging scheduling optimization model; S22: Define the decision variables for the special steel forging scheduling optimization model; S23: Define the constraints for the special steel forging scheduling optimization model; S24: Define the objective function of the special steel forging scheduling optimization model; S25: Establish an optimization model for special steel forging scheduling.

[0010] Further, step S3 includes: S31: Input all the basic data required for scheduling and transform the special steel forging scheduling optimization model into a specific problem instance for actual orders and resources; S32: Based on the input basic data, an executable instance of the special steel forging scheduling optimization model is fully constructed using the modeling interface of the mathematical optimization solver. S33: On the executable instance of the special steel forging scheduling optimization model constructed in S32, configure the solution parameters and call the optimization engine of the mathematical optimization solver to solve the problem and obtain the values ​​of each decision variable in the model; S34: Analyze the numerical solutions of the decision variables obtained in S33 to generate scheduling plans and reports that can be directly used to guide production.

[0011] Furthermore, in step S12, the specification relationship diagram is a two-dimensional grid diagram, with the horizontal axis representing pre-forging specification category B and the vertical axis representing post-forging specification category C. Each node in the diagram is located at the intersection of the grid and uniquely corresponds to a combination of "pre-forging specification category - post-forging specification category"; In the diagram, two nodes that are adjacent in the horizontal or vertical direction are defined as adjacent in the processing dimension, corresponding to directly adjacent categories in the preset classification sequence for pre-forging or post-forging specifications.

[0012] Furthermore, in step S13, the canonical multivariate decomposition is a CP decomposition; The objective function of the rapid forging time tensor Includes data fitting terms, L2 regularization terms, and terms based on the Laplacian matrix. The Laplace regularization term is as follows:

[0013] The data fitting term is as follows: The L2 regularization term is: Laplace matrix The Laplace regularization term is: ; in, These are three fast forging regularization parameters; These are three rapid forging factor matrices; The rank of the CP decomposition; Represents the trace of a matrix; The algorithm is as follows ; It is the Frobenius norm; The objective function of the radial forging time tensor Specifically as follows:

[0014] in, These are three radial forging regularization parameters; These are three radial forging factor matrices; The rank of the CP decomposition; Represents the trace of a matrix; The algorithm is as follows ; It is the Frobenius norm.

[0015] Furthermore, in step S21, the core elements include orders, production resources, and production time parameters; The complete set of orders is Based on different production process paths, the complete order set Divided into three mutually exclusive subsets: the subset of orders that only require rapid forging. A subset of orders that only require radial forging. A subset of joint orders requiring rapid forging followed by radial forging ; The production resources include: the set of equipment consisting of all available fast forging machines in the system. The system comprises all available radial forging equipment. The resource set consisting of all radial forging machine hammers in the system. Forging machines with specific diameters Hammerhead subset ; The production time parameters include: , indicating an order In a high-speed forging machine The standard processing time is used to predict the tensor by querying the rapid forging time. It can be obtained; , indicating an order On a radial forging machine The standard machining time is used to predict the tensor by querying the radial forging time. It can be obtained; If order The processing time on any radial forging machine is... Similarly, if the order The processing time on any high-speed forging machine is... ; make This indicates the maximum permissible total construction period.

[0016] Furthermore, in step S22, the decision variables include resource allocation decision variables, process sequence decision variables, time planning continuous variables, and hammer replacement identifier binary variables; The resource allocation decision variables are described using the following binary decision variables: For any order Any fast forging machine ,when When, it indicates an order. Assigned to the fast forging machine Process it; otherwise, the value is 0. For any order Arbitrary diameter forging machine ,when When, it indicates an order. Assigned to radial forging machine Process it; otherwise, the value is 0. For any order Arbitrary hammerhead ,when When, it indicates an order. Hammers are used in the radial forging stage. Otherwise, the value is 0. The process sequence decision variables are described using the following binary decision variables to describe the processing order of orders on the same resource: For any two different orders Any fast forging machine Decision variables Indicates a fast forging machine Place an order Is the processing sequence superior to the order? If so, then If not, then ; For any two different orders Arbitrary diameter forging machine Decision variables Indicates radial forging machine Place an order Is the processing sequence superior to the order? If so, then If not, then ; For any two different orders Arbitrary hammerhead Decision variables Indicates hammerhead Place an order Is the processing sequence superior to the order? If so, then If not, then ; The continuous variables for time planning use the following continuous decision variables to define the time attributes of the scheduling: For any order Any fast forging machine , Indicates order In a high-speed forging machine The planned start time on the above, and its corresponding planned completion time is: ; For any order Arbitrary diameter forging machine , Indicates order In the radial forging machine The planned start time on the above, and its corresponding planned completion time is: ; The binary variable for the hammerhead replacement identifier is: For any order , Indicates order The hammer type required in the radial forging stage is considered to be a valid hammer change operation only when two orders with different hammer types required are consecutively assigned to the same radial forging machine. For any two different orders Arbitrary hammerhead ,make Indicates order With orders Is it on the hammer? If it is continuous processing, then If not, then take 0.

[0017] Furthermore, in step S23, the constraints include resource allocation completeness constraints, equipment processing sequence constraints, cross-stage process dependency constraints, hammer replacement logic constraints, total project duration constraints, and sequential logic completeness constraints. The resource allocation completeness constraint ensures that each order is uniquely allocated to the required high-speed forging mill, radial forging mill, and hammer. The equipment processing timing constraints ensure that the time windows of orders processed on the same resource do not overlap. The cross-stage process dependency constraint ensures that for joint orders that require rapid forging followed by radial forging, the start time of radial forging is later than the end time of rapid forging. The hammer replacement logic constraint is used to identify and count replacement events caused by orders requiring different hammer types for continuous processing; The total project duration constraint ensures that the total project duration is not less than the completion time of any order and does not exceed the maximum allowable value; The sequential logic completeness constraint ensures mutual exclusion between sequential variables and their dependence on resource allocation.

[0018] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described special steel forging production scheduling method for sparse data.

[0019] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects: 1. The method of this invention constructs a forging time prediction model based on sparse tensor completion. For the first time, the process specification relationship diagram is embedded into the learning framework in the form of Laplace regularization, so that the prediction process is guided by physical laws, providing a high-precision and reliable input for scheduling optimization, and solving the problem of prediction inaccuracy caused by sparse production data.

[0020] 2. The method of this invention designs a special steel forging scheduling optimization model that integrates multi-layer resources and process dependencies. It uniformly describes the allocation and timing of fast forging machines, radial forging machines and hammers in the form of mixed integer programming, and coordinates the dual objectives of "minimizing the total construction period" and "reducing hammer replacement" for optimization, providing an accurate and complete mathematical model paradigm for complex forging scheduling.

[0021] 3. The method of this invention constructs an integrated "prediction-optimization" solution framework, tightly coupling the upper and lower layers of the model to form a closed-loop optimization link from data to decision, achieving a synergistic improvement in prediction accuracy and scheduling efficiency. This method can generate feasible and globally optimal or near-optimal production scheduling solutions, significantly improving equipment utilization, shortening manufacturing cycles, reducing production energy consumption and tool wear, and demonstrating excellent practicality and stability in complex production scenarios with multiple process paths and small-batch orders.

[0022] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objects and other advantages of this invention can be realized and obtained from what is particularly pointed out in the description and drawings. Attached Figure Description

[0023] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0024] Figure 1 This is a schematic diagram of the technical route for the special steel forging production scheduling method for sparse data according to the present invention. Figure 2 This is a schematic diagram illustrating the technical route for constructing the forging time prediction model and predicting the rapid forging time and radial forging time of new orders to be scheduled, as per the present invention. Figure 3 This is a schematic diagram illustrating the technical route for constructing and solving the special steel forging scheduling optimization model of the present invention. Detailed Implementation

[0025] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0026] This invention provides a special steel forging production scheduling method for sparse data, comprising: S1: Based on historical forging order data, construct a forging time prediction model, and use the model to predict the standard processing time of new orders to be scheduled on the high-speed forging mill and the radial forging mill; Specifically, step S1 includes the following steps: S11: Based on historical forging order data, construct dimensionally aligned fast forging time tensors and radial forging time tensors respectively, and store the historical forging time under different process combinations in a structured manner. Specifically, the historical forging order data includes the order steel grade, pre-forging billet specifications, and post-forging finished product specifications. Three dimensions are defined: Dimension A represents the order steel grade classification, Dimension B represents the pre-forging billet specification classification, and Dimension C represents the post-forging finished product specification classification. Based on this, two dimensionally aligned third-order sparse tensors are constructed: the rapid forging time tensor. With radial forging time tensor ,in Tensor storage provides historical rapid forging times under specific process combinations. Tensor storage is used to store historical radial forging times for specific process combinations. Due to the discrete nature of production order combinations, not all order steel grades have forging records for all specification combinations. tensor and The tensors are all sparse tensors, with a large number of missing values ​​that need to be filled. For example, the steel grades in the orders include alloy structural steel 40Cr, die steel 4Cr5MoSiV1, etc. It should be noted that in this invention, the steel grade classification, pre-forging specification classification, and post-forging specification classification all constitute predefined, finite discrete sets; the content of these sets is based on domain knowledge, production history, and enterprise standards, and can be configured and updated during system initialization. Specific rules are as follows: Steel grade classification: The basic classification unit is the specific steel grade (such as 40Cr alloy structural steel, 4Cr5MoSiV1 mold steel, etc.) in national or enterprise standards. Steel grades with the same grade have consistent composition and processing characteristics and are classified into one category. In practice, a very small number of specific grades may also be merged based on the similarity of composition and performance.

[0027] Pre-forging / Post-forging Specification Classification: A composite hierarchical rule of "shape-weight range-size range" is adopted. First, it is classified according to the main shape (e.g., round steel, square steel, flat steel, etc.). Then, under each shape, it is divided into continuous numerical ranges according to weight (tons). Next, for specifications within a weight range, it is further divided into size ranges according to the key cross-sectional dimensions (millimeters). A specific specification classification is uniquely determined by the shape, the corresponding weight range, and the corresponding size range. For example, the small weight range is greater than 0 tons and not more than 3 tons (0 < weight ≤ 3 tons), the medium weight range is greater than 3 tons and not more than 6 tons (3 < weight ≤ 6 tons), and the large weight range is greater than 6 tons and not more than 10 tons (6 < weight ≤ 10 tons). For example, pre-forging billet specifications include 5T round steel 410mm... 530mm, 10T square steel 220mm 400mm, etc., finished product specifications after forging include 3T octagonal 150mm, etc. 420mm, 5T flat steel 240mm 90mm, etc.

[0028] The core principle of this invention's classification of historical forging orders is that "orders sharing the same or extremely similar processing parameters are grouped into the same category." Therefore, classification according to predefined rules for steel grades and pre- / post-forging specifications ensures that historical forging orders with similar processes are grouped into the same or adjacent categories, laying the foundation for subsequently constructing a tensor dimension and specification relationship diagram with process significance. The process parameters of any actual order can be uniquely mapped to a specific category within these three classification sets.

[0029] S12: Construct specification relationship diagrams for fast forging and radial forging processes respectively, and calculate the corresponding Laplace matrix to transform the domain knowledge of forging processes into computable spatial smoothness constraints. Specifically, to characterize the process relationships between different specifications, specification relationship diagrams for rapid forging and radial forging processes are constructed separately, and the corresponding Laplace matrices are calculated to transform the neighborhood knowledge of forging processes into computable spatial smoothness constraints; specifically, for the rapid forging process, its two-dimensional specification diagram is constructed. In the graph, nodes correspond to various specification categories. If two specifications are adjacent in terms of processing dimensions (such as continuous weight or cross-sectional size ranges), a connecting edge is established between their corresponding nodes. Based on the graph... adjacency matrix degree matrix Calculate its Laplace matrix. Similarly, for the radial forging process, the above process is repeated to obtain the degree matrix of the radial forging slices. and adjacency matrix And calculate the Laplace matrix of radial forging. This step transforms the neighborhood knowledge of the forging process into computable spatial smoothness constraints.

[0030] It should be noted that the method for establishing the two-dimensional specification relationship diagram is as follows: An undirected graph is independently constructed for both the rapid forging process and the radial forging process. This graph is a two-dimensional mesh graph, where the horizontal axis (X dimension) represents the pre-forging specification category B (i.e., the value of dimension B, such as B1, B2, ..., B...). n The vertical axis (Y-axis) represents the forging specification category C (i.e., the value of dimension C, such as C1, C2, ..., C...). n Each node in the diagram is located at the intersection of the grid and uniquely corresponds to a combination of "pre-forging specification category - post-forging specification category", i.e., a (B) i C j For example, assuming there are three pre-forging specifications (B1, B2, B3) and two post-forging specifications (C1, C2), then the graph would have 3 × 2 = 6 nodes, corresponding to (B1, C1), (B1, C2), (B2, C1)... (B3, C2). For the rapid forging time tensor... or radial forging time tensor When a certain steel grade A is fixed m When (i.e., a specific value of dimension A) is obtained, a two-dimensional matrix in dimensions B and C can be obtained. Each element position (i, j) in this matrix, that is, the combination of the i-th pre-forging specification and the j-th post-forging specification, corresponds exactly to a node (B) in the two-dimensional specification relationship diagram. i C j In other words, the set of nodes in the specification relationship graph is the same as the set of all possible combinations of the time tensor in the two dimensions B and C. The graph is constructed to characterize the process relationships between these different specification combinations.

[0031] In a two-dimensional specification diagram, two nodes that are adjacent in the horizontal or vertical direction are defined as "adjacent in the processing dimension." This corresponds to the following two quantifiable cases of process similarity: Laterally adjacent (horizontal edge): Two nodes have the same post-forging specification C, but their pre-forging specification B are directly adjacent categories in the preset classification sequence (e.g., B2 and B3 are adjacent). This means that the billet weight or size differs by a preset range, and the forging deformation is similar.

[0032] Vertically adjacent (vertical edge): Two nodes have the same pre-forging specification B, but their post-forging specification C are directly adjacent categories in the preset classification sequence. This means that the target size of the finished product differs by a preset range, and the processing difficulty and steps are similar.

[0033] The calculated graph Laplacian matrix and , are the structure matrices corresponding to the specification relationship diagrams of the fast forging process and the radial forging process, respectively. Their number of rows and columns are both equal to B × C, i.e., (number of specification categories before forging) × (number of specification categories after forging), corresponding to the order of all (B, C) combination nodes in the two-dimensional specification relationship diagram after expanding into a one-dimensional list. This step transforms the neighborhood knowledge of the forging process into a computable spatial smoothness constraint. Its core principle is: if two specification combinations are similar in process (i.e., adjacent nodes in the diagram), then their corresponding processing times should also be similar; the introduction of the Laplace matrix is ​​precisely to reflect this process law in the model, ensuring that the predicted processing time maintains a smooth change at adjacent nodes.

[0034] S13: Based on the normalized multivariate decomposition framework, design objective functions with spatial regularization terms for the rapid forging time tensor and the radial forging time tensor, respectively. Specifically, based on the canonical multivariate decomposition framework (exemplarily, CP decomposition), objective functions with spatial regularization terms are designed for the rapid forging time tensor and the radial forging time tensor, respectively. The objective function for the rapid forging time tensor is... Includes data fitting terms, L2 regularization terms, and terms based on the Laplacian matrix. The Laplace regularization term is as follows:

[0035] The data fitting term is as follows: The L2 regularization term is: Laplace matrix The Laplace regularization term is: ; in, These are three fast forging regularization parameters; These are three rapid forging factor matrices; The rank of the CP decomposition; Represents the trace of a matrix; The algorithm is as follows ; It is the Frobenius norm.

[0036] Similarly, the objective function of the radial forging time tensor Constructed in the same form, the objective function Specifically as follows:

[0037] in, These are three radial forging regularization parameters; These are three radial forging factor matrices; The rank of the CP decomposition; Represents the trace of a matrix; The algorithm is as follows ; It is the Frobenius norm.

[0038] It should be noted that the objective function and This is a tensor completion model used to complete the time tensors of rapid forging and radial forging; in the objective function and In this model, the data fitting term is used to improve the fitting accuracy, ensuring that the tensor reconstructed by the tensor completion model is as close as possible to the true observed value at the known (non-missing) data location, thereby minimizing the reconstruction error; the L2 regularization term prevents overfitting; and the Laplace regularization term injects the spatial constraints of the fast forging process and the radial forging process into the corresponding tensor completion models, forcing that the adjacent specifications of the fast forging process or the radial forging process on the corresponding two-dimensional specification diagram structure also tend to have similar factor matrix characteristics, thereby guiding the tensor completion model to conform to the physical process law when completing missing values.

[0039] Laplace matrix acting on tensor factor matrix (Dimensions are B × R) and (When the size is C × R) it needs to be transposed and deformed. Specifically, in middle, Each row represents a feature vector of a pre-forging specification B in the latent space (R-dimensional), but in order to make it compatible with a (B×C) dimensional vector... To multiply, you need to first... and The feature matrix is ​​formed by combining elements using methods such as the Kronecker product, which corresponds to the node order. In other words, the Laplace regularization term constrains the factor matrix... and In this context, the row vectors corresponding to adjacent categories should be as similar as possible.

[0040] Will Adding a smoothness constraint term, such as the Laplacian regularization term, to the objective function means that during model training (tensor completion), not only is fitting existing historical data required, but also a smoothness constraint term based on the specification graph structure is introduced, namely the factor matrix (as mentioned above). , , , These factor matrices maintain a smooth transition across the corresponding specification relationship graph. This smoothness constraint reflects domain knowledge of the forging process: adjacent nodes in the specification relationship graph (i.e., pre-forging or post-forging specifications with similar processes) should have similar characteristic representations in their corresponding factor matrices. By minimizing this regularization term, the model can be guided to make the factor matrix vectors corresponding to adjacent specifications tend to be similar during the learning process, thereby embedding the process continuity regularity into the tensor completion model. Under the condition of sparse historical data (i.e., a large number of missing process-time correspondences), this smoothness constraint can effectively guide the model to make reasonable missing value inferences based on process similarity, avoiding blind interpolation due to insufficient data, thereby significantly improving the accuracy and physical rationality of the prediction results.

[0041] It should be noted that the regularization parameter (λ) and CP decomposition rank (R) in the objective function are not fixed empirical values. Their optimal values ​​are determined through a standard data-driven optimization process to ensure the model's generalization ability under sparse data.

[0042] The rank (R) of the CP decomposition is determined using the validation set method, which includes the following steps: In the historical data used for training, a portion of known processing time entries are pre-defined as a validation set. Pre-set a set of candidate rank values, for example, R=3, 4, 5, 6, 7; For each candidate rank R, a tensor completion model is trained using the remaining historical data, and its prediction accuracy is evaluated on the validation set (e.g., the root mean square error is calculated). The R with the smallest prediction error and the smallest rank value on the validation set is selected from the candidate ranks as the final decomposition rank. Based on the characteristics of actual forging data, the final determined rank is generally between 3 and 7, which can ensure the model's fitting ability while avoiding overfitting.

[0043] Determining the regularization parameter (λ): A method combining K-fold cross-validation and parameter search (such as grid search) is adopted, specifically including the following steps: Based on the model structure and prior knowledge of the process, several sets of regularized parameter combinations to be tested are set to form a parameter search space; The historical known data is evenly divided into K mutually exclusive subsets. Each subset is used as the validation set, and the remaining K-1 subsets are combined as the training set. For each set of candidate parameters, perform K rounds of training and validation: in each round, train the tensor completion model using the current training set and calculate the prediction error index on the corresponding validation set; Calculate the average prediction error of each set of parameters in K rounds of validation, and select the parameter combination with the smallest average error as the final model hyperparameters; Through the above cross-validation and parameter search process, regularization parameters can be determined systematically and objectively, thereby achieving an optimal balance between data fitting accuracy, process smoothness constraints, and model generalization ability.

[0044] S14: Use the stochastic gradient descent algorithm to evaluate the objective function. and Parallel optimization is performed to obtain the optimal factor matrix; Specifically, the stochastic gradient descent algorithm is used to apply the objective function. and Parallel optimization is performed, and the solution process includes: optimizing the objective function separately. and The factor matrices are initialized using a normal distribution with random initialization, and the initial learning rate, maximum number of iterations, batch size, and convergence threshold are set. In each iteration, a batch of triplet observation data is randomly sampled, and the gradient of the objective function with respect to each factor matrix is ​​calculated through backpropagation. Subsequently, the parameters of all factor matrices are updated synchronously according to the gradient direction and learning rate. The iterative process continues until the reconstruction error is lower than the preset threshold or the maximum number of iterations is reached, and finally, the optimal fast-forging factor matrix is ​​output. With the radial forging factor matrix .

[0045] It should be noted that the "parallel optimization solution" refers to: the rapid forging time prediction model (objective function) ) and radial forging time prediction model (objective function) In computers, training and solving are performed simultaneously (in parallel) as two independent tasks, with no computational dependency between them; this is task-level parallelism, designed to improve overall solution efficiency. During the training of a single model, the automatic parallel capabilities of modern computing frameworks (such as PyTorch and TensorFlow) can also be used to accelerate tensor operations.

[0046] It should be noted that the settings for the initial learning rate, maximum number of iterations, batch size, and convergence threshold follow the general principles of training neural networks and tensor decomposition models. The initial learning rate is typically set to a small positive value (e.g., 0.01 or 0.001), and a learning rate decay strategy (e.g., decaying during the validation error plateau) can be used to improve convergence stability. The maximum number of iterations is set to a sufficiently large value (e.g., 2000 or 5000) to ensure sufficient training. The convergence threshold is set to a small positive number (e.g., 1e-5), and the iterations terminate early when the objective function value drops below this threshold. The specific values ​​of these parameters can be determined through small-scale trial training and validation on historical data, which is standard engineering practice for implementing this type of optimization algorithm.

[0047] It should be noted that in each iteration, a batch of triplet observation data is randomly sampled, and the gradient of the objective function with respect to each factor matrix is ​​calculated through backpropagation. The batch size refers to the number of valid observation entries (i.e., combinations of "steel grade - pre-forging specifications - post-forging specifications" with known processing times) randomly sampled in each parameter update of stochastic gradient descent. For example, a batch size of n means that in each iteration, n entries are randomly selected from all known time data (combinations of "steel grade - pre-forging specifications - post-forging specifications") for calculating the gradient and updating model parameters. This value should generally be as large as possible, within the limits of computational resources, to improve the stability of gradient estimation and accelerate model convergence. Furthermore, the "triplet observation data" contains complete training information, specifically: an index triplet (a, b, c), corresponding to the steel grade category index, the pre-forging specification category index, and the post-forging specification category index, respectively, and the index in the sparse tensor. or The corresponding known processing time observation value.

[0048] S15: Reconstruct the complete fast forging and radial forging time tensors using the obtained optimal fast forging factor matrix and optimal radial forging factor matrix respectively, so as to provide new order query and prediction of processing time.

[0049] Specifically, the optimal rapid forging factor matrix obtained by solving the problem is used. Reconstruct the complete rapid forging time prediction tensor The optimal forging factor matrix obtained by solving the problem is used. Reconstruct the complete radial forging time prediction tensor .

[0050] For a new order, after determining the indices (a, b, c) corresponding to its steel grade classification A, pre-forging specification B, and post-forging specification C, the rapid forging time prediction tensor is obtained based on these indices. The value located at that index is the predicted standard processing time for fast forging; similarly, to obtain... Predicting tensor of radial forging time The value located at the same index is the predicted standard machining time for radial forging.

[0051] S2: Based on the predicted standard processing time for fast forging and standard processing time for radial forging, a special steel forging scheduling optimization model is defined; Specifically, step S2 includes: S21: Define the core elements of the special steel forging scheduling optimization model; Specifically, the core elements include orders, production resources, and production time parameters.

[0052] Specifically, the complete order set is Based on different production process paths, the complete order set Divided into three mutually exclusive subsets: the subset of orders that only require rapid forging. A subset of orders that only require radial forging. A subset of joint orders requiring rapid forging followed by radial forging .

[0053] It should be noted that the core task of the rapid forging stage is to process all orders that require rapid forging (i.e., Allocate appropriate high-speed forging mill resources and determine their processing sequence on each piece of equipment. The core task of the radial forging stage is to process all orders requiring radial forging (i.e., Allocate appropriate radial forging machine resources and the hammer resources attached to them, and determine the processing sequence. The scheduling scheme for the radial forging stage must follow the process dependencies generated in the rapid forging stage to ensure the process sequence of joint orders. That is, when arranging radial forging machine and hammer resources for all orders that require radial forging (including joint orders and orders that only require radial forging), the radial forging time of joint orders cannot be arbitrarily arranged. When scheduling, it must be ensured that the start time of radial forging arranged for a certain joint order must be later than the end time of rapid forging that has been arranged in the rapid forging stage. This is "following the process dependencies generated in the rapid forging stage" to ensure that the process sequence of "rapid forging first, then radial forging" is strictly executed in time and that the logical error of "radial forging is arranged before rapid forging" does not occur.

[0054] Specifically, the production resource set includes: the set of all available fast forging machines in the system. The system comprises all available radial forging equipment. The resource set consisting of all radial forging machine hammers in the system. Forging machines with specific diameters Hammerhead subset (i.e., the hammer resources available for this radial forging mill).

[0055] Specifically, the production time parameters include: , indicating an order In a high-speed forging machine The standard processing time is used to predict the tensor by querying the rapid forging time. It can be obtained; , indicating an order On a radial forging machine The standard machining time is used to predict the tensor by querying the radial forging time. It can be obtained; It should be noted that, based on the definition of an order subset, it can be naturally concluded that if an order... The processing time on any radial forging machine is... Similarly, if the order The processing time on any high-speed forging machine is... .make This indicates the maximum permissible total construction period.

[0056] S22: Define the decision variables for the special steel forging scheduling optimization model; Specifically, decision variables are defined to describe resource allocation, process sequence, time planning, and hammer replacement events, in order to comprehensively characterize the special steel forging scheduling scheme.

[0057] Specifically, the following decision variables are defined: Resource allocation decision variables: The special steel forging scheduling optimization model uses the following binary decision variables to describe the resource allocation scheme: For any order Any fast forging machine ,when When, it indicates an order. Assigned to the fast forging machine Process it; otherwise, take the value 0.

[0058] For any order Arbitrary diameter forging machine ,when When, it indicates an order. Assigned to radial forging machine Process it; otherwise, take the value 0.

[0059] For any order Arbitrary hammerhead ,when When, it indicates an order. Hammers are used in the radial forging stage. Otherwise, the value is 0.

[0060] The special steel forging scheduling optimization model uses the following binary decision variables to describe the processing sequence of orders on the same resource: For any two different orders Any fast forging machine Decision variables Indicates a fast forging machine Place an order Is the processing sequence superior to the order? If so, then If not, then ; For any two different orders Arbitrary diameter forging machine Decision variables Indicates radial forging machine Place an order Is the processing sequence superior to the order? If so, then If not, then ; For any two different orders Arbitrary hammerhead Decision variables Indicates hammerhead Place an order Is the processing sequence superior to the order? If so, then If not, then .

[0061] For time-planning continuous variables, the special steel forging scheduling optimization model uses the following continuous decision variables to define the time attributes of the scheduling: For any order Any fast forging machine , Indicates order In a high-speed forging machine The planned start time on the above, and its corresponding planned completion time is: ; For any order Arbitrary diameter forging machine , Indicates order In the radial forging machine The planned start time on the above, and its corresponding planned completion time is: .

[0062] Hammerhead replacement identifier binary variable: For any order , Indicates order The hammer type required in the radial forging stage is considered to be the only valid hammer change operation when two orders requiring different hammer types are consecutively assigned to the same radial forging machine.

[0063] For any two different orders Arbitrary hammerhead ,make Indicates order With orders Is it on the hammer? If it is continuous processing, then If not, then take zero.

[0064] S23: Define the constraints for the special steel forging scheduling optimization model; Specifically, a series of constraints are established to ensure that the scheduling scheme meets all production rules and resource limitations. These constraints include resource allocation completeness constraints, equipment processing sequence constraints, cross-stage process dependency constraints, hammer replacement logic constraints, total project duration constraints, and sequential logic completeness constraints. The resource allocation completeness constraint ensures that each order is uniquely allocated to the required high-speed forging mill, radial forging mill, and hammer, including: Uniqueness constraint of high-speed forging mill: Each order requiring rapid forging must be assigned to one and only one rapid forging machine; Uniqueness constraint of radial forging mill: Each order requiring radial forging must be assigned to one and only one radial forging machine; Hammerhead allocation consistency constraint: Each order requiring radial forging must be assigned one and only one hammer, and that hammer must belong to the radial forging machine to which it is assigned.

[0065] The equipment processing timing constraints ensure that the time windows of orders processed on the same resource do not overlap. The processing timing constraints of the equipment are defined as a sufficiently large positive constant, including: High-speed forging mill timing constraints: In any high-speed forging mill If the order In orders Previously processed, then the order The start time must not be earlier than the order. End time;

[0066] Timing constraints for radial forging mills: In any radial forging mill If the order In orders Previously processed, then the order The start time must not be earlier than the order. The end time.

[0067]

[0068] Hammerhead usage timing constraints: In any hammerhead If the order In orders Previously processed, then the order The start time must not be earlier than the order. The end time. This constraint only applies if both orders use the same hammerhead.

[0069]

[0070] The cross-stage process dependency constraint is: For any joint order If it is assigned to a fast forging machine With radial forging machine Therefore, the start time of the radial forging process must be later than the end time of the rapid forging process. The connection constraint between rapid forging and radial forging is the core of coupling the two stages of rapid forging and radial forging.

[0071] The hammerhead replacement logic constraint is as follows:

[0072] Among them, hammerhead type consistency indicator factor Defined as:

[0073] The hammer replacement logic constraint is used to accurately identify and count hammer replacement events if and only if the two required hammer types are different (i.e., An order is counted as a valid hammer change only when the order is processed continuously on the same hammer.

[0074] The total project duration constraint defines and limits the total project duration. ,include: Lower bound constraint on project duration (rapid forging): The total project duration must not be less than the completion time of any order on its assigned rapid forging mill. Not assigned to fast forging machine When this constraint is a constant Relaxed management .

[0075] Lower bound constraint on lead time (radial forging): The total lead time must not be less than the completion time of any order on its assigned radial forging mill. When an order Not assigned to radial forging machine When this constraint is a constant Relaxed management .

[0076] Maximum project duration constraint: The total project duration shall not exceed the preset maximum allowable value. , .

[0077] The sequential logic completeness constraint ensures the logical consistency and rationality among sequential decision variables, including: High-speed forging mill sequence completeness constraint: In any high-speed forging mill In this context, the processing order of any two different orders is mutually exclusive, and the validity of the order variable is contingent upon resource allocation.

[0078]

[0079] Radial forging mill sequence completeness constraint: in any radial forging mill In this context, the processing order of any two different orders is mutually exclusive, and the validity of the order variable is contingent upon resource allocation.

[0080]

[0081] Hammer order completeness constraint: In any hammer order In this context, the processing order of any two different orders is mutually exclusive, and the validity of the order variable is contingent upon resource allocation.

[0082]

[0083] S24: Define the objective function of the special steel forging scheduling optimization model The special steel forging scheduling model aims to minimize the total project duration and reduce the total number of hammer replacements. If we change the penalty coefficient for the hammerhead, then the objective function becomes:

[0084] S25: Establishing an optimization model for special steel forging scheduling Combining the defined core elements, constraints, and objective function, The special steel forging scheduling model can be summarized as follows:

[0085]

[0086] It should be noted that, by specifying the input parameters and set (S21), all basic data required by the model, such as orders, resources, and time, are determined; decision variables are defined (S22), introducing mathematical variables to represent all decisions to be determined in the scheduling scheme; formalizing the constraints (S23), the production rules are translated into mathematical equations or inequalities that the decision variables must satisfy; constructing the objective function (S24), the optimization objective is expressed as a mathematical function of the decision variables; by executing the above steps S21 to S24, the definition of the special steel forging scheduling optimization model is completed. This model is a mixed integer programming problem with a clear mathematical expression. The model is completely characterized by its defined mathematical elements, variables, constraints, and objective function.

[0087] S3: Solve the special steel forging scheduling optimization model and output the scheduling scheme.

[0088] Specifically, step S3 includes the following steps: S31: Input all the basic data required for scheduling and transform the special steel forging scheduling optimization model into a specific problem instance for actual orders and resources; It should be noted that the special steel forging scheduling optimization model constructed in step S2 is in mathematical form, where multiple sets and parameters are represented by symbols. Inputting all the basic data required for scheduling involves assigning specific numerical values ​​to these symbols, transforming the "mathematical form" into a specific problem instance tailored to the current actual orders and resources. Specifically, all the input basic data includes: Order data: Complete order list and its subsets ( , , Standard processing time for each order on high-speed forging mills and radial forging mills , Hammer type required for radial forging orders ; Resource Data: Collection of High-Speed ​​Forging Machines 1. Radial forging machine assembly Hammer head collection and their subordinate relationships ; Model parameters: Maximum allowable construction period Hammer head replacement penalty coefficient linearization constant .

[0089] S32: Based on the input basic data, an executable instance of the special steel forging scheduling optimization model is fully constructed using the modeling interface of the mathematical optimization solver. Specifically, the process includes: creating all decision variables and model variables, including resource allocation variables, within the programming environment of the selected mathematical optimization solver (e.g., CPLEX, Gurobi, or an open-source solver), based on the definition of S22 and the specific data in S31. Ordinal variables Time variables and hammerhead replacement identifier variable ; Based on the definition of S23 and the specific data of S31, add instances of all six types of constraints (resource allocation completeness, equipment processing sequence, cross-stage process dependency, hammer replacement logic, total project duration, and sequential logic completeness).

[0090] According to the definition in S24, set the objective function as follows:

[0091] Thus, a complete and structured special steel forging scheduling optimization model (i.e., a mixed integer programming problem model) is formed inside the solver, and it awaits the solution instruction.

[0092] S33: On the executable instance of the special steel forging scheduling optimization model constructed in S32, configure the solution parameters and call the optimization engine of the mathematical optimization solver to solve the problem and obtain the values ​​of each decision variable in the model; Specifically, before starting the solution process, configure the solution parameters of the mathematical optimization solver, including computation time limits and optimality gap tolerance, and then start the solution process. After configuration, call the solver's solution functions (such as model.solve() or model.optimize()); the solver will run its built-in optimization algorithms (such as branch and bound, cut plane) to automatically optimize the model until the preset termination conditions are met (such as reaching the time limit or optimality gap); after the solution is completed, the solver will output the solution status (such as marked as "optimal solution" or "feasible solution") and the specific values ​​of each decision variable in the model.

[0093] It's important to note that to ensure timely generation of scheduling solutions for production decision-making, a maximum allowable computation time must be set, known as the computation time limit. This limit is not fixed but dynamically determined based on the real-time requirements and scale of the scheduling problem (such as the number of orders and resources). A typical setting principle is: for daily scheduling, it can be set to several minutes to an hour; for urgent order insertions or small-scale rescheduling, it can be set to several seconds to several minutes. Once this time limit is reached, the solver will stop and return to the currently found best feasible solution.

[0094] The optimality gap tolerance is an indicator of solution quality, defined as (target value of the current optimal solution - current optimal lower bound) / |current optimal lower bound|. Setting an optimality gap tolerance (e.g., 0.5%-2%) means that the solver can terminate the solution when it proves that the target value of the current solution is close to the theoretical optimum within this tolerance range. This avoids spending excessive computation time in pursuit of an absolutely optimal solution. The principle for setting it is: for production scheduling applications, the optimality gap tolerance is usually set between 0.5% and 2% to achieve an engineering balance between solution quality and computational efficiency.

[0095] The solution process terminates when any of the following conditions are met: (1) the solver finds an optimal solution that is proven to be within the optimality gap tolerance (i.e., it has been proven that there is no solution that is above the current optimality gap tolerance range); (2) the solution reaches the preset computation time limit; (3) the solver finds the theoretically absolute optimal solution (gap is 0).

[0096] S34: Analyze the numerical solutions of the decision variables obtained in S33 to generate scheduling plans and reports that can be directly used to guide production.

[0097] It should be noted that the quality of the solution is determined based on the solution status returned by the solver. If the status is "optimal," or "feasible" and the objective function value meets the preset optimality gap requirement, then the numerical solution is considered a high-quality scheduling scheme, and further processing is performed on it. Specifically, this includes: Extracting and analyzing the optimal solution: Read the optimal values ​​of all decision variables from the results returned by the solver that meet the quality requirements; Generate Gantt chart: based on variables We can create Gantt charts for order scheduling on high-speed forging machines, radial forging machines, and hammers to visually display equipment load and order progress.

[0098] Generate scheduling reports: Compile and output key performance indicators, including total project duration. Total number of hammer replacements.

[0099] Generate production instructions: Transform the scheduling plan into a specific list of production instructions, specifying when and what resources will be used for processing each order.

[0100] It should be noted that the "optimal scheduling scheme" refers to the solver output that satisfies one of the following conditions: (1) a scheme that has been proven by the solver to be the globally optimal solution; or (2) a feasible scheme with the best objective function value within a preset optimality gap tolerance range. The latter is an engineering practice adopted in large-scale complex problems to balance solution efficiency and scheme quality. Finally, the solver outputs a scheduling scheme that satisfies all constraints (i.e., the assignment results of all decision variables).

[0101] This invention proposes a special steel forging production scheduling method for sparse data to overcome the challenges of accurate prediction and global optimization driven by data. First, a forging time prediction model based on sparse tensor completion is constructed. For the first time, the process specification relationship diagram is embedded into the learning framework using Laplace regularization, guiding the prediction process with physical laws and providing a high-precision, reliable input for scheduling optimization, thus solving the prediction inaccuracy problem caused by sparse production data. Second, a special steel forging scheduling optimization model integrating multi-layered resources and process dependencies is designed. A mixed-integer programming approach is used to uniformly characterize the allocation and timing of the high-speed forging machine, radial forging machine, and hammers. The dual objectives of "minimizing the total project duration" and "reducing hammer replacements" are optimized collaboratively, providing an accurate and complete mathematical model paradigm for complex forging scheduling. Finally, by constructing an integrated "prediction-optimization" solution framework, the upper and lower layers of the model are tightly coupled, forming a closed-loop optimization link from data to decision, achieving a synergistic improvement in prediction accuracy and scheduling efficiency. The proposed method can generate feasible and globally optimal or near-optimal production scheduling solutions, significantly improving equipment utilization, shortening manufacturing cycle, reducing production energy consumption and tool wear, and demonstrating excellent practicality and stability for complex production scenarios with multiple process paths and small batch orders.

[0102] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware, and the program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.

[0103] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A special steel forging production scheduling method for sparse data, characterized in that, Includes the following steps: S1: Based on historical forging order data, construct a forging time prediction model, and use the model to predict the standard processing time of new orders to be scheduled on the high-speed forging mill and the radial forging mill; S2: Based on the predicted standard processing time for fast forging and standard processing time for radial forging, a special steel forging scheduling optimization model is defined; S3: Solve the special steel forging scheduling optimization model and output the scheduling scheme; The historical forging order data includes the steel type of the order, the specifications of the billet before forging, and the specifications of the finished product after forging.

2. The special steel forging production scheduling method according to claim 1, characterized in that, Step S1 includes: S11: Based on historical forging order data, construct dimensionally aligned fast forging time tensors respectively. With radial forging time tensor Structured storage of historical forging times under different process combinations; S12: Construct specification relationship diagrams for both rapid forging and radial forging processes, and calculate the corresponding Laplace matrices. and This allows domain knowledge of forging processes to be transformed into computable spatial smoothness constraints. S13: Based on the normalized multivariate decomposition framework, design objective functions with spatial regularization terms for the rapid forging time tensor and the radial forging time tensor, respectively. and ; S14: Use the stochastic gradient descent algorithm to evaluate the objective function. and Parallel optimization is performed to obtain the optimal factor matrix; S15: Reconstruct the complete fast forging and radial forging time tensors using the optimal fast forging factor matrix and the optimal radial forging factor matrix obtained from the solution, respectively, so as to provide a new order query to predict the processing time; In step S11, the dimensions include: dimension A represents the steel type classification of the order, dimension B represents the pre-forging billet specification classification, and dimension C represents the post-forging finished product specification classification.

3. The special steel forging production scheduling method according to claim 1, characterized in that, Step S2 includes: S21: Define the core elements of the special steel forging scheduling optimization model; S22: Define the decision variables for the special steel forging scheduling optimization model; S23: Define the constraints for the special steel forging scheduling optimization model; S24: Define the objective function of the special steel forging scheduling optimization model; S25: Establish an optimization model for special steel forging scheduling.

4. The special steel forging production scheduling method according to claim 1, characterized in that, Step S3 includes: S31: Input all the basic data required for scheduling and transform the special steel forging scheduling optimization model into a specific problem instance for actual orders and resources; S32: Based on the input basic data, an executable instance of the special steel forging scheduling optimization model is fully constructed using the modeling interface of the mathematical optimization solver. S33: On the executable instance of the special steel forging scheduling optimization model constructed in S32, configure the solution parameters and call the optimization engine of the mathematical optimization solver to solve the problem and obtain the values ​​of each decision variable in the model; S34: Analyze the numerical solutions of the decision variables obtained in S33 to generate scheduling plans and reports that can be directly used to guide production.

5. The special steel forging production scheduling method according to claim 2, characterized in that, In step S12, the specification relationship diagram is a two-dimensional grid diagram, with the horizontal axis representing pre-forging specification category B and the vertical axis representing post-forging specification category C. Each node in the diagram is located at the intersection of the grid and uniquely corresponds to a combination of "pre-forging specification category - post-forging specification category"; In the diagram, two nodes that are adjacent in the horizontal or vertical direction are defined as adjacent in the processing dimension, corresponding to directly adjacent categories in the preset classification sequence for pre-forging or post-forging specifications.

6. The special steel forging production scheduling method according to claim 2, characterized in that, In step S13, the canonical multivariate decomposition is a CP decomposition; The objective function of the rapid forging time tensor Includes data fitting terms, L2 regularization terms, and terms based on the Laplacian matrix. The Laplace regularization term is as follows: The data fitting term is as follows: The L2 regularization term is: Laplace matrix The Laplace regularization term is: ; in, These are three rapid forging regularization parameters; These are three rapid forging factor matrices; The rank of the CP decomposition; Represents the trace of a matrix; The algorithm is ; It is the Frobenius norm; The objective function of the radial forging time tensor Specifically as follows: in, These are three radial forging regularization parameters; These are three radial forging factor matrices; The rank of the CP decomposition; Represents the trace of a matrix; The algorithm is ; It is the Frobenius norm.

7. The special steel forging production scheduling method according to claim 3, characterized in that, In step S21, the core elements include orders, production resources, and production time parameters; The complete set of orders is Based on different production process paths, the complete order set Divided into three mutually exclusive subsets: the subset of orders that only require rapid forging. A subset of orders that only require radial forging. A subset of joint orders requiring rapid forging followed by radial forging ; The production resources include: the set of equipment consisting of all available fast forging machines in the system. The system comprises all available radial forging equipment. The resource set consisting of all radial forging machine hammers in the system. Forging machines with specific diameters Hammerhead subset ; The production time parameters include: , indicating an order In a high-speed forging machine The standard processing time is used to predict the tensor by querying the rapid forging time. It can be obtained; , indicating an order On a radial forging machine The standard machining time is used to predict the tensor by querying the radial forging time. It can be obtained; If order The processing time on any radial forging machine is... Similarly, if the order The processing time on any high-speed forging machine is... ; make This indicates the maximum permissible total construction period.

8. The special steel forging production scheduling method according to claim 3, characterized in that, In step S22, the decision variables include resource allocation decision variables, process sequence decision variables, time planning continuous variables, and hammer replacement identifier binary variables; The resource allocation decision variables are described using the following binary decision variables: For any order Any fast forging machine ,when When, it indicates an order. Assigned to the fast forging machine Process it; otherwise, the value is 0. For any order Arbitrary diameter forging machine ,when When, it indicates an order. Assigned to radial forging machine Process it; otherwise, the value is 0. For any order Arbitrary hammerhead ,when When, it indicates an order. Hammers are used in the radial forging stage. Otherwise, the value is 0. The process sequence decision variables are described using the following binary decision variables to describe the processing order of orders on the same resource: For any two different orders Any fast forging machine Decision variables Indicates a fast forging machine Place an order Is the processing sequence superior to the order? If so, then If not, then ; For any two different orders Arbitrary diameter forging machine Decision variables Indicates radial forging machine Place an order Is the processing sequence superior to the order? If so, then If not, then ; For any two different orders Arbitrary hammerhead Decision variables Indicates hammerhead Place an order Is the processing sequence superior to the order? If so, then If not, then ; The continuous variables for time planning use the following continuous decision variables to define the time attributes of the scheduling: For any order Any fast forging machine , Indicates order In a high-speed forging machine The planned start time on the above, and its corresponding planned completion time is: ; For any order Arbitrary diameter forging machine , Indicates order In the radial forging machine The planned start time on the above, and its corresponding planned completion time is: ; The binary variable for the hammerhead replacement identifier is: For any order , Indicates order The hammer type required in the radial forging stage is considered to be a valid hammer change operation only when two orders with different hammer types required are consecutively assigned to the same radial forging machine. For any two different orders Arbitrary hammerhead ,make Indicates order With orders Is it on the hammer? If it is continuous processing, then If not, then take 0.

9. The special steel forging production scheduling method according to claim 3, characterized in that, In step S23, the constraints include resource allocation completeness constraints, equipment processing timing constraints, cross-stage process dependency constraints, hammer replacement logic constraints, total project duration constraints, and sequential logic completeness constraints. The resource allocation completeness constraint ensures that each order is uniquely allocated to the required high-speed forging mill, radial forging mill, and hammer. The equipment processing timing constraints ensure that the time windows of orders processed on the same resource do not overlap. The cross-stage process dependency constraint ensures that for joint orders that require rapid forging followed by radial forging, the start time of radial forging is later than the end time of rapid forging. The hammer replacement logic constraint is used to identify and count replacement events caused by orders requiring different hammer types for continuous processing; The total project duration constraint ensures that the total project duration is not less than the completion time of any order and does not exceed the maximum allowable value; The sequential logic completeness constraint ensures mutual exclusion between sequential variables and their dependence on resource allocation.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by the processor, the program implements a special steel forging production scheduling method for sparse data as described in any one of claims 1 to 9.

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