A distributed assembly flow shop scheduling algorithm recommendation method based on feature global score screening and stacking integrated model

Abstract

The application discloses a distributed assembly flow shop scheduling algorithm recommendation method based on feature global score screening and a stacking integrated model. In view of the problems that the performance of a single algorithm in a distributed assembly flow shop scheduling problem depends on instance features, manual selection is low in efficiency and prone to errors, a candidate algorithm library containing nine meta-heuristic algorithms is constructed, the optimal algorithm label is marked for each instance through an epsilon-approximate optimal strategy, a 56-dimensional meta-feature vector containing basic, statistical and composite features is extracted, and an adaptive constraint-oriented logic reconstruction enhancement strategy is proposed to solve the class imbalance problem, SHAP values and incremental feature selection are used to realize feature dimension reduction and optimization, and then a two-level heterogeneous integrated model based on stacking is constructed, the base learner and the meta-learner are optimized through cross-validation, and adaptive mapping from instance features to the optimal algorithm is realized. The application realizes automatic algorithm recommendation.

Description

Technical Field

[0001] This invention belongs to the field of assembly line workshop scheduling technology, specifically relating to an algorithm recommendation method for distributed assembly line workshop scheduling problems, and in particular, a distributed assembly line workshop scheduling algorithm recommendation method based on feature global score filtering and Stacking ensemble model. Background Technology

[0002] The Distributed Assembly Flow Shop Scheduling Problem (DAFSP) is widely found in modern discrete manufacturing fields such as automotive manufacturing, computer assembly, and plastic products. In this problem, parts are first processed in multiple distributed factories, then assembled according to product structure in an assembly plant, and finally delivered to different customers. Unlike traditional single-factory scheduling, DAFSP involves both the allocation decisions of parts across multiple factories and the time coupling constraints between the manufacturing and assembly stages. Its scheduling objectives typically include minimizing the maximum completion time, total inventory cost, delay penalty cost, and transportation cost. This problem has been proven to be an NP-hard combinatorial optimization problem; the difficulty increases dramatically with the number of factories, product types, and assembly relationships.

[0003] Currently, solutions to DAFSP mainly focus on heuristic rules and metaheuristic algorithms, such as genetic algorithms, differential evolution, distribution estimation algorithms, iterative local search, and their hybrid strategies. These methods can achieve good results under specific scales or constraints, but they generally suffer from the limitation that performance heavily depends on instance characteristics. According to the No Free Lunch (NFL) theorem, no single algorithm can consistently outperform other algorithms on all instances; the performance of the same algorithm varies significantly under different scales, assembly structures, or cost weights. In actual industrial production, due to the lack of prior knowledge and expert experience, manually selecting algorithms through trial and error is costly and inefficient, making it difficult to meet the needs of real-time scheduling and multi-scenario adaptation.

[0004] To address these issues, algorithm selection technology has emerged. Its core idea is to automatically recommend the optimal algorithm from a set of candidate algorithms by analyzing the characteristics of problem instances. In recent years, meta-learning has been introduced into the field of algorithm selection, improving the model's cross-scenario generalization ability by extracting common patterns across multiple tasks or instances. Meanwhile, ensemble learning enhances the stability of algorithm performance predictions by combining multiple prediction models. However, existing meta-learning-based algorithm selection research is mostly limited to single-stage or standard combinatorial optimization problems (such as the Traveling Salesman Problem and the Job Shop Scheduling Problem). For DAFSP, which has a two-stage coupling characteristic of manufacturing and assembly, a systematic algorithm selection framework has not yet been formed. Furthermore, existing methods have significant shortcomings in feature construction, class imbalance handling, feature selection, and base learner configuration: First, the meta-features are not comprehensive and lack a deep representation of the coupling relationship between the manufacturing and assembly stages; second, the algorithm performance datasets generally exhibit long-tailed class distributions, and the sparse samples of a few winning algorithms lead to model prediction bias; third, the selection of meta-learners in existing Stacking ensemble structures largely relies on experience and lacks a systematic dynamic optimization mechanism.

[0005] Therefore, how to construct a DAFSP instance that can adapt to different sizes, assembly constraints and cost structures, and realize a high-precision and highly robust algorithmic automatic recommendation method is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0006] To address the above technical problems, this invention proposes a distributed assembly line workshop scheduling algorithm recommendation method based on feature global score filtering and a Stacking ensemble model, comprising the following steps: B1. Obtaining an Instance The set, each instance For the distributed assembly line scheduling problem, the objective is to minimize the total cost (including inventory cost, delay cost, and transportation cost) while satisfying the constraints. For each instance, all candidate algorithms are run, and the average total cost and average running time of the instance under each candidate algorithm are obtained. A set of approximately optimal candidate algorithms is then selected, ensuring that the average cost relative to the global optimum does not exceed the tolerance. ,exist The candidate algorithm with the shortest average running time is selected as the optimal algorithm label for this instance. ; B2. Extract each instance dimensional eigenvectors Includes basic meta-features Statistical meta-features and features of random composite elements Scale-dependent characteristics This forms a feature vector containing instances. Labels with the optimal algorithm The initial meta-dataset; The features include the number of workpieces. Product Count Number of factories that replace the assembly line structure Machine Number Number of customers And the maximum and minimum values ​​of the following characteristics: part processing time, product assembly time, order delivery time, customer delivery time, unit inventory cost, unit late penalty fee, transportation cost, number of parts in the product, and number of products in the customer order; The features in the data are the mean, variance, coefficient of variation, skewness, and kurtosis calculated for part processing time, product assembly time, order delivery time, inventory holding weight, and late penalty weight, respectively. The features include: , , , , The features include: , , , , For products Unit inventory cost Delay penalty fee for customer h unit, The preset delivery time for customer h, Indicates belonging to the customer A collection of products, Indicates relation to product Related assembly time, The number of components for each product i; B3. Calculate the global importance score of each feature using a pre-trained base classifier and sort them in descending order to obtain the feature priority sequence. Construct candidate feature subsets ,in Include before sorting One feature, for The predictive performance was evaluated to obtain the average classification accuracy and From the relationship curve, select the feature with the fewest features within the interval where the average classification accuracy is stable and highest. As the final optimal feature subset ; B4: Construct and train a Stacking ensemble model containing a base learning layer and a meta-decision layer, where the base learning layer is... The input is the feature space. Each base learner outputs the predicted probability of all candidate algorithms. The meta-decision layer is used to perform nonlinear fusion of the predicted probabilities output by the base learning layer. For each candidate algorithm, the meta-decision layer inference probability is output. Then, the candidate algorithm with the highest meta-decision layer inference probability is selected as the final optimal algorithm category. B5: Use the trained Stacking ensemble model to recommend algorithms for instances of the new distributed assembly line scheduling problem.

[0007] Furthermore, each instance will One workpiece was assigned to A factory with a replaced assembly line structure, respectively composed of... The machines process the products in a fixed sequence, and then the assembly plant assembles them. Each belongs to Products for different customers, each product i consists of several non-repeating parts, with a unit expected inventory cost of... i Each customer The preset delivery date is Late delivery incurs penalties, affecting everyone from the assembly plant to the customer. The transportation cost is h .

[0008] Furthermore, the construction of the candidate algorithm library in step S1 specifically includes selecting a combination of at least one of the following algorithms: a global iterative greedy algorithm based on workpiece block intersection, a discrete invading weed algorithm, a distribution estimation algorithm, and an iterative local search algorithm.

[0009] Furthermore, the pre-trained base classifier mentioned in B3 is LightGBM, and step S3 is included between steps B2 and B3: in the randomly generated domain The internal synthesis samples are generated based on an adaptive strategy and then incorporated. , The generated synthetic samples are sequentially subjected to physical feasibility corrections to eliminate logical violations, resulting in corrected samples. Extraction is then performed from these corrected samples. , , , , Reconstruct and combine into Merging , and To form an enhanced training set.

[0010] Furthermore, in step B3, a pre-trained base classifier is used to calculate the global importance score of each feature in the augmented training set. : ; In step B3, a pre-trained base classifier is used to calculate the global importance score of each feature in the augmented training set. : ; ; For the complete feature set, A subset of features is derived from the full feature set. Remove the current feature Then, any permutation or combination that the remaining features can form. Representing a feature subset The predicted output after inputting into the base classifier. Indicating in the feature subset Based on this, the features After being added, the new prediction result calculated by the base classifier and This indicates the number of features contained in the entire feature set and the feature subset. To represent factorial, S represents removing the current feature from the full feature set F. Then, any subset composed of the remaining features, It iterates through and summarizes all features that are not included. The weighted expectation of the prediction increment of the base classifier is obtained from the feature combination S.

[0011] Furthermore, in step S3, in the random generation domain The process of generating synthetic samples based on an adaptive strategy includes: adaptive sampling and generation; for minority class samples, a conservative interpolation strategy or a random perturbation strategy based on the absolute deviation of the median is used to generate synthetic samples, depending on the sample size; physical feasibility corrections are then performed on the generated synthetic samples, including: Perform discrete parameter integerization, coupling feature consistency correction, and distribution drift truncation operations on the generated synthetic samples: Discrete parameter integerization: for parameters defined in the discrete domain ( The basic discrete parameters are subjected to the nearest integer projection and the minimum lower bound truncation to satisfy the integer constraint of the value range; Coupling feature consistency correction: For coupled feature pairs that satisfy the physical partial order relationship, symmetric mean adjustment is performed to reorder them to ensure that the generated samples satisfy the partial order constraint; in, The mean of the feature pairs, It is the absolute difference; Distribution drift truncation constraint: A two-way extreme value pruning based on interquartile range is adopted to limit the value of each feature dimension to the effective physical interval obtained by the minority class samples, so as to avoid the generated samples from exceeding the reasonable statistical boundary.

[0012] Furthermore, the IFS strategy described in step B4 specifically includes: sorting the meta-features in descending order based on the SHAP global importance score, constructing a nested sequence of candidate feature subsets, evaluating the classification accuracy of each subset through cross-validation, and selecting the subset with the lowest accuracy and the fewest number of features as the optimal feature subset.

[0013] Furthermore, in step B4, the candidate base learners for the base learning layer include tree models and / or support vector machines; the candidate meta-learners for the meta-decision layer include logistic regression, random forest, LightGBM, or XGBoost.

[0014] Furthermore, step B4 involves constructing and training a Stacking ensemble model that includes a base learning layer and a meta-decision layer, including: The original metadata is } Divided into training set ; Phase 1 Base Learner Selection: The candidate base learner set is evaluated using 5-fold cross-validation on the training set, and the set of base learners with the best generalization performance is selected. Stage binary learner training: Generate out-of-fold prediction probabilities on the training set using the selected set of base learners, and construct the training dataset for the meta-learner using these probabilities; train and evaluate candidate meta-learners on the meta-learner training dataset, and select the model with the best comprehensive performance index as the final meta-decision maker; Phase 3 Global Retraining: With a fixed set of selected base learners and meta-decision makers, all models are retrained on the complete training set to obtain the final Stacking ensemble model.

[0015] A distributed assembly line workshop scheduling algorithm recommendation system based on feature global score filtering and Stacking ensemble model is used to execute the method described in any one of the above.

[0016] Compared with the prior art, the beneficial effects of the present invention are: 1. This invention systematically characterizes the features of problem instances and learns the mapping relationship between the instance feature space and the performance of candidate algorithms, thereby transforming the traditional algorithm selection process that relies on human experience and trial and error into a data-driven supervised learning problem.

[0017] 2. This invention constructs a two-level heterogeneous ensemble learning framework based on Stacking. By integrating the complementary advantages of base learners such as Random Forest, XGBoost, LightGBM, CatBoost and Support Vector Machine, and combining the optimal meta-learner selected through experiments, it achieves a high-precision mapping between instances of the Distributed Assembly Flow Shop Scheduling (DAFSP) problem and the optimal solution algorithm.

[0018] 3. This invention proposes an Adaptive Constraint-Oriented Logical Reconstruction Enhancement Strategy (AC-LR), which synthesizes new training samples without violating the DAFSP system constraints by performing conservative interpolation and robust perturbation on the feature space of minority class samples under physical consistency constraints, thereby reconstructing the original long-tail distribution into a balanced distribution and effectively solving the problem of extreme class imbalance in the dataset selection by the algorithm.

[0019] 4. This invention addresses the two-stage coupling characteristics of manufacturing and assembly in DAFSP by designing a three-layer progressive meta-feature characterization method of "scale-distribution-structure". These features fully characterize the search space scale, parameter distribution heterogeneity, and resource coupling relationship between the three stages of manufacturing, assembly, and distribution. This provides a highly discriminative and informative input representation for algorithm performance prediction, overcoming the shortcomings of existing feature engineering methods that are difficult to adapt to two-stage scheduling problems.

[0020] 5. This invention integrates the SHAP feature contribution evaluation and incremental feature selection (IFS) strategy to perform global importance ranking and dynamic optimization on the 55 initial meta-features. Finally, the top 15 features with the highest contribution are selected to form the optimal subset. This mechanism eliminates redundant or noisy features while maintaining prediction accuracy, reduces the risk of dimensionality curse, improves the training efficiency and generalization stability of the model, and overcomes the shortcomings of traditional feature selection methods that rely on a single index and lack dynamic optimization capabilities. Attached Figure Description

[0021] Figure 1 Select an overall framework for the algorithm proposed in this invention; Figure 2 The number and proportion distribution of samples with algorithmic tags in the DAFSP metadata set; Figure 3 The top 15 features by SHAP value; Figure 4 This is a schematic diagram of feature importance analysis; Figure 5 This is a schematic diagram illustrating the relationship between accuracy and the number of features. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0023] Terminology Explanation Replacement assembly line structure, referring to each factory having a... The processing sequence of all workpieces on multiple machines is fixed, and the processing sequence of workpieces on each machine remains consistent.

[0024] The coefficient of variation, also known as the coefficient of dispersion, is an indicator used to measure the relative dispersion of data.

[0025] Skewness, also known as the skewness coefficient, is an indicator used to measure the asymmetry of data distribution.

[0026] Kurtosis, also known as the kurtosis coefficient, is an indicator used to measure the steepness of the data distribution and the thickness of the tails.

[0027] Example This embodiment constructs a distributed assembly line workshop scheduling algorithm recommendation method based on feature global score filtering and a Stacking ensemble model, establishing a mapping from problem instance features to the optimal solution algorithm, such as... Figure 1 As shown, the main steps include: Step S1: Problem Modeling and Data Preprocessing Step S1.1, Problem Modeling The Distributed Assembly Flow Shop Scheduling Problem (DAFSP) consists of two main phases: the manufacturing phase and the assembly phase. In the manufacturing phase, there are... There are several identical factories, each employing a method that includes... The structure of the replacement assembly line workshop for the machines. (Total number of machines) Each workpiece needs to be assigned to different manufacturing plants, and within each plant, it needs to be... Each machine processes components in a fixed sequence. During the assembly phase, a single factory is responsible for assembly. Each product i consists of several non-repeating workpieces. With expected unit inventory cost i . Each product belongs to Each different customer A predetermined delivery period is provided. If delivery to customers exceeds their due date, additional lateness penalty costs are incurred. Furthermore, there are additional costs from the assembly plant to each customer. Transportation costs also need to be paid during the transportation process. h .

[0028] The goal of the Distributed Assembly Flow Shop Scheduling Problem (DAPFSP) is to minimize inventory costs. Delay costs and transportation costs Total cost of composition Minimize: in: In the formula, This represents the set of products belonging to customer h. ; This indicates the actual delivery arrival time for customer h; The completion time of product i at the assembly plant; This represents the unit delay penalty fee for customer h; This indicates the overdue time for all products belonging to customer h.

[0029] In addition to the optimization objectives, the scheduling scheme must also meet the following constraints regarding parts allocation and sequencing, manufacturing phase completion time, product sequencing, assembly phase completion time, delivery and delays, and variable types: (1) Part allocation and sequencing constraints, which are used to specify the allocation of workpieces among manufacturing plants and the processing sequence of workpieces within each plant: Unique precondition: Each non-virtual workpiece ( For non-virtual workpieces, there is one and only one direct predecessor workpiece (including virtual workpiece 0), where workpiece j is the direct predecessor of j'. =1; otherwise =0. At most one post-constraint: per non-virtual workpiece ( (For non-virtual workpieces) There can be at most one direct successor workpiece: Out-degree of virtual workpiece 0: The total number of times virtual workpiece 0 is a direct predecessor workpiece equal to... : The in-degree of virtual workpiece 0 (this virtual workpiece is not a real workpiece, but a start or end node): the sum of the number of times a real workpiece is a direct predecessor of virtual workpiece 0 equals... : No mutual inverse constraint: Any two different workpieces cannot be direct predecessors of each other. (2) Machine completion time constraints during the manufacturing phase, which define the completion time of the workpiece on each machine within the manufacturing plant: Machine sequence constraints within the same workpiece: workpiece In the machine The completion time of the above machine shall not be less than that of the previous machine. Completion time plus processing time: in, Indicates parts In the machine The completion time.

[0030] Workpiece sequence constraints on the same machine: If workpieces It is a workpiece The direct pre-processing (on the same machine in the same factory) of the workpiece Must be on the workpiece Processing can only begin after this is completed. It is a sufficiently large positive number.

[0031] Non-negative completion time: The completion time of all workpieces (including virtual workpiece 0) on all machines is non-negative. Initial conditions for virtual machine 0: The completion time of all artifacts on virtual machine 0 is 0 (i.e., all artifacts are ready at time 0): (3) Product sequencing constraints, which specify the assembly sequence of products during the assembly stage: The only direct precursor: for any real product (Non-virtual) Among all possible products (including virtual starting point 0), there is one and only one direct predecessor product: At most one direct successor: for any real product (Non-virtual) There is at most one direct successor product: Out-degree of virtual product 0: The total number of real products immediately following virtual product 0 equals: The in-degree of virtual product 0: The total number of real products pointing to virtual product 0 equals: No mutual inverse constraint: No two different products can be direct predecessors of each other. (4) Assembly phase completion time constraints, which define the completion time of the product in the assembly plant: Assembly start conditions: Product The assembly completion time shall not be less than the maximum completion time of all its constituent parts on the last manufacturing machine plus the assembly time: Product sequence constraint: If the product... It is a product The direct precursor of the product Must be in the product Assembly can only begin after all other components have been assembled. Assembly completion time is non-negative: The assembly completion time for all products is non-negative. Initial conditions for virtual product 0: The assembly completion time for virtual product 0 is 0. (5) Delivery time and delay constraints, which link product completion time with customer delivery time, transportation time and delay costs: Delivery arrival time definition: Customer The actual delivery arrival time shall not be less than the maximum assembly completion time of all products in the order: Transportation time considerations: actual arrival time plus transportation time It should be no less than the delivery period (This formula is used to ensure that delivery time requirements are met; in practice, it means that the arrival time must meet the following:) Overdue time definition: If Then the overdue period Equal to the excess portion; otherwise =0: Non-negative overdue time: Early arrival is not considered overdue (i.e., overdue time cannot be negative): (6) Variable type constraints: For any two different parts and (Including virtual part 0), decision variables The value can only be 1 or 0: For any two different products and (Including virtual product 0), decision variables The value can only be 1 or 0: A problem instance library is constructed from the parameter set required for modeling given DAFSP (Manufacturing Phase) and DAPFSP (Assembly / Delivery Phase) problems. For each size category Based on the replacement flow workshop structure, relevant data for the manufacturing stage are generated (such as the processing time of workpieces on each machine and their technological relationships), and the workpiece composition relationships required for product assembly are randomly constructed; at the same time, for each customer Generate its delivery date And the corresponding inventory / delay / transportation cost parameters. After generation, the instances are checked for consistency and feasibility (e.g., no duplicate workpieces within the product, customer affiliation constraints, etc.). If the conditions are not met, resampling / correction is performed to obtain a set of independent instances that can be used for algorithm solution. .

[0032] Step S1.2: Construct a candidate algorithm library To ensure that the algorithm selection model has efficient solution capabilities when facing DAFSP instances of different sizes and constraints, this invention selects nine metaheuristic algorithms with different search mechanisms and solution characteristics to construct a candidate algorithm library. The algorithms selected in this implementation include: a global iterative greedy algorithm based on workpiece block crossover and adaptive mutation (gIGA), a discrete invading weed algorithm incorporating tournament selection (TDIWO), a distribution estimation algorithm based on a probability model (MCEDA), and three iterative local search algorithms (ILS1, ILS2, and ILS3) with different perturbation strategies, as shown in Table 1. These algorithms cover three typical paradigms: evolutionary computation, swarm intelligence, and iterative local search, ensuring the diversity of the decision space.

[0033] Table 1 Step S1.3: Generate the optimal algorithm label (ε-approximate optimal strategy) In this embodiment, the problem instance library contains 1710 independent DAFSP benchmark cases, covering various combinations of scenarios with different part sizes, number of factories, product structures, and constraint characteristics. The problem instance library refers to a set of specific parameter instances of a DAPFSP (or DAFSP) problem to be solved. For each instance in the problem instance library... Use each algorithm in algorithm library A in turn. Solve independently. To ensure fair competition among different algorithms on the same benchmark, the termination condition for all algorithms is uniformly set to CPU runtime based on the problem size, i.e. Milliseconds. Given the randomness of metaheuristic algorithms, each algorithm runs independently on each instance. Record the objective function value (total cost) for each run. and running time And calculate its average total production cost and average operating time, denoted as , respectively. and : Due to the randomness of algorithms and the fluctuations in the actual production environment, small cost differences are often considered ineffective gains in practice. Therefore, computational efficiency becomes a key indicator determining the quality of an algorithm. Based on this, this invention introduces a tolerance threshold. (In this embodiment, it is set to) Construct a set of near-optimal candidate algorithms Approximate optimal candidate algorithm set Includes all cost variances Algorithms within the range: in, , which represents the global minimum average cost obtained by this instance across all algorithms.

[0034] In the determined approximate optimal candidate set In the middle, select the average running time Minimal Algorithm As an example Optimal algorithm label : Through the above process, the scheduling optimization problem is transformed into a 9-class classification problem, where each instance... Corresponding to a unique category label .

[0035] Step S2: Extract meta-features of DAFSP instances For each DAFSP instance Extract a 56-dimensional meta-feature vector. This vector It consists of the following three sets of features: Basic meta-features (Feature IDs 1-23, see Table 2 for details): These 23 dimensions are extracted directly from the original problem parameters and are used to define the search space size and numerical boundaries of the problem. Specifically, they include the total number of parts n, the total number of products s, the total number of manufacturing plants f, the total number of machines in the manufacturing plants m, the total number of customers b, and the maximum and minimum values ​​of the following features: part processing time, product assembly time, delivery time, customer delivery time, unit inventory cost, unit delay penalty cost, transportation cost, number of parts contained in a product, and the maximum and minimum values ​​of the number of products in a customer order.

[0036] Table 2 Basic Meta-Features Statistical meta-features (Feature ID 24-48, see Table 3 for details): For the five key parameters—part processing time, product assembly time, order delivery time, inventory holding weight, and late penalty weight—calculate the mean value of each key parameter. ),variance( ), coefficient of variation ( ), skewness ( ) and kurtosis ( This is used to mine the distribution characteristics of data and quantify the difficulty of solving instances.

[0037] Table 3 Statistical Meta-characteristics Composite element characteristics (Feature IDs 49-56, see Table 4 for details): Dimensionless ratio indicators are constructed based on domain knowledge, with a total of 8 dimensions, to reveal the constraints between the manufacturing, assembly and distribution stages. These composite element features provide key physical criteria for algorithm selection.

[0038] Table 4 Characteristics of Composite Elements For products Unit inventory cost Delay penalty fee for customer h unit, The preset delivery time for customer h, Indicates belonging to the customer A collection of products, Indicates relation to product The relevant assembly time, For each product The number of workpieces.

[0039] Through the above steps, unstructured DAFSP instances are transformed into normalized feature vectors. and the algorithm label generated in step 1 Link and construct the initial meta-dataset It contains a total of 1710 samples.

[0040] Step S3: Perform Adaptive Constraint-Guided Logic Refactoring Enhancement (AC-LR) To address the extreme class imbalance problem in the initial metadata set (such as...) Figure 2 gIGA performed best in over 34.9% of instances, dominating the market, while TDIWO, ILS3, MCEDA, etc. only won in less than 5% of edge scenarios. The AC-LR data augmentation strategy is implemented as follows: Step S3.1, Feature Decoupling The 56-dimensional feature space is divided into two operational domains: Randomly generated domain The randomly generated domain is defined as the union of independent feature sets, formally expressed as: Includes basic meta-features Statistical meta-features and random composite subsets In the data augmentation process, it can be regarded as a free variable for interpolation and directly participate in subsequent interpolation and perturbation generation.

[0041] Deterministic Reconstruction Domain This domain consists of scale-dependent features, defined as follows: The features within this domain are not randomly generated, but are reconstructed through the deterministic function in step S3.4.

[0042] Among them, composite element characteristics Divided into random composite subsets and size-dependent subsets Features 49-51 of the composite elements in Table 4 belong to random composite subsets. Features 52-56 of the composite element belong to a size-dependent subset. .

[0043] Step S3.2: For the randomly generated domain Adaptive sampling and generation of samples within the range If sample size Relatively sufficient A conservative interpolation strategy is adopted. For each seed sample... and its nearest neighbor samples Synthesize new samples : Among them, interpolation coefficients The values ​​are strictly constrained within the range of [0.4, 0.6]. This centralization constraint ensures that the newly generated samples are located in the high-confidence core region with the highest cluster probability density, which not only guarantees the physical authenticity of the generated data but also effectively prevents the synthetic samples from drifting to the majority class region.

[0044] If the sample size is insufficient A stochastic perturbation model is employed. To ensure robust scaling estimation under small sample conditions, the median absolute deviation (MAD) is used as a robust scaling estimator. Specifically, for the first class... Dimensional features, median absolute deviation for: In the formula, This indicates that the category is in the Median of the dimensional features This indicates traversing the category. All samples in. This indicates that it belongs to the current specific category. For all samples, perform a median calculation.

[0045] Then, for each seed sample Synthesize new samples : in, The standard Gaussian white noise term is responsible for introducing the random diversity of the generated data. This is the perturbation intensity coefficient, used to scale and constrain the noise amplitude.

[0046] Step S3.3, Strict Physical Correction For the synthetic sample generated in step S3.2 To eliminate logic violations, three strict physical constraint chains are applied step-by-step to correct them: (1) Integerization of discrete parameters: for parameters defined in the discrete domain , Basic parameters The original floating-point value is calculated using the nearest integer projection strategy. Round the result to the nearest whole number, then compare the result with 1 and take the maximum value: in, These are the original parameter values ​​before integerization. This represents the rounding function.

[0047] (2) Coupling feature consistency correction: For coupled feature pairs with logical partial order relationships (such as...) If the generated samples violate this logical partial order relation, they are reordered using symmetric mean adjustment. For feature pairs... The corrected formula is defined as follows: in, The mean of the feature pairs, This is an absolute difference. This operation forcibly restores the physical partial order while preserving the statistical moments of both.

[0048] The aforementioned logical partial order relation refers to coupled feature pairs with a "minimum-maximum" correspondence, including but not limited to: minimum and maximum processing time of a part, minimum and maximum assembly time of a product, minimum and maximum delivery time, minimum and maximum unit inventory cost, etc. These feature pairs must satisfy physical conditions. The partial order constraint is applied, and if the order relationship is violated in the synthetic sample, it is corrected by adjusting the symmetric mean.

[0049] (3) Distribution drift truncation: To prevent generated samples from overflowing the reasonable statistical boundaries, a bidirectional extreme value truncation based on the interquartile range is applied. For each feature dimension, its effective physical interval is defined. : in, and These are the lower and upper quartiles of the original minority class sample, respectively. It is the interquartile range.

[0050] Finally, the corrected sample was obtained. : In the formula, and They are intervals The lower and upper bounds.

[0051] Step S3.4: Deterministic Analytical Reconstruction From the corrected sample Extracting basic parameters (such as) , , , , The deterministic reconstruction domain is reconstructed through the deterministic mapping function M. The features in the domain are used to combine the five basic parameters extracted into four new ratio indicators according to a specific logic: Through the above process, a sufficient number of synthetic samples are generated for each minority class until the number of samples in each class reaches a preset balance threshold (the preset balance value is set to about 500 samples in each class, that is, the number of samples in the majority class in the training set is used as the upper limit, and the minority class samples are supplemented to a level close to this level through the AC-LR strategy, so that the original long-tail distribution is reconstructed into a relatively balanced distribution shape. Specifically, the number of samples in each class after augmentation is between 500 and 560), and finally the augmented training set is obtained.

[0052] Step S4: Feature optimization based on SHAP and incremental feature selection (IFS) The meta-feature set constructed in step 2 provides a detailed description of the problem, but the resulting high-dimensional input space inevitably introduces information redundancy and noise interference. The interference terms not only dilute the discriminative power of key features, but are also more likely to induce the curse of dimensionality. This step is based on a two-stage hybrid selection strategy of SHAP and incremental feature selection (IFS) to accurately lock the optimal feature subset from the two dimensions of physical meaning and predictive contribution.

[0053] Step S4.1: SHAP Global Importance Ranking Using a pre-trained base classifier (such as LightGBM) as the base model, the SHAP value of each feature is calculated on the augmented training set generated in step 3. Specifically, for any sample... and characteristics Its SHAP value Defined as adding this feature to different feature subsets The weighted expectation of the base classifier prediction increment brought about by the subsequent addition: in, For the complete feature set, A subset of features is derived from the full feature set. Remove the current feature Then, any permutation or combination that the remaining features can form. Representing a feature subset The predicted output after inputting into the base classifier. Indicating in the feature subset Based on this, the features After adding it, the base classifier gives a new prediction result. and This indicates the number of features contained in the entire feature set and the feature subset. To represent factorial, S represents removing the current feature from the full feature set F. Then, any subset consisting of the remaining features. It iterates through and summarizes all features that are not included. The weighted expectation of the prediction increment of the base classifier is obtained from the feature combination S.

[0054] To measure the general value of a feature across the entire dataset, define the feature. Global importance score The mean of the absolute values ​​of SHAP across the entire sample space: like Figure 3 As shown, the top 15 features with the highest SHAP values ​​were selected based on... Sort all 56-dimensional features in descending order, such as Figure 4 Generate a priority sequence: Step S4.2: IFS determines the optimal subset. Based on priority sequence Construct a set of strictly nested candidate feature subset sequences. , ,in Include before sorting Each feature subset is evaluated using 5-fold cross-validation while maintaining consistency in the classification model structure and hyperparameter settings. The evaluation process involves using four training samples and one test sample in rotation, and then averaging the results to evaluate each candidate feature subset. The average classification accuracy is achieved, where, to avoid data leakage, the cross-validation process is only performed within the training set.

[0055] like Figure 5 After obtaining all candidate feature subsets After determining the accuracy, a curve is plotted showing the number of features (w) versus the average classification accuracy. On this curve, a stable performance interval is identified (the region where multiple models simultaneously achieve high and relatively stable performance within a similar feature size range). Then, the feature subset with the fewest features within this interval is selected as the final optimal feature subset. .

[0056] Optimal Feature Subset Including the number of workpieces Product Count And the minimum unit inventory cost and the maximum transportation cost, the mean of parts processing time and delay penalty weights, and the kurtosis of product assembly time. and Features of [the text].

[0057] Step S5: Building and training the Stacking meta-learning framework Obtaining the optimal feature subset through the IFS strategy Then, this step designed a cascaded mapping structure that includes a base learning layer (Level-0) and a meta-decision layer (Level-1).

[0058] Level-0 Base Learning Layer: This layer acts as a feature space transformer and has M base learners, denoted as... It is responsible for mapping meta-features to the probability distribution of the algorithm. Each base learner Receive instance features Output Prediction confidence vectors for each candidate algorithm category : in This represents the predicted instance of the z-th base learner. Belongs to the k-th candidate algorithm The probability, ...,K, and satisfying .

[0059] Level-1 Meta-Decision Layer: This layer acts as a global correction arbitrator. Instead of directly processing the original features, it concatenates all the confidence vectors output from Level-0 to construct the prediction layer representation vector. : Meta-learner The base learner outputs are nonlinearly fused, and the optimal algorithm is locked based on the maximum inference probability of the meta-decision layer. : in, Indicates the candidate algorithm The probability of inference from the meta-decision layer. : Take the independent variable that makes the quantity inside the parentheses reach its maximum value.

[0060] The effectiveness of ensemble learning is highly dependent on the differences in base models. Therefore, this embodiment selects five candidate base learners from different learning paradigms, including Random Forest (RF), XGBoost (XGB), LightGBM (LGB), CatBoost (Cat), and Support Vector Machine (SVM). RF reduces model variance through bootstrap sampling and feature randomization mechanisms; the Boosting series models (XGB, LGB, Cat) capture the fine-grained nonlinear relationship between features and algorithm performance by progressively correcting prediction errors; and SVM characterizes instance distribution features from a global geometric perspective based on kernel functions, providing a complement to tree models. The differences in inductive bias among these models enable the Level-0 layer to generate complementary prediction confidences.

[0061] Since different meta-learners have varying sensitivities and generalization properties to input feature distributions, this embodiment abandons prior assumptions about meta-learner types and adopts an experiment-driven posterior selection strategy. A candidate meta-learner set is constructed. Under the condition of uniform 5-fold cross-validation, the higher-order feature vectors output at Level-0 are... The model is trained and evaluated based on the input. Finally, based on the combined performance of metrics such as classification accuracy and F1-score, the model with the best generalization performance and the most stable performance across different data is selected as the final Level-1 decision-maker.

[0062] To achieve effective training of the Stacking meta-learning framework, this embodiment constructs a standardized two-stage training process. Let the original meta-dataset be... The specific steps are as follows: Step 1: Divide the original metadata into training sets. All subsequent model training and selection processes are based on Finish.

[0063] Step 2: In the training set A 5-fold cross-validation mechanism is employed. First, stratified sampling is used to divide the data into five mutually exclusive subsets with consistent class distributions. In the In the round of iteration, using division The four subsets other than the one used to train the candidate base learners set in the Level-0 layer. and in the verification subset The predictive performance was evaluated. Based on the average performance metrics and stability of each base learner under 5-fold cross-validation, the candidate base learners were selected from the set of candidate base learners. Select the best performing ones These models constitute the final set of base learners for the Level-0 layer. .

[0064] Step 3: In the defined set of base learners The 5-fold cross-validation mechanism will continue to be used. In the... As a compromise, the base learner is trained using all data in the training set except for the current validation fold sample, and generates out-of-fold prediction confidence on that validation fold. The trained... Let each model be denoted as And generate a prediction confidence vector on the current validation subset: Step 4: By summarizing the prediction results across all folds, construct a corresponding Level-1 input representation for each instance in the training set, which is the prediction layer representation vector formed by concatenating the prediction confidence scores of each base learner: This forms a dataset for training the meta-learner. }

[0065] Step 5: In The candidate meta-learners are trained and their performance evaluated. The model with the best performance is selected as the final Level-1 decision-maker. .

[0066] Step 6: After determining the base learner set and meta-learner structure, fix the model structure and parameter settings, and run the training on the complete training set. All base learners are retrained, while the meta-learner remains based on the out-of-fold prediction probability dataset from step 5. The trained model parameters remain unchanged to obtain the final Stacking ensemble model. This model is then applied to an independent test set. Performance evaluation was conducted on the above.

[0067] Through the above steps, this embodiment completes the construction and training of the Stacking meta-learning framework, laying the model foundation for subsequent algorithmic adaptive recommendation.

[0068] Step S6: Online Deployment and Algorithm-Adaptive Recommendation for New Instances The trained DAFSP-ASF model is deployed in the algorithm recommendation module of the production scheduling system. For any new, unseen DAFSP instance, an automatic mapping from problem features to scheduling algorithm categories is completed. The algorithm recommendation process is as follows: Step 6.1: Problem Meta-Feature Extraction and Preprocessing. Extract the scale, structure, and assembly relationship features of the new instance to form the original meta-feature vector. Based on the SHAP feature selection results determined in Step 4, retain only the optimal feature subset. The retained features are then Z-score standardized to generate standardized feature vectors. .

[0069] Step 6.2: Base Learner Mapping. Utilize the base learner set retrained on the complete training set. For eigenvectors Perform parallel mapping. Each base learner outputs one... Prediction confidence vector: in, This represents the probability that the z-th base learner predicts the current instance belongs to the k-th candidate algorithm. .

[0070] Step 6.3: Constructing the prediction layer representation vector. Concatenate the prediction confidence vectors output by all base learners to form the prediction layer representation vector. , which serves as the input condition for the meta-decision layer.

[0071] Step 6.4: Meta-learner decision-making and algorithm recommendation. The prediction layer representation vector... Input the trained meta-learner The meta-learner outputs the final algorithm class prediction result: in, This is the optimal scheduling algorithm recommended by the system. This recommendation can be used to guide subsequent scheduling optimization solutions.

[0072] To verify the effectiveness of this invention, detailed experimental verification was conducted in this embodiment. All experiments were performed in a computing environment configured with an AMD Ryzen 9 7945HX CPU, 32GB of memory, and a Windows 11 operating system. The underlying scheduling algorithm and DAFSP-ASF model were implemented using Python 3.11.

[0073] The experimental data came from 1710 DAFSP benchmark examples constructed by Zhang et al. Nine metaheuristic algorithms belonging to different optimization paradigms were selected to construct a candidate algorithm library. An optimal algorithm label was generated for each example using an ε-approximate optimal label generation strategy, forming a meta-dataset of "example meta-features - optimal algorithm label". The original dataset contained 1710 samples across 9 categories, exhibiting significant class imbalance (majority class accounting for 34.9%, minority class only 3.4%).

[0074] To completely avoid data leakage, the experiment strictly followed the "split first, augmentation then feature selection" standard. The 1710 original real samples were divided into a stratified sampling strategy at a ratio of 7:3 into a training set of 1197 samples and an independent test set of 513 samples. The test set was sealed throughout the process and did not participate in any data augmentation, feature selection or model training process. It was only used for the final model generalization performance evaluation.

[0075] To address the issue of imbalanced sample classes, an AC-LR adaptive constraint-guided data augmentation strategy is adopted for the training set to achieve a balanced proportion of samples of each class, as shown in Table 5.

[0076] Table 5 To ensure fairness and reproducibility, all machine learning models employed 5-fold hierarchical cross-validation for hyperparameter optimization, with a fixed global random seed of 42. Hyperparameters of the base learners (RF, XGBoost, LightGBM, CatBoost, SVM) and meta-learners (LR, RF, LightGBM, XGBoost) were tuned using grid search; the specific search range and optimal values ​​are shown in Tables 6 and 7, respectively. To reduce dimensionality and remove noise, SHAP was used to evaluate feature importance, and an incremental feature selection (IFS) strategy was combined to determine the optimal feature subset. Based on the relationship between the number of features and model accuracy, the top 15 features with the highest SHAP values ​​were selected as the optimal feature subset.

[0077] Table 6 shows the specific parameter ranges and optimal values ​​for grid search overtuning of the base learner. Table 7 shows the specific parameter ranges and optimal values ​​for grid search in over-tuning the meta-learner. In the experiments, the model was evaluated using a test set, and accuracy, precision, recall, F1 score, and AUC were selected as the core classification performance metrics. Furthermore, to measure the quality of scheduling optimization, mean relative percentage bias (ARPD) and hit rate were used as core optimization quality metrics.

[0078] DAFSP-ASF Validation: The core decision module of the DAFSP-ASF framework proposed in this embodiment is a two-level stacking heterogeneous integrated architecture built based on a Top-K selection strategy for cross-validation performance. The Level-0 base learner performs Top-K selection based on 5-fold cross-validation generalization performance ranking, while the Level-1 meta-learner uses the best-performing LightGBM (LGB). The final experimental results are shown in Table 8. Table 8 The experimental results in the table above show that the final architecture of DAFSP-ASF (Stacking-LGB-Top4) achieves globally optimal comprehensive classification performance on the test set, with an accuracy of 92.99%. The macro-average precision, macro-average recall, macro-average F1 score, and AUC reach 0.9310, 0.9299, 0.9303, and 0.9851, respectively, all outperforming the five single machine learning benchmark models. Compared to the best-performing single model, LightGBM, it improves accuracy by 4.46%, macro-average recall by 5.05%, macro-average F1 score by 5.34%, and AUC by 0.0283. The gradient-based K-value comparison experiment shows that the Top-4 optimization strategy achieves the best comprehensive performance among all meta-learner schemes and is even better than the Top-5 architecture, verifying that this strategy can effectively avoid the overfitting risk caused by redundant base learners. With the same base learner configuration, the Stacking scheme using LightGBM as the meta-learner is superior to the comparison scheme using LR, RF, and XGBoost as meta-learners.

[0079] To further verify the independent contributions of each core component, this embodiment also designed a systematic ablation experiment, with all experiments conducted on independent test sets. Based on the complete Variant-0 model (including AC-LR, SHAP+IFS, and Stacking ensemble), three variants were constructed: Variant-1 removing AC-LR data augmentation (i.e., directly using the original imbalanced dataset for training), Variant-2 removing SHAP+IFS feature selection (i.e., directly using all 55 original meta-features as input), and Variant-3 removing the Stacking ensemble architecture (degenerating into a single LightGBM, i.e., a base model in the Level-0 layer). The final experimental results are shown in Table 9. Table 9 Experimental results show that removing AC-LR reduces the F1-score by 6.01% and the AUC by 5.11%, indicating that this strategy is crucial for mitigating long-tail distribution; removing SHAP+IFS reduces the F1-score by 1.63% and the AUC by 1.26%, confirming the effectiveness of feature selection; removing Stacking integration reduces the F1-score by 3.45% and the AUC by 4.53%, verifying the generalization advantage of the heterogeneous fusion strategy.

[0080] To further verify the practical application value of DAFSP-ASF, 200 complex DAFSP instances closely matching actual production characteristics were randomly selected from the test set. The instance parameters covered the full range of actual manufacturing scenarios: number of parts Number of manufacturing plants Number of machines per factory Product Count Number of customers It also covers core constraints in actual production, such as different part-product assembly structures, cross-factory capacity constraints, order delivery date priorities, and differences in inventory-delay cost weights. Furthermore, all instances were not involved in model training, hyperparameter optimization, or preprocessing, completely simulating the real scheduling scenario of a factory facing unknown new orders. A comparison of DAFSP-ASF with fixed algorithm strategies (globally using the highest win rate gIGA), random algorithm strategies, and the theoretically optimal Oracle strategy is shown in Table 10. Table 10 Experimental results show that DAFSP-ASF has an average ARPD of only 0.82%, significantly outperforming the fixed algorithm strategy (9.47%) and the random strategy (21.58%); the optimal solution hit rate reaches 90.50%, highly close to the Oracle strategy (100%). In terms of cost, compared with the fixed algorithm strategy, DAFSP-ASF reduces the average latency penalty cost from 28,500 yuan to 21,300 yuan, fully demonstrating its superiority in comprehensive optimization.

[0081] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A recommended method for a distributed assembly line workshop scheduling algorithm based on feature global score filtering and a Stacking ensemble model, characterized in that, Includes the following steps: B1. Obtaining an Instance The set, each instance For the distributed assembly line scheduling problem, the objective is to minimize the total cost (including inventory cost, delay cost, and transportation cost) while satisfying the constraints. For each instance, all candidate algorithms are run, and the average total cost and average running time of the instance under each candidate algorithm are obtained. A set of approximately optimal candidate algorithms is then selected, ensuring that the average cost relative to the global optimum does not exceed the tolerance. ,exist The candidate algorithm with the shortest average running time is selected as the optimal algorithm label for this instance. ; B2. Extract each instance dimensional eigenvectors Includes basic meta-features Statistical meta-characteristics and features of random composite elements Scale-dependent characteristics This forms a feature vector containing instances. Labels related to the optimal algorithm The initial meta-dataset; The features include the number of workpieces. Product Count Number of factories that replace the assembly line structure Machine Number Number of customers And the maximum and minimum values ​​of the following characteristics: part processing time, product assembly time, order delivery time, customer delivery time, unit inventory cost, unit late penalty fee, transportation cost, number of parts in the product, and number of products in the customer order; The features in the data are the mean, variance, coefficient of variation, skewness, and kurtosis calculated for part processing time, product assembly time, order delivery time, inventory holding weight, and late penalty weight, respectively. The features include: , , , , The features include: , , , , Let i be the unit inventory cost of product i. Delay penalty fee for customer h unit, The preset delivery time for customer h, Indicates belonging to the customer A collection of products, Indicates relation to product The relevant assembly time, For each product The number of workpieces; B3. Calculate the global importance score of each feature using a pre-trained base classifier and sort them in descending order to obtain the feature priority sequence. Construct candidate feature subsets ,in Include before sorting One feature, for The predictive performance was evaluated to obtain the average classification accuracy and From the relationship curve, select the feature with the fewest features within the interval where the average classification accuracy is stable and highest. As the final optimal feature subset ; B4: Construct and train a Stacking ensemble model containing a base learning layer and a meta-decision layer, where the base learning layer is... The input is the feature space. Each base learner outputs the predicted probability of all candidate algorithms. The meta-decision layer is used to perform nonlinear fusion of the predicted probabilities output by the base learning layer. For each candidate algorithm, the meta-decision layer inference probability is output. Then, the candidate algorithm with the highest meta-decision layer inference probability is selected as the final optimal algorithm category. B5: Use the trained Stacking ensemble model to recommend algorithms for instances of the new distributed assembly line scheduling problem.

2. The method according to claim 1, characterized in that, Each instance will One workpiece was assigned to A factory with a replaced assembly line structure, respectively composed of... The machines process the products in a fixed sequence, and then the assembly plant assembles them. Each belongs to Products for different customers, each product i consists of several non-repeating parts, with a unit expected inventory cost of... i Each customer The preset delivery date is Late delivery incurs penalties, affecting everyone from the assembly plant to the customer. The transportation cost is h .

3. The method according to claim 1, characterized in that, In step B1, the candidate algorithms include at least one of the following: a global iterative greedy algorithm based on workpiece block intersection, a discrete intrusion weed algorithm, a distribution estimation algorithm, and an iterative local search algorithm.

4. The method according to claim 1, characterized in that, The pre-trained base classifier mentioned in B3 is LightGBM, and step S3 is included between steps B2 and B3: in the randomly generated domain The internal synthesis samples are generated based on an adaptive strategy and then incorporated. , The generated synthetic samples are sequentially subjected to physical feasibility corrections to eliminate logical violations, resulting in corrected samples. Extraction is then performed from these corrected samples. , , , , Reconstruct and combine into Merging , and To form an enhanced training set.

5. The method according to claim 1, characterized in that, In step B3, a pre-trained base classifier is used to calculate the global importance score of each feature in the augmented training set. : ； ； In the formula, For the complete feature set, A subset of features is derived from the full feature set. Remove the current feature Then, any permutation or combination that the remaining features can form. Representing a feature subset The predicted output after inputting into the base classifier. Indicating in the feature subset Based on this, the features After being added, the new prediction result calculated by the base classifier and This indicates the number of features contained in the entire feature set and the feature subset. To represent factorial, S means removing the current feature from the full feature set F. Then, any subset composed of the remaining features, It iterates through and summarizes all features that are not included. The weighted expectation of the prediction increment of the base classifier is obtained from the feature combination S.

6. The method according to claim 4, characterized in that, In step S3, in the random generation domain The process of generating synthetic samples based on an adaptive strategy includes: adaptive sampling and generation; for minority class samples, a conservative interpolation strategy or a random perturbation strategy based on the absolute deviation of the median is used to generate synthetic samples, depending on the sample size; physical feasibility corrections are then performed on the generated synthetic samples, including: Perform discrete parameter integerization, coupling feature consistency correction, and distribution drift truncation operations on the generated synthetic samples: Discrete parameter integerization: for parameters defined in the discrete domain ( The basic discrete parameters are subjected to the nearest integer projection and the minimum lower bound truncation to satisfy the integer constraint of the value range; Coupling feature consistency correction: For coupled feature pairs that satisfy the physical partial order relationship, symmetric mean adjustment is performed to reorder them to ensure that the generated samples satisfy the partial order constraint; in, The mean of the feature pairs, It is the absolute difference; Distribution drift truncation constraint: A two-way extreme value pruning based on interquartile range is adopted to limit the value of each feature dimension to the effective physical interval obtained by the minority class samples, so as to avoid the generated samples from exceeding the reasonable statistical boundary.

7. The method according to claim 1, characterized in that, In step B4, the candidate base learners for the base learning layer include tree models and / or support vector machines; the candidate meta-learners for the meta-decision layer include logistic regression, random forest, LightGBM, or XGBoost.

8. The method according to claim 1, characterized in that, Step B4 involves constructing and training a Stacking ensemble model containing a base learning layer and a meta-decision layer, including: The original metadata is } Divided into training set ; Phase 1 Base Learner Selection: The candidate base learner set is evaluated using 5-fold cross-validation on the training set, and the set of base learners with the best generalization performance is selected. Stage binary learner training: Generate out-of-fold prediction probabilities on the training set using the selected set of base learners, and construct the training dataset for the meta-learner using these probabilities; train and evaluate candidate meta-learners on the meta-learner training dataset, and select the model with the best comprehensive performance index as the final meta-decision maker; Phase 3 Global Retraining: With a fixed set of selected base learners and meta-decision makers, all models are retrained on the complete training set to obtain the final Stacking ensemble model.

9. A distributed assembly line workshop scheduling algorithm recommendation system based on feature global score filtering and Stacking ensemble model, characterized in that, Used to perform the method according to any one of claims 1 to 8.

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