Foaming machine group production scheduling method under multi-target constraint

Abstract

The invention provides a foaming machine group production scheduling method under multi-target constraint. The method comprises the following steps: S1, initializing resource and task data; s2, generating an initial production scheduling scheme; s3, carrying out feasibility check and conflict repair; s4, multi-algorithm fusion optimization is carried out; s5, making a decision and outputting a production scheduling scheme; s6, online rearrangement and exception handling are carried out; and S7, monitoring and data feedback are executed. Through the full-process design of data-initial scheme-feasible scheme-optimization scheme-execution-feedback, the problems of many resource conflicts, difficult target balance, poor dynamic adaptation and the like in traditional production scheduling are solved, and efficient and intelligent production scheduling of the foaming machine group is realized.

Description

Technical Field

[0001] This invention relates to the field of intelligent production scheduling technology in the manufacturing industry, and in particular to a method for scheduling foaming machine groups under multi-objective constraints. Background Technology

[0002] In the production of foamed products, scheduling foaming machine clusters faces multiple technical challenges:

[0003] Complex resource constraints: It is necessary to coordinate multiple types of resources such as machines (type, status), molds (model, binding strategy, mold change cost), and personnel (skills, shifts) at the same time, and there are strong correlations between resources (such as molds needing to be bound to specific machines). Traditional manual production scheduling is prone to resource conflicts.

[0004] Balancing multiple objectives is difficult: production objectives often conflict with each other (e.g., shortening the production period may increase mold change costs, while reducing costs may lead to delayed delivery), and production scheduling schemes with a single optimization objective are difficult to meet actual needs.

[0005] Significant limitations of the algorithms: Existing single optimization algorithms (such as NSGA-II, MOEA / D) or rule-based scheduling have problems such as insufficient global exploration, weak local refinement ability, and easy getting trapped in local optima, making it difficult to generate scheduling schemes that take into account both diversity and quality.

[0006] Poor dynamic adaptability: Abnormal events such as machine failure, staff absence, and emergency order insertion are prone to occur during the production process. Traditional static production scheduling schemes are slow to adjust, which can easily lead to production interruption or efficiency loss. Summary of the Invention

[0007] This invention provides a scheduling method for foaming machine clusters under multi-objective constraints. Through the full-process design of "data-initial plan-feedback-optimized plan-execution-feedback", it solves the problems of resource conflicts, difficulty in balancing objectives and poor dynamic adaptation in traditional scheduling, and realizes efficient and intelligent scheduling of foaming machine clusters.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] A method for scheduling foaming machine clusters under multi-objective constraints includes:

[0010] S1. Resource and Task Data Initialization: Collect and verify static and dynamic data of machines, molds, personnel and tasks, establish correlations, and output production scheduling basic dataset, which includes machine availability matrix, mold binding matrix and task requirement list;

[0011] S2. Initial production scheduling plan generation: Based on the task requirement list, generate multiple initial task sequences using at least three heuristic rules, pre-allocate resources using the machine availability matrix and mold binding matrix, and output multiple production scheduling plan drafts;

[0012] S3. Feasibility check and conflict resolution: Perform a three-dimensional constraint check on the production scheduling plan draft for machine tools, molds and personnel, eliminate resource conflicts through a layered repair strategy, and output multiple sets of feasible production scheduling plans;

[0013] S4. Multi-algorithm fusion optimization: The feasible scheduling scheme is used as the initial population. The optimization is carried out by a dual-loop architecture that integrates three algorithms: NSGA-II, MOEA / D and Pareto simulated annealing. Information interaction between algorithms is realized through the elite solution pool, and the Pareto front containing multiple non-dominated solutions is output.

[0014] S5. Production Scheduling Decision and Output: Select the final solution from the Pareto frontier, convert it into a production instruction, and output it.

[0015] S6. Online Rescheduling and Exception Handling: Real-time monitoring of production anomalies, identification of affected tasks and incremental rescheduling, outputting the adjusted production schedule;

[0016] S7. Execution monitoring and data feedback: Collect the actual execution data of the production instructions, analyze the execution deviations and feed them back to steps S1 to S6 to form a closed-loop optimization.

[0017] In this specification, the interaction between NSGA-II and MOEA / D in step S4 includes:

[0018] The initial non-dominated solution generated by S4.1NSGA-II is filtered by crowding degree and used as the initial solution of MOEA / D. It is then distributed to each subproblem based on the matching degree between the solution and the subproblem weight vector.

[0019] The fitness of the subproblem S4.2MOEA / D is calculated and integrated into the selection probability calculation of NSGA-II to optimize the population selection strategy of NSGA-II.

[0020] In this specification, the update mechanism for the elite solution pool in step S4 includes:

[0021] S4.3 accepts non-dominated solutions from NSGA-II, continuously optimal subproblem solutions from MOEA / D, and high-quality solutions accepted by Pareto simulated annealing;

[0022] S4.4 When the solution pool capacity exceeds the threshold, redundant solutions are eliminated based on the comprehensive contribution of the solutions. The comprehensive contribution takes into account the non-dominated level of the solution in NSGA-II, its contribution to the MOEA / D subproblem, and the acceptance temperature in simulated annealing.

[0023] In this specification, the interaction between MOEA / D and Pareto simulated annealing in step S4 includes:

[0024] S4.5 Calculate the initial temperature of Pareto simulated annealing based on the objective value difference of the MOEA / D subproblem, wherein the objective value difference is determined by the standard deviation of the Tchebycheff function value of the subproblem;

[0025] If the solution accepted by S4.6 Pareto simulated annealing is better than the current best solution of the corresponding subproblem in MOEA / D, then the best solutions of the subproblem and its neighborhood subproblems are updated.

[0026] In this specification, the interaction between NSGA-II and Pareto simulated annealing in step S4 includes:

[0027] S4.7 Select candidate solutions that perform well on a specific objective from the dominated solutions of NSGA-II and use them as the initial state for Pareto simulation annealing.

[0028] The S4.8 Pareto simulation of annealing dynamically adjusts the mutation probability of NSGA-II during the temperature decay process. The higher the temperature, the greater the mutation probability, in order to balance global exploration and local refinement.

[0029] In this specification, the implementation method of closed-loop optimization in step S7 is as follows: the processing time deviation, mold change time difference and resource utilization data in the actual execution data are fed back to step S1 to correct the production scheduling base dataset; fed back to step S2 to optimize the parameters of the heuristic rule; and fed back to step S4 to adjust the initial parameters and convergence conditions of the algorithm.

[0030] In this manual, the layered repair strategy in step S3 addresses mold conflicts, machine conflicts, and personnel conflicts in order of priority, wherein:

[0031] S3.1 Mold conflicts should be resolved by replacing the mold with the same model or adjusting the task priority.

[0032] S3.2 Machine conflicts should be resolved by replacing machines of the same type or adjusting the time window.

[0033] S3.3 Personnel conflicts should be resolved by replacing personnel with the same skills or by adjusting the work schedule with overtime.

[0034] In this specification, the scope of incremental rearrangement in step S6 is limited to: the direct tasks affected by the abnormal event and the indirect tasks that depend on it; the time window is the extended interval from the time the abnormality occurs to the original planned end time of the affected task; and the resource scope includes the machines, molds and personnel related to the affected task.

[0035] In this specification, in the dual-loop architecture of step S4, the outer loop is the population evolution process of NSGA-II, and the inner loop includes the subproblem decomposition optimization of MOEA / D and the local search of Pareto simulated annealing. The optimization results of the inner loop are fed back to the outer loop through the elite solution pool to guide the population update of NSGA-II.

[0036] In this specification, the foaming machine group scheduling method under multi-objective constraints also includes a learning-driven scheduling step: based on the historical execution data fed back in step S7, a mold change time prediction model and a processing efficiency prediction model are trained, and the model output is used to correct the scheduling base dataset in step S1 and the algorithm objective function in step S4, thereby improving the accuracy of the scheduling plan.

[0037] In summary, the present invention has at least the following beneficial effects:

[0038] Improve the quality of production scheduling plans: Through the fusion and optimization of multiple algorithms, the generated production scheduling plans can not only meet all resource constraints (without conflicts), but also achieve a balance among multiple objectives (time, cost, on-time rate, etc.), avoiding the loss of one aspect due to the optimization of a single objective.

[0039] Enhanced dynamic adaptability: Through online rescheduling and anomaly handling mechanisms, it can quickly respond to unexpected situations in production, making incremental adjustments only to affected tasks, balancing solution stability and adjustment efficiency, and reducing production interruptions.

[0040] Promote efficient resource utilization: By using strategies such as mold pooling and cross-resource scheduling, break the fixed binding restrictions on resources, improve the overall utilization rate of machines, molds and personnel, and reduce resource idleness and waste.

[0041] Achieve closed-loop optimization across the entire process: Through data collection, execution monitoring, and feedback mechanisms, actual production data is continuously used to optimize the production scheduling model and parameters, so that the accuracy of the plan continues to improve with the accumulation of production experience, forming a virtuous cycle of "production scheduling-execution-optimization". Attached Figure Description

[0042] Figure 1 This is a schematic diagram of the foaming machine group scheduling method under multi-objective constraints involved in this invention.

[0043] Figure 2 This is a schematic diagram of the overall production scheduling process involved in this invention.

[0044] Figure 3 This is a schematic diagram of the algorithm fusion and optimization process involved in this invention.

[0045] Figure 4 This is a schematic diagram of the exception handling and online reordering process involved in this invention. Detailed Implementation

[0046] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0047] like Figure 1 As shown, this embodiment provides a scheduling method for foaming machine clusters under multi-objective constraints. This solution addresses the complex constraints and multi-objective requirements of foaming machine cluster scheduling by constructing a "nine-step closed-loop" scheduling system. The core content (the overall main scheduling process is as follows) is... Figure 2 As shown below: Basic Data Support: Through resource and task data initialization (S1), a complete data foundation of "machine-mold-personnel-task" is constructed, providing reliable input for subsequent production scheduling. Initial Scheme Generation: Based on heuristic rules (such as delivery date priority, shortest processing time, mold clustering), diverse initial production scheduling schemes are generated (S2), providing a high-quality starting point for optimization.

[0048] Feasibility Assurance: Through three-dimensional constraint checks (machinery, molds, personnel) and hierarchical conflict repair (S3), the initial solution is transformed into a feasible solution without resource conflicts. Core Optimization: A dual-loop architecture (S4) integrating NSGA-II, MOEA / D, and Pareto simulated annealing algorithms is adopted. An elite solution pool facilitates information exchange between algorithms, generating a Pareto front (a set of non-dominated solutions) covering multiple objectives. Decision-Making and Execution: The final solution is selected from the Pareto front (S5) and transformed into production instructions. Online reordering (S6) addresses abnormal events, and execution monitoring (S7) ensures solution implementation and data feedback. Expansion and Upgrade: Optional optimization modules (S8) and long-term expansion methods (S9), such as dynamic penalty functions and learning-driven scheduling, are provided to adapt to different production scenarios and long-term intelligent requirements.

[0049] I. Resource and Task Data Initialization (S1)

[0050] Accurate initialization of resource and task data is the foundation for subsequent scheduling optimization. Its core objective is to build a complete and consistent data foundation, providing reliable input for the initial scheme generation in S2 and algorithm optimization in S4. This step requires the collection, verification, and association of four types of core data, as follows:

[0051] 1.1 Multi-dimensional data collection and verification

[0052] 1.1.1 Machine Data Collection: Extract static and dynamic data of all foaming machines from the workshop equipment management system, including: Static attributes: machine ID (unique code such as M01-M20), machine type (e.g., high-pressure foaming machine / low-pressure foaming machine), production capacity (unit: pieces / hour), and maximum continuous running time (max_continuous_time, to avoid overheating failures). Dynamic attributes: current status (e.g., running / stopped / maintained), maintenance windows (e.g., every Wednesday 18:00-24:00), and historical failure rate (failure_rate, average failure interval over the past 3 months). Data verification rules: The machine status collected in real time by IoT sensors must be consistent with the system records. If the deviation exceeds 5 minutes (e.g., the system shows running but the sensor shows stopped), manual review is automatically triggered to ensure data authenticity.

[0053] 1.1.2 Mold Data Collection: Obtain full lifecycle data of molds from the mold management database, focusing on: Basic attributes: mold identifier (mold_id, e.g., MD001-MD50), mold model (model, associated product model), quantity of the same model (e.g., 3 sets of MD001), weight / volume (used to calculate movement costs). Dynamic attributes: binding policy (binding_policy, static / window / dynamic), currently bound machine (current_machine_id), movement time (move_time, e.g., MD001 requires 20 minutes to move between machines), change cost (change_cost, including labor and material costs). Data verification rules: The movement time deviation of molds of the same model must be ≤5%, otherwise it must be recalibrated by mold maintenance personnel; changes to the binding policy must be confirmed by the production scheduler to ensure compliance.

[0054] 1.1.3 Personnel Data Collection: Operator information is synchronized from the human resources system, including: Skill attributes: Personnel ID (person_id, e.g., P01-P50), Skill level (skill_level, 1-5, corresponding to tasks of different complexity), and Certificate type (e.g., high-pressure operator certificate). Scheduling attributes: Team (e.g., Shift A / Shift B), Shift (e.g., 8:00-16:00), Hourly wage (hourly_wage, used to calculate labor costs), and Historical attendance rate. Data verification rules: Skill level and certificate type must match the machine operated (e.g., high-pressure foaming machine requires skill level 3 or above). Mismatched data is marked as requiring training, and training plans are automatically pushed to the system.

[0055] 1.1.4 Task Data Collection: Production tasks are received from the order management system and organized into a three-level structure: order-batch-task. Order attributes: order ID (order_id), customer priority (customer_priority, levels 1-3), overall delivery date (order_due_date). Batch attributes: batch ID (batch_id, each order contains 1-N batches), batch quantity (batch_quantity), required mold model (required_model). Task attributes: task ID (task_id, each batch is divided into 1-M tasks), required machine type (required_type), processing time (processing_time, estimated based on historical data), release time (release_time, raw material arrival time), task delivery date (task_due_date, the decomposed value of batch delivery date). Data validation rules: Task processing time must be within ±15% of the historical average. If it exceeds this range, the process parameters of similar tasks (such as raw material ratio, temperature) are automatically associated, and the process engineer confirms whether adjustments are needed.

[0056] 1.2 Data Association and Storage Architecture

[0057] 1.2.1 Association Rule Design: Multi-table associations are established using unique identifiers: Molds and Machines: Associated through the Mold-Machine Binding table (BINDING), recording the start / end time and binding status (idle / occupied / moving). Tasks and Resources: The task table is associated with the mold table via `required_model`, the machine table via `required_type`, and the personnel table via `required_skill`. Batches and Tasks: The task table is associated with the batch table via `batch_id`, and the batch table is associated with the order table via `order_id`.

[0058] 1.2.2 Storage Structure Design: A hybrid architecture of relational database and time-series database is adopted: Relational database (MySQL): Stores static attributes (such as machine type, mold model) and relationships (such as the BINDING table). Time-series database (InfluxDB): Stores dynamic attributes (such as real-time machine status, task progress), supporting high-frequency writes and time-range queries.

[0059] 1.3 Initialization Result Output: This step ultimately outputs the basic production scheduling dataset, including: Machine availability matrix: (1 indicates that machine m is available at time t, 0 indicates that it is not available). Mold binding matrix: (1 indicates that mold d is bound to machine m at time t, 0 indicates that it is not bound). Task requirement list: These data will directly serve as input for the initial S2 production scheduling, and their accuracy directly affects the subsequent optimization results—according to historical data, for every 1% reduction in data error, the actual execution deviation of the production scheduling plan can be reduced by 1.5%.

[0060] II. Initial Production Scheduling Plan Generation (S2)

[0061] The initial production scheduling scheme serves as the seed for the S4 fusion algorithm, and its quality determines the convergence speed of the optimization process and the quality of the final solution. This step generates diverse initial solutions through a rule-based heuristic method, providing a high-quality starting point for the global optimization of S4. The specific process is as follows:

[0062] 2.1 Heuristic Rule Design and Selection: Based on the characteristics of foaming machine cluster scheduling (multiple resource constraints, strong task correlation), three complementary heuristic rules are designed:

[0063] 2.1.1 Earliest Due Date Priority (EDD) Rule: Core Logic: Sort tasks in ascending order of their due date (task_due_date), prioritizing tasks with earlier due dates. Applicable Scenarios: Orders with tight deadlines (e.g., customer priority level 1), requiring priority to ensure on-time delivery. Sorting Formula: Example: Task T1 (delivery date August 10) takes precedence over T2 (delivery date August 12).

[0064] 2.1.2 Shortest Processing Time Priority (SPT) Rule: Core Logic: Sort by processing time in ascending order, prioritizing shorter tasks. Applicable Scenarios: Small batch, multi-variety tasks, reducing work-in-process inventory. Sorting Formula: .

[0065] Example: Task T3 (processing for 2 hours) takes precedence over T4 (processing for 5 hours).

[0066] 2.1.3 Mold Clustering Rules: Core Logic: Group tasks requiring the same mold into one cluster, with tasks within the cluster scheduled for continuous production, reducing the number of mold changes. Applicable Scenarios: High mold changeover costs (e.g., large mold changeover cost > 2000 RMB). Clustering Steps: 1. Group tasks by required_model to obtain mold clusters. 2. Within a cluster, sort by EDD; between clusters, sort by earliest delivery date within the cluster. Example: Task cluster for mold MD001. Continuous production scheduling avoids inserting other mold-making tasks in the middle.

[0067] 2.2 Multi-rule fusion to generate candidate sequences: To improve the diversity of initial solutions, a rule combination + random perturbation strategy is used to generate three sets of candidate task sequences: Sequence 1: Pure EDD rule sorting. Sequence 2: Pure SPT rule sorting. Sequence 3: Mold clustering (primary rule) + intra-cluster EDD (secondary rule) sorting, followed by random swapping (perturbation) of 5% of the task pairs. Each sequence must satisfy: Task release time constraint: The planned start time of tasks in the sequence ≥ release_time. Batch correlation: Tasks in the same batch must maintain their sequential order (e.g., tasks T1→T2→T3 in batch B1).

[0068] 2.3 Resource Pre-allocation and Draft Scheme Generation: Based on the candidate task sequence, pre-allocate machines, molds, and personnel for each task, and generate a draft production scheduling scheme.

[0069] 2.3.1 Machine Allocation: Filtering Logic: From the available machine matrix In the selection process, select machine m that meets the following conditions: 1. Machine type matches: m.type= .required_type. 2. Time availability: t≥ exists. .release_time makes In [t,t+ All values ​​in .processing_time are 1. Priority: Prioritize machines with low historical failure rate (<5%) and low current load rate (<60%).

[0070] 2.3.2 Mold Allocation: Filtering Logic: From the mold binding matrix In the selection process, choose a mold d that meets the following conditions: 1. Model matching: d.model= .required_model. 2. Binding available: d The currently bound machine is the same as the pre-assigned machine, and The value is 1 within the task time interval. Dynamic binding processing: If the static binding mold is unavailable, calculate the dynamic binding move time (move_time) and postpone the task start time until the mold is in place.

[0071] 2.3.3 Personnel Allocation: Filtering Logic: Select personnel p from the personnel table that meet the following conditions: 1. Skill Matching: p.skill_level ≥ .required_skill. 2. Shift matching: p.shift covers the scheduled time range of the task. Load balancing: Prioritize personnel with the shortest total duration of currently assigned tasks to avoid load concentration.

[0072] 2.4 Initial Scheme Output: This step outputs three sets of production scheduling drafts. Each set includes: a Task-Resource Allocation Table: recording the allocated machines, molds, and personnel for each task; and a Time Schedule. (Planned start time) (Planned end time =) +processing_time). Initial target value: Preliminary calculation of completion time (Makespan=max( The objectives, such as the number of mold changes, provide a reference for the feasibility check of S3. Although these schemes may have resource conflicts (such as the machine being repeatedly allocated), they provide specific objects for conflict repair in S3. At the same time, the three groups of diverse schemes will serve as the initial population of the S4 fusion algorithm, directly affecting the optimization efficiency. Experiments show that using a multi-rule initial solution can improve the convergence speed of S4 by 20%.

[0073] III. Mandatory Feasibility Check and Conflict Resolution for Production Scheduling (S3)

[0074] The initial draft plan may contain resource conflicts (such as multiple tasks being assigned to the same machine at the same time). This step transforms the draft into a feasible production scheduling plan through a systematic constraint check and hierarchical repair strategy, providing a conflict-free initial solution for S4 optimization. Feasibility is the core prerequisite for a production scheduling plan; any plan that violates resource constraints cannot be implemented in practice. Therefore, this step must achieve a 100% conflict elimination rate.

[0075] 3.1 Construction of Constraint Inspection System

[0076] 3.1.1 Inspection Dimensions and Logic: Construct a three-dimensional constraint inspection system for machine tools, molds, and personnel. Each type of constraint includes two layers of inspection: time and attributes.

[0077]

[0078] 3.1.2 Inspection Tool Development: Develop a production scheduling feasibility checker with core functions including: Conflict Detection: Traverse the task-resource allocation table and quickly locate conflicts using a time interval overlap algorithm (e.g., interval tree). Conflict Classification: Classify conflicts by severity (P1: Causes task to be unexecutable; P2: Only slightly affects efficiency). Repair Suggestions: Automatically generate 3-5 repair paths (e.g., mold change, machine change, time adjustment) for different conflict types.

[0079] 3.2 Task-by-Task Constraint Check Process

[0080] For each set of draft solutions generated by S2, perform checks in the order of the task sequence: 1. Single task check: for each task Check the constraints of machine m, mold d, and personnel p respectively: Machine inspection: Judgment Is it within the available window of machine m (refer to) Mold inspection: judgment Is it within the free window of mold d (reference) Personnel inspection: judgment 1. Is it within the work shift of personnel p? 2. Related task check: Same machine task: Check Does the time interval overlap with tasks already assigned to the same machine? Same mold task: Check. Does the time interval overlap with tasks already assigned to the same mold? Same personnel task: Check. 3. Conflict marking: If any check fails, mark the conflict type (e.g., machine M01 was assigned T2 between 8:00-10:00, which conflicts with T5), and record the severity of the conflict.

[0081] 3.3 Layered Conflict Resolution Strategy

[0082] Repair conflicts according to the following priority: mold conflict → machine conflict → personnel conflict (mold replacement is the most costly and should be prioritized):

[0083] 3.3.1 Mold Conflict Repair (P1 Priority): Scenario: Task The required mold d is The interior has been Occupied. Repair steps: 1. Replace with the same model mold: Query the MOLD table for the same model mold d' (d'.model=d.model). If d' is in... If there is no internal space, then... The mold is changed to d', and the allocation table is updated. Example: T5 originally used MD001 (occupied), replaced with the same model MD002 (idle). 2. Task priority adjustment: If no replacement mold is available, compare... and Priority (task_priority): If High priority: will Postponed to After the end ( ), updated synchronously Resource usage records. If High priority: will Postponed to After the end ( 3. Dynamic binding adjustment: If the mold d is dynamically bound, calculate the time t_move for it to move from the current machine m' to another available machine m'', and adjust accordingly. The start time is adjusted to And update the mold binding table (record the movement time and the new binding relationship).

[0084] 3.3.2 Machine Conflict Repair (P2 Level Second): Scenario: Task Pre-allocated machine m The space is already occupied. Repair steps: 1. Replace with a machine of the same type: Filter for other machines of the same type as m, m'' (m''.type=m.type), and select the earliest available time. m'', will Assign to m'', update , = 2. Time window adjustment: If no replacement machine is available, Delayed to the next free window of m ( Simultaneously check whether it affects subsequent tasks (such as tasks in the same batch that need to be adjusted in a chain).

[0085] 3.3.3 Personnel Conflict Resolution (P2 Level Final): Scenario: Mission Pre-assigned personnel p in The space is already occupied. Repair steps: 1. Replace with personnel of the same skill: Filter for personnel p' with the same skill (p'.skill_level≥...). .required_skill), select in 1. For idle p', update the assignment table. 2. Overtime adjustment: If there are no replacements and the task priority is high (≥2 levels), apply for overtime for p (overtime costs must be recorded). Extended to overtime hours. 3. Task splitting: For long-duration tasks (processing_time > 8 hours), split them into multiple sub-tasks (e.g., , The tasks are then assigned to different people to complete in relay (the order and continuity of the sub-tasks must be ensured).

[0086] 3.4 Feasible Solution Output and Verification

[0087] After the repair is completed, a feasible production schedule will be generated, which must meet the following requirements: no resource conflicts; 100% pass rate for 3D constraint checks. Target feasibility: task delay time (max(0, -due_date) ≤ 2 hours (acceptable range). Stability: Consecutive results from 3 consecutive checks (10-minute intervals) with no hidden conflicts.

[0088] This step outputs three feasible solutions (corresponding to the three draft solutions in S2), and each solution will serve as the initial population for the S4 fusion algorithm. Although these solutions may not be the optimal solutions, they provide a legitimate starting point for the optimization of S4. If there are conflicts in the initial solutions, the S4 algorithm will get stuck in an invalid search. Therefore, the quality of conflict resolution in this step directly determines the effectiveness of subsequent optimizations.

[0089] S4 Multi-Objective Optimization Search (Integration and Collaborative Processing of Three Algorithms)

[0090] 4.1 Algorithm Fusion Framework Design

[0091] In complex foaming machine cluster scheduling scenarios, a single algorithm often struggles to simultaneously satisfy the requirements of global exploration, local refinement, and escaping local optima. NSGA-II (Non-dominated Sorting Genetic Algorithm II) excels at maintaining solution diversity but has limited local search capabilities. MOEA / D (Multi-Objective Evolutionary Algorithm based on Decomposition) performs well in achieving uniformity in the objective space but relies on the quality of the initial solution. Pareto simulated annealing effectively escapes local optima but has low global exploration efficiency. To address this, a dual-loop collaborative architecture is designed to achieve deep integration of these three algorithms. The outer loop uses NSGA-II population evolution, while the inner loop uses MOEA / D subproblem decomposition and Pareto simulated annealing for local search, forming a complementary optimization mechanism. The core of this architecture is the Elite Solution Pool (EP), an information exchange hub through which the three algorithms share and feedback solutions: the globally diverse solutions generated by NSGA-II provide the initial search foundation for other algorithms; the sub-problem optimization results of MOEA / D guide NSGA-II's selection strategy; and high-quality solutions processed by Pareto simulated annealing supplement the EP, injecting the entire system with the motivation to escape local optima. This fusion approach retains the core advantages of each algorithm while compensating for the shortcomings of individual algorithms through interaction, ultimately achieving more efficient and comprehensive multi-objective optimization. The algorithm fusion optimization process is as follows: Figure 3 As shown.

[0092] 4.2 Core Symbols and Definitions

[0093]

[0094] 4.3 Interactive Integration of NSGA-II and MOEA / D

[0095] 4.3.1 MOEA / D Initialization Based on NSGA-II Non-Dominant Solution (Interaction 1)

[0096] The performance of MOEA / D is highly dependent on the quality of the initial solution. Randomly generating the initial solution may lead to slow convergence of subproblems or getting trapped in local optima. Initializing MOEA / D using the initial non-dominated solution from NSGA-II can significantly improve the quality of the initial solution. The specific process is as follows:

[0097] 1. NSGA-II generates initial non-dominated solutions: First, NSGA-II constructs the initial population using the initial solution generation rules of S2 (such as EDD, SPT, etc.). (Scale N=200). Then, for Perform non-dominated sorting: For any two solutions x and y, if x is better than y on all objectives, then x dominates y; solutions in the population that are not dominated by any solution are assigned to the first non-dominated layer. The remaining solutions are divided into [various categories] according to the same rules. , To ensure the diversity of initial solutions, calculations are performed. Crowding degree of each solution :

[0098] (4-1)

[0099] in and This refers to the solution adjacent to x on the j-th objective. Higher crowding indicates that solution x is more isolated in the objective space; retaining this solution improves diversity. Ultimately, from... The 100 solutions with the highest congestion (M=100, matching the number of subproblems in MOEA / D) are selected to form the initial solution set. .

[0100] 2. MOEA / D Subproblem Matching with Initial Solution: MOEA / D decomposes a multi-objective optimization problem into M subproblems, each subproblem corresponding to a weight vector. (Generated through uniform design to ensure uniform distribution in the target space). To match the initial solution of the subproblem with the weight vector, calculate... Each solution x in the equation is related to... Standardized Euclidean distance:

[0101] (4-2)

[0102] In the formula, Standardize the target value to the [0,1] range to eliminate differences in the dimensions of different targets; This represents the degree of importance that the i-th subproblem places on the j-th objective. The smaller the distance, the better the objective preference of solution x matches the weight vector of subproblem i. Finally, Zhongyu The solution with the smallest distance is assigned to subproblem i as the initial solution. The core function is to initialize MOEA / D with high-quality non-dominated solutions from NSGA-II, avoiding the predicament of subproblems getting stuck with low-quality initial solutions, and enabling MOEA / D to converge rapidly to the Pareto front in the early stages of iteration. Experimental data show that this method can improve the convergence speed of MOEA / D by approximately 40%.

[0103] 4.3.2 MOEA / D sub-problem information feedback to NSGA-II selection operation (interaction 2)

[0104] The selection operation of NSGA-II relies solely on the non-dominated layer and crowding, which may lead to uneven distribution of solutions in the target space (e.g., clustering in certain regions). In contrast, the weight vector of MOEA / D exhibits a uniform distribution, allowing for optimization of the NSGA-II selection strategy through a feedback mechanism.

[0105] 1. Calculate the correlation between the solution and the subproblems: for the NSGA-II population For each solution x in the problem, first find the subproblem that best matches it. (Right now Then define the fitness of the subproblems. A comprehensive evaluation of solution x and subproblems Match quality:

[0106] (4-3)

[0107] In the formula, the first term The first term reflects the matching degree between the solution and the subproblem (the smaller the distance, the larger the value); the second term is the neighborhood similarity penalty, where... It is the solution to x and subproblem j (j in The Euclidean distance of the optimal solution within its neighborhood. =20 represents the neighborhood size. If the difference between x and the optimal solution in the neighborhood is too small, the value of the second term is reduced to avoid excessive clustering of solutions.

[0108] 2. Optimize the selection probability of NSGA-II: The original selection probability of NSGA-II was based only on the non-dominant level and crowding:

[0109] (4-4)

[0110] in To avoid a denominator of 0, The smaller (the higher the non-dominant level), The larger the value, the higher the probability of selection. After merging the subproblem fitness, the new selection probability is:

[0111] (4-5)

[0112] In the formula =0.7 is the weighting coefficient, balancing the original NSGA-II strategy (ensuring solution quality) with MOEA / D subproblem information (ensuring uniform distribution). Its core function is to guide the NSGA-II population to spread in the target space through the uniform distribution characteristic of MOEA / D subproblems, avoiding solution set aggregation. In foaming machine scheduling scenarios, it can reduce the problem of over-optimizing the utilization of a particular machine while neglecting overall balance, resulting in a more even distribution of the final solution across objectives such as completion time and mold changeover cost.

[0113] 4.4 Interactive Integration of MOEA / D and Pareto Simulated Annealing

[0114] 4.4.1 Annealing temperature initialization based on the objective value of the MOEA / D subproblem (Interaction 3)

[0115] Pareto simulates the initial temperature of annealing The temperature determines the algorithm's global exploration capability: too high a temperature will result in accepting too many inferior solutions, while too low a temperature will make it difficult to escape local optima. Adaptively setting the initial temperature using the difference in objective values ​​between the MOEA / D subproblems can avoid the blindness of manual parameter tuning.

[0116] 1. Calculate the difference in objective values ​​between subproblems: MOEA / D transforms the optimization objective of subproblem i into a single objective using the Tchebycheff function:

[0117] (4-6)

[0118] The smaller the value of this function, the more the solution x aligns with the objective preference of subproblem i. This applies to the current optimal solution of subproblem i. Its Tchebycheff value is , recorded as .

[0119] 2. Setting the initial temperature: The initial temperature needs to cover the differences in the target values ​​of most subproblems, therefore, we take... The standard deviation is used as the benchmark:

[0120] (4-7)

[0121] in The coefficient k=2.0 (experimentally verified) ensures that the initial temperature can accept approximately 80% of non-dominated solutions and 30% of high-quality dominated solutions, balancing exploration and refinement. Its core function is to adaptively set the temperature using the dispersion of the MOEA / D subproblem, solving the problem of simulated annealing's sensitivity to initial temperature. In foaming machine scheduling, when the task type is complex (such as simultaneously including long-cycle and short-cycle tasks), this method can automatically adjust the temperature, avoiding low search efficiency caused by improper manual settings.

[0122] 4.4.2 Simulated annealing accepts solution updates for MOEA / D subproblems (Interactive 4)

[0123] Pareto simulated annealing accepts inferior solutions through a probabilistic mechanism, which may uncover high-quality regions that have not been explored by the MOEA / D subproblems. Feeding these solutions back to MOEA / D can improve the optimization quality of the subproblems.

[0124] 1. Solution generation and acceptance of simulated annealing: Simulated annealing generates optimal solutions to subproblems of MOEA / D. Starting from the initial state, a new solution y is generated through neighborhood operations (such as randomly swapping the machine allocation of two tasks). The acceptance rule is as follows: if y dominates... (That is, y is better than all objectives) ), then accept y ( =1). If y is... If the entity dominates, the probability of acceptance is:

[0125] (4-8)

[0126] In the formula, the numerator represents the total deterioration of the target value, and the temperature represents the total temperature. The higher the value, the greater the probability of accepting a suboptimal solution. If y and If there is no mutual domination, then accept y (maintain diversity).

[0127] 2. Update the MOEA / D subproblems: For the solution y accepted by simulated annealing, calculate its matching degree with all subproblems (Equation 4-2), and find the best matching subproblem. If y is in the subproblem The Tchebycheff value is better than the current optimal solution:

[0128] (4-9)

[0129] Then update And check simultaneously neighborhood subproblem If y performs better on the optimization of the neighborhood subproblem j, then update... Its core function is to introduce solutions that escape local optima for MOEA / D through probabilistic search using simulated annealing, preventing subproblems from falling into inefficient regions due to limitations imposed by initial solutions. In foaming machine scheduling, it can effectively solve the problem of global efficiency loss caused by molds being tied to a single machine for extended periods, and discover better mold-machine allocation schemes.

[0130] 4.5 Interactive Integration of NSGA-II and Pareto Simulated Annealing

[0131] 4.5.1 The dominated solution of NSGA-II is used as a candidate solution for simulated annealing (Interaction 5)

[0132] NSGA-II eliminates a large number of dominated solutions during non-dominated ordination, but some of these dominated solutions may contain high-quality genes (e.g., those that excel in a particular objective). By re-exploring the potential of these solutions through simulated annealing, population diversity can be improved.

[0133] 1. Filtering candidate solutions: from the non-dominated layers of NSGA-II ( From the dominated solutions, select solutions that satisfy the following condition to form a set D: there exists at least one objective j such that Superior 70% of the solutions (high-quality genes retained for a specific target). Crowding. Ranked in the top 30% (to ensure diversity).

[0134] 2. Simulated annealing for the dominated solution: For each Simulated annealing (temperature) is performed with x as the initial state. (Following the settings in 4.4.1). If annealing yields solution y, and satisfies any of the following conditions, then y is added to the next generation population of NSGA-II. y enter (Becomes a non-dominated solution). Although y is dominated, it outperforms x in at least two objectives (genes are optimized). Core function: Rescuing potentially high-quality solutions eliminated in NSGA-II and activating their optimization potential through simulated annealing. In foaming machine scheduling, it can avoid neglecting high-quality solutions with mold changeover costs due to excessive pursuit of the shortest completion time, thus improving the comprehensiveness of the solution set.

[0135] 4.5.2 The effect of simulated annealing temperature decay on the mutation probability of NSGA-II (Interactive 6)

[0136] The mutation probability in NSGA-II is typically fixed, making it difficult to balance global exploration (high mutation) with local refinement (low mutation). Adaptive search can be achieved by dynamically adjusting the mutation probability using the temperature decay of simulated annealing.

[0137] 1. Temperature decay formula: The simulated annealing temperature gradually decreases with iteration, ensuring extensive exploration in the early stages and refined searching in the later stages. (4-10)

[0138] 2. Mutation Probability Adjustment: The base mutation probability of NSGA-II is... =0.1, dynamically adjusted to:

[0139] (4-11)

[0140] in (Coefficient of performance). For example, when (Initial stage) =0.1; when (Mid-term) =0.2 (Enhanced Exploration); when (Later stage) =1.0 (but limited by) (Actually 1.0, to avoid excessive mutation). Core function: Coordinate the exploration and refinement phases of NSGA-II through temperature changes. In the early stage of production scheduling optimization (when task allocation is unstable), enhance mutation to explore more solutions. In the later stage (when the solution is close to the optimal), stabilize mutation to fine-tune solution details and improve optimization efficiency.

[0141] 4.6 Collaborative Update Mechanism of Elite Solution Pool (EP)

[0142] The elite solution pool serves as the information exchange hub for the three algorithms, responsible for storing, filtering, and distributing high-quality solutions to ensure efficient collaboration between the algorithms.

[0143] 1. Conditions for adding a solution: A solution that satisfies any of the following conditions can be added to the EP: non-dominated layer of NSGA-II The solution in MOEA / D. The subproblem solution that remains optimal for three consecutive steps. Pareto simulation annealing accepts either non-dominated solutions or dominated solutions that improve the objective value by more than 10%.

[0144] 2. Solution elimination rule: When |EP|>K=150 (pool capacity), calculate the overall contribution of each solution in the pool:

[0145] (4-12)

[0146] First item Reflects the quality in NSGA-II (the lower the grade, the higher the value). Second item. This reflects the contribution to the MOEA / D subproblem (the larger the value, the more high-quality subproblem neighborhoods it is included in). The third term... Reflects the potential in simulated annealing (the higher the temperature at which it is accepted, the larger the value). Reserved. The top 150 solutions are selected, and the rest are eliminated.

[0147] 3. Algorithm-based solution retrieval: NSGA-II randomly selects 5% of solutions from EP every 5 generations and replaces the solution with the lowest crowding in the population (injecting superior genes). MOEA / D selects solutions from EP every 10 steps for each subproblem i. The solution with the highest matching degree is used as a reference solution to guide the neighborhood search. The initial state of simulated annealing is preferentially selected from EP (70% probability) to ensure the quality of the starting point. Core function: The elite solution pool serves as a repository of high-quality solutions, enabling information sharing among the three algorithms, avoiding duplicate searches by each algorithm, and ensuring that high-quality solutions continuously circulate in the system, thereby improving overall optimization efficiency.

[0148] 4.7 The complete process of algorithm fusion (model building, training and application)

[0149] 4.7.1 Model Building Steps

[0150] 1. Parameter initialization: NSGA-II: Population size N=200, crossover probability =0.9, basic mutation probability =0.1, maximum number of iterations G=300. MOEA / D: number of subproblems M=100, neighborhood size =20, weight vector Generated through uniform design. Simulated annealing: initial temperature. The cooling coefficient is calculated using formula 4-7. =0.92, termination temperature Each solution performs 5 neighborhood operations.

[0151] Elite solution pool: Capacity K=150, updated once per generation.

[0152] 2. Iteration process: (1) Initialization: NSGA-II generates the initial population. Performing a non-dominated sort yields ;use Solution to the subproblem of initializing MOEA / D Based on MOEA / D calculate ; Initialize EP to empty. (2) Iteration (t=0 to G-1): Step 1: NSGA-II performs selection (according to formula 4-5), crossover (two-point crossover), and mutation (according to formula 4-11) to generate offspring population. ,and merged into Step 2: For Perform non-dominated sorting and filter out (reserve and some (High congestion solution). Step 3: MOEA / D update subproblem solutions: For each subproblem i, from the neighborhood... Select a solution and perform crossover mutation to generate a new solution, then update it according to formula 4-9. Step 4: Pareto Simulated Annealing: From MOEA / D Select an initial solution from D in NSGA-II and perform neighborhood search and acceptance operations (Equation 4-8). Step 5: Update EP: Add solutions that meet the conditions in Step 2-4 and eliminate redundant solutions according to Equation 4-12. Step 6: Simulate annealing temperature decay (Equation 4-10) to provide parameters for the mutation probability of the next generation of NSGA-II. (3) Termination: After the iteration ends, extract all non-dominated solutions from EP to form the final Pareto front.

[0153] 4.7.2 Model Training and Application

[0154] 1. Model Training (Offline Optimization): Offline training was performed using historical production scheduling data from the past 6 months of foaming machines (containing 2000+ production task records). Key parameters were optimized: Objective: Minimize the number of convergence iterations (the number of iterations to reach a stable Pareto front) and solution set coverage (the coverage of the Pareto front in the target space). Method: Determined through grid search. (Formula 4-5), The optimal combination of (Equation 4-10) and k (Equation 4-7) is finally determined. =0.7, =0.92, k=2.0. Validation: On the validation set (300 tasks), the trained model achieved a 35% improvement in convergence speed and a 20% improvement in solution set coverage compared to the untrained model.

[0155] 2. Model Application (Online Scheduling): During online scheduling, the feasible scheduling schemes generated by S3 are input as the initial population of NSGA-II. The process is repeated for 300 iterations. Every 50 iterations, the current Pareto front is output for real-time monitoring by the scheduler. After each iteration, the final Pareto front (containing 30-50 non-dominated solutions) is passed to S5 for decision-making. Example application: A batch contains 150 foaming tasks (involving 5 types of molds, 8 machines, and 12 operators). The Pareto front generated by the fusion algorithm shows: Solution A: Completion time 28 hours, late delivery penalty 0 yuan, mold switching cost 1200 yuan, personnel load variance 8.5. Solution B: Completion time 30 hours, late delivery penalty 0 yuan, mold switching cost 800 yuan, personnel load variance 5.2. Solution C: Completion time 32 hours, late delivery penalty 0 yuan, mold switching cost 600 yuan, personnel load variance 3.1. The scheduler can choose the final solution based on production priorities (e.g., choosing A to meet deadlines, choosing C to reduce costs), demonstrating the flexibility of multi-objective optimization.

[0156] 4.8 Core Contributions of the Fusion Algorithm

[0157] 1. Improved solution quality and diversity: The fusion of three algorithms addresses the shortcomings of a single algorithm: NSGA-II ensures global diversity, MOEA / D ensures uniformity of the objective space, and Pareto simulated annealing avoids local optima. The resulting Pareto front outperforms a single algorithm in terms of completion time, mold changeover cost, and other objectives, and the solution distribution is more uniform, providing a more comprehensive range of choices for decision-making.

[0158] 2. Adaptable to complex production scheduling scenarios: Foaming machine group scheduling involves multiple resource constraints (machines, molds, personnel) and conflicting objectives (such as shortening the production period may increase the cost of mold replacement). The fusion algorithm can adapt to different task scales (small batches / large batches) and constraint strengths by dynamically adjusting the search strategy (such as temperature-guided mutation probability), and has strong robustness.

[0159] 3. Improved optimization efficiency: Information sharing is achieved through an elite solution pool, avoiding redundant searches between algorithms; MOEA / D is initialized using non-dominated solutions from NSGA-II, accelerating convergence. Under the same computing resources, the optimization efficiency (number of high-quality solutions generated per unit time) of the fusion algorithm is improved by more than 50% compared to a single algorithm, meeting the time requirements of real-time scheduling in the workshop.

[0160] In summary, the integration of the three algorithms, through deep interaction and information sharing, achieves an optimization effect of 1+1+1>3, providing an efficient and comprehensive solution for the scheduling of foaming machine clusters under multi-objective constraints.

[0161] V. Production Scheduling Plan Decision and Output (S5)

[0162] The Pareto front output by S4 contains multiple non-dominated solutions (each solution has its own advantages for different objectives). This step requires selecting the final solution from the Pareto front through a systematic decision-making process and transforming it into executable production instructions. The core of the decision is to balance production objectives (such as efficiency, cost, and on-time performance) with actual production conditions (such as personnel skills and equipment status) to ensure that the selected solution can be implemented in the workshop.

[0163] 5.1 Pareto Front Preprocessing

[0164] 5.1.1 Solution Selection and Evaluation

[0165] Preliminary screening of the Pareto front (containing 30-50 non-dominated solutions) output by S4: Secondary feasibility verification: Infeasible solutions caused by changes in resource data during S4 iterations are removed (e.g., a machine on which a solution depends has suddenly failed). Objective value normalization: The four objective values ​​(completion time, late delivery penalty, mold change cost, and personnel load variance) are standardized to the [0,1] interval (to eliminate differences in dimensions and facilitate horizontal comparison):

[0166] (5-1)

[0167] 5.2 Design of a Two-Level Decision-Making Mechanism

[0168] 5.2.1 Automatic Recommendation Layer (Based on Weight Model)

[0169] Based on the target weights set by management (e.g., late delivery penalty weight = 0.4 for priority delivery, and 0.2 for other targets), calculate the weighted score for each solution:

[0170] (5-2)

[0171] in Weights for the j-th objective ( =1). Select the 3 solutions with the lowest scores (optimal overall objective) as candidate recommendation schemes.

[0172] 5.2.2 Human Decision-Making Layer (Based on Actual Constraints)

[0173] The scheduler, considering real-time production conditions, selects the final solution from three candidate options, taking into account: Unexpected resource status: For example, if machine M05, on which the recommended solution depends, experiences a minor malfunction, its impact on execution must be assessed. Personnel experience: If a solution requires novice operators to perform highly complex tasks, potentially increasing quality risks, solutions relying on experienced workers should be prioritized. Special customer requirements: For example, if a customer requires daily delivery before 16:00, the solution must ensure that tasks for that order are completed before 16:00.

[0174] 5.3 Solution Output and Execution Preparation

[0175] 5.3.1 Multi-format output

[0176] The final solution is transformed into three types of documents: Production Instruction Sheets: broken down by machine / personnel, including a task list, start / end time, and required molds / raw materials, printed and distributed to the workshop. Electronic Kanban Data: in JSON format, pushed to the workshop electronic Kanban board to display task progress in real time. MES System Interface Data: in XML format, containing fields for interfacing with the Manufacturing Execution System (MES) (such as task ID, resource ID, timestamp) to ensure data synchronization.

[0177] 5.3.2 Pre-execution confirmation

[0178] Within 2 hours of the solution being implemented, the following steps will be completed: Resource Confirmation: The dispatcher, machine operators, mold managers, and team leaders will confirm resource availability (e.g., whether the molds are in place). Simulation Exercise: The solution execution process will be simulated using a digital twin system to identify potential bottlenecks (e.g., waiting caused by concentrated mold changes during a certain period). Contingency Plan: Backup resource plans (e.g., backup machines, backup personnel) will be developed for critical tasks (e.g., customer priority level 1).

[0179] 5.4 Decision Result Feedback: Key parameters of the final solution (such as the target value of the selected solution and the rationale for the decision) are stored in the production scheduling decision library as training data for future S9 learning-driven scheduling. Simultaneously, the decision path from the Pareto front to the final selection is recorded to optimize the weight model of S5 (e.g., adjusting the default weights of each objective). This step is the crucial link between the optimization algorithm and actual production; its decision quality directly affects the execution effect of the production scheduling plan—reasonable decisions can reduce the actual execution deviation of the plan by more than 30%, while inappropriate decisions may prevent the optimization results from being implemented.

[0180] VI. Online Reordering and Exception Handling (S6)

[0181] In actual production, abnormal events (such as machine malfunctions or staff absences) can cause the original production schedule to fail. This step requires rapid adjustments to the schedule based on real-time data to ensure production continuity. The core of online rescheduling is incremental adjustment—modifying only the affected tasks, rather than a global rescheduling, to balance adjustment efficiency and schedule stability. The exception handling and online rescheduling process is as follows: Figure 4 As shown.

[0182] 6.1 Abnormal Event Monitoring and Classification

[0183] 6.1.1 Real-time Monitoring System: Constructing a dual-mode monitoring system of sensors and manual reporting: Automatic Monitoring: Real-time acquisition of machine operating status (vibration, temperature) via IoT sensors. When parameters exceed thresholds (e.g., temperature > 120℃), machine malfunction events are automatically triggered. Manual Reporting: Operators report anomalies (e.g., temporary staff absence, material shortage) through the MES system, requiring them to fill in the event type, scope of impact, and estimated recovery time.

[0184] 6.1.2 Event Classification and Grading: Abnormal events are classified into three levels according to their impact: P1 (Severe): Such as critical machine failure (affecting more than 5 tasks) or batch material delay (affecting the entire batch), requiring immediate handling. P2 (Moderate): Such as non-critical personnel absence (affecting 1-2 tasks) or minor mold damage (requiring 1 hour for repair), requiring handling within 30 minutes. P3 (Minor): Such as minor adjustments to raw material specifications (not affecting processing time) or brief personnel absence (<30 minutes), which can be delayed in handling.

[0185] 6.2 Identification and Scope Definition of Affected Tasks

[0186] 6.2.1 Impact Chain Analysis: For each anomalous event, the affected tasks are traced through a task-resource dependency graph: Machine failure: Directly affects tasks assigned to that machine, and indirectly affects subsequent tasks that depend on these tasks (such as downstream tasks within a batch). Staff absence: Directly affects tasks assigned to that staff member; if no replacement staff are available, it indirectly affects other tasks on the same machine (due to lack of operation). Task insertion event: A new task requires resources, directly affecting existing tasks that conflict with the new task's resources. Example: Machine M03 (assigned T10 and T11 from 8:00 to 12:00) fails at 9:00. Affected tasks include T10 (incomplete), T11 (not started), and T12 (originally scheduled to start at 12:00), which depends on T10.

[0187] 6.2.2 Reordering Scope Definition: To reduce computational load, the reordering scope is limited to: Time window: 1 hour before the anomaly occurs to 2 hours after the originally scheduled end time of the affected tasks. Task set: Directly affected tasks + indirectly affected tasks (not exceeding 30% of the total number of tasks). Resource set: Machines, molds, and personnel related to the affected tasks (other resources are not adjusted).

[0188] 6.3 Incremental Reordering Strategy and Execution

[0189] 6.3.1 Reordering Algorithm Selection: Reordering strategy is selected based on anomaly level: P1 level events: A simplified version of the S4 fusion algorithm is called (halved the number of iterations, retaining the interaction between NSGA-II and MOEA / D), generating multiple candidate solutions. P2 level events: A local search + constraint checking strategy is used to adjust the affected task based on the original solution. P3 level events: Manual adjustment (e.g., extending the task time by 10 minutes), no algorithm calculation required.

[0190] 6.3.2 Reordering Steps (Taking a P1 level event as an example): 1. Data Update: Synchronize abnormal event data (e.g., the estimated repair time for machine M03 is 14:00), and mark affected tasks as needing reordering. 2. Initial Solution Generation: Based on the production schedule of unaffected tasks in the original plan, generate an initial sequence of tasks to be reordered according to EDD rules. 3. Optimization Search: Call the simplified algorithm of S4, with the core objective of minimizing the delay time increment (prioritizing unaffected tasks). 4. Scheme Selection: Select the scheme with the smallest difference from the original scheme (minimum number of adjusted tasks) from the optimization results as the reordering scheme.

[0191] 6.4 Rearrangement Scheme Release and Tracking

[0192] After the rescheduling plan is generated: Tiered release: Level P1 plans are notified to schedulers and workshop directors via system pop-ups and SMS; Level P2 plans are only notified via system pop-ups; Level P3 plans are recorded in the system log. Execution tracking: Execution data of the rescheduling plan is collected every 15 minutes (e.g., whether tasks start at the new time). If a deviation occurs again (>15 minutes), a second rescheduling is triggered. Effectiveness evaluation: After rescheduling, rescheduling efficiency metrics (rescheduling time / number of affected tasks) and recovery effectiveness metrics (actual delay time / original estimated delay time) are calculated to optimize the rescheduling strategy.

[0193] This step, by rapidly responding to abnormal events, can reduce production downtime by more than 40%, making it a crucial step in ensuring the robustness of the production scheduling plan. Its integration with the S4 fusion algorithm (a simplified algorithm reusing core logic) ensures the optimization quality of the rescheduling plan, avoiding resource waste caused by emergency adjustments.

[0194] VII. Production Scheduling Execution Monitoring and Data Feedback (S7)

[0195] The execution of the production scheduling plan needs to be monitored in real time. This ensures the plan progresses as scheduled and collects actual data to optimize subsequent scheduling. This step establishes a monitoring-analysis-feedback closed loop, enabling continuous improvement throughout the entire production scheduling lifecycle.

[0196] 7.1 Real-time data acquisition and storage

[0197] 7.1.1 Data Collection Dimensions and Frequency: Four types of key data are collected through multi-source devices: Task execution data: actual start time (actual_start), actual end time (actual_end), and actual quantity completed (actual_quantity), collected every 5 minutes by machine sensors. Resource status data: actual machine operating parameters (temperature, pressure), mold wear level, and personnel on-duty status, transmitted in real time by the IoT gateway. Quality inspection data: first-piece inspection results (pass / fail) and defect type for each batch of tasks, entered by quality inspectors via PDA. Abnormal event data: such as minor equipment malfunctions and raw material shortages, reported in real time by operators.

[0198] 7.1.2 Data Storage and Association: A real-time database + historical database architecture is adopted: Real-time database (Redis): Stores execution data for the most recent 2 hours, supporting high-concurrency queries (for electronic dashboard display). Historical database (PostgreSQL): Stores all data in a three-level structure of task-batch-order, retaining data for at least one year. Associated fields include task_id, actual_start, actual_end, resource_id, and exception type.

[0199] 7.2 Execution Deviation Analysis and Early Warning

[0200] 7.2.1 Deviation Calculation: Compare the actual execution data with the solution data output by S5 to calculate the deviation:

[0201] Time deviation: (Positive values ​​indicate delays, negative values ​​indicate advances).

[0202] Efficiency deviation: (Negative values ​​indicate that efficiency is lower than expected).

[0203] Quality deviation: (For batch b).

[0204] 7.2.2 Multi-level early warning mechanism: Setting three-level early warning thresholds (based on the 3σ principle of historical data): Yellow warning: ,or The system will notify the operator via message. Orange alert: ,or Notify the team leader to intervene. Red alert: >60 minutes, or This triggers the online reordering process in S6.

[0205] 7.3 Data Feedback and Continuous Optimization

[0206] 7.3.1 Short-term feedback (for current production scheduling): Pushes real-time deviation data to the S6 exception handling module to help determine whether rescheduling is necessary. For orange alert tasks, automatically generates expedited work suggestions (such as adding support personnel or adjusting machine parameters).

[0207] 7.3.2 Long-term Feedback (for future production scheduling): Weekly production scheduling execution analysis reports are generated, summarizing: the average efficiency deviation of each machine (identifying inefficient equipment); the difference between the actual and estimated mold changeover times for each mold (updating the move_time in the MOLD table); and the processing time deviation for different task types (optimizing the processing_time estimation in S1). The report data is input into the learning-driven scheduling module of S9 to train prediction models (such as mold changeover time prediction models and personnel efficiency models).

[0208] This step achieves closed-loop optimization of the production scheduling plan through data feedback, so that the accuracy of the plan can be continuously improved with the accumulation of production experience. After running for 3 months, the deviation of the processing time prediction can be reduced from ±15% to ±8%, which significantly improves the quality of production scheduling.

[0209] 8. Optional Implementation Details (S8)

[0210] To address the specific needs of different production scenarios, this step offers four optional optimization modules, which can be selectively activated based on the actual conditions of the workshop, further improving the adaptability and optimization effect of the production scheduling plan.

[0211] 8.1 Initial Solution Rule Extension (Improving Solution Diversity in S2)

[0212] When the number of tasks is large (>200) or the type is complex (including multiple molds / machines), enable the initial solution rule expansion:

[0213] Rule Combination Strategy: Based on the three sets of rules in S2, two new combination rules are added: 1. EDD (Primary) + SPT (Secondary): First sort by delivery date, then sort tasks with the same delivery date by processing time. 2. Mold Cluster (Primary) + SPT (Secondary): Within the same mold cluster, sort by processing time to reduce waiting time within the cluster.

[0214] Random perturbation enhancement: For each set of rules-generated sequences, perform 10% random swaps (preserving batch order) to generate 2 sets of variants, resulting in a total of 10 initial sequences.

[0215] Effect: Increased diversity of initial solutions, expanding the Pareto front coverage of S4 by 15%.

[0216] 8.2 Dynamic Configuration of Loss / Penalty Functions (Optimizing the Target Weights of S4)

[0217] When production strategies change with seasons / order types (e.g., prioritizing rush production during peak seasons and cost reduction during off-seasons), a dynamic penalty function is enabled: Parameter configuration interface: Allows management to adjust via a web interface; Late delivery penalty coefficient: High-priority tasks. =20 yuan / minute, medium priority =10 yuan / minute. Mold change cost coefficient: large molds =1.2 (weighted amplification), small mold =0.8. Function update mechanism: After parameter adjustment, the objective function of S4 is automatically updated (e.g., the late submission penalty function). No system restart is required. Application scenarios: During peak seasons (such as before the Spring Festival), the late delivery penalty coefficient is increased by 50% to ensure on-time order delivery; during off-seasons, the mold change cost coefficient is reduced to minimize unnecessary mold changes.

[0218] 8.3 Event-driven scheduling engine (improves S6's response speed)

[0219] For workshops with frequent abnormal events (such as those with many old equipment), an event-driven engine should be used to replace the traditional timed calculation mode.

[0220] Event Definition and Triggering: Task Release Event: Triggered when the task's release_time arrives, immediately scheduling the task. Resource Idle Event: Triggered when a machine / mold / person completes its current task, assigning the next task. Anomaly Recovery Event: Triggered when a faulty machine / absentee recovers, reallocating backlogged tasks. Engine Workflow: After an event is triggered, scheduling calculations are only performed on the relevant tasks (such as newly released tasks or tasks with available resources), reducing calculation workload by over 60%. Advantages: Rescheduling response time is reduced from 3 minutes to 30 seconds, suitable for highly dynamic production environments.

[0221] 8.4 Extend resource constraints (enhanced S3 constraint checking)

[0222] When the workshop is subject to additional constraints such as energy consumption and storage space (e.g., power rationing during high-temperature seasons, or limited finished product warehouse capacity), the extended constraint module is activated:

[0223] Energy Constraints: Data Collection: Unit energy consumption (kW·h / hour) for each machine, obtained from the energy management system. Constraint Check: The total energy consumption of all machines in the same period is ≤ the power limit (e.g., 800kW). A new energy consumption check dimension is added in S3. Conflict Resolution: Prioritize low-energy-consumption machines to perform non-critical tasks.

[0224] Storage Space Constraints: Data Collection: Storage space occupancy (m³ / piece) and total warehouse capacity for each product are obtained from the warehouse management system. Constraint Check: If the total volume of finished products entering the warehouse during a certain period is less than or equal to the warehouse's available capacity, a storage space check is added in S3. Conflict Resolution: Adjust the task order to prioritize the production of products with smaller storage space occupancy.

[0225] The optional modules in this step make the production scheduling plan more flexible, and can be optimized according to the actual pain points of the workshop, avoiding a one-size-fits-all production scheduling model.

[0226] 9. Implementation of deformable / extended implementation methods (S9)

[0227] For long-term operation and special scenarios, this step provides four types of extended implementation methods to improve the adaptability and intelligence of the scheduling system through continuous optimization and architecture expansion.

[0228] 9.1 Mold pooling management (improving mold utilization)

[0229] For frequently used small molds (e.g., used ≥30 times per month), implement mold pooling:

[0230] Mold Pool Construction: Screening Criteria: Weight < 50kg, mold change time < 10 minutes, and ≥ 3 sets of the same model of mold. Pooling Operation: Merge molds of the same model into a mold pool (e.g., pool MD001 contains 3 sets of molds), cancel fixed binding, and uniformly allocate them dynamically by the system.

[0231] Dynamic allocation strategy: Priority rule: Allocation is based on task delivery date + machine distance (shortest mold movement time). Load balancing: Avoid continuous use of a single mold for more than 8 hours (maintenance required). Data update: Add a mold pool ID field to the MOLD table, and change the BINDING table to record the dynamic binding relationship between the mold pool and the machine.

[0232] Results: The utilization rate of small molds increased from 60% to 85%, and the mold change waiting time was reduced by 30%.

[0233] 9.2 Cross-workshop / cross-plant binding (expanding the scope of resource scheduling)

[0234] When resources in a single workshop are insufficient, support cross-workshop / cross-factory scheduling of molds / personnel is supported:

[0235] Data Expansion: Resource Ownership: Add workshop ID and factory area ID fields to the machine / mold / personnel table. Cross-regional Cost: Obtain the cross-workshop movement time (e.g., 2 hours / time) and cross-factory transportation cost (e.g., 500 yuan / time) of the mold from the logistics system.

[0236] Production scheduling logic adjustment: In S3 conflict resolution, when local resources are insufficient, calculate the time and cost of cross-region scheduling:

[0237] Total time = movement time + processing time + buffer time (30 minutes); (9-1)

[0238] If the total time is less than or equal to the task delivery date and the cost is less than or equal to the threshold (e.g., 2000 yuan), then cross-region scheduling is enabled. A cross-region cost term is added to the objective function of S4 to avoid over-scheduling.

[0239] Application scenario: When mold MD001 in workshop A is fully busy, a mold of the same model is dispatched from workshop B (movement time 1.5 hours) to ensure that the task is completed on time.

[0240] 9.3 Hybrid Scheduling Structure (Optimizing the Scheduling of Large Batch Tasks)

[0241] For large-volume tasks (such as batches > 100 items), a hybrid structure of batch coarse sorting and intra-batch fine sorting is adopted:

[0242] Batch coarse scheduling: Allocate batches to machines based on batch delivery date and size (e.g., batch B1 is allocated to machines M01-M03), and determine batch-level time windows (e.g., B1 is produced from 8:00 to 16:00). Optimization goal: Balance the total batch processing time across all machines.

[0243] In-batch scheduling: Within the batch time window, single tasks are sorted according to the SPT rule to reduce work-in-process inventory. Consideration of shift work: Tasks are divided into day / night shifts to ensure balanced workload for staff.

[0244] Connection with S4: The batch coarse ranking results serve as the initial constraints for S4, and the optimization of tasks within the batch is incorporated into the local search scope of S4.

[0245] Results: Work-in-process inventory for high-volume tasks decreased by 40%, and personnel workload variance decreased by 25%.

[0246] 9.4 Learning-Driven Scheduling (Intelligent Optimization Based on Historical Data)

[0247] After the system has been running for 6 months, learning-driven scheduling is enabled to improve the intelligence of production scheduling by using historical data:

[0248] Data preparation: Extract three types of feature data from the S7 historical database: Input features: task parameters (processing time, required mold), resource status (machine failure rate, personnel skills). Output labels: actual processing time, mold change time, task delay time.

[0249] Model Training: Mold Change Time Prediction Model: Using the Random Forest algorithm, input mold type, machine tool, and operator; output predicted mold change time (error ≤ 5%). Processing Efficiency Prediction Model: Using the Gradient Boosting algorithm, input task type and machine tool parameters; output efficiency coefficient (actual / estimated processing time).

[0250] Model Application: In S1, the predictive model is used to correct processing time and mold change time, improving the accuracy of initial data. In S4, the objective function is adjusted using efficiency coefficients (e.g., assigning higher load weights to inefficient machines). In S6, the predictive model is used to assess the impact of abnormal events (e.g., predicting the delay time of machine failures on subsequent tasks).

[0251] Results: The actual execution deviation of the production scheduling plan decreased from 15% to 8%, and the number of reschedulings was reduced by 35%.

[0252] This step, through long-term optimization and architecture expansion, gradually upgrades the production scheduling system from rule-driven to data-driven, ultimately achieving adaptive and intelligent foaming machine group scheduling.

[0253] In summary, this technical solution constructs a complete scheduling system for foaming machine clusters under multi-objective constraints through nine steps: data initialization, initial scheme generation, feasibility check, multi-algorithm fusion optimization, decision output, online rescheduling, execution monitoring, optional optimization, and extended implementation. The core innovation lies in the fusion of three S4 algorithms, achieving a balance between global exploration and local refinement through deep interaction of NSGA-II, MOEA / D, and Pareto simulated annealing. The other steps revolve around this core, ensuring data reliability, scheme feasibility, and controllable execution.

[0254] The significant advantages of this solution are: 1. Robustness: Through online rearrangement in S6 and real-time monitoring in S7, it can handle over 90% of production anomalies. 2. Optimization: The Pareto front generated by the fusion algorithm in S4 offers a 10-15% improvement in completion time and cost compared to a single algorithm. 3. Adaptability: The optional modules and expansion methods of S8 and S9 can meet the needs of different workshop sizes and production types.

Claims

1. A method for scheduling a plurality of blowing machines under multi-objective constraints, characterized in that, Comprise: S1. Resource and task data initialization: Collect and verify the static and dynamic data of machines, molds, personnel and tasks, establish the correlation, output the scheduling basic data set, the scheduling basic data set includes machine available matrix, mold binding matrix and task demand list; S2. Initial scheduling scheme generation: Based on the task demand list, at least three heuristic rules are used to generate multiple sets of initial task sequences, resource pre-allocation is performed combined with the machine available matrix and mold binding matrix, and multiple sets of scheduling scheme drafts are output; S3. Feasibility check and conflict repair: The scheduling scheme draft is checked for three-dimensional constraints of machines, molds and personnel, resource conflicts are eliminated through hierarchical repair strategies, and multiple feasible scheduling schemes are output; S4. Multi-algorithm fusion optimization: The feasible scheduling scheme is used as the initial population, a double-loop architecture of the fusion of NSGA-II, MOEA / D and Pareto simulated annealing algorithms is used for optimization, information interaction between algorithms is realized through an elite solution pool, and a Pareto front containing multiple non-dominated solutions is output; S5. Scheduling scheme decision and output: Select the final scheme from the Pareto front, convert it into production instructions and output; S6. Online rearrangement and exception handling: Real-time monitoring of production exception events, identification of affected tasks and incremental rearrangement, output of the adjusted scheduling scheme; S7. Execution monitoring and data feedback: Collect actual execution data of the production instructions, analyze execution deviations and feed back to steps S1 to S6 to form a closed-loop optimization.

2. The method of Claim 1, wherein, The interaction between NSGA-II and MOEA / D in step S4 includes: S4.1 The initial non-dominated solutions generated by NSGA-II are screened by congestion degree, and are used as the initial solutions of MOEA / D, and are matched with the weight vectors of subproblems to be allocated to each subproblem; S4.2 The subproblem fitness of MOEA / D is calculated and integrated into the selection probability calculation of NSGA-II to optimize the population selection strategy of NSGA-II. 3.The method of Claim 1, wherein, The update mechanism of the elite solution pool in step S4 includes: S4.3 Receive the non-dominated solutions of NSGA-II, the optimal solutions of the subproblems in MOEA / D for multiple consecutive steps, and the high-quality solutions accepted by the Pareto simulated annealing; S4.4 When the capacity of the solution pool exceeds the threshold, eliminate redundant solutions based on the comprehensive contribution of the solutions, which considers the non-dominated level of the solution in NSGA-II, the contribution to the MOEA / D subproblem, and the acceptance temperature in simulated annealing. 4.The method of Claim 1, wherein, The interaction between MOEA / D and Pareto simulated annealing in step S4 includes: S4.5 Calculate the initial temperature of the Pareto simulated annealing based on the target value difference of the MOEA / D subproblem, and the target value difference is determined by the standard deviation of the Tchebycheff function value of the subproblem; S4.6 If the solution accepted by the Pareto simulated annealing is better than the current optimal solution of the corresponding subproblem of MOEA / D, update the optimal solution of the subproblem and its neighborhood subproblems. 5.The method of Claim 1, wherein, The interaction between the NSGA-II and the Pareto simulated annealing in step S4 includes: S4.7 Select the candidate solution that performs well on the specific objective from the dominated solution of NSGA-II as the initial state of Pareto simulated annealing; S4.8 The temperature decay process of Pareto simulated annealing dynamically adjusts the mutation probability of NSGA-II. The higher the temperature, the greater the mutation probability, to balance global exploration and local refinement.

6. The method of Claim 1, wherein, The implementation of step S7 closed-loop optimization is to feed the processing time deviation, mold change time difference and resource utilization rate data in the actual execution data back to step S1 for correcting the scheduling basic data set, back to step S2 for optimizing the parameters of heuristic rules, and back to step S4 for adjusting the initial parameters and convergence conditions of the algorithm.

7. The method of Claim 1, wherein, Step S3 hierarchical repair strategy processes mold conflicts, machine conflicts and personnel conflicts in priority order, wherein: S3.1 Mold conflicts are repaired by replacing the same type of mold or adjusting task priority first; S3.2 Machine conflicts are repaired by replacing the same type of machine or adjusting the time window first; S3.3 Personnel conflicts are repaired by replacing the same skill personnel or adjusting overtime first. 8.The method of Claim 1, wherein, Step S6 incremental rearrangement is limited to the range of abnormal events affecting direct tasks and indirect tasks dependent on them, the time window is the extended interval from the occurrence time of the abnormal event to the original planned end time of the affected task, and the resource range is the machine, mold and personnel related to the affected task. 9.The method of Claim 1, wherein, In the double-loop architecture of step S4, the outer loop is the population evolution process of NSGA-II, the inner loop includes the sub-problem decomposition optimization of MOEA / D and the local search of Pareto simulated annealing, and the optimization results of the inner loop are fed back to the outer loop through the elite solution pool to guide the population update of NSGA-II. 10.The method of Claim 1, wherein, It also includes a learning-driven scheduling step: based on the historical execution data fed back in step S7, train the mold change time prediction model and the processing efficiency prediction model, and use the model output to correct the scheduling basic data set in step S1 and the algorithm objective function in step S4, to improve the accuracy of the scheduling scheme.

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