Distributed heterogeneous flexible flow shop batch processing scheduling method and system

Abstract

The invention discloses a distributed heterogeneous flexible flow shop batch processing scheduling method and system, relates to the technical field of distributed production scheduling in the manufacturing industry, and aims to solve the problems that an existing scheduling method is not comprehensive in constraint consideration, poor in energy consumption optimization and low in algorithm efficiency. According to the method, a mixed integer linear programming model containing multiple constraints such as release time and sequence-related preparation time is constructed, a learning-assisted dual-objective co-evolution framework is established, and the maximum completion time and the total energy consumption are synchronously optimized by combining mixed initialization, global-local search collaboration, decision reinforcement learning operator selection and a collaborative energy-saving strategy. The release time, the sequence-related preparation time, the inter-stage transportation time and the batch processing scheduling are simultaneously considered in the distributed heterogeneous flexible flow shop scheduling for the first time, the established mixed integer linear programming model better fits the actual production scene, and the method fits the actual production scene, is good in energy consumption optimization effect and can be adapted to the non-ferrous metal metallurgy aluminum production process.

Description

Technical Field

[0001] This invention relates to the field of distributed production scheduling technology in the manufacturing industry, and in particular to a distributed heterogeneous flexible assembly line workshop batch processing scheduling method and system. Background Technology

[0002] The flexible flow shop scheduling problem has been proven to be NP-hard. With the continued deepening of economic globalization, the systematic research on distributed flexible flow shop scheduling has received increasing attention. Given the differences in the number and function of new and old machines in various factories during actual production, research on distributed heterogeneous flexible flow shop scheduling is particularly important. Research from the basic flexible flow shop scheduling problem to the distributed heterogeneous flexible flow shop scheduling problem has attracted widespread attention from industry and academia; however, existing research is inefficient and cannot meet the actual needs of enterprises.

[0003] As an effective manufacturing method, batch flow technology utilizes the divide-and-conquer principle to decompose production batches into several sub-batches to improve processing efficiency. However, existing research has significant limitations: it rarely considers release time, sequence-dependent preparation time, and inter-stage transport time in the distributed heterogeneous flexible flow shop scheduling problem simultaneously, neglecting the impact of these factors on actual production and the core competitiveness of enterprises; furthermore, batch scheduling is rarely included in the research scope of the distributed heterogeneous flexible flow shop scheduling problem.

[0004] The shortcomings of existing technologies are mainly reflected in two aspects: First, the constraints are not fully considered, failing to simultaneously cover release time, sequence-related preparation time, inter-stage transportation time, and batch processing scheduling requirements, thus being out of touch with actual production scenarios; Second, the energy consumption optimization effect is poor, and there are a large number of invalid searches during the solution process, resulting in low algorithm efficiency and difficulty in simultaneously optimizing the maximum completion time and total energy consumption of the scheduling scheme. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a distributed heterogeneous flexible workflow workshop batch processing scheduling method and system.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows:

[0007] A distributed heterogeneous flexible workflow workshop batch processing scheduling method includes the following steps:

[0008] S1. Construct a mixed-integer linear programming model for the batch processing energy efficiency scheduling problem in a distributed heterogeneous flexible flow shop. The constraints of the model simultaneously include release time, sequence-dependent preparation time, inter-stage transportation time, and batch processing scheduling requirements. The optimization objective is to minimize the maximum completion time (C0). max ) and Total Energy Consumption (TEC);

[0009] S2. Construct a dual-objective co-evolutionary framework based on learning assistance. The framework includes a problem encoding / decoding module, a hybrid initialization module, a global search operator module, a knowledge-driven local search operator module, a learning selection module based on adversarial reinforcement learning, and a collaborative energy-saving strategy module.

[0010] S3. Use the hybrid initialization module to generate a global population. The hybrid initialization module uses load balancing rules, sorting rules, and random rules to generate 1 / 5, 1 / 5, and 3 / 5 of the population individuals, respectively.

[0011] S4. Perform a global search on the global population, sequentially performing mating selection, crossover update, mutation update, and environment selection;

[0012] S5. Extract Pareto solutions as elite solutions from the population after global search, and perform local search on the elite solutions through the knowledge-driven local search operator module. The knowledge-driven local search operator module includes 8 single-factory knowledge-driven operators and 10 multi-factory knowledge-driven operators.

[0013] S6. A learning selection module based on duel reinforcement learning is adopted, and the optimal local search operator is dynamically selected for each Pareto solution through a triple combined duel dual deep Q network (DuelingDDQN).

[0014] S7. Optimize the energy consumption of the Pareto solution after local search using the collaborative energy-saving strategy module. The collaborative energy-saving strategy module includes ES1 strategy and ES2 strategy. ES1 strategy reduces the total energy consumption by adjusting the machine start time and ES2 strategy reduces the total energy consumption by reallocating the workpiece processing machine.

[0015] S8. Repeat steps S4-S7 until the iteration termination condition is met, and output the final Pareto solution set.

[0016] The constraints of the mixed-integer linear programming model in step S1 specifically include: the processing sequence constraints of the workpiece in each factory and stage, the sub-batch processing constraints of the batch processing equipment, the release time constraints, the sequence-related preparation time constraints, the inter-stage transportation time constraints, and the calculation constraints of machine processing energy consumption and transportation energy consumption.

[0017] In step S3:

[0018] The load balancing rule defines the factory workload as the sum of the processing time of all workpieces in each stage, and prioritizes assigning tasks to factories with less workload.

[0019] The sorting rule first arranges the workpieces in ascending order by release time and in ascending order by order association preparation time between sub-batch, resulting in two index arrays. After calculating and accumulating the selection probabilities of the two arrays, individuals are generated by sorting them in descending order.

[0020] The random rule replenishes the remaining individuals through random initialization to enhance population diversity.

[0021] In step S5:

[0022] The single-factory knowledge-driven operator includes:

[0023] A single-factory internal exchange operator that exchanges adjacent or any two workpieces in the critical factory Fc.

[0024] A single-factory adjacent exchange operator exchanges adjacent workpieces in Fc and Ft of the energy-critical factory.

[0025] The single-factory internal insertion operator inserts 1-2 workpieces into other positions in Fc;

[0026] A single-factory internal flip operator reverses the workpiece sequences in Fc and Ft;

[0027] The multi-factory knowledge-driven operator includes:

[0028] The exchange operator between multiple factories exchanges 1-3 adjacent workpieces in Fc / Ft with 1-3 adjacent workpieces in other factories;

[0029] The inter-factory insertion operator inserts 1-3 adjacent workpieces or any 1 workpiece from Fc into other factories;

[0030] The critical plant Fc is defined as the plant with the worst performance in the maximum time to completion indicator, and the critical plant Ft is defined as the plant with the worst performance in the total energy consumption indicator.

[0031] The workflow of the learning selection module based on duel reinforcement learning described in step S6 includes:

[0032] Calculate the initial state of the scheduling environment;

[0033] Based on the initial state, select the local search operator to be executed at the decision point;

[0034] Optimize the scheduling scheme using the selected operators;

[0035] Evaluate the reward of the selected operator and update the scheduling environment state for subsequent decision points.

[0036] In step S7:

[0037] The ES1 strategy employs a machine delay processing strategy in the first stage, postponing the machine's start processing time to match the workpiece release time. In the second to S stages, the machine delays processing during the initial processing transport time.

[0038] The ES2 strategy keeps the machine allocation unchanged within the factory corresponding to the maximum completion time. For workpieces from other factories, it prioritizes the allocation to the machine with the lowest processing energy consumption in each processing stage, and the allocation rules between each stage are consistent with the decoding mode of the encoding and decoding module.

[0039] A distributed heterogeneous flexible workflow workshop batch processing scheduling system includes:

[0040] Model building module: used to build the mixed integer linear programming model in step S1 of claim 1;

[0041] Framework building module: used to build the learning-assisted dual-objective co-evolutionary framework in step S2 of claim 1;

[0042] Population generation module: used to generate the global population in step S3 of claim 1;

[0043] Global search module: used to perform the global search in step S4 of claim 1;

[0044] Local search module: used to implement the local search in step S5 of claim 1;

[0045] Operator selection module: used to implement the operator selection based on confrontation reinforcement learning in step S6 of claim 1;

[0046] Energy consumption optimization module: used to implement the collaborative energy-saving optimization in step S7 of claim 1;

[0047] Iteration output module: Used to control the iteration process and output the final Pareto solution set.

[0048] This method can be applied to the aluminum production process in the non-ferrous metals metallurgical industry, including the scheduling optimization of the electrolysis, casting, cold rolling, and hot rolling stages. The electrolytic cells in the electrolysis stage, the continuous casting machines in the casting stage, and the rolling equipment in the rolling stage are all treated as parallel processing machines. The batch transportation and processing of molten aluminum correspond to batch processing scheduling, transportation time, and sequence-related preparation time constraints, respectively.

[0049] Compared with the prior art, the beneficial effects of the present invention are:

[0050] 1. For the first time, in the scheduling of a distributed heterogeneous flexible flow shop, release time, sequence-related preparation time, inter-stage transportation time and batch processing scheduling are considered simultaneously. The established mixed-integer linear programming model is more in line with the actual production scenario and solves the problem of the disconnect between existing technology and reality.

[0051] 2. By using a learning-assisted dual-objective co-evolutionary framework, the maximum completion time and total energy consumption are optimized simultaneously. Furthermore, the collaborative energy-saving strategy can further reduce energy consumption without extending the completion time, which is superior to the non-dominated solution set of existing algorithms.

[0052] 3. Eighteen knowledge-driven local search operators are designed, and the optimal operator is dynamically selected through a triple-combined duel dual-deep Q-network, which significantly reduces invalid searches. At the same time, the hybrid initialization module improves the quality of the initial population, and the global and local searches are coordinated and balanced, resulting in higher learning efficiency and faster iterative convergence than traditional algorithms.

[0053] 4. Customized adaptation for aluminum production processes in the non-ferrous metals industry solves the challenges of equipment scheduling and energy consumption optimization in this industry, providing a scalable technical solution for scheduling optimization in similar discrete manufacturing scenarios. Attached Figure Description

[0054] Figure 1 This is a system flowchart of the present invention;

[0055] Figure 2 This is a comparison chart of the dual-objective evaluation metrics of the present invention and existing algorithms;

[0056] Figure 3 A schematic diagram of the aluminum production process in the non-ferrous metals metallurgical industry.

[0057] Figure 4 Pareto front diagram of Example 1;

[0058] Figure 5 Pareto front diagram of Example 2;

[0059] Figure 6 This is the Pareto front diagram for Example 3. Detailed Implementation

[0060] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments. It should be understood that these descriptions are merely exemplary and not intended to limit the scope of the invention. Furthermore, descriptions of well-known structures and technologies are omitted in the following description to avoid unnecessarily obscuring the concepts of the invention.

[0061] Example 1: Application of aluminum production scheduling with 3 workpiece sub-batches

[0062] (I) Application Scenario Parameters: This embodiment targets the aluminum production process in the non-ferrous metals metallurgical industry, involving two distributed heterogeneous factories (Factory A and Factory B). The production stages include electrolysis (Stage 1), casting (Stage 2), cold rolling (Stage 3), and hot rolling (Stage 4), requiring the scheduling of 10 workpieces.

[0063] Key parameters of the workpiece: Release time: The release times for workpieces 1-10 are 0, 10, 15, 20, 22, 25, 28, 30, 12, and 18 minutes, respectively;

[0064] Processing time: Taking workpiece 1 as an example, the processing times for stages 1-4 in factory A are 30, 25, 22, and 18 minutes respectively, and the processing times for stages 1-4 in factory B are 32, 24, 20, and 16 minutes respectively.

[0065] Transportation time: 8 minutes for phase 1-2, 7 minutes for phase 2-3, and 6 minutes for phase 3-4;

[0066] Preparation time related to sequence: 3-8 minutes between sub-batches, such as 5 minutes for sub-batch 1-2 of workpiece 1.

[0067] Optimization objectives: Cmax ≤ 420 minutes, TEC ≤ 1.3 × 10⁻⁶ minutes 5 kWh.

[0068] (II) System Deployment and Core Parameters

[0069] Parameter configuration:

[0070] Hybrid initialization: Population size 50, load balancing rule generates 10 individuals, sorting rule generates 10 individuals, and random rule generates 30 individuals;

[0071] Energy-saving strategy: ES1 delay time ≤ transportation time, ES2 low energy consumption machine judgment standard is power less than 10% of the stage average power.

[0072] (III) Implementation Process and Results

[0073] Initial population generation: The load balancing rule assigns the workpieces with the longest processing time (1-3) to factories A, B, and A respectively. The sorting rule generates the processing order based on the combined probability of release time and preparation time. The initial population average Cmax = 450 minutes, TEC = 1.38 × 10 5 kWh.

[0074] Global-Local Search: The global search optimizes the population through crossover and mutation. In the local search, DuelingDDQN selects the "inter-factory insertion operator" to insert workpiece 5 from factory A (Fc, Cmax = 430 minutes) into factory B, thus reducing Cmax to 415 minutes.

[0075] Energy saving optimization: The ES1 strategy postpones the start-up time of machine 2 in phase 1 of factory A to the release time of workpiece 3 (15 minutes), reducing idling energy consumption by 750kWh; the ES2 strategy allocates workpiece 4 in phase 2 of factory B from an 80kW machine to a 75kW machine, reducing energy consumption by 35kWh.

[0076] Final result: After 100 iterations, the optimal solution Cmax = 405 minutes, TEC = 1.22 × 10⁻⁶. 5 The tWh was 10% shorter than the initial population Cmax, the TEC was reduced by 11.6%, and the Pareto front was closer to the origin than the comparative algorithm NSGA-II (IGD index was reduced by 28%).

[0077] Example 2: Application of aluminum production scheduling with 4 workpiece sub-batches

[0078] (I) Application Scenario Parameters

[0079] The factory machine configuration in this embodiment is the same as that in Embodiment 1. The core difference is that the 10 workpieces are processed in 4 sub-batches. The key parameters of the workpieces are adjusted as follows:

[0080] Processing time: As the batch size increases, the processing time for each workpiece increases by 10%-15%. For example, the processing time for workpiece 1 in stage 1 of factory A increases from 30 minutes to 34 minutes, and in stage 2 it increases from 25 minutes to 28 minutes.

[0081] Sequence-related preparation time: The increase in the number of sub-batches leads to an increase in the frequency of preparation time. The preparation time between sub-batches is adjusted to 4-9 minutes, such as the preparation time of sub-batches 2-3 of workpiece 2 is 6 minutes.

[0082] Optimization goals: Cmax ≤ 480 minutes, TEC ≤ 1.5 × 10⁻⁶ minutes 5 kWh.

[0083] (II) Core Parameter Adjustment

[0084] Hybrid initialization: The selection probability weights for release time and preparation time in the sorting rules are adjusted to 0.4 and 0.6, respectively, with greater emphasis on the impact of preparation time on the processing order;

[0085] Local search: The frequency of critical factory Fc and Ft determination has been adjusted from 10 iterations / time to 8 iterations / time to adapt to the dynamic changes after the increase of sub-batches;

[0086] Number of iterations: As the number of factor batches increases, the solution space expands, so the number of iterations is adjusted to 120.

[0087] (III) Implementation Process and Results

[0088] Initial population generation: Initial population mean Cmax = 520 minutes, TEC = 1.62 × 10⁻⁶.5 kWh, of which Plant A has fewer stage 4 hot rolling mills (3 units), becoming Fc (Cmax = 535 minutes);

[0089] Global-Local Search: The global search assigns two jobs from factory A to factory B through crossover mutation, reducing Cmax to 500 minutes; in the local search, DuelingDDQN selects the "single factory internal flip operator" to reverse the job sequence of stage 4 in factory A, further reducing Cmax to 485 minutes.

[0090] Energy saving optimization: In Phase 2 of Factory B, the ES1 strategy delays the start-up time of Machine 3 until the end of the transportation time (7 minutes), reducing idling energy consumption by 560kWh; the ES2 strategy reassigns 3 workpieces in Phase 3 of Factory A from the 60kW machine to the 58kW machine, reducing energy consumption by 420kWh.

[0091] Final result: After 120 iterations, the optimal solution Cmax = 470 minutes, TEC = 1.43 × 10⁻⁶. 5 Compared to the initial population, the Cmax was shortened by 9.6% and the TEC was reduced by 11.7%. Compared to the Pareto solution of the comparison algorithm TS-NSGA-II, the Cmax was shortened by an average of 7% and the TEC was reduced by an average of 8%.

[0092] Example 3: Application of aluminum production scheduling with 5 workpiece sub-batches

[0093] (I) Application Scenario Parameters

[0094] This example illustrates a large-batch scheduling scenario in aluminum production, where 10 workpieces are divided into 5 sub-batch processing sessions. The factory machine configuration is consistent with Example 1, but the key parameters of the workpieces are adjusted as follows:

[0095] Processing time: With the further increase in the number of sub-batches, the processing time of each workpiece is extended by 20%-25% compared to Example 1. For example, the processing time of workpiece 1 in stage 1 of factory A increases from 30 minutes to 37 minutes, and in stage 2 it increases from 25 minutes to 31 minutes.

[0096] Transportation time: Due to the increase in the frequency of batch transportation, the transportation time between stages will be extended by 2 minutes. For example, the transportation time between stages 1 and 2 will increase from 8 minutes to 10 minutes.

[0097] Optimization objectives: Cmax ≤ 550 minutes, TEC ≤ 1.8 × 10⁻⁶ minutes 5 kWh.

[0098] (II) Core Parameter Adjustment

[0099] Hybrid initialization: The proportion of individuals generated by random rules is adjusted from 3 / 5 to 2 / 5, increasing the proportion of high-quality individuals generated by load balancing and sorting rules (each accounting for 3 / 10);

[0100] Learning Options: The DuelingDDQN experience replay pool capacity has been increased from 1000 to 1500 to accommodate more complex solution spaces;

[0101] Energy-saving strategy: In the ES2 strategy, the criteria for judging low-energy-consuming machines are relaxed to "power is less than 12% of the average power of the stage", increasing the range of machines that can be allocated.

[0102] (III) Implementation Process and Results

[0103] Initial population formation: Initial population average Cmax = 600 minutes, TEC = 1.95 × 10⁻⁶ minutes. 5 kWh, both Plant A Phase 4 (3 hot rolling mills) and Plant B Phase 2 (3 continuous casting machines) are critical plants, Fc = Plant A (Cmax = 610 minutes), Ft = Plant B (TEC = 1.02 × 10⁻⁶ minutes). 5 kWh);

[0104] Global-Local Search: The global search redistributes the 3 workpieces from factory A and the 2 workpieces from factory B, balancing the load of the two factories, and reducing Cmax to 570 minutes; in the local search, DuelingDDQN selects the "inter-factory exchange operator", exchanging 2 workpieces from factories A and B, and reducing Cmax to 555 minutes.

[0105] Energy saving optimization: The ES1 strategy delayed machine start-up time at each stage in both factories, resulting in a cumulative reduction of idling energy consumption of 2100kWh; the ES2 strategy redistributed 8 workpieces in the low-load stage of both factories to low-power machines, reducing energy consumption by 850kWh.

[0106] Final result: After 150 iterations, the optimal solution Cmax = 540 minutes, TEC = 1.72 × 10⁻⁶. 5 The solution yields a 10% reduction in Cmax compared to the initial population and an 11.8% reduction in TEC. Among all comparative algorithms, the Pareto solution of this invention exhibits the best distribution uniformity (Spacing index 0.12, lower than 0.18 of NSGA-II).

[0107] from Figure 2As can be seen, this invention has the best multi-objective evaluation index because it effectively balances global and local search while preserving high-quality elite solutions. The reverse generation distance index of this invention is the smallest because it designs efficient single-factory local search operators and multi-factory search operators, further optimizing elite solutions. The results of this invention are closer to the origin and coordinate axes, indicating that it can obtain a better non-dominated solution set than existing algorithms. This invention employs a learning-based dueling dual deep reinforcement learning selection mechanism to select the optimal local search operator for each solution, avoiding ineffective searches. This learning-based dueling dual deep reinforcement learning selection mechanism further balances the resource allocation of global and local search. Furthermore, the collaborative energy-saving strategy further optimizes energy consumption while maintaining the maximum completion time.

[0108] Figure 3 This paper illustrates the general process flow of aluminum production in the non-ferrous metallurgical industry, including electrolysis, casting, cold rolling, and hot rolling. In electrolysis, pure aluminum is extracted from alumina using multiple parallel electrolytic cells. Subsequently, the molten aluminum in each electrolytic cell is absorbed in batches by a vacuum ladle for further processing. Considering the different completion times of the molten aluminum in each electrolytic cell, the release time for each batch of molten aluminum to reach the converter is set. In continuous casting, molten aluminum is processed on multiple parallel continuous casting machines, and each aluminum sheet needs to be completed as early as possible to avoid solidification. Molten aluminum in the rolling process is also processed on multiple parallel machines. Sequential preparation time is required when changing molds or cleaning machines. Transport time is generated between these stages via vacuum ladle transport of molten aluminum, and the operation of the machines during transport generates transport energy consumption. In the production process, two conflicting objectives are typically involved: equipment utilization and energy efficiency. Minimizing the maximum completion time (Cmax) is similar to improving equipment utilization, while minimizing total energy consumption is similar to improving energy efficiency.

[0109] This invention generates three real-world cases from the non-ferrous metals metallurgy industry to further evaluate the effectiveness and practicality of the algorithm. All comparison algorithms were tested on these three real-world cases, which represent actual production scenarios in the aluminum production process within the non-ferrous metals metallurgy industry. In Example 1, the first factory has 5, 3, 5, and 3 parallel processing machines at each stage, and the second factory has 5, 3, 5, and 5 parallel processing machines at each stage. In Example 1, each workpiece is divided into 3 sub-batches. In Example 2, each workpiece is divided into 4 sub-batches, and in Example 3, each workpiece is divided into 5 sub-batches. The processing time, release time, transport time, and sequence-related preparation time differ for each workpiece in different factories, but the start time for all workpieces is the same. All algorithms are run independently 20 times. Figure 4 , 5Table 6 shows the Pareto fronts of all algorithms in three practical cases. The results of this invention shown in all three embodiments are closer to the origin and coordinate axes, indicating that this invention can obtain a superior Pareto solution compared to the comparative algorithms. Under the same cutoff criterion, the convergence of other methods is inferior to that of this invention. This is because this method designs local search operators for single-factory and multi-factory applications based on problem characteristics, and selects the optimal search operator for each solution through a learning-based dual deep Q-network selection mechanism, thereby avoiding invalid searches. Furthermore, a collaborative energy-saving strategy further optimizes the total energy consumption of the problem.

[0110] It should be understood that the specific embodiments described above are merely illustrative or explanatory of the principles of the invention and do not constitute a limitation thereof. Therefore, any modifications, equivalent substitutions, improvements, etc., made without departing from the spirit and scope of the invention should be included within the protection scope of the invention. Furthermore, the appended claims are intended to cover all variations and modifications falling within the scope and boundaries of the appended claims, or equivalent forms of such scope and boundaries.

Claims

1. A distributed heterogeneous flexible workflow workshop batch processing scheduling method, characterized in that, Includes the following steps: S1. Construct a mixed-integer linear programming model for the batch processing energy efficiency scheduling problem in a distributed heterogeneous flexible flow shop. The constraints of the model simultaneously include release time, sequence-dependent preparation time, inter-stage transportation time, and batch processing scheduling requirements. The optimization objective is to minimize the maximum completion time (C0). max ) and Total Energy Consumption (TEC); S2. Construct a dual-objective co-evolutionary framework based on learning assistance. The framework includes a problem encoding / decoding module, a hybrid initialization module, a global search operator module, a knowledge-driven local search operator module, a learning selection module based on adversarial reinforcement learning, and a collaborative energy-saving strategy module. S3. Use the hybrid initialization module to generate a global population. The hybrid initialization module uses load balancing rules, sorting rules, and random rules to generate 1 / 5, 1 / 5, and 3 / 5 of the population individuals, respectively. S4. Perform a global search on the global population, sequentially performing mating selection, crossover update, mutation update, and environment selection; S5. Extract Pareto solutions as elite solutions from the population after global search, and perform local search on the elite solutions through the knowledge-driven local search operator module. The knowledge-driven local search operator module includes 8 single-factory knowledge-driven operators and 10 multi-factory knowledge-driven operators. S6. A learning selection module based on duel reinforcement learning is adopted, and the optimal local search operator is dynamically selected for each Pareto solution through a triple combined duel dual deep Q network (DuelingDDQN). S7. Optimize the energy consumption of the Pareto solution after local search using the collaborative energy-saving strategy module. The collaborative energy-saving strategy module includes ES1 strategy and ES2 strategy. ES1 strategy reduces the total energy consumption by adjusting the machine start time and ES2 strategy reduces the total energy consumption by reallocating the workpiece processing machine. S8. Repeat steps S4-S7 until the iteration termination condition is met, and output the final Pareto solution set.

2. The distributed heterogeneous flexible workflow workshop batch processing scheduling method according to claim 1, characterized in that, The constraints of the mixed-integer linear programming model in step S1 specifically include: the processing sequence constraints of the workpiece in each factory and stage, the sub-batch processing constraints of the batch processing equipment, the release time constraints, the sequence-related preparation time constraints, the inter-stage transportation time constraints, and the calculation constraints of machine processing energy consumption and transportation energy consumption.

3. The distributed heterogeneous flexible workflow workshop batch processing scheduling method according to claim 1, characterized in that, In step S3: The load balancing rule defines the factory workload as the sum of the processing time of all workpieces in each stage, and prioritizes assigning tasks to factories with less workload. The sorting rule first arranges the workpieces in ascending order by release time and in ascending order by order association preparation time between sub-batch, resulting in two index arrays. After calculating and accumulating the selection probabilities of the two arrays, individuals are generated by sorting them in descending order. The random rule replenishes the remaining individuals through random initialization to enhance population diversity.

4. The distributed heterogeneous flexible workflow workshop batch processing scheduling method according to claim 1, characterized in that, In step S5: The single-factory knowledge-driven operators include: a single-factory internal exchange operator, which exchanges adjacent or any two workpieces in the critical factory Fc; a single-factory adjacent exchange operator, which exchanges adjacent workpieces in Fc and the energy-consuming critical factory Ft; a single-factory internal insertion operator, which inserts 1-2 workpieces in Fc to other positions; and a single-factory internal flip operator, which reverses the workpiece sequence in Fc and Ft. The multi-factory knowledge-driven operator includes a multi-factory exchange operator, which exchanges 1-3 adjacent workpieces in Fc / Ft with 1-3 adjacent workpieces in other factories; The inter-factory insertion operator inserts 1-3 adjacent workpieces or any 1 workpiece into other factories in Fc; The critical plant Fc is defined as the plant with the worst performance in the maximum time to completion indicator, and the critical plant Ft is defined as the plant with the worst performance in the total energy consumption indicator.

5. A distributed heterogeneous flexible workflow workshop batch processing scheduling method according to claim 1, characterized in that, The workflow of the learning selection module based on duel reinforcement learning described in step S6 includes: Calculate the initial state of the scheduling environment; Based on the initial state, select the local search operator to be executed at the decision point; Optimize the scheduling scheme using the selected operators; Evaluate the reward of the selected operator and update the scheduling environment state for subsequent decision points.

6. The distributed heterogeneous flexible workflow workshop batch processing scheduling method according to claim 1, characterized in that, In step S7: The ES1 strategy employs a machine delay processing strategy in the first stage, postponing the machine's start processing time to match the workpiece release time. In the second to S stages, the machine delays processing during the initial processing transport time. The ES2 strategy keeps the machine allocation unchanged within the factory corresponding to the maximum completion time. For workpieces from other factories, it prioritizes the allocation to the machine with the lowest processing energy consumption in each processing stage, and the allocation rules between each stage are consistent with the decoding mode of the encoding and decoding module.

7. A distributed heterogeneous flexible workflow workshop batch processing scheduling system, characterized in that, include: Model building module: used to build the mixed integer linear programming model in step S1 of claim 1; Framework building module: used to build the learning-assisted dual-objective co-evolutionary framework in step S2 of claim 1; Population generation module: used to generate the global population in step S3 of claim 1; Global search module: used to perform the global search in step S4 of claim 1; Local search module: used to implement the local search in step S5 of claim 1; Operator selection module: used to implement the operator selection based on confrontation reinforcement learning in step S6 of claim 1; Energy consumption optimization module: used to implement the collaborative energy-saving optimization in step S7 of claim 1; Iteration output module: Used to control the iteration process and output the final Pareto solution set.

8. A distributed heterogeneous flexible workflow workshop batch processing scheduling system according to claim 7, characterized in that, This method can be applied to the aluminum production process in the non-ferrous metals metallurgical industry, including the scheduling optimization of the electrolysis, casting, cold rolling, and hot rolling stages. The electrolytic cells in the electrolysis stage, the continuous casting machines in the casting stage, and the rolling equipment in the rolling stage are all treated as parallel processing machines. The batch transportation and processing of molten aluminum correspond to batch processing scheduling, transportation time, and sequence-related preparation time constraints, respectively.

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