Energy-saving fuzzy cascade scheduling method and system for regional gathering cooperative production

Abstract

The invention relates to the technical field of intelligent production and manufacturing, in particular to an energy-saving fuzzy cascade scheduling method and system for regional gathering cooperative production, and aims to solve the composite problems of supply chain cascade scheduling heterogeneous factory resource allocation, multi-stage time accumulation effect, uncertainty interference and the like in regional cooperative transformation in the manufacturing industry. According to the method, a double-layer collaborative optimization framework is assisted through integrated learning, the uncertainty of quintuple interval fuzzy quantization processing, transportation and assembly time is adopted, an initial Q value matrix is generated through a pre-training layer, self-adaptive operator selection is achieved in combination with a dynamic decision-making layer, and local search, damage recombination and genetic operation are executed by multiple sub-groups. According to the method, the energy-saving second-class fuzzy distributed flow shop and multi-flexible job shop cascade scheduling problem model is effectively defined, three-segment coding and full-process energy consumption calculation are supported, and the overall scheduling efficiency and the energy efficiency balance capability of the regional aggregation industry are remarkably improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of intelligent production manufacturing, in particular to an energy-saving fuzzy cascade scheduling method and system for regional agglomeration collaborative production. BACKGROUND

[0002] With the gradual transformation of global manufacturing towards regionalization and collaboration, the supply chain production system is facing the dual challenges of multi-factory collaborative scheduling and dynamic uncertainty. In complex production scenarios, how to coordinate the resource allocation, job sequencing and fuzzy time constraints among multi-stage factories, while achieving energy efficiency optimization, has become a core problem that needs to be solved. However, the existing technology still has the following shortcomings: limitations of scheduling models: traditional scheduling models mainly focus on single factory or homogeneous environment, which is difficult to adapt to the complex needs of multi-factory heterogeneous collaborative production, especially in regional agglomeration industries, upstream and downstream enterprises need to realize the cascade collaboration of distributed flow shop and flexible job shop, the existing models have significant defects in dynamic uncertainty processing, multi-objective collaborative optimization, etc., and cannot meet the actual production needs; efficiency bottleneck of algorithm framework: existing algorithm frameworks, such as genetic algorithm and destruction and recombination algorithm, highly depend on fixed search strategies, resulting in strong early search blindness and insufficient global convergence ability; balance problem of energy efficiency and response speed: in the cascade scheduling scenario, the maximum completion time directly affects the response ability of the supply chain, while the total energy consumption is related to the sustainable development goal of the enterprise, the existing methods mostly use single-objective optimization or simple weighting strategy, which cannot effectively balance the dynamic balance of efficiency and energy consumption, resulting in low resource utilization and difficulty in achieving green production goals; deficiency of uncertainty modeling: in actual production environment, processing, transportation and assembly time are affected by equipment state, order fluctuation and other factors, showing significant fuzziness, traditional scheduling models mostly use deterministic or one-type fuzzy system, which is difficult to accurately describe the distribution characteristics of complex uncertainty. In recent years, regional agglomeration production mode provides a new idea for multi-factory collaboration by integrating the collaborative advantages of distributed flow shop and flexible job shop, however, such mode needs to solve the problems of cross-factory job allocation, process connection under fuzzy time constraints and dynamic optimization of energy consumption, existing researches still have significant shortcomings in dynamic decision-making, multi-objective collaboration and uncertainty handling, although they try to integrate distributed flow and assembly scheduling. SUMMARY

[0003] The present application provides an energy-saving fuzzy cascade scheduling method and system for regional agglomeration collaborative production to solve the problems existing in the above background.

[0004] In order to achieve the above purpose, the technical scheme adopted by the present application is as follows: The energy-saving fuzzy cascade scheduling system for regional agglomeration collaborative production is characterized by comprising a modeling module, an encoding module, an optimization module and an output module.

[0005] The modeling module is used for constructing a mathematical model of an energy-saving two-type fuzzy distributed flow shop and multi-flexible job shop cascading scheduling problem ET2FDFS-MFJSCSP.

[0006] The encoding module is used for generating a three-section encoding of job sequencing JS, machine selection MS and operation sequencing OS.

[0007] The optimization module is used for executing an LBCOF algorithm, including population initialization, sub-population division, Q-learning decision and decoupled crossover.

[0008] The output module is used for outputting a Pareto optimal solution set and a corresponding scheduling scheme.

[0009] The energy-saving fuzzy cascading scheduling method for regional cluster collaborative production comprises the following processes: Step 1, a mathematical model of an energy-saving two-type fuzzy distributed flow shop and multi-flexible job shop cascading scheduling problem ET2FDFS-MFJSCSP is established, and minimization of maximum completion time and total energy consumption is set as double objectives, the mathematical model of the energy-saving two-type fuzzy distributed flow shop and multi-flexible job shop cascading scheduling problem ET2FDFS-MFJSCSP includes fuzzy time and energy consumption models of processing stages, transportation stages and assembly stages, wherein processing time, transportation time and assembly time are represented and calculated by using five-tuple interval two-type fuzzy numbers IT2F.

[0010] Wherein, a five-tuple interval two-type fuzzy number set IT2F is represented by a five-tuple , wherein is a centroid of a two-type fuzzy set , and are used for constraining upper membership boundaries of , and are used for constraining lower membership boundaries of , and the upper membership boundaries and the lower membership boundaries determine the range of the two-type fuzzy set.

[0011] Step 2, a three-section encoding mode is designed, including job sequencing JS, machine selection MS and operation sequencing OS, and a corresponding decoding strategy is designed, the decoding strategy includes calculating job completion time according to job sequencing JS encoding, determining transportation time and calculating job arrival assembly plant time according to product relationship, determining earliest product start assembly time and distributing operations to machines according to operation sequencing OS and machine selection MS encoding, and an activity scheduling strategy is used to generate a scheduling scheme.

[0012] Step 3, an initial population is generated by using a mixed initialization strategy, and is divided into multiple sub-populations, the mixed initialization strategy includes that the job sequencing JS encoding uses a product set rule or a random rule, the machine selection MS encoding uses a minimum time rule, a minimum load rule or a random rule, the operation sequencing OS encoding uses a first-in-first-processing rule, a machine greedy rule or a random rule, and the initial population is generated by combining the five rules.

[0013] Step 4, a learning-assisted double-layer co-evolution optimization framework LBCOF is constructed, including a pre-training layer and a dynamic decision layer.

[0014] Step 5, in the pre-training layer of the step 4, three sub-populations respectively perform three search operations: a local search operation, a destruction and recombination operation and a genetic operation, and the success rates of the operations are recorded to a Q table.

[0015] Step 6, in the dynamic decision layer of the step 4, search operations are adaptively selected based on the Q table and an epsilon-greedy learning-assisted strategy, and a decoupled crossover strategy is performed on parent individuals to enhance search diversity.

[0016] Step 7, finally, the population is updated by environmental selection and non-dominated sorting, and a Pareto optimal solution set is output.

[0017] Further, the three search operations in the step 5 include a local search operation based on a variable neighborhood descent VND strategy, including four neighborhood structures of js_out_insert, ms_select, os_swap and js_in_swap; a destruction and recombination operation on key jobs, machines and operations; and a genetic operation using POX crossover and uniform crossover combined with mutation operation.

[0018] Further, the Q table and the epsilon-greedy learning-assisted strategy in the step 6 include that a state space is composed of the evaluation times and the success times of each search operation, an action space is three search operations, a reward function is based on the difference between the current success rate and the historical average success rate, and a hierarchical Q-learning mechanism is used, the pre-training layer is learned offline, and the decision layer dynamically selects operations online.

[0019] Further, the decoupled crossover strategy in the step 6 is to separate and recombine the job sequencing JS of the processing stage encoding of the parent individuals and the machine selection MS and operation sequencing OS of the assembly stage encoding to generate offspring individuals.

[0020] The present application has the following beneficial effects: The application firstly defines a mathematical model of an energy-saving type two-class fuzzy distributed flow shop and multi-flexible job shop cascade scheduling problem ET2FDFS-MFJSCSP, and proposes a calculation criterion with Cmax and TEC as double targets, thereby providing a systematic theoretical framework for multi-factory collaborative optimization; three differentiated search strategies of local search, destruction and recombination and genetic operation are designed according to the characteristics of the mathematical model of the energy-saving type two-class fuzzy distributed flow shop and multi-flexible job shop cascade scheduling problem ET2FDFS-MFJSCSP, which are respectively used for improving solution quality, enhancing global exploration and maintaining population diversity, so as to realize the balance of performance and efficiency; a learning auxiliary search strategy is introduced, and through a hierarchical training mechanism, the adaptive adjustment of operator selection is realized, the influence of strategy randomness on search efficiency is significantly reduced, and the stability and convergence speed of the algorithm are improved; a decoupling crossover strategy is proposed, the coding recombination process of the processing stage and the assembly stage is separated and processed, the search range of the solution space is effectively expanded, and the adaptability of the algorithm to complex scenes is enhanced; the overall system logic is clear and simple, easy to realize and expand, and can adapt to most dynamic scheduling scenes in the field of intelligent manufacturing, especially showing good robustness and scalability in the multi-factory heterogeneous environment, and meeting the actual production demand. BRIEF DESCRIPTION OF DRAWINGS

[0021] Figure 1 is a structural schematic diagram of the mathematical model of the energy-saving type two-class fuzzy distributed flow shop and multi-flexible job shop cascade scheduling problem ET2FDFS-MFJSCSP in the application.

[0022] Figure 2 is a three-section coding method in the application.

[0023] Figure 3 is a double-layer collaborative evolution architecture in the application.

[0024] Figure 4 is an algorithm flowchart in the application.

[0025] Figure 5 is an embodiment in the application.

[0026] Figure 6 is a box plot of four algorithms under the HV index in the application.

[0027] Figure 7 is a box plot of four algorithms under the IGD index in the application.

[0028] Figure 8 is a Pareto front comparison chart under the condition of S06.

[0029] Figure 9 is a Pareto front comparison chart under the condition of S14.

[0030] Figure 10 is a Pareto frontier contrast plot under L01 condition.

[0031] Figure 11 is a Pareto frontier contrast plot under L12 condition. DETAILED DESCRIPTION

[0032] The application will be further described below in connection with the accompanying drawings and specific examples.

[0033] The energy-saving fuzzy cascade scheduling method and system for regional cluster collaboration production provided by the application are based on a learning-assisted double-layer collaborative evolution optimization framework LBCOF, and are realized through the following steps: First step, establishment of a mathematical model of an energy-saving type two-class fuzzy distributed flow shop and multi-flexible job shop cascade scheduling problem ET2FDFS-MFJSCSP.

[0034] Table 1, mathematical model annotation

[0035]

[0036] The objective of the mathematical model of the energy-saving type two-class fuzzy distributed flow shop and multi-flexible job shop cascade scheduling problem ET2FDFS-MFJSCSP is to minimize the maximum completion time Cmax and the total energy consumption TEC.

[0037]

[0038]

[0039]

[0040]

[0041] Second step, coding and decoding design.

[0042] In the mathematical model of the energy-saving type two-class fuzzy distributed flow shop and multi-flexible job shop cascade scheduling problem ET2FDFS-MFJSCSP, the production stage needs to determine the factory allocation of workpieces and the processing sequence of the workpieces in each factory, and the assembly stage needs to determine the machine selection and process sequence of each assembly factory. For example, Figure 2As shown, the distributed flow shop solution of the production stage is encoded by a vector denoted as job sequence JS, in which the job sequence between different factories is separated by 0. For the assembly stage, the solution of multiple flexible job shop is encoded by two vectors, machine selection MS and operation sequence OS. The assembly stage is arranged according to the order of assembly factories, and within each assembly factory, the machine selection MS is arranged according to the product and operation sequence of the factory, and the processing machine selected by the current operation is used as the encoding gene; while the operation sequence OS uses the operation-based encoding method, directly using the product number as the encoding gene. Therefore, the overall encoding of the solution of the mathematical model of the energy-saving type II fuzzy distributed flow shop and multiple flexible job shop cascade scheduling problem ET2FDFS-MFJSCSP is composed of a triple {JS, MS, OS}, in which the triple is composed of job sequence JS, machine selection MS and operation sequence OS.

[0043] Since the mathematical model of the energy-saving type II fuzzy distributed flow shop and multiple flexible job shop cascade scheduling problem ET2FDFS-MFJSCSP contains two interrelated stages of production and assembly, the earliest assembly time of all products is determined by the time when the last job of the product arrives at the assembly factory. In addition, since the assembly stage involves multiple flexible job shops, an activity scheduling strategy can be used to improve scheduling flexibility. The steps of the decoding process are as follows: 1. Calculate the completion time of each job according to the job sequence of the job sequence JS, and record it as .

[0044] 2. Determine the transportation time of each job according to its product structure relationship, denoted as ; then calculate by type II fuzzy addition to obtain the arrival time of each job at the designated assembly factory.

[0045] 3. Take the completion time of the last job of all jobs required by each product as the earliest assembly start time of the product.

[0046] 4. According to the order specified by the operation sequence OS and the earliest assembly start time of each product, assign the operations of each product to the machine selection MS of the corresponding machine in turn, where the earliest start time of each operation depends on the completion time of the previous operation or the earliest arrival time of the job.

[0047] 5. Based on the earliest start time of the operation and the current scheduling state of the machine, determine whether the operation can be inserted before other operations on the current machine. If the insertion condition is met, perform the front insertion operation; otherwise, arrange it at the end of the machine scheduling sequence. Thus, the decoding process is completed, and the corresponding activity scheduling scheme is generated.

[0048] The third step is to use the LBCOF algorithm to solve the mathematical model of the energy-saving type II fuzzy distributed flow shop and multiple flexible work shop cascade scheduling problem ET2FDFS-MFJSCSP.

[0049] The flowchart of the proposed LBCOF algorithm is as follows: Figure 4 As shown, the algorithm description is in Algorithm 1, and its termination condition is set to the total number of fitness evaluations TNFEs.

[0050] Algorithm 1

[0051] A hybrid initialization rule was used to generate the initial population, and differentiated initialization rules were designed based on the characteristics of each coding segment. The initialization rules for the three coding segments are given below: the workpiece sorting JS uses two rules, namely product set and random; the machine selection MS introduces three rules, namely time optimal, load balancing and random allocation; and the process sorting OS developed three rules, namely first-come-first-served, machine greedy and random.

[0052] The specific combination methods of the basic rules for workpiece sorting (JS), machine selection (MS), and process sorting (OS) are shown in Table 2.

[0053] Table 2. Combination Methods

[0054] This strategy generates five complementary initial solution generation strategies using the combination methods shown in Table 2, where IJR, IMR, and IOR represent the initialization rules for the corresponding coding segments. Each strategy independently generates a subpopulation of size PS / 5, and the complete initial population is finally constructed by merging the subpopulations.

[0055] The algorithm employs a two-layer computational resource allocation mechanism, where parameters... Control the resource allocation in the first phase. Define the greedy factor for the second stage of Q-learning. The first stage (steps 2-14) constructs a system containing... through a hybrid initialization strategy. The initial population of solutions is determined and evenly divided into groups. Three subpopulations. Each subpopulation has a preset fitness window. The evolutionary process is performed independently within each iteration. After each iteration, an environment selection mechanism based on fast non-dominated sorting and crowding distance metric is executed, simultaneously updating the current number of evaluations (NFEs) and the Q-table. The second stage (steps 15-26) first merges the three subpopulations to construct a new initial population, introducing a decoupling crossover strategy to expand the search range, and employing... The strategy dynamically selects search operators. By merging parent and child generations to perform multi-objective environment selection, an elite preservation strategy is ultimately employed to extract the Pareto front solution set from the updated population. .

[0056] Fourthly, simulation results and analysis of LBCOF.

[0057] To verify the effectiveness of LBCOF in solving the mathematical model of energy-saving type two-class fuzzy distributed flow shop and multi-flexible job shop cascading scheduling problem ET2FDFS-MFJSCSP, a dataset containing 32 test instances is constructed. Among them, the number of workpieces in small-scale instances is {20, 30}, and the number of products t is {6, 8}; the number of workpieces in large-scale instances is {80, 100}, and the number of products t is {20, 30}. In each instance, the number of processing workstations F is {2, 3}, the number of assembly workstations Q is {2, 3}, the number of machines m is randomly selected from {6, 7, 8}, and the number of operations o required for each product is randomly selected from {4, 5, 6}. The processing time of workpieces and the assembly time of products both follow a uniform distribution in the interval [10, 50]; the transportation time follows a uniform distribution in the interval [50, 100]. The processing power and assembly power are both 3.0 kilowatt-hours, the transportation power is 2.0 kilowatt-hours, and the idle power of the device is 1.0 kilowatt-hours. All instances are independently run 10 times, and the algorithm termination condition is set to .

[0058] All experiments are implemented in Python 3.11 environment, running on Windows 11 operating system, with hardware configuration of 12th generation Intel (R) Core (TM) i7-12700H processor (clock speed 2.30 GHz) and memory capacity of 332 GB. The performance of PBIGA algorithm is evaluated by two evaluation indicators: hyper volume (HV) and inverse generational distance (IGD) to ensure the scientificity and reliability of experimental results.

[0059] In the parameter calibration experiment, three key parameters, population size , division ratio , and greed factor , are selected for analysis. The value range of each parameter is determined based on preliminary experimental results. Table 2 shows the ANOVA results under the IGD index, and statistical analysis shows that under the HV index, is a significant influencing factor; while under the IGD index, and have significant influence. Among them, and The p values of all are less than 0.05, indicating that both have important roles in the performance of the algorithm. In combination with the evaluation results, when the parameter combination is set as , the LBCOF algorithm shows the best performance.

[0060] Table 3, ANOVA results of LBCOF under IGD index

[0061] The LBCOF algorithm and three current mainstream advanced algorithms, KNSGA-II, KBOA and LBPEA, were compared in the experiment. The performance results of the four algorithms in HV (hypervolume) and IGD (inverse generational distance) indexes are shown in Table 3. From the experimental results, it can be seen that LBCOF is superior to the comparison algorithms in both convergence performance and balance of solution set distribution. From the overall trend analysis, the HV value of LBCOF on all test data sets remains leading, indicating that the generated solution set can more widely cover the high-quality target space region. This advantage is mainly due to the hierarchical cooperative mechanism adopted in the algorithm design, which effectively improves the cooperative efficiency between global exploration and local development by dynamically deploying differentiated search strategies.

[0062] Table 4, average indexes of four algorithms on 32 data sets

[0063] Figure 6 、 Figure 7 The box plots of the four algorithms based on HV (hypervolume) and IGD (inverse generational distance) indexes are shown. In these box plots, the horizontal lines inside the box represent the median of the data, and the hollow square points represent the average value. From the overall distribution trend, LBCOF shows significant performance advantage and higher stability in both evaluation indexes.

[0064] Under the HV index, the median and average of LBCOF are significantly higher than those of the other three algorithms, indicating that it has stronger optimization capability in solution set coverage and quality. In addition, the interquartile ranges of the four algorithms are similar, indicating that they are basically consistent in solution stability and data dispersion. In terms of IGD index, the median and average of LBCOF are significantly lower than those of the other algorithms, reflecting its superior performance in approximating the true Pareto front. At the same time, the interquartile range of LBCOF is the smallest among the four algorithms, further verifying its good convergence ability under the fuzzy time constraint and cascading scheduling mechanism.

[0065] In contrast, the median and mean of KBOA are higher than LBPEA, which may be due to the fixed strategy selection mechanism of KBOA is less adaptive in dealing with complex energy consumption constraints. KNSGA-II shows the highest median and mean, as well as the largest interquartile range, indicating that traditional multi-objective algorithms are less robust in complex problem environments, especially in large-scale datasets, the dispersion of IGD values is more significant.

[0066] Figures 8-11 The Pareto front distribution shown further intuitively demonstrates the significant advantage of LBCOF in the field of multi-objective optimization. As can be seen from the figure, the solution set generated by LBCOF exhibits better convergence and distribution uniformity in the two-objective space. The overall solution set is closer to the origin, indicating that the algorithm is closer to the theoretical global optimal solution in minimizing the two objective functions. This advantage is not only reflected in the position of the solution set, but also in the quality and distribution density of the solution, further verifying the effectiveness and stability of LBCOF in multi-objective scheduling problems.

Claims

1. An energy-saving fuzzy cascade scheduling system for regional clustered collaborative production, characterized in that: It includes a modeling module, a coding module, an optimization module, and an output module; The modeling module is used to construct a mathematical model for the energy-saving type II fuzzy distributed flow shop and multi-flexible operation shop cascade scheduling problem ET2FDFS-MFJSCSP; The encoding module is used to generate a three-segment encoding of workpiece sorting (JS), machine selection (MS), and process sorting (OS). The optimization module is used to execute the LBCOF algorithm, including population initialization, subpopulation partitioning, Q-learning decision-making, and decoupling crossover; The output module is used to output the Pareto optimal solution set and its corresponding scheduling scheme.

2. An energy-saving fuzzy cascade scheduling method for regional clustered collaborative production, characterized by: The process includes the following steps: Step 1: Establish a mathematical model for the energy-saving type II fuzzy distributed flow shop and multiple flexible work shop cascade scheduling problem ET2FDFS-MFJSCSP. Set minimizing the maximum completion time and total energy consumption as the dual objectives. The mathematical model of the energy-saving type II fuzzy distributed flow shop and multiple flexible work shop cascade scheduling problem ET2FDFS-MFJSCSP includes fuzzy time and energy consumption models for the processing stage, transportation stage and assembly stage. The processing time, transportation time and assembly time are all represented and calculated using the five-tuple interval type II fuzzy number IT2F. Step 2: Design a three-segment coding method, including workpiece sorting (JS), machine selection (MS), and process sorting (OS), and design corresponding decoding strategies. The decoding strategies include calculating the workpiece completion time based on the workpiece sorting (JS) code, determining the transportation time based on product relationships and calculating the workpiece arrival time at the assembly plant, determining the earliest start time for product assembly, and allocating processes to machines based on the process sorting (OS) and machine selection (MS) codes. An active scheduling strategy is used to generate a scheduling scheme. Step 3: Generate an initial population using a hybrid initialization strategy and divide it into multiple subpopulations. The hybrid initialization strategy includes: the workpiece sorting JS code adopts a product set rule or a random rule; the machine selection MS code adopts a minimum time rule, a minimum load rule or a random rule; the process sorting OS code adopts a first-come-first-served rule, a machine greedy rule or a random rule; and the initial population is generated by combining five rules. Step 4: Construct a learning-assisted two-layer co-evolutionary optimization framework LBCOF, including a pre-training layer and a dynamic decision layer; Step 5: In the pre-training layer of Step 4, the three subpopulations perform three search operations respectively: local search operation, disruptive recombination operation and genetic operation, and record the success rate of each operation in the Q table; Step 6: In the dynamic decision-making layer of Step 4, the search operation is adaptively selected based on the Q-table and ε-greedy learning auxiliary strategy, and a decoupling crossover strategy is executed on the parent individuals to enhance search diversity; Step 7: Finally, update the population through environmental selection and non-dominated sorting, and output the Pareto optimal solution set.

3. The energy-saving fuzzy cascade scheduling method for regional clustered collaborative production according to claim 2, characterized in that: The three search operations in step 5 include local search operations: based on the variable neighborhood descent VND strategy, including four neighborhood structures: js_out_insert, ms_select, os_swap, and js_in_swap; destruction and recombination operations: small-scale destruction and recombination of workpieces, machines, and processes in key plants; and genetic operations: using POX crossover and uniform crossover, combined with mutation operations.

4. The energy-saving fuzzy cascade scheduling method for regional clustered collaborative production according to claim 2, characterized in that: The Q-table and ε-greedy learning assistance strategy in step 6 include: the state space consists of the number of evaluations and successes of each search operation; the action space consists of three types of search operations; the reward function is based on the difference between the current success rate and the historical average success rate; and a hierarchical Q-learning mechanism is adopted, with the pre-training layer learning offline and the decision layer dynamically selecting operations online.

5. The energy-saving fuzzy cascade scheduling method for regional clustered collaborative production according to claim 4, characterized in that: The decoupling and crossover strategy in step 6 is as follows: the processing stage coding workpiece sorting JS of the parent individual is separated and recombined with the assembly stage coding machine selection MS and process sorting OS to generate the child individual.

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