Scheduling method of distributed flexible flow shop in uncertain environment based on learning-driven empire butterfly optimization, storage medium and terminal thereof

Abstract

The invention discloses a method for scheduling a distributed flexible flow shop in an uncertain environment based on learning-driven empire butterfly optimization, and belongs to the technical field of shop scheduling, the method is used for adjusting a production scheme when order information in the flow shop changes, and the scheduling method comprises a static scheduling stage and a dynamic scheduling stage, according to the method, in a static scheduling stage, a learning-driven empire butterfly optimization method fuses a self-adaptive migration operator and a butterfly adjustment operator, and local search is carried out on a production scheme; in the dynamic scheduling stage, the scheduling method aims at minimizing the maximum completion time of a production scheme, and an iterative greedy method is used for identifying an order insertion position with changed information; finally, the final scheduling scheme is determined after rescheduling is conducted in the static scheduling stage and the dynamic scheduling stage, the scheduling method has high robustness and accuracy, and smooth proceeding of the workshop production plan is guaranteed.

Description

Technical Field

[0001] The present invention belongs to the technical field of workshop scheduling, and in particular, relates to a scheduling method for a distributed flexible flow workshop in an uncertain environment based on learning-driven monarch butterfly optimization. Background Art

[0002] In modern manufacturing, scheduling is a key issue to improve production efficiency and resource utilization. Manufacturing companies with only one factory have decreased, while supply chains involving multiple factories have become more and more common. Among the scheduling models widely adopted in manufacturing, the flow shop scheduling problem is one of the most widely studied production scheduling problems. The problem involves processing a set of workpieces through a series of predetermined processing stages or machines, where each workpiece must follow the same sequence of operations, and the goal is to find an optimal workpiece sequence that minimizes a specific performance indicator, such as completion time, workpiece completion time, or the number of delayed workpieces.

[0003] In modern manufacturing, companies often use flow shop production lines to improve productivity and reduce costs. However, traditional flow shop scheduling models usually assume that each process is restricted to a specific machine, which is unrealistic in real-world production scenarios. To overcome this limitation, the concept of flexible flow shop scheduling (FFSP) was introduced. FFSP allows certain operations to be performed on multiple different machines, thereby increasing scheduling flexibility. This scheduling method is of great significance to improving production efficiency and reducing costs.

[0004] Manufacturing companies usually adopt two main scheduling strategies: static scheduling and dynamic scheduling. Static scheduling means that once the production and processing plan is determined, it must be completed according to the original plan without considering changes. However, in complex manufacturing systems, uncertainties and unexpected events in the workshop will disrupt the production plan and, in some cases, reduce the productivity of the production line. Dynamic scheduling refers to rescheduling in response to changes in dynamic events, where dynamic events include events related to order changes, machine-related events, and process-related events. Among them, order-related dynamic events are prevalent in workshop scheduling.

[0005] There are two main approaches to rescheduling in response to changes in dynamic events. One is the real-time scheduling process, and the other is the rescheduling process. Real-time scheduling is a dynamic approach in which manufacturing facilities abandon pre-established production plans and instead dynamically develop scheduling strategies based on immediate orders. It is worth noting that each new order triggers a recalibration of the scheduling framework. In contrast, rescheduling production starts with the initial production blueprint and modifies it based on unforeseen events. The essential difference lies in how rescheduling incorporates the production process that existed before the disruptive event into the new planning strategy. In actual manufacturing scenarios, companies face the challenge of rescheduling more frequently because they need to adapt to fluctuating environments.

[0006] In recent years, the rescheduling problem has attracted a lot of research. Existing rescheduling research mainly focuses on flexible job shops, which urgently need to solve the rescheduling problem. Research on distributed flexible flow shop scheduling mainly focuses on solving static problems characterized by complex constraints. For more complex dynamic problems, at present, based on two dynamic events of comprehensive machine failure and random workpiece arrival, a multi-objective mathematical model with the goal of minimizing maximum tardiness, machine idle energy consumption and maximum completion time is established in this field, and a genetic programming hyper-heuristic method that uses terminal sets to generate advanced scheduling rules is applied to solve the dynamic energy-saving hybrid flow shop scheduling problem. In addition, X.-R.Tao, Q.-K.Pan, H.-Y.Sang, L.Gao, A.-L.Yang, and M.Rong, "Nondominated sorting genetic algorithm-II with Q-learning for the distributed permutation flowshop rescheduling problem," Knowledge-Based Systems, vol.278, pp.110880, 2023 / 10 / 25 / , 2023 discloses a NSGA-II method based on Q-learning to solve the real-time scheduling challenges in the context of sustainable production. However, the existing workshop scheduling methods still have the following defects: traditional methods cannot adapt to the dynamic nature of scheduling problems and the complexity of the solution process; machine learning methods usually require a lot of time and data training, and cannot adapt to short-term rescheduling needs when dynamic orders change. Existing research mainly focuses on solving the rescheduling problem after the arrival of new orders, without fully considering other dynamic orders.

[0007] In view of the above limitations and difficulties, this paper aims to study the theoretical framework and practical application of distributed flexible flow shop scheduling problems (DFFSJP). A scheduling method for distributed flexible flow shop under uncertain environment based on learning-driven monarch butterfly optimization is proposed to obtain high-quality solutions in the first stage; in the rescheduling stage, various rules are tailored for different dynamic events to obtain rescheduling solutions online in a short time. Summary of the invention

[0008] The purpose of this section is to summarize some aspects of embodiments of the present invention and briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section and the specification abstract and the invention title of this application to avoid blurring the purpose of this section, the specification abstract and the invention title, and such simplifications or omissions cannot be used to limit the scope of the present invention.

[0009] To solve the above problems, the present invention adopts the following technical solutions.

[0010] A scheduling method for a distributed flexible flow shop in an uncertain environment based on learning-driven monarch butterfly optimization is used to adjust the production plan when the order information in the flow shop changes. The scheduling method includes a static scheduling stage and a dynamic scheduling stage, and is characterized by:

[0011] In the static scheduling stage, the learning-driven monarch butterfly optimization method combines the adaptive migration operator and the butterfly adjustment operator to perform local search on the production plan;

[0012] In the dynamic scheduling stage, the scheduling method aims to minimize the maximum completion time of the production plan and uses an iterative greedy method to identify the order insertion position with information changes;

[0013] Finally, the final scheduling plan is determined after rescheduling through the above-mentioned static scheduling stage and dynamic scheduling stage.

[0014] Preferably, in the above scheduling method, the objective function of the scheduling scheme is:

[0015] Objective function: min(C max )=min(C n,m ) (1)

[0016] Among them, the constraints in the objective function are:

[0017]

[0018] Formula (1) indicates that the objective function is to minimize the completion time.

[0019] Equation (2) states that each slot can only have at most one order.

[0020] Formula (3) ensures that the factory cannot be changed after each order is assigned.

[0021] Equation (4) requires that when an order at a factory location is processed on a machine, it must have been processed on the preceding machine first.

[0022] Equation (5) indicates that when machine i in a factory is processing an order at a location, it needs to wait for the order previously processed on the same machine to be completed before starting the subsequent task.

[0023] Constraint (6) captures the correlation between the departure times of two consecutive orders. The target for completion time is formally specified as Equation (7).

[0024] (8) and (9) give the specific value ranges of the decision variables.

[0025] Preferably, in the above scheduling method, the learning-driven monarch butterfly optimization solution mainly consists of three parts:

[0026] Heuristic initialization method;

[0027] Local search method based on driven learning;

[0028] Dynamic rule-based search process.

[0029] Preferably, in the above scheduling method, the population generated by the heuristic initialization method is used as the initial population for collaborative monarch butterfly optimization; the population is divided into sub-population 1 and sub-population 2, and the number of individuals in sub-population 1 and sub-population 2 are NP1 and NP2 respectively, as shown in the following formula.

[0030]

[0031] Where NP is the size of the initial population, and p=5 / 12 represents the mobility of subpopulation 1.

[0032] Preferably, in the above scheduling method, the local search includes 6 local search schemes, namely:

[0033] Orders are inserted or exchanged within the factory;

[0034] Orders are inserted or exchanged between plants;

[0035] Orders are inserted or exchanged within key plants;

[0036] Among them: the factory with the longest completion time for processing the order is the key factory.

[0037] Preferably, in the above scheduling method, for the dynamic scheduling stage, the scheduling scheme schedules three kinds of dynamic events, which are:

[0038] Insertion of orders, cancellation of orders and changes in order processing times.

[0039] Preferably, in the above scheduling method, the method is evaluated and analyzed by the average relative percentage deviation, which is specifically obtained by the following formula:

[0040]

[0041] Among them, C i is the result of the ith run of the current instance; R is the number of independent runs; C best is the best result for the current instance.

[0042] Preferably, in the above scheduling method, the parameters of the scheduling method include group size N, mobility p and migration period x;

[0043] Among them, N = {20, 50, 100, 200}, p = {0.3, 0.4, 0.5, 0.6}, x = {0.9, 1.1, 1.3}.

[0044] On the other hand, the present invention also provides a storage medium for executing the above method, and the computer program stored in the storage medium enables the electronic device to execute the scheduling method of distributed flexible assembly line workshops in an uncertain environment based on learning-driven monarch butterfly optimization as described above.

[0045] On the other hand, the present invention also provides an information data processing terminal, which includes a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the scheduling method of distributed flexible assembly line workshops in an uncertain environment based on learning-driven monarch butterfly optimization as described above.

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] The scheduling method in the present invention is modeled in two stages: a static scheduling stage and a rescheduling stage. In the static scheduling stage, the scheduling method integrates an adaptive migration operator and a butterfly adjustment operator. It regards the local search operation as an action under the reinforcement learning framework, in which the learning-driven monarch butterfly optimization method is used to select the optimal action according to the status of the order. In the dynamic scheduling stage, with the goal of minimizing the maximum completion time, an iterative greedy method is used to identify all potential insertion locations. Finally, the learning-driven experience obtained in the static stage is used as knowledge to extract the final scheduling plan. The present invention conducts effectiveness analysis experiments on the various components of the scheduling method and compares the performance with the current mainstream methods. The experimental results show that the scheduling method in the present invention is highly competitive. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 A flowchart for order insertion in the present invention;

[0049] Figure 2 A flowchart of order cancellation in the present invention;

[0050] Figure 3 A flowchart of order changes in the present invention;

[0051] Figure 4 is a flow chart of the scheduling method in the present invention;

[0052] Figure 5 is a coding diagram of the scheduling method in the present invention;

[0053] Figure 6 Flowchart of the learning-driven monarch butterfly optimization method;

[0054] Figure 7 A block diagram of a local search in the present invention;

[0055] Figure 8 It is a parameter analysis diagram of the monarch butterfly optimization method based on learning drive in the present invention;

[0056] Fig. 9 A graph showing the impact of different components on the performance of the learning-driven monarch butterfly optimization method;

[0057] Fig.10 The mean ARPD values ​​and box plots of QLMBO and comparison methods in different scenarios;

[0058] Fig.11 Diagram for the Friedman test structure. DETAILED DESCRIPTION

[0059] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the accompanying drawings.

[0060] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein, and those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0061] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure or characteristic that may be included in at least one implementation of the present invention. The term "in one embodiment" that appears in different places in this specification does not refer to the same embodiment, nor is it a separate or selective embodiment that is mutually exclusive with other embodiments. The present invention provides the following embodiments.

[0062] In this embodiment, the scheduling method (DDFFSP) of the distributed flexible flow shop under uncertain environment is to reschedule the original scheduling method (DFFSP) of the distributed flexible flow shop after the dynamic event occurs. In this embodiment, three types of dynamic events are mainly considered: order arrival, order cancellation and order processing time change. In order to more clearly explain the problem to be solved by this embodiment, this embodiment is described as follows for the problem to be solved by the present invention. In this embodiment, the mathematical model of the scheduling method (DFFSP) of the distributed flexible flow shop is shown in Table 1.

[0063] Table 1 Mathematical model of the scheduling method of distributed flexible flow shop

[0064]

[0065] The mathematical static DFFSP model is built like this. There is a set of F factories, each containing the same flow shop configuration. The flow shop consists of a series of machines. It is necessary to assign a set of orders to F factories for processing. Order processing starts with machine 1, then machine 2, and so on, until machine M.

[0066] Among them, the mathematical model of static DFFSP is as follows:

[0067] Objective function: min(C max )=min(C n,m ) (1)

[0068] Constraints:

[0069]

[0070] Formula (1) indicates that the objective function is to minimize the completion time.

[0071] According to equation (2), each slot can only have one order at most.

[0072] Formula (3) ensures that the factory cannot be changed after each order is assigned.

[0073] According to equation (4), when an order at a factory location is required to be processed on a machine, it must first be processed on the preceding machine.

[0074] Equation (5) indicates that when machine i in a factory is processing an order at a location, it needs to wait for the order previously processed on the same machine to be completed before starting the subsequent task.

[0075] Constraint (6) captures the correlation between the departure times of two consecutive orders. The target for completion time is formally specified as Equation (7).

[0076] (8) and (9) give the specific value ranges of the decision variables.

[0077] However, in manufacturing, the phenomenon of new order insertion is a common phenomenon in remanufacturing environments. When a new order (at a specific time t) is introduced into a schedule that is being executed on a shop floor, it becomes necessary to include a rescheduling operation. The problem is described as follows: In the case of several factories operating according to a predetermined schedule, a set of new orders {NO1, NO2, …, NO u} Arrives randomly and needs to be assigned to the corresponding factory at the designated decision point. Unprocessed and newly inserted orders need to be rescheduled at the arrival time. The rescheduling of existing orders is determined by the time of insertion of the order or the time when the current processing program is completed. The starting time of rescheduling on each machine is determined by the insertion time or the time when the current operation is completed on that machine. Emergency orders arriving at random times in dynamic events are considered. According to the newly arrived emergency orders, the factory needs to be based on the urgency of the order and C max Arrange the production of new orders. In the rescheduling stage, the flow time of the new job is determined according to its arrival time and completion time. The optimization goal is to minimize C max Deviation, as shown in equation (1).

[0078] In order to more clearly demonstrate the technical solution in this embodiment, this embodiment provides the following diagram for the problem to be solved by the present invention, such as Figures 1 to 3 shown.

[0079] like Figure 1As shown in FIG. 1 , when an enterprise has two identical factories, each factory is equipped with 3 machines, and each factory uses the existing optimization solution before the new order arrives. Due to the urgency of the order, the new order arrives on time. Subsequently, the scheduling method in this embodiment will make a rescheduling decision at the decision point based on the production situation of the factory.

[0080] When a manufacturing company receives a series of orders, some orders may be cancelled during the production process. The problem is described as follows: when multiple factories are running according to the scheduled plan, old orders need to be cancelled for some reason, so the unprocessed orders need to be rescheduled. The rescheduling of existing orders depends on the time when the current order is cancelled and the time when the current process is completed. The start time of rescheduling on each machine is determined by the cancellation time and completion time of the current operation performed on the machine. Figure 2 As shown in Figure 1, before the new order arrives, each factory uses the existing optimization plan, cancels the old order, and then regenerates the scheduling plan based on the factory's production situation.

[0081] When executing a pre-set production schedule in a multi-factory environment, some scheduled order processing times may change for a variety of reasons. Such changes require that unfinished orders be rescheduled into the production process quickly and efficiently. The rescheduling task needs to take into account the variables of each machine's current processing schedule. Figure 3 As shown, after the old order processing time changes, the scheduling system needs to immediately evaluate and generate a new production scheduling plan to ensure that factory production continues to proceed efficiently and orderly.

[0082] In order to solve the above problem that the factory production plan needs to be readjusted due to dynamic reality, this embodiment provides a distributed flexible flow shop scheduling method (DDFFSP) under uncertain environment. The flowchart of the method is as follows: Figure 4 As shown by Figure 4 It can be seen that the framework of the scheduling method for a distributed flexible flow shop under an uncertain environment in this embodiment mainly includes the scheduling method for a distributed flexible flow shop under an uncertain environment.

[0083] In this embodiment, the problems to be solved by the distributed flexible flow shop scheduling method (DDFFSP) under uncertain environment can be divided into two categories, one is the job allocation problem for the factory, and the other is the job scheduling problem within the factory. Therefore, in order to solve the DDFFSP problem, a permutation-based solution representation method is usually adopted, in which each solution represents a specific sequence of workpieces to be processed. This method allows a direct and intuitive mapping between the solution space and the order of operations in the flow shop environment. For this problem, a two-dimensional vector representation method is used to represent each solution, where the first dimension is the factory vector. In addition, the second dimension organizes the tasks specified for each factory and lists the precise order in which each job should be processed. The solution is represented as follows Figure 5 shown.

[0084] In addition, in order to improve the rationality of the scheduling method of the distributed flexible flow shop under uncertain environment in this embodiment, and improve the iterative search capability to ensure the effectiveness of scheduling, the scheduling method of the distributed flexible flow shop under uncertain environment in this embodiment adds the monarch butterfly optimization method (MBO) to ensure the scheduling effect in this embodiment. The monarch butterfly optimization method (MBO) has the characteristics of simple structure, few parameters, easy implementation, strong robustness, etc. Therefore, the monarch butterfly optimization method (MBO) has been successfully applied to various fields, such as global numerical optimization, combinatorial optimization problems, neural network training, etc. At the same time, existing studies have shown that the monarch butterfly optimization method (MBO) is prone to fall into local optimality. In view of the problems existing in the static optimization stage of the scheduling method of the distributed flexible flow shop under uncertain environment (DDFFS) and the above-mentioned shortcomings of the monarch butterfly optimization method (MBO), the scheduling method of the distributed flexible flow shop under uncertain environment based on learning-driven monarch butterfly optimization in this embodiment introduces the Q-learning mechanism in reinforcement learning to enhance the search capability of the monarch butterfly optimization method (MBO).

[0085] In this embodiment, the model based on the learning-driven monarch butterfly optimization method (QLMBO) is as follows Figure 6 As shown. Figure 6 It can be seen that the monarch butterfly optimization method based on reinforcement learning mechanism first initializes the population to obtain the initial solution, and then optimizes the initial solution through the monarch butterfly optimization method based on reinforcement learning mechanism. After obtaining the new solution, the new solution is evaluated. When the new solution is better than the initial solution, the new solution is used to replace the initial solution, and local search is performed based on learning-driven. The new solution is optimized again and replaces the new solution, and finally a scheduling plan is obtained.

[0086] QLMBO performs iterative search in a population of initial size, where each individual represents a complete scheduling sequence and also represents the position of the monarch butterfly in the search space. The quality of the initial solution in the population has an important impact on the performance of the QLMBO method. Therefore, a hybrid method is used to ensure the quality and diversity of the solutions in the population. The first individual in the population is generated by a heuristic method (NEH), and the other individuals are generated by random initialization. The population generated by the hybrid method is used as the initial population of the collaborative monarch butterfly optimization method. The population is then divided into subpopulation 1 and subpopulation 2, and the number of individuals in subpopulation 1 and subpopulation 2 are NP1 and NP2, respectively, as shown in the following formula.

[0087]

[0088] Where NP is the size of the initial population, and p=5 / 12 represents the mobility of subpopulation 1.

[0089] The local search process plays an important role in the performance of the QLMBO method. In view of the particularity of the problem, this embodiment adopts 6 local search methods to improve the solution accuracy. This method considers key plants and ordinary plants, such as Figure 7 As shown. The neighborhood structure is a method of generating new feasible solutions by performing certain neighborhood operations on existing feasible solutions. QLMBO uses traditional neighborhood structures and block-based neighborhood structures to explore the solution space. The traditional neighborhood structure is a neighborhood operation based on insertion and exchange. For ordinary factories, four traditional neighborhood structures are used as the initial four heuristic methods (LLHs), including intra-factory exchange, inter-factory exchange, intra-factory insertion, and inter-factory insertion. During the optimization process, the factory with the largest C_max is defined as the key factory. The remaining two local search operations are used for key factories, which are exchange operations inserted between factories.

[0090] The states and actions of QLHH_DIR are S={s1,s2,…,s n} and A={LLH1,LLH2,…,LLH n}. The reward obtained by this method is recorded as reward t+1 , the Q table is used to store the experience that the agent has learned from the environment during the entire iteration process, and the Q value is calculated using formula (11).

[0091] Q(s t ,a t )←Q(s t ,a t )+α*(reward t+1 +β*maxQ(s t+1 ,a t+1 )-Q(s t ,a t)) (11)

[0092] Where Q(s t ,a t ) represents the Q value associated with the action selected in each generation, which depends on the state. α∈(0,1] and γ∈(0,1] represent the learning rate and discount factor, respectively. maxQ(s t+1 ,a t+1 ) represents the maximum Q value that can be achieved in the subsequent state when executing the subsequent action.

[0093] In the proposed method, rewards are used to capture the effectiveness of the selected actions and their subsequent results. The Q-learning mechanism aims to select a local search strategy that maximizes the reward. The main goal of the method is to minimize the make span, optimizing it to the smallest possible value. To achieve this goal, the method in this embodiment distributes rewards based on the selection of the most effective action to achieve the goal. If the selected action results in a smaller makespan after updating the state, the method receives a reward. On the contrary, if the selected action does not result in a shorter make span, no reward is given. By rewarding actions that contribute to a shorter make span and penalizing those that do not contribute, the method learns to make choices that lead to improved scheduling results. This reinforcement learning approach helps guide the method to find better solutions over time. The reward function is represented by equation (12).

[0094]

[0095] If the action taken leads to a new best solution that is better than the previous best solution, the chosen action will be strengthened or enhanced. Conversely, if the new solution is worse than the previous best solution, the action may be penalized or discouraged. Q-learning learns the optimal choices under different states based on the evolution of the method and the experience of executing different stages. It adjusts and updates the strategy by leveraging the knowledge gained in the previous iteration to guide decision-making in subsequent iterations. This iterative learning process helps the method converge to the optimal area. Therefore, the learning-driven monarch butterfly optimization in this embodiment is applied to the scheduling method of distributed flexible assembly line workshops in uncertain environments, so that the final scheduling plan can be guaranteed through the iterative learning process during scheduling to facilitate factory production.

[0096] In addition, in this embodiment, dynamic scheduling rules are provided for three dynamic events (order insertion, order cancellation, and order processing time change). After a dynamic event occurs, the original factory will generate a new scheduling plan as soon as possible based on the original scheduling plan. The specific rules are as follows.

[0097]

[0098] This embodiment conducts experiments on the above scheduling method. The specific experimental conditions are: the number of workshops f∈3,4,5,6,7}, the number of workpieces n∈{20,50,100,200}, and the number of machines m∈{5,10,20}. And the number of equivalent parallel machines τ k ∈{3,4}. Therefore, the benchmark consists of 120 combinations. In addition, each combination generates 10 different instances, resulting in 120×10=1200 instances. i,j ∈U[1,99], the processing time of each workpiece is randomly distributed. Each instance is executed 5 times independently. All programs are implemented in Matlab to ensure the fairness of the experiment. All experiments are completed on a computer with a 3.40GHz AMD-Ryzen71700X CPU, 16G RAM and a 64-bit operating system. The performance of all methods is evaluated and analyzed by the average relative percentage deviation (ARPD) calculated by formula 13.

[0099]

[0100] Among them C i is the result of the i-th run of the current instance. R is the number of independent runs. best is the best result for the current instance.

[0101] The parameters of QLMBO include population size N, migration rate p, and migration period x. The parameter levels are set as: N = {20, 50, 100, 200}, p = {0.3, 0.4, 0.5, 0.6}, x = {0.9, 1.1, 1.3}, with a total of 4 × 4 × 3 = 48 control parameter combinations. To ensure stability, each parameter combination is executed 20 times and the average value is reported. The variance analysis of N, p, and x is shown in Table 2.

[0102] Table 2 ANOVA results of QLMBO parameters

[0103]

[0104] By analyzing the data in Table 2, the probability values ​​of parameters p and N are both less than 0.05, indicating that they are key parameters. This shows that the adjustment of p and N will lead to significant changes in QLMBO performance within the 95% confidence interval. In addition, the F-ratio of p and N exceeds that of other parameters, further confirming their substantial impact on QLMBO.

[0105] The main effect analysis of QLMBO parameters is shown in the figure Figure 8 As shown, more information is provided. Figure 8(a) It can be seen that when the parameters are configured as p = 0.4, N = 100, x = 0.9, the ARPD value of QLMBO is the smallest.

[0106] The interaction effect was tested, as shown in Table 2. It was found that the probability values ​​of the p*N and N*x interactions were both less than 0.05. This requires further research on these parameter combinations through interaction effect diagrams. Figure 8 (b) and Figure 8 (c) The interaction effect diagrams of p*N and N*x. Figure 1 The optimal parameter configuration is p=0.4, N=100, and x=1.1.

[0107] In summary, the optimal control parameter combination of QLMBO is p = 0.4, N = 100, and x = 1.1.

[0108] The learning-driven monarch butterfly optimization method in this embodiment mainly consists of three parts:

[0109] (1) Heuristic initialization method;

[0110] (2) Local search method based on Q-learning (driven learning);

[0111] (3) Search process based on dynamic rules.

[0112] In order to verify the effectiveness of these components, this embodiment provides three variants of QLMBO: QLMBO1 with a random initialization method, QLMBO2 without Q-learning operation, and QLMBO3 without a dynamic rule-based search process. And the QLMBO variants were tested to verify the effectiveness of each component. The termination condition was set to ((t = c × n × m × f) milliseconds of CPU running time, and each QLMBO variant was executed independently 10 times on each instance. The experimental results are shown in Table 3.

[0113]

[0114] The results show that the overall average ARPD of QLMBO is higher than that of other QLMBO variants. The mean and box plots of the average relative percentage deviation (ARPD) under different problem sizes and termination conditions are shown in Figure 2. Fig. 9 shown. Fig. 9 (a) shows the average ARPD for different numbers of plants, from which it can be observed that QLMBO outperforms other variants with a significant overall performance improvement. Fig. 9The box plots in (b), 9(c), and 9(d) show the dispersion of the data results, further reflecting the stability of the overall performance of the method in this embodiment. From the results shown in the figure, it can be seen that under different problem scales and termination conditions, the box plot length (upper quartile-lower quartile) of QLMBO is smaller than that of other variant methods. Therefore, the results of QLMBO are more stable. In other words, the QLMBO method shows more stable performance on instances of different scales and termination conditions.

[0115] In order to further verify the accuracy of the scheduling method in this embodiment, the proposed QLMBO is compared with three well-known methods for solving DDHFSP. The following methods are selected as comparison methods: QLHHEA (q-learningbased hyper heuristic evolutionary algorithm), BMBO (Binary MBO) and SACMBO (MBO algorithm with Self-adaptive Crossover).

[0116] The termination condition is set to (t = c × n × m × f) milliseconds of CPU running time, and each method is executed 10 times independently for each instance. Table 4-6 shows the performance of the QLMBO method and the comparison method under different problem sizes and termination conditions, among which the ARPD value of the QLMBO method is the smallest. The results show that the QLMBO method performs best on large-scale instances in different scenarios, such as Fig.10 As shown in (a), under the same conditions, the QLMBO method shows advantages over other comparison methods. Fig.10 (b) Fig.10 (c) Fig.10 (d) The box plots of the three methods show that QLMBO has smaller fluctuations and stronger stability. Comprehensive analysis shows that the QLMBO method is superior to other methods in terms of efficiency and stability.

[0117]

[0118]

[0119]

[0120] In addition, in this embodiment, the Friedman test is used to perform statistical analysis on QLMBO and other methods, and the results are shown in Table 7. The Friedman test is a non-parametric statistical technique used to determine the significant differences between multiple (related) samples. Fig.11As shown, it shows that QLMBO has the smallest average rank value. In the 90% and 95% confidence intervals, the performance of QLMBO is significantly better than other methods.

[0121] Table 7 Results of Friedman test

[0122]

[0123] The Wilcoxon test was used to verify the performance difference between QLMBO and other methods. The results of the Wilcoxon test are shown in Tables 8, 9, and 10. In the Wilcoxon test, if the p value is less than the significance level α, it indicates that there is a significant difference between the two methods. As shown in Tables 8, 9, and 10, the p values ​​are all less than 0.05, indicating that the QLMBO method is significantly better than other methods.

[0124] Table 8 Wilcoxon signed rank test results of QLMBO and comparison methods (c=20)

[0125]

[0126] Table 9 Wilcoxon signed rank test results of QLMBO and comparison methods (c=40)

[0127]

[0128] Table 10 Wilcoxon signed rank test results of QLMBO and comparison methods (c=60)

[0129]

[0130] From the above, we can see that the QLMBO method outperforms the existing benchmark methods in terms of solution quality. Therefore, QLMBO with dynamic rules is an effective method for generating static scheduling solutions and rescheduling solutions in response to dynamic events. The proposed two-stage modeling approach and its corresponding methods provide an effective approach to solving the dynamic shop scheduling problem.

[0131] In addition, on the other hand, this embodiment also provides a storage medium for receiving the above-mentioned computer program input by the user, and the stored computer program enables the electronic device to execute the above-mentioned scheduling method of distributed flexible assembly line workshops under uncertain environment based on learning-driven monarch butterfly optimization, and the above-mentioned storage medium is assembled in an information data processing terminal, which includes a memory and a processor, and the memory stores the above-mentioned computer program. When the computer program is executed by the processor, the processor executes the above-mentioned scheduling method of distributed flexible assembly line workshops under uncertain environment based on learning-driven monarch butterfly optimization to solve the scheduling problem of the workshop.

[0132] The above content is a further detailed description of the present invention in combination with specific implementation methods. It cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as belonging to the scope of protection determined by the claims submitted for the present invention.

Claims

1. A scheduling method for a distributed flexible flow shop in an uncertain environment based on learning-driven monarch butterfly optimization, which is used to adjust the production plan when the order information in the flow shop changes. The scheduling method includes a static scheduling stage and a dynamic scheduling stage, and is characterized by: In the static scheduling stage, the learning-driven monarch butterfly optimization method combines the adaptive migration operator and the butterfly adjustment operator to perform local search on the production plan; In the dynamic scheduling stage, the scheduling method aims to minimize the maximum completion time of the production plan and uses an iterative greedy method to identify the order insertion position with information changes; Finally, the final scheduling plan is determined after rescheduling through the above-mentioned static scheduling stage and dynamic scheduling stage.

2. The scheduling method of distributed flexible flow shop under uncertain environment based on learning-driven monarch butterfly optimization according to claim 1 is characterized in that: The objective function of this scheduling scheme is: Objective function: min(C max )=min(C n,m ) (1) Among them, the constraints in the objective function are: Formula (1) indicates that the objective function is to minimize the completion time; Equation (2) stipulates that each slot can only have one order at most; Formula (3) ensures that the factory cannot be changed after each order is assigned; Equation (4) requires that when an order at a factory location is processed on a machine, it must first be processed on the preceding machine; Equation (5) indicates that when machine i in a factory is processing an order at a location, it needs to wait for the order previously processed on the same machine to be completed before starting the subsequent task; Constraint (6) captures the correlation between the departure times of two consecutive orders; the target of completion time is formally specified as equation (7); (8) and (9) give the specific value ranges of the decision variables.

3. The scheduling method of distributed flexible flow shop under uncertain environment based on learning-driven monarch butterfly optimization according to claim 2 is characterized in that: The learning-driven monarch butterfly optimization solution mainly consists of three parts: Heuristic initialization method; Local search method based on driven learning; Dynamic rule-based search process.

4. The method for scheduling a distributed flexible flow shop under uncertain environment based on learning-driven monarch butterfly optimization according to claim 3 is characterized in that: The population generated by the heuristic initialization method is used as the initial population of the collaborative monarch butterfly optimization method; the population is divided into sub-population 1 and sub-population 2, and the number of individuals in sub-population 1 and sub-population 2 are NP1 and NP2 respectively, as shown in the following formula; Where NP is the size of the initial population, and p=5 / 12 represents the mobility of subpopulation 1.

5. The method for scheduling a distributed flexible flow shop under uncertain environment based on learning-driven monarch butterfly optimization according to claim 3 is characterized in that: The local search includes 6 local search schemes, namely: Orders are inserted or exchanged within the factory; Orders are inserted or exchanged between plants; Orders are inserted or exchanged within key plants; Among them: the factory with the longest completion time for processing the order is the key factory.

6. The method for scheduling a distributed flexible flow shop in an uncertain environment based on learning-driven monarch butterfly optimization according to claim 3 is characterized in that: In the dynamic scheduling stage, the scheduling scheme schedules three dynamic events, which are: Insertion of orders, cancellation of orders and changes in order processing times.

7. The method for scheduling a distributed flexible flow shop based on learning-driven monarch butterfly optimization in an uncertain environment according to any one of claims 1 to 6, characterized in that: This method is evaluated and analyzed by the average relative percentage deviation, which is obtained by the following formula: Among them, C i is the result of the ith run of the current instance; R is the number of independent runs; C best is the best result for the current instance.

8. The method for scheduling a distributed flexible flow shop under uncertain environment based on learning-driven monarch butterfly optimization according to claim 7 is characterized in that: The parameters of the scheduling method include group size N, mobility p, and migration period x; Among them, N={20,50,100,200}, p={0.3,0.4,0.5,0.6}, x={0.9,1.1,1.3}.

9. A storage medium for receiving a user input program, characterized in that: The stored computer program enables the electronic device to execute the scheduling method of a distributed flexible assembly line workshop in an uncertain environment based on learning-driven monarch butterfly optimization as described in claim 8.

10. An information data processing terminal, characterized in that: The terminal includes a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the scheduling method for distributed flexible assembly lines in an uncertain environment based on learning-driven monarch butterfly optimization as described in claim 8.

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