Three-stage remanufacturing blocking scheduling method based on machine deterioration and maintenance strategy

Abstract

The application belongs to the technical field of remanufacturing scheduling, and discloses a three-stage remanufacturing blocking scheduling method based on machine deterioration and maintenance strategy, which comprises the following steps: taking the rate adjustment activity as the maintenance strategy of the remanufacturing machine in the remanufacturing stage, and constructing a deterioration model considering the time-dependent deterioration problem and the maintenance strategy; based on the deterioration model of the remanufacturing machine, setting the constraints of the disassembly stage, the remanufacturing stage and the reassembly stage respectively, so as to construct a three-stage remanufacturing blocking scheduling model, and adopting the monarch butterfly optimization algorithm to solve the three-stage remanufacturing blocking scheduling model, and outputting the optimal three-stage remanufacturing blocking scheduling scheme, wherein the monarch butterfly optimization algorithm adopts the greedy acceptance strategy to update the sub-population. The application can obtain a high-quality three-stage remanufacturing blocking scheduling scheme.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of remanufacturing scheduling, and particularly relates to a three-stage remanufacturing blocking scheduling method based on machine deterioration and maintenance strategy. BACKGROUND

[0002] A classic remanufacturing system consists of three core stages: disassembly, reprocessing, and reassembly. When a batch of end-of-life products enters the remanufacturing system, they are first disassembled into individual components in the disassembly workshop, and then these components are restored to a near-new state through different operations in the reprocessing workshop. Finally, all the reprocessed components are assembled into remanufactured products in the reassembly stage. Compared with single-stage or two-stage remanufacturing systems, three-stage remanufacturing systems are more complex and have more extensive applications because they optimize the performance of the entire system.

[0003] Machine blocking refers to the phenomenon that a workpiece remains on the current machine after the machine completes processing the workpiece. Blocking frequently occurs in actual scheduling due to reasons such as buffer capacity limitations, technical limitations, and production characteristics. Blocking can significantly reduce overall scheduling efficiency, so it is of great practical significance to study how to reduce or eliminate blocking in actual scheduling.

[0004] In traditional scheduling problems, processing time is usually considered a fixed parameter. However, due to factors such as worker fatigue, tool misplacement, and machine deterioration, processing time often changes in actual production environments. In particular, under the influence of time-dependent deterioration, the later a workpiece is processed, the longer its processing time will be. If not controlled, the effects of time-dependent deterioration will gradually accumulate and have a negative impact on processing efficiency. Therefore, decision-makers usually implement maintenance activities to alleviate the effects of time-dependent deterioration. Rate-modifying activities (RMAs) are a common type of maintenance activity, and by implementing RMAs, machines can be restored to a "near-new state" or a "less deteriorated state".

[0005] At present, remanufacturing scheduling problems, especially three-stage remanufacturing scheduling problems, have attracted widespread attention. Existing technology has researched integrated process planning and scheduling problems in three-stage remanufacturing processes and proposed an improved spider monkey optimization algorithm to solve the problem. In addition, considering that reprocessed parts can be used for the reassembly of other products, a three-stage remanufacturing model considering part versatility has been proposed. Scholars have also proposed a three-stage remanufacturing scheduling model based on batch flow production mode, taking completion time and total energy consumption as optimization objectives. Or a three-stage remanufacturing system scheduling problem based on energy awareness has been constructed, which minimizes total energy consumption by adopting a power-on / off strategy. However, the above research on remanufacturing scheduling often ignores complex practical factors, especially the combined effects of factors such as machine blocking and deterioration. SUMMARY

[0006] The application aims to provide a three-stage remanufacturing blocking scheduling method based on machine degradation and maintenance strategy, which can obtain a high-quality three-stage remanufacturing blocking scheduling scheme.

[0007] To achieve the above-mentioned purpose, the technical solution adopted by the application is:

[0008] A three-stage remanufacturing blocking scheduling method based on machine degradation and maintenance strategy, the three stages including a disassembly stage, a reprocessing stage and a reassembly stage, the three-stage remanufacturing blocking scheduling method based on machine degradation and maintenance strategy comprising:

[0009] Taking the rate adjustment activity as the maintenance strategy of the reprocessing machine in the reprocessing stage, a degradation model considering the time-dependent degradation problem and the maintenance strategy is constructed;

[0010] Based on the degradation model of the reprocessing machine, a three-stage remanufacturing blocking scheduling model is constructed by setting the constraints of the disassembly stage, the constraints of the reprocessing stage and the constraints of the reassembly stage respectively, with the objective of minimizing the completion time;

[0011] The monarch butterfly optimization algorithm is used to solve the three-stage remanufacturing blocking scheduling model, and the optimal three-stage remanufacturing blocking scheduling scheme is output, and the monarch butterfly optimization algorithm uses the greedy acceptance strategy to update the sub-population.

[0012] The three-stage remanufacturing blocking scheduling method based on machine degradation and maintenance strategy provided by the application, in order to more effectively guide the remanufacturing scheduling in the real scene, proposes a class of blocking scheduling problems considering time-dependent degradation and taking the rate adjustment activity (RMA) as the machine maintenance strategy. In order to solve the above-mentioned problems, firstly, a degradation model integrating RMAs is proposed to determine the actual reprocessing time and RMA execution strategy. On this basis, a new blocking scheduling model is constructed to minimize the completion time. And the monarch butterfly optimization algorithm is used to obtain a high-quality three-stage remanufacturing blocking scheduling scheme within a reasonable time. BRIEF DESCRIPTION OF DRAWINGS

[0013] Figure 1 The overall layout of the three-stage remanufacturing system researched by the application;

[0014] Figure 2 The flowchart of the three-stage remanufacturing blocking scheduling method based on machine degradation and maintenance strategy of the application;

[0015] Figure 3 The Gantt chart of the solution of the remanufacturing process in which RMAs are performed and the Gantt chart of the solution of the remanufacturing process in which RMAs are not performed in the example of the application;

[0016] Figure 4 Flow chart for solving three-stage remanufacturing blocking scheduling model by monarch butterfly optimization algorithm for the present application;

[0017] Figure 5 Schematic diagram of individual represented by three-layer structure for the present application;

[0018] Figure 6 Schematic diagram of product variation assigned to remanufacturing machine before and after MLB strategy is executed for the present application;

[0019] Figure 7 Schematic diagram of one embodiment of performing type I exchange mutation on individual of sub-population 1 for the present application;

[0020] Figure 8 Schematic diagram of one embodiment of performing type II exchange mutation or insertion mutation on first layer of individual in sub-population 2 for the present application;

[0021] Figure 9 C max Average value of each parameter at different levels in experiment for the present application;

[0022] Figure 10 Box plot of five algorithms in medium and large test instances in experiment for the present application. DETAILED DESCRIPTION

[0023] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the scope of protection of the present application.

[0024] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the present application belongs. The terms used in the specification of the present application are only for the purpose of describing specific embodiments and are not intended to limit the present application.

[0025] Figure 1The overall layout of the three-stage remanufacturing system studied in this invention is shown, which consists of a disassembly shop, a reprocessing shop and an assembly shop. The disassembly shop is equipped with parallel disassembly machines (DWs, also referred to as disassembly workstations), the reprocessing shop is equipped with parallel reprocessing lines (RLs), and each reprocessing line is equipped with reprocessing machines (RWs), and the assembly shop is equipped with parallel assembly machines (AWs, also referred to as assembly workstations). Different colors are used to distinguish end-of-life products (EOL) with different defect states, and different geometric shapes are used to represent different parts of the product. First, a batch of end-of-life products with similar structure and remanufacturing value enters the system. In the first stage, these products are disassembled into corresponding parts. It should be noted that the disassembly task can be assigned to any one of the parallel disassembly machines. In the second stage, a series of reprocessing operations are performed on the parts on the parallel reprocessing lines. It is worth noting that different reprocessing lines are equipped with a series of specific reprocessing machines to handle specific types of parts. In the third stage, the reprocessed parts are assembled into remanufactured products. Similar to the disassembly workstations, the assembly task can be assigned to any one of the parallel assembly machines.

[0026] The problem is described as follows: there are I end-of-life products, each consisting of J parts, which need to be assigned to a remanufacturing system for processing. The system consists of G parallel DWs, J parallel special RLs and R parallel AWs. The jth RL contains K j The buffer capacity between reprocessing machines is assumed to be zero, i.e. when the next machine is not available, the part cannot be released from the current machine even if the reprocessing operation has been completed (i.e. it will be blocked on the current machine). In addition, to address the time-dependent deterioration problem, each reprocessing machine can perform a rate adjustment activity (rate adjustment activity as a maintenance strategy RMA) after processing a part, and the operation time of each RMA is fixed. During the reprocessing of a part or when the part is blocked, RMA cannot be performed. Performing RMA can affect the work of the previous machine, because before RMA is completed, the part can be blocked on the previous machine, making the machine unavailable.

[0027] The method of the invention first determines the execution strategy of the rate adjustment activity. On this basis, the disassembly machines are assigned to the end-of-life products and the disassembly sequence of the end-of-life products on each disassembly machine is determined, then the processing sequence of the parts in the reprocessing shop is determined, and finally the assembly machines are assigned to the remanufactured products and the assembly sequence of the remanufactured products on each assembly machine is determined to minimize the completion time.

[0028] In addition, the following assumptions are made: all machines are initially in normal and available state. No machine can process two or more parts or products simultaneously, and each part or product can only be processed once on a specific machine. Disassembly, reprocessing and reassembly operations cannot be interrupted once started. The preparation time is independent of the sequence of operations. The transportation time is negligible.

[0029] As shown in FIG. 1, the three-stage remanufacturing blocking scheduling method based on machine deterioration and maintenance strategy of the embodiment includes the following steps: Figure 2

[0030] Step 1, constructing a deterioration model considering time-dependent deterioration problem and maintenance strategy as a maintenance strategy of reprocessing machines in the reprocessing stage.

[0031] In order to determine the actual reprocessing time and the execution strategy of RMA, the embodiment proposes a deterioration model integrating RMAs. It should be noted that each reprocessing machine needs to reprocess I products. Considering the extreme case, RMA is performed after each component is reprocessed. Since performing RMA after reprocessing the last component will not affect the completion time, at most I-1 RMAs can be performed on each reprocessing machine. Here, I-1 represents the maximum number of RMAs that can be performed on each RM, because in most cases, I-1 RMAs do not need to be performed.

[0032] The actual processing time of a workpiece is usually represented as a linear function of the interval between the end time of the last RMA (or the start time of the first job in the RM) and the start processing time of the workpiece. In the embodiment, the actual reprocessing time of a part is also defined in a similar way, as shown in equation (1).

[0033]

[0034] Obviously, for those parts that are first reprocessed on the RM jk or immediately after RMA, the actual reprocessing time is equal to the expected reprocessing time, because is zero. Otherwise, due to the deterioration factor, the actual reprocessing time of the part will exceed the expected reprocessing time. The actual reprocessing time is calculated by equation (2).

[0035]

[0036] where, is the completion time of RMA jk0 , i.e. the assumed 0th RMA on each RM jk . By assuming RMA jk0 ​For any part reprocessed on a RM, there will always be a nearest RMA to mathematically model the actual reprocessing time of the part. is equal to the reprocessing start time of the part reprocessed first on the RM jk as shown in equation (3):

[0037]

[0038] Equation (4) ensures that the completion time of a potential RMA only makes sense if it is actually performed:

[0039]

[0040] λ jkl and λ ij ′ kl are related as shown in equation (5):

[0041]

[0042] Equations (6) and (7) specify the number of RMA performed on each RM. Equation (8) ensures that there is and only one RMA nearest to any part reprocessed on a RM before the part is reprocessed on the RM.

[0043]

[0044] In the extreme case, an RMA can be performed after each part reprocessing, but can result in significant resource waste. Therefore, as shown in equation (9), an RMA is only performed on a RM jk if the reprocessing time due to degradation of the part to be reprocessed on the RM RMA is greater than t jk . Then, the part will be blocked on the previous RM j(k-1) until the RMA is completed. Equation (10) further ensures that for a part reprocessed on a RM, the reprocessing time due to degradation is less than t RMA .

[0045]

[0046]

[0047] Step 2, based on the degradation model of the reprocessing machine, a three-stage remanufacturing blocking scheduling model is constructed with the objective of minimizing the completion time and setting the constraints of the disassembly stage, the reprocessing stage and the reassembly stage respectively.

[0048] (1) Objective function:

[0049]

[0050] (2) Constraints in the disassembly stage:

[0051]

[0052]

[0053] Equation (12) ensures that each end-of-life product can only be disassembled at one DW. Equations (13) and (14) specify the disassembly sequence of end-of-life products. Equation (15) specifies that when two end-of-life products are assigned to the same DW, they should be disassembled in sequence

[0054] (3) Constraints in the remanufacturing stage:

[0055]

[0056]

[0057]

[0058] Equation (16) specifies that the remanufacturing of a product must start after the disassembly of the product is completed. Equations (17) and (18) specify the relationship between the departure time and the completion time of a part by considering the blocking effect. Equation (19) explains that the start time of a part's remanufacturing at an RM is equal to its departure time from the previous RM. Equation (20) ensures the time relationship between parts that need to be remanufactured at the same RM by considering the blocking effect. Equation (21) specifies the time relationship between a RMA and its previous part. Equation (22) specifies the remanufacturing sequence of parts.

[0059] (4) Constraints in the reassembly stage:

[0060]

[0061]

[0062]

[0063] Equation (23) specifies that each remanufactured product can only be reassembled at one AW. Equation (24) specifies the remanufacturing and reassembly sequence of products. Equation (25) specifies that two remanufactured products cannot be reassembled at the same AW. Equations (26) and (27) specify the reassembly sequence of products.

[0064] In addition, the constraints of binary variables are shown in Equations (28)-(31):

[0065]

[0066]

[0067]

[0068] In this embodiment, the parameters and variables are defined as follows: i, i′ are product indices and i, i′ ∈ {1,..., I}; j is the part / RL index, j ∈ {1,..., J}, since parts and reprocessing lines have a corresponding relationship, they use the same index; g is the DW index, g ∈ {1,..., G}; k is the RM index, k ∈ {1,..., K}. j}; k is the RM index, k∈{1,...,K} j}; r is the AW index, r∈{1,...,R}; l is the RMA index, l∈{0,1,...,I-1}; P i P i′ For the i-th or i′-th scrapped or remanufactured product, in this embodiment, the product is referred to as a scrapped product during the disassembly and reprocessing stages, and as a remanufactured product during the reassembly stage; C ij For P i The j-th part; DW g For the gth DW; RL j For the j-th RL; RM jk For RL j The kth station RM; AW r For the rth AW; RMA jkl For RM jk The first RMA; t RMA α represents the execution time of the RMA (duration); M is an infinitely large positive number; α is the machine degradation rate. For P i Disassembly time (duration); C ij In RM jk The expected reprocessing time (in duration); For P i Reassembly time; C max The completion time of the remanufacturing schedule (in seconds); C ij In RM jk Actual reprocessing time (in duration); FT i D For P i The completion time of the dismantling (at a specific moment); C ij In RM jk The start time of the reprocessing (at time t); For RMA jklThe completion time (in seconds); C ij In RM jk The completion time of the reprocessing (at time FT); i A For P i Reassembly completion time; η ig Let P be the decision variable, expressed as if P i In DW g If the upper part is disassembled, then η ig =1; otherwise η ig =0; η i ′ i'g Let be the decision variable, expressed as in DW g If P i In P i′ If it was previously disassembled, then η' ii'g =1; otherwise η' ii' =0; λ jkl Let RMA be the decision variable, expressed as if RMA jkl In RM jk If the above is executed, then λ jkl =1; otherwise λ jkl =0; λ ij ′ kl Let be the decision variable, represented as in RM jk Reprocessing C ij Previously, if RMA jkl If it is the most recently executed RMA, then λ' ijkl =1; otherwise λ' ijkl =0; γ ii′jk Let be the decision variable, represented as in RM jk Above, if C ij In C i′j If it has been reprocessed before, then γ ii′jk =1; otherwise γ ii′jk =0; μ ir Let P be the decision variable, expressed as if P i In AW r If the above is reassembled, then μ ir =1; otherwise μ ir =0; μ i ′ i'r Let be the decision variable, expressed as in AW r If P i It is in P i′ If it is reassembled previously, then μ' ii'r =1; otherwise μ' ii'r =0.

[0069] This embodiment illustrates the advantages of RMA for remanufacturing scheduling with an example:

[0070] Suppose there are three scrapped damping supports, denoted as P1, P2 and P3. Two related parts, plate and bushing, are evaluated to have remanufacturing value. The remanufacturing operation process of the plate is cleaning→laser processing→general milling, and the remanufacturing process of the bushing is cleaning→laser processing. Two DWs and two AWs are provided for this purpose. In the reprocessing workshop, RL1 has a cleaning machine (RM 11 ), a laser machine (RM 12 ) and a numerical control milling machine (RM 13 ), and RL2 has a cleaning machine (RM 21 ) and a laser machine (RM 22 ). The deterioration rate of the machine is set to 0.1, t RMA is set to 5, and other parameters are shown in Table 1.

[0071] A feasible solution is: in the disassembly stage, disassemble P2 and P1 on DW1, and the disassembly sequence is P2→P1, and disassemble P3 on DW2; in the reprocessing stage, the sequence is P2→P3→P1; in the reassembly stage, reassemble P2 and P1 on AW1, and the reassembly sequence is P2→P1, and reassemble P3 on AW2. If the reprocessing time caused by deterioration is greater than t RMA , the RMAs are performed.

[0072] Table 1 shows the parameter values of the example

[0073]

[0074]

[0075] In order to intuitively show the influence of RMA on the scheduling result, two Gantt charts are drawn for the solution considering RMA execution in this embodiment, as shown in Figure 3 . The C max value of the solution of the remanufacturing process in which the RMAs are performed is 227.8, which is better than the C max value 230.98 of the solution of the remanufacturing process without performing the RMAs, indicating that the RMA execution strategy adopted in this embodiment is effective. It should be noted that the number of scrapped products in this example is small. With the further increase of the number of scrapped products, the negative influence of deterioration on the scheduling efficiency will continue to increase if an appropriate RMA strategy is not adopted. Therefore, RMA is of great significance to improve the remanufacturing scheduling efficiency.

[0076] A three-stage remanufacturing blocking scheduling problem is proposed in this embodiment, considering time-dependent deterioration and RMAs execution strategy. In order to solve this problem, an integrated RMAs deterioration model is proposed to describe the dynamic changes of actual processing time and determine the position and number of RMAs on each machine during reprocessing. In addition, a new blocking scheduling model is established to minimize the makespan by considering the time waste caused by blocking.

[0077] Step 3, solve the three-stage remanufacturing blocking scheduling model by using the monarch butterfly optimization algorithm, and output the optimal three-stage remanufacturing blocking scheduling scheme. As shown in Figure 4 , the specific steps are as follows:

[0078] Step 3.1, set the population size to N, to balance the quality and diversity of the solution, use the constructive heuristic method and machine load balancing strategy to initialize N / 2 individuals, and randomly initialize the remaining N / 2 individuals, each individual represents a three-stage remanufacturing blocking scheduling scheme, that is, each monarch butterfly individual represents a feasible scheduling solution.

[0079] In order to encode the solution containing product / part sequence and workstation allocation, the individual of this embodiment uses a three-layer structure to represent, and the individual can be represented as , where the first layer, the second layer and the third layer can be represented as π={π1,π2,...,π I}, ψ={ψ1,ψ2,...,ψ I} and ξ={ξ1,ξ2,...,ξ I} respectively. Elements π h , ψ h , ξ h (h∈{1,...,I}) represent product index, DW index and AW index respectively. π h in π is a non-repeating integer selected from {1,...,I}, ψ h in ψ and ξ h in ξ are integers selected from {1,...,G} and {1,...R} respectively. The elements corresponding to the positions in the first layer and the second layer represent that the products are disassembled on the disassembly machine, if the elements with the same value in the second layer correspond to multiple elements in the first layer, it means that multiple products are disassembled on the disassembly machine, and the product at the front position is disassembled first; the elements corresponding to the positions in the first layer and the third layer represent that the products are reassembled on the reassembly machine, if the elements with the same value in the third layer correspond to multiple elements in the first layer, it means that multiple products are reassembled on the reassembly machine, and the product at the front position is reassembled first.

[0080] Figure 5 An example of the solution is given, that is The decoding process is as follows: in the disassembly stage, P5 and P4 are disassembled on DW2, P3 and P2 are disassembled on DW1, and P1 is disassembled on DW3. The disassembly order on the disassembly station is P5→P4 and P3→P2, respectively. In the reassembly stage, P3, P2 and P1 are reassembled on AW2, and P5 and P4 are reassembled on AW1 and AW3, respectively. In addition, considering the connection between the three stages, the first-come-first-served (FCFS) heuristic method is used to determine the order of components in the reprocessing stage and the order of remanufactured products in the reassembly stage. Due to the specificity of RL, the allocation of RL does not need to be considered. Only when the reprocessing time caused by degradation exceeds t RMA , RMA is performed.

[0081] The quality of the initial solution has a great influence on the performance of the metaheuristic algorithm. Compared with the completely random initialization method, the initialization method based on specific problems can often obtain better results in acceptable time. Therefore, this embodiment proposes a new constructive heuristic method and MLB strategy to generate high-quality initial solutions.

[0082] A, first, a constructive heuristic method is used to generate the first and second layers of individuals.

[0083] According to a specific sorting rule, I EOL products are sorted and represented as a sequence θ = {P θ(1) ,...,P θ(G) ,...,P θ(I)}. P θ(h) represents the hth product in the sequence θ, where h∈{1,...,I}. Second, the first G products of the sequence θ are assigned to G parallel DWs in turn. Then, for the remaining products of the sequence θ, from P θ(G+1) to P θ(I) , the possible insertion positions of the product on the DWs are checked in turn, and the maximum departure time of the reprocessing stage caused by the current insertion position is calculated. Finally, P θ(h) is inserted into the position that minimizes the maximum departure time. The four sorting rules used in this embodiment are as follows, one of which is selected for execution:

[0084] (1) LTT (Longest Total Time) rule: products are sorted in non-increasing order according to their total processing time TT i , the formula of which is shown in equation (32):

[0085]

[0086] (2) STT (Shortest Total Time) rule: products are sorted in non-decreasing order according to their total processing time TT i .

[0087] (3) LSDT (Long-Short Disassembly Time) rule: First, the products are sorted in non-increasing order of their disassembly times, and then the first and the last products are iteratively selected from the sorted sequence until all products are selected. This rule attempts to reduce the idle time by assigning products with large difference in disassembly time to different DWs. For example, if the products are sorted in non-increasing order of their disassembly times as 123456, then the final ordering is 162534.

[0088] (4) LSTT (Long-Short Total Time) rule: The only difference between this rule and the LSDT rule is that the products are sorted in non-increasing order of their total times instead of disassembly times. That is, first, the products are sorted in non-increasing order of their total processing times, and then the first and the last products are iteratively selected from the sorted sequence until all products are selected, generating the final ordering.

[0089] B, second, a machine load balancing strategy is employed to generate the third layer of the individual.

[0090] By the above constructive heuristic method, the allocation scheme of DWs and the disassembly sequence of products in each initial solution can be determined. However, in the third layer of the solution, if the elements representing the AW allocation are randomly generated, the quality of the solution and the convergence speed of the algorithm can be reduced. In some extreme cases, most of the remanufactured products can be allocated to the same AW, resulting in other AWs being completely idle. Therefore, the machine load balancing (MLB) strategy is proposed in this embodiment to balance the load of AWs, and the main steps are as follows:

[0091] (1) Randomly generate the elements ξ h from the reassembly machine index range {1,..,R} in turn, where h e {1,...,I} and R is the total number of reassembly machines and I is the total number of products.

[0092] (2) Calculate the total reassembly time of each reassembly machine, and denote the reassembly machine with the maximum total reassembly time as AW max , and denote the reassembly machine with the minimum total reassembly time as AW min ; if the total reassembly times of multiple AWs are the same, one of them is randomly selected.

[0093] (3) If AW max allocates the most products and AW min allocates the least products, or if AW max allocates the least products and AW min allocates the least products, then step (4) is performed; otherwise, the process is ended, the third layer is output, and the individual initialization is completed.

[0094] (4) randomly select one product from AW max and assign it to AW min , go back to step (2).

[0095] An example of executing the MLB strategy is shown below. Initially, P1, P3, P5, P6 are assigned to AW1, and P2, P4 are assigned to AW3. The reassembly times of P1, P2, P3, P4, P5, P6 are 35, 25, 38, 37, 30, 32 respectively. As shown in Figure 6 , after executing the MLB strategy, the number of products assigned to AW1 is reduced from 4 to 2. Obviously, the AW utilization of the reassembly workshop is improved.

[0096] Step 3.2, calculate the fitness value of each individual in the population. Since a smaller C max value represents a better solution, the fitness value is taken as the reciprocal of the makespan C max in this embodiment.

[0097] Step 3.3, sort the entire population in non-ascending order based on the fitness value, and divide the population into a first sub-population (sub-population 1) and a second sub-population (sub-population 2) according to the sorting result. The fitness value of the individuals in the first sub-population is greater than that of the individuals in the second sub-population. Let sub-population 1 be the top N1 better individuals, and sub-population 2 be the remaining N-N1 individuals. N1 = Ceil(p-N), and p represents the proportion of butterflies from sub-population 1. Ceil(p-N) represents the smallest integer not less than p-N.

[0098] Step 3.4, execute the migration operator on the first sub-population and update the first sub-population using the greedy acceptance strategy; execute the adjustment operator on the second sub-population and update the second sub-population using the greedy acceptance strategy.

[0099] In each iteration of the basic monarch butterfly optimization algorithm (MBO), each element of each butterfly in sub-population 1 is updated by the migration operator. However, since most individuals in sub-population 1 have high quality, modifying the three levels of elements may cause the quality of most individuals to decrease. In order to reduce excessive disturbance, the migration operator is improved as follows in this embodiment.

[0100] First, perform type I swap mutation on each individual of sub-population 1. Specifically, based on the elements of the first and second levels, randomly select a disassembly machine that has two or more products being disassembled. Then, randomly select two products on the disassembly machine and swap their positions in the first level. For example, Figure 7As shown, the disassembling machine with index 2 is selected, and the products being disassembled on the disassembling machine are products 4 and 5. Therefore, products 4 and 5 are exchanged in position.

[0101] Secondly, the elements of the third layer are updated using formula (33).

[0102]

[0103] wherein, represents the hth element of the third layer of the st individual in subpopulation 1 in the t+1th generation. and represents the hth element of the third layer of the st individual in subpopulation 1 in the tth generation, wherein s1 and s2 represent the individuals randomly selected from subpopulation 1 and subpopulation 2, respectively. p is a parameter representing the proportion of butterflies from subpopulation 1. r = rand * peri, wherein rand is a random number generated from [0, 1], and peri is the migration period.

[0104] Finally, the greedy acceptance strategy is applied to each individual in subpopulation 1. The fitness value of each individual after the migration operation is calculated. If the fitness value after migration is higher than that before migration, the updated individual is selected to enter the next generation; otherwise, the original individual is retained to enter the next generation.

[0105] Unlike subpopulation 1, the individuals in subpopulation 2 have relatively low quality. Therefore, the improved butterfly adjustment operator adopts a large-scale element disturbance strategy to efficiently search the solution space.

[0106] Firstly, type II exchange mutation or insertion mutation is randomly performed on the first layer of each individual in subpopulation 2 to change the product sequence, as shown in Figure 8 (a) and Figure 8 (b). For type II exchange mutation, two different elements 3 and 1 are randomly selected and their positions are exchanged. For insertion mutation, element 4 is randomly selected and inserted into a random position between elements 5 and 3.

[0107] Secondly, the elements of the second layer are updated using formula (34) and rounded off:

[0108]

[0109] wherein, represents the hth element of the second layer of the st individual in subpopulation 2 in the t+1th generation. represents the hth element of the second layer of the best individual in the whole population in the tth generation. represents the hth element of the second layer of the s2th individual randomly selected in sub-population 2. BAR is the adjustment rate. λ is set to 1.5 in Lévy flight. ε represents the weight coefficient, which is defined in equation (35):

[0110] ε = S max / t 2 (35)

[0111] where S max is the maximum step size, which is set to 1 in this embodiment.

[0112] Then, the elements of the third layer are updated in the same way as the second layer, that is, the elements of the second layer are updated using equation (34) and rounded.

[0113] Finally, the greedy acceptance strategy is applied to each individual of sub-population 2.

[0114] Step 3.5, merge the updated first sub-population and the second sub-population as a new population, if the iteration end condition (the end condition can be the maximum number of iterations) is not reached, return to step 3.3 to continue iteration; otherwise, output the individual with the maximum fitness value in the new population as the optimal three-stage remanufacturing blocking scheduling scheme.

[0115] In this embodiment, a constructive heuristic method based on problem characteristics and a new machine load balancing strategy are introduced based on the monarch butterfly optimization algorithm to generate high-quality initial solutions. In addition, two improved operators suitable for the representation mechanism of the solution are designed to achieve a comprehensive search of the solution space.

[0116] In order to demonstrate the advantages of the improved monarch butterfly optimization (MMBO) algorithm proposed in the present application, the following experiments are performed. First, the optimal algorithm parameter combination and ordering rule are determined through experiments to optimize the performance of the algorithm as much as possible. Then, the branch and bound solver GUROBI is called to solve the proposed model, and the results are compared with those of the MMBO algorithm. Next, the MMBO algorithm is compared with other benchmark algorithms to verify its superiority. The MMBO algorithm is written in Python language, and the experiment is run on a PC with a 3.20GHz AMD Ryzen 7 CPU, 16GB RAM and Windows 11 64-bit system.

[0117] I. Experimental design.

[0118] The method of randomly generating instances is used to test the comparative algorithm in this embodiment. In the generation of instances, four parameters such as product number, part / RL number, DW number and AW number are given different levels of values, respectively I ∈ {5, 10, 15, 20, 30}, J ∈ {3, 4, 5}, G ∈ {3, 4, 5}, R ∈ {3, 4, 5}. Then, they are combined with each other to form different test instances, which can be represented as ti(I / J / G / R). For each test instance, the α of all RMs is set to 0.1, and t RMA is set to 8. K j 、 The values of the parameters are randomly generated from the integer sets [2, 5], [25, 50], [10, 30], [25, 50], respectively.

[0119] The experimental results of each test instance are evaluated using the relative percentage deviation (RPD), which is calculated as follows:

[0120]

[0121] In the formula, C max represents the maximum completion time obtained by a certain algorithm on a specific test instance, represents the best C max obtained by all comparative algorithms on the same test instance.

[0122] II. Parameter combination of the algorithm

[0123] The parameters used by the MMBO algorithm include migration period peri, migration ratio p, butterfly adjustment rate BAR, population size N and maximum iteration number N it . In order to determine the optimal combination of peri, p and BAR, the Taguchi method is used to divide the different values of the parameters into levels, as shown in Table 2. In this experiment, ti(20 / 3 / 4 / 4) is used as the test instance, and the algorithm is run independently 5 times on this instance. To ensure the convergence of the algorithm, N is set to 40, and N it is set to 800. In addition, only the LTT sorting rule is selected for testing.

[0124] Table 3 shows the average C max of different parameter level combinations. Table 4 shows the average C max of each parameter at different levels. The larger the range value, the greater the impact of the parameter on the performance of the algorithm. From Figure 9 it can be seen that, Figure 9 the broken line in the figure corresponds to the parameters peri, p and BAR from left to right, and when the levels of peri, p and BAR are 1, 2 and 1 respectively, the MMBO algorithm performs best, with the corresponding parameter values being 1, 1 / 2 and 5 / 12. Therefore, this parameter combination will be used in the subsequent experiments.

[0125] Ranking of different parameter values

[0126] Parameter Parameter level 1 Parameter level 2 Parameter level 3 peri 1 65 75 p 512 1 / 2 712 BAR 512 1 / 2 712

[0127] C of different ranking combinations max Average

[0128] Level combination peri p BAR Average C max ]] C1 1 1 1 366.96 C2 1 2 2 367.63 C3 1 3 3 373.44 C4 2 1 3 370.39 C5 2 2 1 367.98 C6 2 3 2 372.06 C7 3 1 2 370.31 C8 3 2 3 368.13 C9 3 3 1 370.45

[0129] C of parameter at different rankings max Average

[0130] Level peri p BAR 1 369.34 369.22 368.46 2 370.14 367.91 370.00 3 369.63 371.98 370.65 Range value 0.80 4.07 2.19

[0131] III. Evaluation of the constructive heuristic method under different ranking rules.

[0132] To determine the best ranking rule for the improved NEH-based heuristic method, the test instances were run to compare the four ranking rules. The population size was set to 40 and the maximum number of iterations was set to 800. Each test instance was run independently for 5 times. Table 5 records the best relative percentage deviation (RPD) value and the average RPD value. The MMBO algorithms using the four ranking rules are denoted as MMBO_LTT, MMBO_STT, MMBO_LSDT and MMBO_LSTT, respectively.

[0133] As shown in Table 5, for the small test instances containing 5 products and the medium test instances containing 10 products, the MMBO algorithms using the four ranking rules all obtained the best or near-optimal best RPD. With the increase of the size of the test instances, MMBO_LTT and MMBO_LSTT performed relatively worse in terms of the best RPD, while MMBO_STT and MMBO_LSDT performed better or worse. In terms of the average RPD, MMBO_STT and MMBO_LSDT still performed better or worse on different test instances. However, MMBO_LSDT performed the best in terms of the sum of the best RPD and the average RPD. Therefore, MMBO_LSDT was selected as the benchmark algorithm in the subsequent experiments.

[0134] Comparison of MMBO using different ranking rules

[0135]

[0136] Note: The values in the table have scientific notation e-02.

[0137] IV. Model evaluation.

[0138] The GUROBI solver is called to solve the model to verify its effectiveness. Meanwhile, the results obtained by the GUROBI solver are compared with the results obtained by the MMBO_LSDT algorithm. The deterioration model and the three-stage remanufacturing blocking scheduling model proposed in the present application can be simplified as:

[0139] min f = C max

[0140] s.t. x e X

[0141] where x is the decision variable vector and X is the feasible region defined by equations (1)-(31). This model is solved directly by the GUROBI solver. Experiments are conducted on three small test instances (ti(5 / 3 / 3 / 3), ti(5 / 4 / 4 / 4), ti(5 / 5 / 3 / 4)) and three medium test instances (ti(10 / 3 / 4 / 4), ti(10 / 4 / 3 / 4), ti(10 / 5 / 5 / 4)). The maximum CPU time for the GUROBI solver and the MMBO_LSDT algorithm is set to 1200 seconds.

[0142] Table 6 records the C max values obtained by the GUROBI solver and the MMBO_LSDT algorithm. For small test instances, the GUROBI solver can obtain the optimal C max value in a shorter CPU time. However, for medium test instances, the GUROBI solver cannot obtain the optimal C max value within 1200 seconds on ti(10 / 3 / 4 / 4) and ti(10 / 5 / 5 / 4). In contrast, the MMBO_LSDT algorithm can obtain the optimal or near-optimal C max value within a reasonable CPU time on both small and medium test instances. Therefore, the GUROBI solver is suitable for small-scale problem solving but not for large-scale problem solving. The MMBO algorithm proposed in the present application is suitable for both small-scale and large-scale problem solving.

[0143] Table 6 records the C max values obtained by the GUROBI solver and the MMBO_LSDT algorithm within 1200 seconds

[0144]

[0145] Note: The symbol ' / ' in the table indicates that there is no output within the limited CPU time.

[0146] Five, algorithm evaluation.

[0147] To evaluate the effectiveness and superiority of the MMBO algorithm, it is compared with other benchmark algorithms. The selected benchmark algorithms include improved flower pollination algorithm (IFPA), improved genetic algorithm (IMGA), hybrid genetic algorithm based on variable neighborhood search (GAVNS), and improved artificial bee colony algorithm (IABC). The reasons for selecting the above algorithms are as follows: first, the problem solved in this experiment is a discrete single-objective problem, so the benchmark algorithm should be designed for solving this kind of problem to avoid excessive modification; second, the problem handled by the benchmark algorithm should be related to remanufacturing scheduling to ensure a fair comparison within a similar application field; third, all benchmark algorithms are advanced algorithms whose effectiveness has been verified.

[0148] According to the pre-experiment, the population size and the maximum number of iterations of all algorithms are set to 40 and 800, respectively. Other parameters are set according to the suggestions in the respective literature. Each algorithm is independently run 5 times on each test instance.

[0149] The experimental results are recorded in Table 7 and Table 7 (continued), where Best, Avg, and Var represent the best RPD value, the average RPD value, and the RPD value variance, respectively. MMBO_LSDT obtains the best RPD value on all test instances, and on medium and large test instances, no benchmark algorithm can achieve the same best RPD value as MMBO_LSDT. This indicates that the MMBO_LSDT algorithm has a significant advantage in searching for the optimal solution. In terms of the average RPD value, MMBO_LSDT performs best on 14 out of 15 test instances, further verifying its excellent performance in obtaining the best RPD value. In addition, MMBO_LSDT has a smaller RPD value variance, indicating that it has higher stability in solving this problem.

[0150] To more intuitively show the performance differences between algorithms, Figure 10 boxplots of five algorithms on medium and large test instances are plotted. From Figure 10 (a) to Figure 10 (l), it can be seen that the lower edge of the box of MMBO_LSDT is always at the lowest position, indicating that it can always obtain the best RPD value. At the same time, the entire box of MMBO_LSDT is always at the lowest position, indicating that it can obtain better solutions at each run. In summary, the MMBO_LSDT algorithm has higher efficiency and stability in solving this problem, significantly outperforming other benchmark algorithms.

[0151] Table 7 RPD values of MMBO algorithm and other benchmark algorithms

[0152]

[0153]

[0154] Table 7 and Continued Table 7. The best and average RPD values are followed by the scientific notation e-02.

[0155]

[0156] Note: The best and average RPD values in Table 7 and Continued Table 7 are followed by the scientific notation e-02.

[0157] The present application proposes a new remanufacturing scheduling problem for a three-stage remanufacturing system integrating disassembly, reprocessing and reassembly. The problem considers machine blocking, machine deterioration and rate-modifying activities (RMAs) simultaneously. The present application only considers the restoration of machines to "nearly new" condition to simplify the complexity of the scheduling problem. To solve this NP-hard problem, a new deterioration model is proposed to determine the actual processing time and the location and number of RMAs on each machine. Subsequently, a blocking scheduling model is constructed to minimize the makespan. To obtain efficient and robust solutions, an improved monarch butterfly optimization algorithm is proposed. The algorithm contains constructive heuristics and machine load balancing strategies for solution initialization, and two improved operators are designed to enhance the search ability of the algorithm. Finally, the comparison experiments with four benchmark algorithms verify the significant effectiveness and superiority of the MMBO algorithm in solving the problem proposed in the present application

[0158] The technical features of the above-described embodiments can be combined in any manner. To make the description concise, not all possible combinations of the technical features in the above-described embodiments are described, but it should be considered that any combination of the technical features is within the scope of the present disclosure as long as the combination does not result in contradictions.

[0159] The above-described embodiments only express several implementation manners of the present application, and the description is relatively specific and detailed, but it should not be understood as a limitation on the scope of the present application. It should be noted that, for those skilled in the art, without departing from the concept of the present application, a number of modifications and improvements can be made, which are all within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the appended claims.

Claims

1. A three-stage remanufacturing blocking scheduling method based on machine deterioration and maintenance strategy, characterized in that, The three stages include a disassembly stage, a reprocessing stage and a reassembly stage, and the three-stage remanufacturing blocking scheduling method based on machine deterioration and maintenance strategy comprises: The rate adjustment activity is taken as a maintenance strategy of the reprocessing machine in the reprocessing stage, and a deterioration model considering time-dependent deterioration and maintenance strategy is constructed; A three-stage remanufacturing blocking scheduling model is constructed based on the deterioration model of the reprocessing machine, with the objective of minimizing the completion time, and constraints of the disassembly stage, the reprocessing stage and the reassembly stage are set respectively; The monarch butterfly optimization algorithm is used to solve the three-stage remanufacturing blocking scheduling model, and an optimal three-stage remanufacturing blocking scheduling scheme is output, and the monarch butterfly optimization algorithm uses a greedy acceptance strategy to update the sub-population; The deterioration model considering time-dependent deterioration and maintenance strategy comprises: The actual reprocessing time of the part is calculated according to the following formula: (1) In the formula, Indicates the first The first of the scrapped products The part in the first The first reprocessing line The actual reprocessing time on the reprocessing machine. Indicates the first The first of the scrapped products The part in the first The first reprocessing line The expected reprocessing time on the reprocessing machine. The degradation rate of the reprocessing machine. Indicates the first The first of the scrapped products The part in the first The first reprocessing line The reprocessing interval on the reprocessing machine. For indexing obsolete products, , The total number of scrapped products. For part indexing or reprocessing line indexing, , The number of parts for each scrapped product or the number of parallel lines in the reprocessing line. For reprocessing machine indexing, , Indicates the first The total number of reprocessing machines on each reprocessing line; wherein the reprocessing time interval is calculated as follows: (2) In the formula, , , , represents the start time of reprocessing of the first part of the first scrapped product on the first reprocessing machine of the first reprocessing line, represents the completion time of the first maintenance strategy of the first reprocessing machine of the first reprocessing line, is a maintenance strategy index, is a decision variable, specifically, before the first part of the first scrapped product is reprocessed on the first reprocessing machine of the first reprocessing line, if the first maintenance strategy of the first reprocessing machine of the first reprocessing line is the most recent maintenance strategy executed, ; otherwise ; otherwise ; otherwise​​​​​​​​​​​​​ When maintaining strategy index At this time, it indicates the assumed maintenance strategy for the 0th time. equals first in the The first reprocessing line The start time of reprocessing of parts on the reprocessing machine is shown in formula (3), where , : (3) Equation (4) ensures that the completion time of a maintenance policy only makes sense if the maintenance policy is actually executed, where , , , represents an infinite large positive number, is a decision variable, specifically if the maintenance policy of the reprocessing machine of the reprocessing line is executed on the reprocessing machine of the reprocessing line, then ; otherwise ; (4) And And The relationship between the values of the parameters a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, (5) Equations (6) and (7) specify the number of maintenance strategies performed on each reprocessing machine, where , , , is a decision variable, specifically if the th maintenance strategy of the th reprocessing machine of the th reprocessing line is performed on the th reprocessing machine of the th reprocessing line, then ; otherwise ; equation (8) ensures that there is and only one maintenance strategy closest to any one part before it is reprocessed on a reprocessing machine, where , , : (6) (7) (8) Formula (9) constraint will be in the first line of reprocessing machine of the first reprocessing parts on the reprocessing machine of the first reprocessing line due to deterioration caused by reprocessing time greater than the first reprocessing line of the first reprocessing machine to execute maintenance strategy, wherein , , , the execution time of the maintenance strategy represents the first reprocessing line of the first reprocessing machine of the first maintenance strategy completion time: (9) (10) Equation (10) further constrains the rework time for a part undergoing rework on a rework machine to be less than , where , , .

2. The three-phase remanufacturing blocking scheduling method based on machine degradation and maintenance strategy according to claim 1, characterized in that, The three-stage remanufacturing blocking scheduling model is constructed as follows: (1) The objective function is constructed as follows: (11) wherein, is the objective function, i.e. minimizing the makespan, is the makespan of the three-phase remanufacturing blocking scheduling, is the completion time of the reassembly of the th remanufactured product, is the index of the remanufactured product, , is the total number of remanufactured products; (2) The constraints of the disassembly stage are set as follows: (12) (13) (14) (15) Equation (12) constrains each end-of-life product to be disassembled on only one disassembly machine, where , is a decision variable, specifically if the th end-of-life product is disassembled on the th disassembly machine; otherwise ; is the disassembly machine index, , is the total number of disassembly machines. Equation (13) and Equation (14) define the disassembly sequence of the end-of-life products, where , , is the index of the end-of-life product, is the decision variable, specifically, on the th disassembly machine, if the th end-of-life product is disassembled before the th end-of-life product, then ; otherwise ; is the decision variable, specifically, on the th disassembly machine, if the th end-of-life product is disassembled before the th end-of-life product, then ; otherwise ; is the decision variable, specifically, if the th end-of-life product is disassembled on the th disassembly machine, then ; otherwise ; Formula (15) constrains that when two scrapped products are assigned to the same dismantling machine, they are dismantled sequentially. , , Indicates the first The completion time for dismantling a single scrapped product. Indicates the first The dismantling time of each scrapped product Indicates the first The completion time for dismantling a single scrapped product. It is an infinitely large positive number; (3) The constraints of the reprocessing stage are set as follows: (16) (17) (18) (19) (20) (21) (22) Equation (16) constrains that the reprocessing of a product must start after the disassembly of the product is completed, where , , represents the start time of the reprocessing of the i-th part of the j-th end-of-life product on the 1st reprocessing machine of the i-th reprocessing line, is the part index or the reprocessing line index, is the number of parts per end-of-life product or the number of parallel reprocessing lines.​​​ Equations (17) and (18) constrain the relationship between the departure time and the completion time of a part by considering the blocking effect, where , , , Cij represents the completion time of the jth part of the ith scrapped product reprocessed on the ith reprocessing line, the jth reprocessing machine of the ith reprocessing line, Cij represents the completion time of the jth part of the ith scrapped product reprocessed on the ith reprocessing line, the jth reprocessing machine of the ith reprocessing line, Cij represents the completion time of the jth part of the ith scrapped product reprocessed on the ith reprocessing line, the jth reprocessing machine of the ith reprocessing line, is the index of the reprocessing machine, is the total number of reprocessing machines of the ith reprocessing line, Cij represents the completion time of the jth part of the ith scrapped product reprocessed on the ith reprocessing line, the jth reprocessing machine of the ith reprocessing line, Cij represents the completion time of the jth part of the ith scrapped product reprocessed on the ith reprocessing line, Cij represents the completion time of the jth part of the ith scrapped product reprocessed on the ith reprocessing line, the jth reprocessing machine of the ith reprocessing line.​​​​​​​​​​​​​​​​​​​​ Equation (19) constrains the start time of a part's rework on a rework machine to be equal to its exit time from the previous rework machine, where , , , represents the completion time of the rthpart of the nthscrap product on the sthrework machine of the rthrework line. ​​​​ Formula (20) constrains the time relationship between parts reprocessed on the same reprocessing machine by taking into account the blocking effect. , , , Indicates the first The first of the scrapped products The part in the first The first reprocessing line The start time of reprocessing on the reprocessing machine. For decision variables, specifically in the first... The first reprocessing line On the reprocessing machine, if the first The first of the scrapped products The part in the first The first of the scrapped products If a part was previously reprocessed, then ;otherwise ; Equation (21) constrains the time relationship between the maintenance policy and its preceding parts, where , , , , represents the completion time of the kth maintenance policy of the jth reprocessing machine of the ith reprocessing line, is the execution time of the maintenance policy, is a decision variable, specifically, whether the kth maintenance policy of the jth reprocessing machine of the ith reprocessing line is the most recently executed maintenance policy before the jth reprocessing machine of the ith reprocessing line reprocesses the kth part of the nth end-of-life product, ; otherwise ; is a decision variable, specifically, whether the kth maintenance policy of the jth reprocessing machine of the ith reprocessing line is the most recently executed maintenance policy before the jth reprocessing machine of the ith reprocessing line reprocesses the kth part of the nth end-of-life product, ; otherwise ; is the maintenance policy index;​​​​​​​​​​​​​​​​​ Equation (22) constrains the rework sequence between parts, where , , , is a decision variable, specifically, whether the thpart of the thscrap product is reworked before the thpart of the thscrap product at the thrework machine of the thrework line; otherwise ; otherwise ; (4) The constraints of the reassembly stage are set as follows: (23) (24) (25) (26) (27) Equation (23) constrains each remanufactured product to be reassembled on only one reassembly machine, where , is a decision variable, specifically if the th remanufactured product is reassembled on the th reassembly machine, then ; ; is the reassembly machine index, , is the total number of reassembly machines; Formula (24) constrains the sequence of reprocessing and reassembly of the product, where , For the first The reassembly time of a remanufactured product; Equation (25) constrains that two remanufacturing products cannot be reassembled on one reassembly machine simultaneously, where, , , is the completion time of the reassembly of the th remanufacturing product, is the reassembly time of the th remanufacturing product, is a decision variable, specifically, if the th remanufacturing product is reassembled on the th reassembly machine; ; is a decision variable, specifically, if the th remanufacturing product is reassembled on the th reassembly machine before the th remanufacturing product; otherwise ; Equations (26) and (27) constrain the reassembly order of products, where , , are decision variables, specifically, on the th reassembly machine, if the th remanufactured product is reassembled before the th remanufactured product, then ; otherwise .

3. The three-phase remanufacturing blocking scheduling method based on machine degradation and maintenance strategy according to claim 1, characterized in that, The monarch butterfly optimization algorithm is used to solve the three-stage remanufacturing blocking scheduling model, and an optimal three-stage remanufacturing blocking scheduling scheme is output, and the monarch butterfly optimization algorithm uses a greedy acceptance strategy to update the sub-population; (1) Set the population size as , and initialize individuals by using constructive heuristic method and machine load balancing strategy, and randomly initialize the remaining individuals, each of which represents a three-stage remanufacturing blocking scheduling scheme; (2) The fitness value of each individual in the population is calculated, and the fitness value is the reciprocal of the minimum completion time; (3) The whole population is sorted in non-ascending order based on the fitness value, and the population is divided into a first sub-population and a second sub-population according to the sorting result, and the fitness value of the individual in the first sub-population is greater than that in the second sub-population; (4) The migration operator is executed on the first sub-population, and the first sub-population is updated using the greedy acceptance strategy; the adjustment operator is executed on the second sub-population, and the second sub-population is updated using the greedy acceptance strategy; (5) The updated first sub-population and second sub-population are combined as a new population, and if the iteration end condition is not reached, step (3) is returned to continue iteration; otherwise, the individual with the maximum fitness value in the new population is output as the optimal three-stage remanufacturing blocking scheduling scheme.

4. The three-phase remanufacturing blocking scheduling method based on machine degradation and maintenance strategy according to claim 3, characterized in that, The individual is represented by a three-layer structure, the first layer represents product index, the second layer represents disassembly machine index, and the third layer represents reassembly machine index, and the number of elements in the three layers corresponds; The elements corresponding to the positions in the first layer and the second layer represent that the product is disassembled on the disassembly machine, and if the elements with the same value in the second layer correspond to multiple elements in the first layer, it means that multiple products are disassembled on the disassembly machine, and the products in the front position are disassembled first; The elements corresponding to the positions in the first layer and the third layer represent that the product is reassembled on the reassembly machine, and if the elements with the same value in the third layer correspond to multiple elements in the first layer, it means that multiple products are reassembled on the reassembly machine, and the products in the front position are reassembled first.

5. The three-phase remanufacturing blocking scheduling method based on machine degradation and maintenance strategy according to claim 4, characterized in that, The method for initializing the machine load balancing strategy by using the constructive heuristic method an individual, comprising: A constructive heuristic method is used to generate the first layer and the second layer of the individual; A machine load balancing strategy is used to generate the third layer of the individual, comprising: (1) randomly generating elements of the third layer from the reassembled machine index range in turn is the total number of reassembled machines, is the total number of products;​​​ (2) calculating the total reassembly time of each reassembly machine, and recording the reassembly machine with the maximum total reassembly time as , and recording the reassembly machine with the minimum total reassembly time as ; (3) if the most products are allocated and the least products are allocated, or if the least products are allocated and the least products are allocated, then step (4) is performed; otherwise the process is ended, the third layer is output, and the individual initialization is completed. (4) randomly select one product from and assign it to , go to step (2).

6. The three-phase remanufacturing blocking scheduling method based on machine degradation and maintenance strategy according to claim 5, characterized in that, The sorting rule of the constructive heuristic method is as follows: The products are sorted in a non-increasing order according to the total processing time of the products; Or, the products are sorted in a non-decreasing order according to the total processing time of the products; Or, first, the products are sorted in a non-increasing order according to the disassembly time of the products, and then, the first product and the last product are selected from the sorted sequence iteratively until all products are selected, to generate a final sorting; Or, first, the products are sorted in a non-increasing order according to the total processing time of the products, and then, the first product and the last product are selected from the sorted sequence iteratively until all products are selected, to generate a final sorting.

7. The three-phase remanufacturing blocking scheduling method based on machine degradation and maintenance strategy according to claim 4, characterized in that, The migration operator is executed on the first sub-population, including: Based on the elements of the first layer and the second layer, a disassembly machine is randomly selected, the selected disassembly machine has two or more products being disassembled, then two products are randomly selected on the selected disassembly machine, and the positions of the selected two products are exchanged in the first layer; The elements of the third layer are updated using formula (33): (33) in, Indicates the first In the first generation, the first subpopulation The third layer of individuals One element, and They represent the first time. In the first subpopulation 1 of the generation The individual and the second subpopulation The third layer of individuals There are elements, among which and These represent individuals randomly selected from the first and second subpopulations, respectively. It is a parameter representing the proportion of butterflies from the first subpopulation. It is a periodic parameter, where From Random numbers generated in the process, It is the migration cycle.

8. The three-phase remanufacturing blocking scheduling method based on machine degradation and maintenance strategy according to claim 4, characterized in that, The adjustment operator is executed on the second sub-population, including: For each individual in the second sub-population, a type II exchange mutation or an insertion mutation is randomly selected to be performed on the first layer, for the type II exchange mutation, two different elements are randomly selected and their positions are exchanged; for the insertion mutation, a random element is selected and inserted into a random position; For each individual in the second sub-population, the elements of the second layer and the third layer are updated using formula (34) respectively and rounded to the nearest integer: (34) In the formula, Indicates the first In the second generation, the second subpopulation The second or third layer of an individual One element, Indicates the first In the generation, the second or third layer of the best individual in the entire group One element, Indicates the first randomly selected subpopulation from the second subpopulation The second or third layer of an individual One element, Indicates the weighting coefficient. Set to 1.5 during Lévy flight. From Random numbers generated in the process, It is a parameter representing the proportion of butterflies from the first subpopulation. This is the adjustment rate.

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