A remanufacturing system scheduling method diversifying reprocessing routes

Abstract

The application discloses a remanufacturing system scheduling method of diversified reprocessing routes, and the remanufacturing system comprises a disassembly subsystem, a reprocessing subsystem and a recombination subsystem. In the establishment of a scheduling model, the coordination among the three subsystems is considered, and diversified reprocessing routes are also considered. Then, a hybrid meta-heuristic algorithm is used to solve the scheduling model, the number and sequence of products to be disassembled (recombined) on the disassembly (recombination) workstation are determined, and suitable reprocessing routes are selected to repair defective components with different damage types and damage degrees, and the performance of the solution is improved through the integration of adaptive parameters, efficient migration and mutation operators, local search strategies and restart strategies. The application can quickly obtain a better scheduling scheme, and improves the coordination and efficiency of the remanufacturing system.

Description

Technical Field

[0001] This application belongs to the field of remanufacturing technology, and in particular relates to a remanufacturing system scheduling method with diversified reprocessing routes. Background Technology

[0002] In recent years, remanufacturing has become increasingly popular due to its significant environmental and economic benefits. As an important component of sustainable development, remanufacturing for end-of-life (EOL) products has received widespread attention. In a remanufacturing system, EOL products are restored to a state similar to new products through a series of operations, including complete disassembly, reprocessing, and reassembly. Remanufacturing not only provides new products at a lower cost but also maximizes resource utilization and reduces waste emissions. Successful industrial applications have already been found in various remanufacturing fields, including automotive, electronics, and aerospace remanufacturing.

[0003] EOL (Exhausted Online) products processed by a Remanufacturing System (RMS) can be restored to the same appearance and quality as new products, and may even have better performance and user experience. The Remanufacturing System consists of three coordinated subsystems: a disassembly subsystem, a reprocessing subsystem, and a reassembly subsystem. Unlike traditional manufacturing, remanufacturing utilizes EOL products as raw materials. It is worth noting that the operating conditions and usage processes of EOL products differ from those during their lifespan, making the remanufacturing process more complex. For example, a batch of EOL products often exhibits different types and degrees of damage, leading to diverse reprocessing routes. Therefore, to achieve more efficient remanufacturing system scheduling, the three subsystems should be considered comprehensively, the number of disassembled (assembled) products should be rationally allocated, and the reprocessing route should be determined based on the damage status of the defective components.

[0004] Remanufacturing system scheduling has been extensively studied, but existing remanufacturing system scheduling models mainly focus on the scheduling of individual subsystems of EOL (End-of-Life) products, such as disassembly scheduling, reprocessing scheduling, and assembly scheduling. However, remanufacturing systems involve three subsystems, and considering only one subsystem during scheduling may lead to production conflicts.

[0005] Current research has considered the scheduling of subsystems in remanufacturing systems with different configurations; however, these studies only consider a single reprocessing route and ignore the type and extent of damage to defective components. The actual condition of EOL (End-of-Life) products varies depending on operating conditions, therefore, reprocessing routes are usually not fixed but can be flexibly adjusted according to the actual condition of the damaged components. Because reprocessing routes are not fixed, existing technologies cannot provide adequate scheduling solutions when diverse reprocessing routes exist. Summary of the Invention

[0006] The purpose of this application is to provide a scheduling method for remanufacturing systems with diversified reprocessing routes, which considers not only the coordination of remanufacturing subsystems but also the diversity of reprocessing routes. Based on this, a hybrid metaheuristic algorithm combining differential evolution and biogeographical optimization algorithms is proposed to effectively solve the model.

[0007] To achieve the above objectives, the technical solution of this application is as follows:

[0008] A remanufacturing system scheduling method with diversified reprocessing routes, wherein the remanufacturing system includes a disassembly subsystem, a reprocessing subsystem, and a reassembly subsystem, and the remanufacturing system scheduling method with diversified reprocessing routes includes:

[0009] Establish a mathematical model for the end time of disassembling and remanufacturing products at the disassembly workstation in the disassembly subsystem:

[0010]

[0011] in, This indicates the start time of the i-th product at the s-th disassembly workstation. This represents the end time of the i-th product at the s-th disassembly workstation. DT represents the number of times the i-th product is disassembled at the s-th disassembly workstation. i This represents the time required to disassemble the i-th product;

[0012] Establish a mathematical model for the end time of the reprocessing unit and the remanufactured product component in the reprocessing subsystem:

[0013]

[0014] in, This represents the end time corresponding to the k-th damage type of the j-th component of the i-th product being reprocessed in the n-th reprocessing unit on the v-th reprocessing route; This represents the start time corresponding to the k-th damage type of the j-th component of the i-th product being reprocessed in the n-th reprocessing unit on the v-th reprocessing route. This represents the number of times the j-th component of the i-th product is reprocessed for the k-th damage type in the n-th reprocessing unit on the v-th reprocessing route. This represents the time required to reprocess the j-th component of the i-th product with the k-th damage type on the n-th reprocessing unit of the v-th reprocessing route;

[0015] Establish a mathematical model for the end time of remanufactured products at the remanufacturing workstation in the remanufacturing subsystem:

[0016]

[0017] in, This represents the start time of the i-th product at the u-th reorganization workstation. RT represents the end time of the i-th product at the u-th reorganization workstation. i This represents the time required to reassemble the i-th product. This represents the number of times the i-th product is reassembled on the u-th reassembly workstation;

[0018] Establish a scheduling model with the optimization objective of minimizing the total completion time of all remanufactured products:

[0019]

[0020] Where TT represents the total completion time of all remanufactured products, I is the number of remanufactured product types, and U represents the number of remanufacturing workstations;

[0021] Solve the scheduling model to obtain the scheduling scheme for the remanufacturing system, and then perform scheduling according to the obtained scheduling scheme.

[0022] Furthermore, the solution to the scheduling model employs a hybrid metaheuristic algorithm, in which a habitat consists of two parts: the first part encodes the product allocation information for each disassembly and reassembly workstation, and the second part encodes the operation sequencing information for each subsystem.

[0023] The first part consists of two matrices, which represent the product allocation information of the disassembly or reassembly workstations respectively. The number of columns represents the number of product categories, and the number of rows represents the number of workstations in the disassembly or reassembly subsystem.

[0024] The second part consists of three matrices, which represent the operation sequence information of products or components in the three subsystems. The first and third matrices represent the disassembly and reassembly sequence of products in the disassembly and reassembly subsystems, respectively; the second matrix represents the reprocessing sequence and selected reprocessing route of components with different damage types in the reprocessing subsystem.

[0025] Furthermore, the hybrid metaheuristic algorithm includes:

[0026] Step 5.1: Initialize the population and parameters;

[0027] Step 5.2: Calculate the current adaptive probability, and select the mutation operator to be executed for the first part of the habitat based on the adaptive probability. The mutation operator includes two mutation operators: DE / best / 1 and DE / rand / 2.

[0028] Step 5.3: Execute the crossover operator;

[0029] Step 5.4: Update the product allocation information for the dismantling and reassembly workstations in the habitat;

[0030] Step 5.5: Calculate the immigration rate and emigration rate for each habitat, and apply the migration operator to the second part of the habitat.

[0031] Step 5.6: Calculate the mutation rate for each habitat and execute the mutation operator;

[0032] Step 5.7: Execute the local search strategy;

[0033] Step 5.8: Update the operation sorting information of products or components in the three subsystems;

[0034] Step 5.9: Determine if the restart conditions are met. If they are met, proceed to the next step; otherwise, proceed to step 5.11.

[0035] Step 5.10: Reinitialize the population using the restart strategy;

[0036] Step 5.11: Determine if the stopping condition is met. If it is, stop the iteration and output the optimal scheduling scheme. Otherwise, return to step 5.2 and start iterating again.

[0037] Furthermore, the adaptive probability is calculated using the following formula:

[0038]

[0039] Where P DE This represents the adaptive probability, where maxiter and t represent the maximum number of iterations and the current number of iterations, respectively.

[0040] Furthermore, the immigration rate and immigration rate are calculated using the following formulas:

[0041]

[0042]

[0043] Where λ o μ represents the emigration rate. o E represents the immigration rate. max and I max These represent the highest emigration rate and emigration rate, respectively, S o Let be the number of species in the o-th habitat, and NP be the maximum number of species.

[0044] Furthermore, the calculation of the mutation rate for each habitat includes:

[0045] The mutation rate for the optimal habitat in each generation is set to 0. The mutation rate for other habitats is calculated using the following formula:

[0046]

[0047] Where m max For the maximum mutation rate, G max m represents the probability of species abundance in the maximum habitat. o G represents the mutation rate of the o-th habitat. o Let be the survival probability of the o-th habitat.

[0048] Furthermore, the execution of the local search strategy includes:

[0049] In each iteration, a local search strategy based on two neighborhood structures is performed on the solutions of the previous preset proportion.

[0050] Furthermore, the reinitialization of the population using the restart strategy includes:

[0051] When the restart condition is triggered, the individual is randomly reinitialized;

[0052] The restart conditions are as follows:

[0053]

[0054] If the number of iterations of the unimproved solution exceeds RC, a restart strategy will be triggered, where NI0 is the maximum number of iterations allowed for the initial consecutive unimproved solutions, RN is the number of times the restart strategy is used, and RC is the maximum number of consecutive iterations of the unimproved solution.

[0055] This application proposes a remanufacturing system scheduling method with diversified reprocessing routes, considering the coordination between three subsystems and the diversity of reprocessing routes. It proposes a novel representation scheme and several improved HDEBBO algorithms, including adaptive parameters, a local search strategy, and a restart strategy. This results in a better solution to the scheduling model, determining the quantity and order of products to be disassembled (reassembled) on the disassembly (reassembly) workstation, and selecting appropriate reprocessing routes to repair defective components with different damage types and degrees. The HDEBBO algorithm improves its performance by integrating adaptive parameters, efficient migration and mutation operators, a local search strategy, and a restart strategy. This invention can quickly obtain better scheduling schemes, improving the coordination and efficiency of the remanufacturing system. Experimental results show that the HDEBBO algorithm proposed in this application outperforms other algorithms. Attached Figure Description

[0056] Figure 1 This is a flowchart of the remanufacturing system scheduling method with diversified reprocessing routes in this application;

[0057] Figure 2 This is a schematic diagram illustrating the solution process of the scheduling model in an embodiment of this application;

[0058] Figure 3 This is a schematic diagram of habitat coding in an embodiment of this application;

[0059] Figure 4 This is a schematic diagram of the migration operator in an embodiment of this application;

[0060] Figure 5 This is a schematic diagram of a mutation operator according to this application;

[0061] Figure 6 This is a schematic diagram of a partial search strategy in an embodiment of this application;

[0062] Figure 7 This is a graph comparing the performance of algorithms with different iteration counts in the embodiments of this application. Detailed Implementation

[0063] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0064] This application discloses a remanufacturing system scheduling method with diversified reprocessing routes, used for remanufacturing system scheduling. The remanufacturing system scheduling consists of three coordinated subsystems: a disassembly subsystem, a reprocessing subsystem, and a reassembly subsystem. The disassembly subsystem comprises multiple disassembly workstations, and the reassembly subsystem comprises multiple reassembly workstations. All disassembly (reassembly) workstations are identical, allowing processing to be completed at any disassembly (reassembly) workstation with identical processing times. Furthermore, each disassembly (reassembly) workstation can be considered a machine capable of completely disassembling (reassembling) EOL products. The reprocessing subsystem includes multiple reprocessing units, each containing a machine capable of performing specific operations. Defective components reprocessed through a series of reprocessing units can ultimately be restored to a new state. This application considers batch remanufacturing of EOL products, enabling batch processing of products across the three subsystems. It is noteworthy that a batch of identical products (or components) can only proceed to the next subsystem after being processed in the current subsystem. For a batch of EOL products, determine the quantity and sequence of products to be disassembled (reassembled) on the disassembly (reassembly) workstation, and select an appropriate reprocessing route to repair defective components with different damage types and degrees.

[0065] In one embodiment, such as Figure 1 As shown, a remanufacturing system scheduling method with diversified reprocessing routes is provided, including:

[0066] Step S1: Establish a mathematical model for the end time of disassembling and remanufacturing products at the disassembly workstation in the disassembly subsystem.

[0067] In order to transform the remanufacturing scheduling problem into a mathematical model, this application uses the following notation:

[0068] P i Let i represent the i-th product, i = 1, ..., I, where I is the number of remanufactured product types;

[0069] C ij This represents the j-th component of the i-th product, where j = 1, ..., J. i J i This represents the number of components in the i-th product;

[0070] This represents the k-th damage type (including damage type and damage severity) of the j-th component of the i-th product, where k = 1, ..., K. ij K ij It represents the number of damage types of the j-th component of the i-th product;

[0071] TT represents the total completion time for all remanufactured products;

[0072] BT represents the total budget completion time for all remanufactured products;

[0073] This indicates the start time of the i-th product at the s-th disassembly workstation;

[0074] This represents the end time of the i-th product at the s-th disassembly workstation;

[0075] DT i This represents the time required to disassemble the i-th product;

[0076] DW s Let S represent the s-th disassembly workstation, where s = 1, ..., S, and S is the number of disassembly workstations.

[0077] α i This represents a Boolean variable, where 1 indicates that the i-th product is the first to be disassembled in the disassembly subsystem, and 0 otherwise.

[0078] This means that the vth clause can The possible routes to restore the state to a completely new state are v = 1, ..., V, where V represents the number of possible routes;

[0079] express The nth reprocessing unit on the vth optional route was selected, where n = 1, ..., N. v N v This indicates the number of reprocessing units in the route;

[0080] Indicates in Further processing C ij Start time;

[0081] Indicates in Further processing C ij End time;

[0082] Indicates in Further processing C ij Time required;

[0083] Let this be a Boolean variable, where 1 indicates that the v-th optional route is selected for further processing. Otherwise, it is 0;

[0084] This represents a Boolean variable, where 1 indicates that the nth reprocessing unit of the vth optional route is used for reprocessing. Otherwise, it is 0;

[0085] λ vnv′n′ This represents a Boolean variable, where 1 indicates that the nth reprocessing unit in the vth optional route and the n'th reprocessing unit in the v'th optional route are the same, and 0 otherwise.

[0086] RW u Let represent the u-th reorganization workstation, u = 1, ..., U, where U represents the number of reorganization workstations;

[0087] This indicates the start time of the i-th product at the u-th reorganization workstation;

[0088] This represents the end time of the i-th product at the u-th reorganization workstation;

[0089] RT i This represents the time required to reorganize the i-th product.

[0090] The goal of the scheduling model proposed in this application is to minimize the total completion time TT of all remanufactured products and obtain the optimal scheduling scheme to maximize the efficiency of the remanufacturing system. Therefore, the established scheduling model is to provide a mathematical model of the total completion time of all remanufactured products, which is affected by three subsystems of TT.

[0091] This step is used to determine the end time for the disassembly workstation in the disassembly subsystem to disassemble and remanufacture products.

[0092] Remanufactured product P i The start time is calculated by formula (1), disassembling Pi The end time is calculated using formula (2):

[0093]

[0094]

[0095] in, This indicates the start time of the i-th product at the s-th disassembly workstation. This represents the end time of the i-th product at the s-th disassembly workstation. DT represents the number of times the i-th product is disassembled at the s-th disassembly workstation. i This represents the time required to disassemble the i-th product. DW s This represents the s-th disassembly workstation. In DW s Disassembling P on the workstation i' The end time is earlier than the disassembly of P. i Completed earlier. i' In DW s The i'th product previously disassembled on the workstation. In this embodiment, the remanufactured product is also simply referred to as a product.

[0096] As can be seen from the above formula, the start time of dismantling remanufactured products at the dismantling workstation in the dismantling subsystem is determined by whether there are any products being dismantled previously. If there are no products being dismantled, the i-th product is the first product to be dismantled; otherwise, it is determined by the end time of the previously dismantled products. The end time of the i-th product at the s-th dismantling workstation is related to the start time, the number of products to be dismantled, and the time required to dismantle the i-th product.

[0097] Step S2: Establish a mathematical model for the end time of the reprocessing and remanufacturing of product components in the reprocessing unit of the reprocessing subsystem.

[0098] This step is used to determine the end time for the reprocessing of remanufactured product components by the reprocessing unit in the reprocessing subsystem:

[0099] This represents the k-th damage type of the j-th component of the i-th product, requiring further processing. The start time and P i It is related to the disassembly time. Therefore, reprocessing The start and end times are calculated using formulas (3) and (4), respectively:

[0100]

[0101]

[0102] in, This represents the end time corresponding to the k-th damage type of the j-th component of the i-th product being reprocessed in the n-th reprocessing unit on the v-th reprocessing route; This represents the start time corresponding to the k-th damage type of the j-th component of the i-th product being reprocessed in the n-th reprocessing unit on the v-th reprocessing route. This represents the number of times the j-th component of the i-th product is reprocessed for the k-th damage type in the n-th reprocessing unit on the v-th reprocessing route. This represents the time required to reprocess the k-th type of damage to the j-th component of the i-th product at the n-th reprocessing unit on the v-th reprocessing route.

[0103] because This represents the k-th damage type of the j-th component of the i-th product. express The nth reprocessing unit on the vth optional route was selected; therefore, in this embodiment, according to... The definition of will be elaborated upon.

[0104] Indicates reprocessing End time, and Reprocessing is performed on the same reprocessing unit and completed earlier, that is, on products that were previously processed in that reprocessing unit. express exist The amount of processing.

[0105] Step S3: Establish a mathematical model for the end time of the remanufactured products at the remanufacturing workstation in the remanufacturing subsystem.

[0106] This step is used to determine the end time of the remanufactured products at the remanufacturing workstation in the remanufacturing subsystem. (P in the remanufacturing subsystem) i The start and end times are calculated using formulas (5) and (6) respectively:

[0107]

[0108]

[0109] in Indicates in RW u Recombinant P i' The end time is longer than P. i Complete it earlier. Indicates in RW u Recombinant P i The quantity. This represents the start time of the i-th product at the u-th reorganization workstation. RT represents the end time of the i-th product at the u-th reorganization workstation. i This represents the time required to reassemble the i-th product. This represents the number of times the i-th product is reassembled on the u-th reassembly workstation.

[0110] Step S4: Establish a scheduling model with the goal of minimizing the total completion time of all remanufactured products.

[0111] The scheduling model established in this step is represented as follows:

[0112]

[0113] Where TT represents the total completion time of all remanufactured products, I is the number of remanufactured product types, and U represents the number of remanufacturing workstations.

[0114] It should be noted that the scheduling model in this application must satisfy the following constraints:

[0115]

[0116]

[0117] TT≤BT (10)

[0118] Constraint (8) indicates that only one route can be selected to complete the task. The reprocessing, constraint (9) means that the current operation will not start unless all its previous operations are completed, and constraint (10) guarantees that the TT of the scheduling scheme does not exceed BT.

[0119] To more intuitively and concisely represent the efficiency of the scheduling scheme, the normalized result of TT is used as the final objective function, as shown in equation (11):

[0120]

[0121] Where TT represents the total completion time of all remanufactured products, TT max and TT min These represent the maximum TT and minimum TT required to complete the remanufacturing task, respectively.

[0122] Step S5: Solve the scheduling model to obtain the scheduling scheme of the remanufacturing system, and perform scheduling according to the obtained scheduling scheme.

[0123] This application proposes a hybrid metaheuristic algorithm (HDEBBO) that combines differential evolution (DE) and biogeographic optimization (BBO) to effectively solve scheduling models and find the optimal scheduling scheme.

[0124] The scheduling problem of remanufacturing systems can be viewed as a hybrid discrete problem, which can be decomposed into two subproblems: product allocation and operation sequencing. Basic DE and BBO algorithms excel at solving simple continuous problems but are not suitable for directly solving hybrid discrete problems. Therefore, this application proposes the HDEBBO algorithm after making five improvements to the basic DE and BBO algorithms, including: 1) proposing a new representation scheme to adapt to the proposed model; 2) adopting an adaptive strategy to improve the mutation operator in the DE algorithm to balance local and global search capabilities; 3) introducing an efficient migration mutation operator into the BBO algorithm to solve discrete problems more quickly; 4) adopting a local search strategy to improve the algorithm's convergence and search capability; and 5) adopting a restart strategy to avoid premature convergence.

[0125] This embodiment employs a hybrid metaheuristic algorithm, using the DE algorithm to solve the product allocation subproblem and the BBO algorithm to solve the operation ordering subproblem. However, the original representation schemes of these two basic algorithms cannot be directly used to encode the remanufacturing system scheduling problem. Therefore, this embodiment proposes a novel habitat-based representation scheme. A habitat (representing a scheduling scheme, also called an individual) consists of two parts: the first part encodes the product allocation information for each dismantling (reassembly) workstation, and the second part encodes the operation ordering information for each subsystem.

[0126] like Figure 3 As shown, (1) the first part consists of two matrices, representing the product allocation information for the disassembly and reassembly workstations. In one matrix, the number of columns represents the number of product categories, and the number of rows represents the number of workstations in the disassembly (reassembly) subsystem.

[0127] Figure 3 The example illustrates the allocation of 6 products to 2 disassembly (reassembly) workstations. The first row of the first matrix, {10,30,15,25,20,10}, represents the quantity of each product allocated to the first disassembly workstation as 10, 30, 15, 25, 20, 10 respectively.

[0128] (2) The second part consists of three matrices, which represent the operation ordering information of products or components in the three subsystems.

[0129] The first and third matrices represent the disassembly and reassembly sequences of products in the disassembly and reassembly subsystems, respectively. For example, the first matrix {2,3,5,4,1,6} represents the disassembly sequence of each product in the disassembly subsystem as: P2,P3,P5,P4,P1,P6.

[0130] The second matrix represents the reprocessing sequence and selected reprocessing route for components with different damage types and degrees within the reprocessing subsystem. For example, the first column {2,3,1,4} in the second matrix represents component C. 23 The first type of damage is reprocessed through the first reprocessing unit in the fourth optional route. The second occurrence of {2,3,1,4} in the third column indicates C. 23 The first type of damage is reprocessed again through the fourth candidate route, and at this time, the reprocessing operation is performed in the second reprocessing unit of that route.

[0131] like Figure 2 As shown, the hybrid metaheuristic algorithm (HDEBBO) in this embodiment includes:

[0132] Step 5.1: Initialize the population and parameters.

[0133] For example, in experiments, the cross-factor, F min F max NI0 is set to 0.5, 0.2, 0.8, and 70 respectively. These parameters include all configurable parameters used in the algorithm, which will not be detailed here.

[0134] Step 5.2: Calculate the current adaptive probability, and select the mutation operator to execute based on the adaptive probability. The mutation operator includes two mutation operators: DE / best / 1 and DE / rand / 2.

[0135] This embodiment uses two mutation operators, DE / best / 1 and DE / rand / 2, as shown in formulas (12) and (13), respectively. The former fully utilizes the optimal solution to accelerate the convergence speed of the algorithm, while the latter has good search capabilities due to the two different vectors. After calculating the current adaptive probability, the adaptive probability is compared with a random number. If it is greater than or equal to the random number, the DE / best / 1 mutation operator is executed; otherwise, the DE / rand / 2 mutation operator is executed.

[0136]

[0137]

[0138] in The best individual in population t. and V represents an individual randomly selected from the current population that satisfies the condition a≠b≠c≠d≠e. i t For the i-th individual generated by the mutation operator, F i t and F i Let be the scaling factor for the i-th individual.

[0139] This embodiment introduces an adaptive probability P during the iteration process. DE The mutation operator is switched to balance the local search capability and global search capability of the algorithm.

[0140] P DE The calculation method is shown in formula (14):

[0141]

[0142] Where maxiter and t represent the maximum number of iterations and the current number of iterations, respectively. As t increases, P DE The value of will also increase, making DE / rand / 2 more likely to be selected, thus avoiding premature entrapment in local optima. e is the natural constant.

[0143] The scaling factor has a significant impact on the search range of the DE algorithm, and it needs to be adjusted differently at different times. In this embodiment, the scaling factor of DE / best / 1 is adaptively adjusted based on the fitness of the individual, as described in formula (15). Furthermore, the scaling factor of DE / rand / 2... i The distribution is set to uniform to perturb individuals, making them more likely to escape local optima.

[0144]

[0145] in and Each represents an individual and fitness, F min and F max These are the minimum and maximum values ​​of the scaling factor, respectively. As t increases, and The probability of values ​​being similar increases, and F i t The value also increases, thereby enhancing the algorithm's global search capability in the later stages.

[0146] Step 5.3: Execute the crossover operator.

[0147] Step 5.4, Update Q improve This refers to updating the product allocation information for dismantling and reassembling workstations, which is the first part of the habitat coding.

[0148] Step 5.5: Calculate the immigration rate and emigration rate for each habitat and execute the migration operator.

[0149] Migration operators improve habitats with low HSI values ​​by sharing habitat features or information with high HSI values. Compared to linear migration models, sinusoidal migration models are closer to nature and can better simulate unpredictable events through mutation operators. Based on this model, the emigration rate λ is calculated using equations (16) and (17), respectively. o and immigration rate μ o .

[0150]

[0151]

[0152] Where E max and I max These represent the highest emigration rate and emigration rate, respectively, S o Let be the number of species in the 0th habitat, and NP be the maximum number of species. π is the mathematical constant pi.

[0153] Figure 4 An example of a migration operator is described. Furthermore, this embodiment employs a roulette wheel strategy to select habitats for migration to improve the algorithm's convergence speed. For example... Figure 4 As shown, two points are randomly selected from habitat i, and the species between these two points are copied to habitat i' according to their positions, while the same species in habitat j are removed. Then, the remaining species in habitat j are moved to empty positions in habitat i' in sequence.

[0154] Step 5.6: Calculate the mutation rate for each habitat and execute the mutation operator.

[0155] This embodiment uses the inversion mutation operator to improve the operation sequence information. Figure 5 An example of a mutation operator is depicted, which reverses the order of species between two randomly selected points.

[0156] In addition, to accelerate the convergence speed, the mutation rate of the optimal habitat for each generation is set to 0. The mutation rate of the remaining habitats can be calculated using formula (18).

[0157]

[0158] Where m max For the maximum mutation rate, G max G represents the probability of species abundance in the maximum habitat. o The survival probability of the o-th habitat can be calculated using formula (19).

[0159]

[0160] Here, o-1 and o+1 both represent the habitat sequence number.

[0161] Step 5.7: Execute the local search strategy.

[0162] To improve the algorithm's local search capability and obtain a better operation order, this step performs a local search strategy based on two neighborhood structures on the solutions of the first preset proportion in each iteration.

[0163] For example, in each iteration, a local search strategy based on two neighborhood structures (exchange and insertion) is performed on the top 10% of the solutions. Figure 6 An example is given, where the swap operator is used to exchange corresponding values ​​between two randomly selected points, and the insertion operator is used to randomly select two points and then insert the other point before the first one.

[0164] Step 5.8, Update O improve This refers to updating the operation sorting information of products or components in the three subsystems, which is the second part of the habitat coding.

[0165] Step 5.9: Determine if the restart conditions are met. If they are met, proceed to the next step; otherwise, proceed to step 5.11.

[0166] Step 5.10: Reinitialize the population using the restart strategy.

[0167] A restart strategy can prevent the algorithm from converging prematurely. This embodiment designs a restart strategy that randomly reinitializes individuals when the restart condition is triggered. The restart condition can be calculated using formula (20):

[0168]

[0169] Where NI0 is the maximum number of iterations allowed for the initial continuous non-improved solution, RN is the number of times the restart strategy is used, and RC is the maximum number of consecutive iterations for the non-improved solution. If the number of iterations for the non-improved solution exceeds RC, the restart strategy will be triggered.

[0170] Step 5.11: Determine if the stopping condition is met. If it is, stop the iteration and output the optimal scheduling scheme. Otherwise, return to step 5.2 and start iterating again.

[0171] In another embodiment, the applicant also verified the technical solution proposed in this application through experiments to evaluate the performance of the HDEBBO algorithm in solving the remanufacturing system scheduling model.

[0172] To simulate a real remanufacturing environment, in each instance of this experimental data, the number of product categories was randomly generated between 2 and 10, and the number of products within each category was randomly generated between 10 and 100. For each product, the number of components was randomly generated between 2 and 9. The number of damage types for each component was randomly generated between 1 and 3. The number of operations in each reprocessing route was randomly generated between 2 and 4. The number of parallel workstations in the disassembly (reassembly) subsystem was set to 3.

[0173] Because this problem is a hybrid discrete problem, it is not suitable for direct solution using standard heuristic algorithms. Therefore, this embodiment evaluates the performance of the HDEBBO algorithm by comparing it with other baseline hybrid algorithms. In the experiment, the Flower Pollination (FPA) algorithm, Simulated Annealing (SA) algorithm, DE algorithm, and BBO algorithm were mixed in pairs to alternately solve the product allocation and operation order problem. To avoid confusion, the above four baseline hybrid algorithms are referred to as FPA-BBO, FPA-SA, DE-SA, and DE-BBO algorithms. To enhance the robustness of the experiment, each algorithm was executed 10 times under the same environment, and the average fitness value was used as the final result.

[0174] This embodiment tests the performance of the five algorithms mentioned above under different numbers of iterations, such as Figure 7 As shown, it is intuitive to see that the HDEBBO algorithm can obtain the best results in fewer iterations. The HDEBBO algorithm outperforms other algorithms that require 500 iterations at 200 iterations. It can also be seen that HDEBBO converges at approximately 350 iterations, while other algorithms converge after approximately 430 iterations. This demonstrates that the HDEBBO algorithm has superior convergence ability and optimal solution performance.

[0175] To effectively evaluate the performance differences between the HDEBBO algorithm and four other baseline hybrid algorithms, this embodiment tested multiple instances of different sizes. The comparison results for each instance are shown in Tables 1 and 2:

[0176]

[0177] Table 1

[0178]

[0179]

[0180] Table 2

[0181] Tables 1 and 2 above contain statistical indicators of optimal fitness and average fitness, labeled "optimal" and "average," respectively. It can be seen that the optimal and average fitness values ​​of the HDEBBO algorithm are both better than or equal to the fitness values ​​of other baseline hybrid algorithms, indicating that the HDEBBO algorithm outperforms other baseline hybrid algorithms in solving this model.

[0182] The scheduling model proposed in this application considers both the coordination among the three subsystems and the operation shop-type reprocessing workshops associated with diverse reprocessing routes. The HDEBBO algorithm used is superior to other algorithms.

[0183] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A method of scheduling a remanufacturing system that diversifies reprocessing routes, the remanufacturing system including a disassembly subsystem, a reprocessing subsystem, and a recombination subsystem, the method characterized by, The remanufacturing system scheduling method of the diversified reprocessing route comprises: a mathematical model for establishing end time of disassembly of a disassembly workstation in a disassembly subsystem is established: ； wherein, denotes the start time of the i-th product on the s-th disassembly workstation, denotes the end time of the i-th product on the s-th disassembly workstation, denotes the number of i-th products disassembled on the s-th disassembly workstation, denotes the time required to disassemble the i-th product; a mathematical model for establishing end time of reprocessing of a reprocessing unit in a reprocessing subsystem is established: ； wherein, denotes the end time of the kth damage type of the jth component of the ith product reprocessed on the nth reprocessing unit on the vth reprocessing route; denotes the start time of the kth damage type of the jth component of the ith product reprocessed on the nth reprocessing unit on the vth reprocessing route, denotes the number of processes of the kth damage type of the jth component of the ith product reprocessed on the nth reprocessing unit on the vth reprocessing route, denotes the time required for the kth damage type of the jth component of the ith product reprocessed on the nth reprocessing unit on the vth reprocessing route; a mathematical model for establishing end time of recombination of a recombination workstation in a recombination subsystem is established: ； wherein, denotes the start time of the i-th product at the u-th reconfiguration workstation, denotes the end time of the i-th product at the u-th reconfiguration workstation, denotes the time required to reconfigure the i-th product, denotes the number of i-th products reconfigured at the u-th reconfiguration workstation; a scheduling model with minimum total completion time of all remanufactured products as an optimization objective is established: ； wherein, TT represents total completion time of all remanufactured products, I is the number of remanufactured product types, and U represents the number of recombination workstations; the scheduling model is solved to obtain a scheduling scheme of the remanufacturing system, and scheduling is performed according to the obtained scheduling scheme; wherein, the scheduling model is solved by using a hybrid meta-heuristic algorithm, in which one habitat is composed of two parts, the first part encodes product allocation information of each disassembly and recombination workstation, and the second part encodes operation sequence information of each subsystem; wherein, the first part is composed of two matrices, which respectively represent product allocation information of a disassembly or recombination workstation, the number of columns represents the number of product types, and the number of rows represents the number of workstations in the disassembly or recombination subsystem; the second part is composed of three matrices, which represent operation sequence information of products or components in the three subsystems, wherein the first matrix and the third matrix respectively represent disassembly and recombination sequences of products in the disassembly and recombination subsystems; and the second matrix represents reprocessing sequences and selected reprocessing routes of components with different damage types in the reprocessing subsystem; the hybrid meta-heuristic algorithm comprises: Step 5.1, initializing a population and parameters; Step 5.2, calculating a current adaptive probability, and selecting a mutation operator according to the adaptive probability to execute the mutation operator on the first part of the habitat, wherein the mutation operator comprises DE / best / 1 and DE / rand / 2 mutation operators; Step 5.3, executing a crossover operator; Step 5.4, updating product allocation information of the disassembly and recombination workstations in the habitat; Step 5.5, calculating immigration rate and emigration rate of each habitat, and executing a migration operator on the second part of the habitat; Step 5.6, calculating mutation rate of each habitat, and executing a mutation operator; Step 5.7, executing a local search strategy; Step 5.8, updating operation sequence information of products or components in the three subsystems; Step 5.9, judging whether a restart condition is met, if the restart condition is met, proceeding to the next step, otherwise, proceeding to Step 5.11; Step 5.10, reinitializing the population by using a restart strategy; Step 5.11, judging whether a stop condition is met, if the stop condition is met, stopping iteration, and outputting an optimal scheduling scheme, otherwise, returning to Step 5.2 to reiterate.

2. The remanufacturing system scheduling method of diversification reprocessing routes according to claim 1, characterized in that, The adaptive probability is calculated according to the following formula: ； wherein represents the adaptive probability, maxiter and t represent the maximum number of iterations and the current number of iterations, respectively.

3. The remanufacturing system scheduling method of diversification reprocessing routes according to claim 1, characterized in that, The immigration rate and the emigration rate are calculated according to the following formula: ； ； where represents the emigration rate, represents the immigration rate, E max and I max are the maximum emigration and immigration rates, respectively, is the number of species in the oth habitat, and NP is the maximum number of species.

4. The remanufacturing system scheduling method of diversification reprocessing routes according to claim 1, characterized by, The mutation rate of each habitat is calculated according to the following formula: The mutation rate of each habitat is calculated according to the following formula: ； where m max is the maximum mutation rate, G max is the maximum habitat species number probability, represents the mutation rate of the oth habitat, G o is the survival probability of the oth habitat.

5. The remanufacturing system scheduling method of diversification reprocessing routes according to claim 1, characterized by, The local search strategy comprises: a local search strategy based on two neighborhood structures is executed on a preset proportion of solutions in each iteration.

6. The remanufacturing system scheduling method of diversified reprocessing routes according to claim 1, characterized in that, The using a restart strategy to reinitialize the population comprises: When a restart condition is triggered, randomly reinitialize the individual; Wherein the restart condition is: ； If the number of iterations of non-improved solutions exceeds RC, the restart strategy is triggered, wherein NI0 is the maximum number of iterations allowed for the initial continuous non-improved solution, RN is the number of times the restart strategy is used, and RC is the maximum number of continuous iterations of non-improved solutions.

Images