A decision tree-based uncertainty remanufacturing scheduling method

Abstract

The application discloses a decision tree-based uncertainty remanufacturing scheduling method, which aims at maximizing total remanufacturing profit and minimizing total time required for remanufacturing all waste products, sets the quality grade of the waste products as a fuzzy variable, evaluates the remanufacturability of the waste products by using a decision tree, and selects a remanufacturing line with the maximum expected profit for remanufacturing the waste products. Then, an improved teach-and-learn optimization algorithm is used, in which, in the teacher stage, the learner uses an adaptive inertia weight to update the reprocessing operation sequence, and when falling into a local optimum, the learner simultaneously learns from the teacher, the best learner and the learner with the maximum adaptive value in the last iteration, so as to relieve the algorithm from falling into a local optimum and improve the diversity of the population. The application realizes efficient solution of the model and can obtain a more reasonable scheduling scheme.

Description

Technical Field

[0001] This application belongs to the field of remanufacturing scheduling technology, and in particular relates to an uncertainty remanufacturing scheduling method based on decision trees. Background Technology

[0002] Remanufacturing is a recyclable manufacturing process based on original manufacturing techniques, aiming to unlock the residual value of waste products. With the continuous development of the remanufacturing industry, the issue of remanufacturing scheduling is receiving increasing attention from academia and industry.

[0003] Due to variations in the degree of use of waste products and the efficiency of remanufacturing machines, significant uncertainties exist in the remanufacturing scheduling process, which substantially impacts the assessment of the remanufacturability of waste products and the selection of remanufacturing lines. Remanufacturability refers to the potential for remanufacturing recycled waste products, and can be described as assessing whether waste products are worth remanufacturing. Many factors can have a positive or negative impact on the remanufacturability of waste products. For example, the profit generated from scrapping or remanufacturing waste products; the significant differences in the quality of waste products after varying degrees of use, affecting the profit generated from scrapping or remanufacturing waste products, and thus affecting the remanufacturability of waste products. Furthermore, when remanufacturing waste products of different qualities, remanufacturing lines with different reprocessing operations can be selected, and the time required to remanufacture waste products using different remanufacturing lines varies.

[0004] Current technical solutions for remanufacturing scheduling mostly consider deterministic factors, neglecting the impact of uncertainties. Some scholars have studied uncertain remanufacturing scheduling based on experience or stochastic optimization methods, but have not explicitly described the uncertainty. Other scholars have used fuzzy methods such as fuzzy logic theory and linear fuzzy functions to transform uncertainty in remanufacturing scheduling into determinism, but have not explored the impact of uncertainty on assessing the remanufacturability of scrap products and selecting suitable remanufacturing lines.

[0005] Because the impact of uncertainties on scheduling cannot be ignored, more and more scholars are beginning to focus on uncertain scheduling. Some scholars have proposed a model for an uncertain remanufacturing production optimization scheduling system constrained by two random variables. Others have used experience-based strategies to solve the remanufacturing scheduling problem with uncertain remanufacturing time; and still others have used stochastic simulation models to handle the uncertainty in remanufacturing system scheduling. However, neither stochastic optimization nor experience-based methods can explicitly describe uncertainty, and therefore are only suitable for solving simple uncertain scheduling problems.

[0006] Some scholars have also used fuzzy methods to solve the uncertain remanufacturing scheduling problem, and used fuzzy logic theory to quantify the superposition effect of multiple uncertainties in the remanufacturing scheduling model. However, these methods only transform uncertainty into certainty through certain theories and methods to solve the uncertain remanufacturing scheduling problem, without exploring the impact of uncertainty on remanufacturability assessment and remanufacturing line selection. Summary of the Invention

[0007] The purpose of this application is to provide a decision tree-based uncertainty remanufacturing scheduling method, which addresses the impact of uncertainty by constructing a decision tree and combining it with fuzzy numbers, and proposes remanufacturing strategies related to remanufacturability assessment and remanufacturing line selection.

[0008] To achieve the above objectives, the technical solution of this application is as follows:

[0009] An uncertainty remanufacturing scheduling method based on decision trees, comprising:

[0010] Step 1: Create a remanufacturing optimization model with the goal of maximizing total remanufacturing profit and minimizing the total time required to remanufacture all waste products.

[0011] Step 2: Set the quality grade of the waste products as a fuzzy variable, use a decision tree to evaluate the remanufacturability of the waste products, and select the remanufacturing line with the highest expected profit for remanufacturing the waste products as the remanufacturing line for the waste products.

[0012] Step 3: Using the remanufacturability assessment results of waste products and the selection results of remanufacturing lines as the first dimension of the scheduling scheme, and the reprocessing operation sequence of waste products on the remanufacturing line as the second dimension, generate the initial population.

[0013] Step 4: Determine if the learner is trapped in a local optimum. If not, execute the teacher phase of the teaching and learning optimization algorithm. The learner updates the reprocessing operation sequence using adaptive inertia weights. If the learner is trapped in a local optimum, execute the teacher phase of the teaching and learning optimization algorithm combined with the differential evolution algorithm. The learner learns from the teacher, the best learner, and the learner with the largest improvement in fitness value in the previous iteration, and updates the reprocessing operation sequence.

[0014] Step 5: The learner phase of the teaching and learning optimization algorithm is executed, and the learner updates the reprocessing operation sequence;

[0015] Step 6: Determine if the termination condition is met. If not, return to step 4 to continue iterative optimization. Once the termination condition is met, the optimal remanufacturing scheduling scheme is obtained.

[0016] Furthermore, the first dimension comprises three layers: the first layer represents the serial number of the waste product; the second layer represents the remanufacturability assessment result of the waste product; and the third layer represents the selection result of the remanufacturing line.

[0017] The second dimension comprises two layers. The first layer represents the real number code of the reprocessing operation sequence of the waste product on the corresponding remanufacturing line, and the second layer represents the number of the reprocessing operation sequence of the waste product on the corresponding remanufacturing line.

[0018] Furthermore, the adaptive inertia weight is calculated using the following formula:

[0019]

[0020] in, Represents the current iteration number. Represents the maximum number of iterations. Representing the The number of individuals whose fitness values ​​improved in the next iteration. Represents the total number of individuals in the population.

[0021] Furthermore, the learner updates the reprocessing operation sequence using adaptive inertia weights, including:

[0022] Calculate the real number encoding corresponding to the reprocessing operation sequence using the following formula:

[0023]

[0024] in, The i-th real number encoding corresponding to the reprocessing operation sequence of the new learner individual. This represents the i-th real number encoding corresponding to the reprocessing operation sequence of the original learner. The i-th real number encoding corresponding to the sequence of reprocessing operations for an individual teacher. The average value of the i-th real number encoding corresponding to the reprocessing operation sequence of all individuals in the population; The heuristic step size is a random number between 0 and 2.

[0025] The fitness values ​​of new learners are compared with those of existing learners, and learners with higher fitness values ​​are retained to form a new population.

[0026] Furthermore, the learner simultaneously learns from the teacher, the best learner, and the learner whose fitness value improved the most in the previous iteration, updating the reprocessing operation sequence, including:

[0027] Learners update the real-number encoding corresponding to the reprocessing operation sequence according to the following formula:

[0028]

[0029] in, The i-th real number encoding corresponding to the reprocessing operation sequence of the best learner. The i-th real number encoding corresponding to the reprocessing operation sequence of the learner who has made the greatest improvement in fitness in the previous iteration;

[0030] The fitness values ​​of new learners are compared with those of existing learners, and learners with higher fitness values ​​are retained to form a new population.

[0031] Furthermore, the fitness value is calculated using the following formula:

[0032] … …

[0033] in, Representative of individuals fitness value, , TT represents the total number of individuals in the population. n Represents an individual The total time required to remanufacture all the corresponding waste products.

[0034] This application proposes a decision tree-based uncertainty remanufacturing scheduling method, which uses decision trees to assess the remanufacturability of scrap products and select remanufacturing lines. A novel solution representation scheme is employed, and an adaptive inertia weight adjustment function combined with the differential mutation strategy of differential evolution algorithm is used to alleviate the algorithm's entrapment in local optima and improve population diversity, thereby achieving efficient model solving and obtaining a more reasonable scheduling scheme. Attached Figure Description

[0035] Figure 1 This is a flowchart of the uncertainty remanufacturing scheduling method based on decision trees in this application.

[0036] Figure 2 This is an example of a solution representation of the remanufacturing optimization model of this application. Detailed Implementation

[0037] 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.

[0038] Because recycled waste products vary in their degree of use, their quality levels differ significantly. Remanufacturing waste products incurs production costs, while recycling failed remanufacturing attempts or selling successfully remanufactured products generates revenue. The profit, calculated by subtracting production costs from revenue, is the remanufacturing profit. This profit varies depending on the quality level of the waste products. Furthermore, different remanufacturing lines typically involve different reprocessing operations; therefore, the remanufacturing time and cost required to remanufacture the same waste products will differ depending on the remanufacturing line used.

[0039] This application considers multiple non-equivalent parallel remanufacturing lines: high-level, medium-level, and low-level lines, respectively suitable for remanufacturing waste products of high, medium, and low quality levels. The high-level line contains the simplest reprocessing operations, while the low-level line contains the most complex. Although all three remanufacturing lines can be used to remanufacture waste products of the same quality level, the remanufacturability and time required for remanufacturing will differ depending on the chosen remanufacturing line. While the low-level line, with its most complex reprocessing steps, can remanufacture high-quality waste products, the longer remanufacturing time and higher costs negatively impact the profitability and remanufacturability of waste product remanufacturing.

[0040] This application's remanufacturing scheduling is divided into two stages. The first stage uses a decision tree to assess the remanufacturability of scrap products and select a suitable remanufacturing line to maximize the total remanufacturing profit. The second stage optimizes the reprocessing operation sequence of scrap products on each remanufacturing line to minimize the total time required to remanufacture all scrap products.

[0041] For ease of description, the symbols used in this application are described below:

[0042] The i-th discarded product, ,in This indicates the total number of discarded products.

[0043] The j-th quality level These correspond to high quality, medium quality, and low quality levels, respectively.

[0044] The z-th remanufacturing line These correspond to the high, medium, and low remanufacturing lines, respectively.

[0045] Remanufacturing line The kth reprocessing unit, ,in Indicates remanufacturing line The total number of remanufacturing units.

[0046] The total profit obtained from remanufacturing or scrapping all waste products.

[0047] The total time required to remanufacture all waste products.

[0048] On the remanufacturing line Remanufactured products The profits obtained.

[0049] On the remanufacturing line Remanufactured products The costs incurred.

[0050] The remanufacturing quality level is Products The resulting revenue.

[0051] Scrapped products The profits obtained.

[0052] The scrap quality level is Products The resulting revenue.

[0053] reprocessing unit For the product The start time for reprocessing.

[0054] reprocessing unit For the product The time required for further processing.

[0055] reprocessing unit For the product The end time for further processing.

[0056] Binary decision variables, where 1 represents the product. On the remanufacturing line If it is remanufactured, then it is 0; otherwise, it is 0.

[0057] Binary decision variables, where 1 represents the product. On the remanufacturing line The first one is remanufactured; otherwise, the result is 0.

[0058] Binary decision variables, where 1 represents the product. It is worth remanufacturing; otherwise, it is 0.

[0059] Binary decision variables, where 1 represents the product. Remanufacturing was successfully completed; otherwise, the result is 0.

[0060] One embodiment of this application, such as Figure 1 As shown, an uncertainty remanufacturing scheduling method based on decision trees is provided, including:

[0061] Step S1: Create a remanufacturing optimization model with the goal of maximizing the total profit of remanufacturing and minimizing the total time required to remanufacture all waste products.

[0062] In this embodiment, the total profit consists of two parts: the profit obtained from remanufacturing waste products. Profits from the disposal and scrapping of waste products .

[0063] With the goal of maximizing total remanufacturing profit, the objective function is shown in formula (1):

[0064] (1)

[0065] Profits from remanufacturing waste products Profits from the disposal and scrapping of waste products The values ​​can be calculated using formulas (2) and (3) respectively:

[0066] (2)

[0067] (3)

[0068] To minimize the total time required to remanufacture all waste products, the objective function is shown in formula (4):

[0069] (4)

[0070] Step S2: Set the quality grade of the waste products as a fuzzy variable, use a decision tree to evaluate the remanufacturability of the waste products, and select the remanufacturing line with the highest expected profit for remanufacturing the waste products as the remanufacturing line for the waste products.

[0071] In this embodiment, the possible quality levels of waste products are set as a fuzzy variable. Taking three quality levels as an example, they can be represented by fuzzy functions, as shown in formula (5):

[0072] (5)

[0073] Among them, probability Represents waste products Belongs to quality grade The probability of , and satisfies formula (6):

[0074] (6)

[0075] Decision trees are used to evaluate waste products. Remanufacturability, i.e., assessing the remanufacturability of waste products Whether remanufacturing is worthwhile is as shown in formula (7):

[0076] (7)

[0077] in, Representative at the remanufacturing line Top products The expected profit that can be obtained from remanufacturing. Representative of the product The expected profit that can be obtained from scrapping can be calculated using formulas (8) and (9), respectively:

[0078] (8)

[0079] (9)

[0080] in, and Representing remanufacturing lines For quality grade waste products The success probability and failure probability of remanufacturing are given, and they satisfy formula (10):

[0081] (10)

[0082] if That is, products If it is not worth remanufacturing, the product should be scrapped. .if That is, products If remanufacturing is worthwhile, the decision tree is used again to select a suitable remanufacturing line. Because... It involves calculating and comparing remanufactured products from different remanufacturing lines. The expected profit that can be obtained is therefore obtained when the remanufacturing line For the product Expected profit from remanufacturing The most suitable remanufacturing line is the one that reaches its maximum value.

[0083] A decision tree consists of a decision graph and possible outcomes. In this embodiment, based on the selection of different remanufacturing options, such as whether to remanufacture and on which remanufacturing line, a tree structure is generated. Decision points represent the decision problem, option branches represent available options, and probability branches represent the various possible outcomes of the options. By calculating and comparing the expected profit values ​​under each branch (i.e., various remanufacturing options), a decision-making basis is provided, and the optimal remanufacturing option is selected.

[0084] Step S3: Using the remanufacturability assessment results of waste products and the selection results of remanufacturing lines as the first dimension of the scheduling scheme, and the reprocessing operation sequence of waste products on the remanufacturing line as the second dimension, an initial population is generated.

[0085] The teaching and learning optimization algorithm is a group optimization algorithm proposed to solve engineering optimization problems. It mainly includes two stages: the teacher stage and the learner stage.

[0086] (1) Teacher Phase: In this phase, the individual with the highest fitness value in the population is considered the teacher, and the remaining individuals are considered learners. Learners improve their own fitness value by continuously learning from the teacher, thereby increasing the average fitness value of the entire population.

[0087] (2) Learner stage: In this stage, learners improve their fitness by interacting with another randomly selected learner.

[0088] Differential evolution is a heuristic random search algorithm that includes stages such as initialization, mutation, crossover, and selection. First, two individuals are randomly selected from the population as parents and a difference operation is performed to obtain a difference vector (i.e., the difference in direction and magnitude between the two individuals in the solution space). Then, the difference vector is superimposed on another individual to achieve mutation, generating a mutated individual. Next, crossover operations are performed on the two parent individuals and the mutated individual respectively to produce new offspring individuals. Finally, a selection operation is performed between the parent and offspring individuals, retaining the individuals that meet the requirements as the next generation of the population.

[0089] Teaching and learning optimization algorithms (TLEs) possess advantages such as strong solution space search capability, algorithm simplicity, few parameters, and high adaptability, making them suitable for solving complex optimization problems. However, basic TLEs also suffer from drawbacks such as poor population diversity and a tendency to get trapped in local optima. Differential evolutionary algorithms (DEEs) can improve population diversity and help TLEs escape local optima. Therefore, this application proposes an adaptive hybrid optimization algorithm combining TLEs and DEEs to efficiently solve the proposed remanufacturing optimization model (RSU-DT model). In the adaptive hybrid optimization algorithm, a novel two-dimensional solution representation scheme is proposed to represent the solution of the RSU-DT model; an adaptive inertia weight adjustment function is used to help the algorithm escape local optima; and an improved teacher stage is proposed in conjunction with DEEs to improve population diversity.

[0090] The remanufacturing scheduling problem proposed in this application is a complex discrete optimization problem, consisting of two parts: remanufacturing strategy selection and reprocessing operation sequencing. Since the solution representation scheme of the basic teaching-learning optimization algorithm is one-dimensional and uses continuous real numbers to encode individuals, it cannot be directly applied to the optimization solution of the RSU-DT model. Therefore, this application proposes a novel two-dimensional solution representation scheme to describe the individuals in the population. The RSU-DT model proposes corresponding remanufacturing strategies by constructing a decision tree. The first dimension corresponds to the remanufacturability assessment of scrap products and the remanufacturing line selection results in this remanufacturing strategy. When scrap products are worth remanufacturing, the second dimension corresponds to the encoding of the reprocessing operation sequence of scrap products on each remanufacturing line.

[0091] In one specific embodiment Figure 2 An example of a solution representation scheme is given.

[0092] like Figure 2 As shown in section (a), the first dimension comprises three layers: the first layer represents the scrap product number; the second layer represents the remanufacturability assessment result of the scrap product, i.e., whether the scrap product should be remanufactured; and the third layer represents the remanufacturing line selection result, i.e., which remanufacturing line to select for remanufacturing the scrap product. Note that when the second layer of a scrap product is "0 (scrapped)," its corresponding third layer is represented by 0, meaning that the scrapped scrap product does not need to be selected for remanufacturing. For example, the first column indicates the remanufacturing line... Above the waste products Remanufacturing is carried out; the third column indicates the remanufacturing of waste products. To be scrapped.

[0093] like Figure 2As shown in section (b), the second dimension represents the encoding of the reprocessing operation sequence of waste products on the remanufacturing line. Note that waste products that need to be scrapped do not need to be encoded in the second dimension. Since the teaching and learning optimization algorithm is only applicable to continuous real number encoding schemes, while the reprocessing operation sequence of waste products is discrete, this paper proposes an improved encoding scheme, as follows.

[0094] The second dimension comprises two layers. The first layer represents the real-valued encoding of the reprocessing operation sequence of the waste products on the corresponding remanufacturing line. When generating the initial population, this is a randomly generated series of real numbers between 0 and 1. The second layer represents the serial number of the reprocessing operation sequence of the waste products on the corresponding remanufacturing line, which is a discrete-valued encoding. Taking the remanufacturing high line as an example, the smallest real number corresponds to the sequence number on the remanufacturing line. The waste product with the lowest product number among the products undergoing reprocessing is selected, and so on, until the remanufacturing line is completed. The reprocessing operation sequence is assigned to all remanufactured products on the line. Therefore, the remanufacturing line... The reprocessing sequence of waste products is as follows: - - - ".

[0095] Step S4: Determine if the learner is trapped in a local optimum. If not, execute the teacher phase of the teaching and learning optimization algorithm, where the learner updates the reprocessing operation sequence using adaptive inertia weights. If so, execute the teacher phase of the teaching and learning optimization algorithm combined with the differential evolution algorithm, where the learner learns from the teacher, the best learner, and the learner whose fitness value increased the most in the previous iteration, and updates the reprocessing operation sequence.

[0096] Basic teaching and learning optimization algorithms are prone to getting trapped in local optima, while inertia weights can alleviate this by balancing the algorithm's global and local solution space search capabilities. Therefore, this embodiment utilizes an adaptive inertia weight adjustment function to prevent getting trapped in local optima.

[0097] Inertia weights in the current iteration It can be calculated using formula (11):

[0098] (11)

[0099] in, Represents the current iteration number. Represents the maximum number of iterations. Representing the The number of individuals whose fitness values ​​improved in the next iteration. Represents the total number of individuals in the population.

[0100] To mitigate the algorithm's tendency to get stuck in local optima and enhance population diversity, this embodiment proposes an improved teacher phase. An additional criterion is added to determine if the algorithm is trapped in a local optimum. If not, the learner updates its reprocessing operation sequence using adaptive inertia weights, preventing it from falling into a local optimum. However, if it is already trapped, a teacher phase combining teaching and learning optimization algorithms with differential evolution is executed. The learner simultaneously learns from the teacher, the best learner, and the learner whose fitness value increased the most in the previous iteration, updating the reprocessing operation sequence to escape local optima.

[0101] To determine whether a learner is trapped in a local optimum, the fitness value of the individual after the previous five iterations can be calculated at each step. If the maximum fitness value of the current learner has not improved, it is considered to be trapped in a local optimum.

[0102] Without getting trapped in a local optimum, the learner uses adaptive inertia weights to update the reprocessing operation sequence, that is, updates the real number encoding corresponding to the reprocessing operation sequence according to formula (12):

[0103] (12)

[0104] in, The i-th real number encoding corresponding to the reprocessing operation sequence of the new learner individual. This represents the i-th real number encoding corresponding to the reprocessing operation sequence of the original learner. The i-th real number encoding corresponding to the sequence of reprocessing operations for an individual teacher. The average value of the i-th real number encoding corresponding to the reprocessing operation sequence of all individuals in the population; The heuristic step size is a random number between 0 and 2.

[0105] When trapped in a local optimum, the learner needs to learn simultaneously from the teacher (i.e., the best individual in the population), the best learner (i.e., the second best individual in the population), and the learner whose fitness value improved the most in the previous iteration. The learner updates the real number encoding corresponding to the reprocessing operation sequence according to formula (13):

[0106] (13)

[0107] in, The i-th real number encoding corresponding to the reprocessing operation sequence of the best learner. The i-th real number encoding represents the reprocessing operation sequence corresponding to the learner whose fitness value has increased the most in the previous iteration.

[0108] In this embodiment, the update reprocessing operation sequence compares the fitness values ​​of new learners with those of existing learners, retaining learners with higher fitness values ​​to form a new population. Among these, individuals... The fitness value can be calculated according to formula (14):

[0109] … … (14)

[0110] in, Representative of individuals fitness value, , Represents the total number of individuals in the population. TT n Represents an individual The total time required to remanufacture all the corresponding waste products.

[0111] In this embodiment, the fitness value reflects the difference between the maximum value of the total time required for all individuals to remanufacture all waste products and the total time required for the individual to remanufacture all waste products. The larger the fitness value, the smaller the total time required for the individual to remanufacture all waste products, so as to achieve the optimization objective of this application, namely, to minimize the total time required to remanufacture all waste products.

[0112] Step S5: The learner phase of the teaching and learning optimization algorithm is executed, and the learner updates the reprocessing operation sequence.

[0113] During the learner phase, the current learner randomly selects an individual from the population and learns from that individual to improve its fitness. The learner updates the real-number encoding corresponding to the reprocessing operation sequence according to formula (15):

[0114] (14)

[0115] in, The i-th real number encoding represents the sequence of reprocessing operations for a randomly selected individual in the population. and These represent the fitness values ​​of the current individual and the randomly selected individual, respectively.

[0116] Similarly, when updating the real number encoding corresponding to the reprocessing operation sequence, the fitness values ​​of the new learner individuals are compared with those of the original learner individuals, and learners with higher fitness values ​​are retained to form a new population.

[0117] Step S6: Determine whether the termination condition is met. If not, return to step S4 to continue iterative optimization. After the termination condition is met, the optimal remanufacturing scheduling scheme is obtained.

[0118] The termination condition for iteration can be whether the preset number of iterations has been reached, or whether the maximum fitness value of an individual learner no longer increases. If the termination condition is not met, the iteration continues. If the termination condition has been met, the optimal solution is considered to have been found, that is, the optimal remanufacturing scheduling scheme has been found, and subsequent remanufacturing is arranged according to this scheduling scheme.

[0119] To verify the above technical solution, the applicant conducted simulation and comparative experiments on this method and other baseline algorithms to determine the parameters of the algorithm and evaluate its performance in solving the remanufacturing optimization model (RSU-DT model) of this application.

[0120] The baseline algorithms used in the experiments included Differential Evolutionary Algorithm (DE), Teaching and Learning Optimization (TLBO), Discrete Particle Swarm Optimization (DPSO), and Extended Particle Swarm Optimization (EPSO). Parameters in the simulation dataset were randomly generated within a given interval. To ensure the reliability of the experiments, all experiments were run five times, and the total time required to remanufacture all discarded products was used as the evaluation metric.

[0121] The experiment was conducted on 14 simulation datasets to compare the proposed method with four other baseline algorithms. The experimental results are shown in Tables 1 and 2.

[0122] Table 1

[0123]

[0124] Table 2

[0125]

[0126] Table 1 shows the experimental results of each algorithm in solving the model, with the average and optimal values ​​of TT as evaluation indicators, denoted as "average" and "optimal" respectively. Table 2 shows the experimental results of the algorithms in solving the model, with the standard deviation of TT and the CPU running time of the algorithm as evaluation indicators, denoted as "standard deviation" and "running time" respectively.

[0127] As shown in Table 1, on most datasets, the average and optimal TT values ​​obtained by our method are superior to other baseline algorithms, indicating that our method outperforms other baseline algorithms in solution space search when solving the model. As shown in Table 2, on most datasets, the standard deviation of TT obtained by our method is superior to other baseline algorithms, indicating that our method has better stability when solving the model.

[0128] Remanufacturing has significant economic and social benefits, and remanufacturing scheduling is one of the key processes in remanufacturing. However, the actual remanufacturing scheduling process is always affected by various uncertainties, such as the uncertainty of the quality of used products and the uncertainty of the time required for remanufacturing, which reduces the economic and social benefits of remanufacturing. This application proposes a novel remanufacturing scheduling model that uses decision trees to assess the remanufacturability of used products and select remanufacturing lines. Based on this, a novel solution algorithm is proposed, employing a new solution representation scheme. Furthermore, an adaptive inertia weight adjustment function combined with the differential mutation strategy of differential evolution algorithm is used to alleviate the algorithm's entrapment in local optima and improve population diversity, thereby achieving efficient model solving.

[0129] 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 decision tree based uncertainty remanufacturing scheduling method, characterized in that, The decision tree-based uncertainty remanufacturing scheduling method includes: Step 1: Create a remanufacturing optimization model with the goal of maximizing total remanufacturing profit and minimizing the total time required to remanufacture all waste products. Step 2: Set the quality grade of the waste products as a fuzzy variable, use a decision tree to evaluate the remanufacturability of the waste products, and select the remanufacturing line with the highest expected profit for remanufacturing the waste products as the remanufacturing line for the waste products. Step 3: Using the remanufacturability assessment results of waste products and the selection results of remanufacturing lines as the first dimension of the scheduling scheme, and the reprocessing operation sequence of waste products on the remanufacturing line as the second dimension, generate the initial population. Step 4: Determine if the learner is trapped in a local optimum. If not, execute the teacher phase of the teaching and learning optimization algorithm. The learner updates the reprocessing operation sequence using adaptive inertia weights. If the learner is trapped in a local optimum, execute the teacher phase of the teaching and learning optimization algorithm combined with the differential evolution algorithm. The learner learns from the teacher, the best learner, and the learner with the largest improvement in fitness value in the previous iteration, and updates the reprocessing operation sequence. Step 5: The learner phase of the teaching and learning optimization algorithm is executed, and the learner updates the reprocessing operation sequence; Step 6: Determine if the termination condition is met. If not, return to step 4 to continue iterative optimization. Once the termination condition is met, the optimal remanufacturing scheduling scheme is obtained.

2. The decision tree based uncertainty remanufacturing scheduling method of claim 1, wherein, The first dimension comprises three layers: the first layer represents the serial number of the waste product; the second layer represents the remanufacturability assessment result of the waste product; and the third layer represents the selection result of the remanufacturing line. The second dimension comprises two layers. The first layer represents the real number code of the reprocessing operation sequence of the waste product on the corresponding remanufacturing line, and the second layer represents the number of the reprocessing operation sequence of the waste product on the corresponding remanufacturing line.

3. The decision tree based uncertainty remanufacturing scheduling method of claim 1, wherein, The adaptive inertia weight is calculated using the following formula: in, Represents the current iteration number. Represents the maximum number of iterations. Representing the The number of individuals whose fitness values ​​improved in the next iteration. Represents the total number of individuals in the population.

4. The decision tree based uncertainty remanufacturing scheduling method of claim 3, wherein, The learner updates the reprocessing operation sequence using adaptive inertia weights, including: Calculate the real number encoding corresponding to the reprocessing operation sequence using the following formula: in, The i-th real number encoding corresponding to the reprocessing operation sequence of the new learner individual. This represents the i-th real number encoding corresponding to the reprocessing operation sequence of the original learner. The i-th real number encoding corresponding to the sequence of reprocessing operations for an individual teacher. The average value of the i-th real number encoding corresponding to the reprocessing operation sequence of all individuals in the population; The heuristic step size is a random number between 0 and 2. The fitness values ​​of new learners are compared with those of existing learners, and learners with higher fitness values ​​are retained to form a new population.

5. The decision tree based uncertainty remanufacturing scheduling method of claim 1, wherein, The learner simultaneously learns from the teacher, the best learner, and the learner whose fitness value improved the most in the previous iteration, updating the reprocessing operation sequence, including: Learners update the real-number encoding corresponding to the reprocessing operation sequence according to the following formula: wherein, the ith real number code corresponding to the sequence of post-processing operations of the best learner, the ith real number code corresponding to the sequence of post-processing operations of the learner whose fitness increased the most in the last iteration; The fitness values ​​of new learners are compared with those of existing learners, and learners with higher fitness values ​​are retained to form a new population.

6. The uncertainty remanufacturing scheduling method based on decision trees according to claim 4 or 5, characterized in that, The fitness value is calculated using the following formula: … … in, Representative of individuals fitness value, , TT represents the total number of individuals in the population. n Represents an individual The total time required to remanufacture all the corresponding waste products.

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