A Dynamic Scheduling Method for Remanufacturing Shops Based on Robust Optimization

Abstract

This invention discloses a robust optimization-based dynamic scheduling method for remanufacturing workshops, comprising a pre-scheduling stage and a dynamic scheduling stage. In the pre-scheduling stage, a discrete scenario set is used to describe the arrival and processing times of jobs in the remanufacturing workshop. A robust optimization objective function is established based on minimizing the completion time of the pre-scheduling scheme and the difference in completion time under different scenarios. A biogeographical optimization algorithm is used to output the pre-scheduling scheme. In the dynamic scheduling stage, if a disturbance event occurs, the pre-scheduling scheme is used as the input scheme, and a job right-shifting and rescheduling strategy is executed to obtain the dynamic scheduling scheme. If the dynamic scheduling scheme is equal to or does not dominate the input scheme, the dynamic scheduling scheme is output; otherwise, a dynamic scheduling objective function is established by minimizing efficiency and robustness indices, and a biogeographical optimization algorithm is used to output the dynamic scheduling scheme. This invention considers the problems of multiple uncertainties and the impact of disturbance events, resulting in a better scheduling scheme.

Description

Technical Field

[0001] This invention belongs to the field of remanufacturing workshops, specifically relating to a dynamic scheduling method for remanufacturing workshops based on robust optimization. Background Technology

[0002] Remanufacturing, as a green manufacturing model that balances the recycling of waste materials with low-carbon circular development, has received widespread attention from all sectors of society. Remanufacturing waste products can save 35%-60% in costs, 60% in energy, 70% in materials, and reduce carbon dioxide emissions by 60%, while the selling price is only 30%-40% of that of traditionally manufactured products, bringing significant economic and environmental benefits to society. The large-scale and standardized development of the remanufacturing industry is inseparable from the development of remanufacturing workshop scheduling technology; therefore, research on remanufacturing workshop scheduling optimization has important theoretical and practical significance for promoting the remanufacturing industry.

[0003] Early research primarily focused on scheduling strategies for remanufacturing workshops. Later, some studies shifted to the impact of different remanufacturing system configurations on overall scheduling efficiency. For example, one existing integrated remanufacturing system configuration includes a product disassembly workshop, a dedicated automated reprocessing line workshop, and a reassembly workshop, using minimizing completion time as the optimization objective to determine the processing sequence of products in the three workshops. Other studies have explored remanufacturing system configurations including disassembly, reprocessing, and reassembly workshops, using non-dedicated automated reprocessing lines to handle scrap products with quality variations. However, compared to traditional manufacturing workshops, remanufacturing workshops use scrap products as raw materials and are subject to more uncertainties and disturbances, such as uncertainties in the quality, arrival time, processing time, and processing path of scrap products, as well as disturbances like machine failures.

[0004] In recent years, some studies have begun to focus on the scheduling optimization problem of remanufacturing workshops under uncertain environments. For example, research on the scheduling problem of engine block remanufacturing workshops with batch and parallel machines has employed Petri nets to describe the uncertainties in processing time and paths. Other studies have used random numbers and triangular fuzzy numbers to describe the uncertainties in the quality of scrap products and processing time during remanufacturing, constructing fuzzy models for remanufacturing production scheduling. Still other studies utilize fuzzy optimization methods to construct remanufacturing workshop scheduling models, employing double fuzzy theory to describe the uncertainties in processing time, cost, and reliability during remanufacturing, as well as the mutual influence between these uncertainties, and also considering the uncertainty of processing path selection. Existing technologies have also constructed remanufacturing workshop scheduling models based on game theory relationships, dividing multiple remanufacturing lines according to the uncertainty of scrap product quality, using interval expiration date setting methods to improve the model's flexibility and practicality, and setting sequence correlation adjustment times related to scrap product quality to further enhance the model's practicality. Compared to fuzzy optimization and stochastic optimization methods, robust optimization methods are more suitable for optimization problems with multiple uncertainties where historical data is lacking and data prediction is difficult. However, none of the above studies used robust optimization methods to model the remanufacturing shop optimization scheduling problem with multiple uncertainties.

[0005] In addition, while some studies have begun to focus on robust optimization methods, such as a scenario-based remanufacturing scheduling optimization method, which uses robust optimization to solve remanufacturing scheduling problems in deterministic environments, they have neglected the impact of disturbance events on remanufacturing shop scheduling. Summary of the Invention

[0006] The purpose of this invention is to provide a dynamic scheduling method for remanufacturing workshops based on robust optimization, which takes into account the problems of multiple uncertainties and the impact of disturbance events, and obtains a better scheduling scheme.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] A robust optimization-based dynamic scheduling method for remanufacturing workshops includes a pre-scheduling phase and a dynamic scheduling phase, wherein:

[0009] In the pre-scheduling stage, a discrete scenario set is used to describe the arrival time and processing time of the operations in the remanufacturing workshop. A robust optimization objective function is established based on minimizing the completion time of the pre-scheduling scheme and the difference in completion time under different scenarios. A biogeographical optimization algorithm is used to output the pre-scheduling scheme.

[0010] During the dynamic scheduling phase, if no disturbance event occurs, the remanufacturing workshop is dynamically scheduled according to the pre-scheduling plan; if a disturbance event occurs, the pre-scheduling plan is used as the input plan, and the job right-shift rescheduling strategy is executed to obtain a dynamic scheduling plan. If the obtained dynamic scheduling plan is equal to or does not dominate the input plan, the obtained dynamic scheduling plan is output and the process ends; otherwise, a dynamic scheduling objective function is established by minimizing the efficiency index and robustness index, and a biogeographical optimization algorithm is used to output the dynamic scheduling plan and the process ends.

[0011] Several alternative methods are provided below, but they are not intended as additional limitations on the overall solution above. They are merely further additions or optimizations. Provided there are no technical or logical contradictions, each alternative method can be combined individually with respect to the overall solution above, or multiple alternative methods can be combined with each other.

[0012] Preferably, the robust optimization objective function is as follows:

[0013]

[0014]

[0015]

[0016]

[0017]

[0018]

[0019]

[0020] In the formula, minf1 is the robust optimization objective function, N is the total number of scenes in the discrete scene set, and p n Let n be the probability of scenario n occurring. p represents the maximum completion time of the pre-scheduling phase in scenario n. n' Let n' be the probability of scenario n' occurring. Let I be the maximum completion time in the pre-scheduling phase under scenario n', and let K be the total number of jobs in the remanufacturing shop, R be the total number of machines in the remanufacturing shop, and R be the maximum completion time in the pre-scheduling phase. i For the i-th assignment J i The total number of candidate paths, For the i-th assignment J i The total number of operations on the r-th candidate path, Given a binary variable, if on the k-th machine M k Execute the i-th job J i The r-th candidate path The j-th operation So otherwise, For machine M in scenario n during the pre-scheduling phase k Perform operation End time, For machine M in scenario n' during the pre-scheduling phase k Perform operation End time, For machine M in scenario n during the pre-scheduling phase k Perform operation The start time, For machine M in scenario n' during the pre-scheduling phase k Perform operation The start time, For machine M in scenario n k Perform operation Processing time, For machine M in scenario n' k Perform operation Processing time;

[0021] AT in For scenario n, the task J i Arrival time, For binary variables, if the operation It is machine M k The first operation performed on, then otherwise, For a binary variable, if on the k'th machine M k' Execute the i-th job J i The r-th candidate path The (j-1)th operation So otherwise, For machine M in scenario n during the pre-scheduling phase k' Perform operation End time, If it is a binary variable, then in machine M k Perform operation Adjacent and prior to operation So otherwise, If it is a binary variable, then in machine M k Execute the i'th job J i' The r'th candidate path The j'th operation So otherwise, For machine M in scenario n during the pre-scheduling phase k Execute the i'th job J i' The r-th candidate path AR i r ' The j'th operation The end time, AT in' Assignment J under scenario n' i Arrival time, For machine M in scenario n' during the pre-scheduling phase k' Perform operation End time, For machine M in scenario n' during the pre-scheduling phase k Execute the i'th job J i' The r-th candidate path The j'th operation The end time.

[0022] Preferably, the constraints of the robust optimization objective function are as follows:

[0023] Ensure that each job can only select one candidate path:

[0024]

[0025] Ensure that each machine can only perform one operation at a time:

[0026]

[0027] Ensure the start time on the machine is feasible:

[0028]

[0029] Ensure the end time on the machine is feasible:

[0030]

[0031] In the formula, If the assignment J is a binary variable, then... i If we choose the r-th candidate path, then... otherwise, M is a predefined constant, n = 1, 2, ..., N, i = 1, 2, ..., I, k = 1, 2, ..., K, r = 1, 2, ..., R i .

[0032] Preferably, the execution process of the biogeographical optimization algorithm is as follows:

[0033] (1) Initialize the population and use a two-dimensional unequal length encoding method to represent each habitat in the population;

[0034] (2) Calculate the fitness index value of each habitat based on the robust optimization objective function or the dynamic scheduling objective function, and at the same time use the sinusoidal migration model to calculate the immigration rate and emigration rate of each habitat.

[0035] (3) Execute the migration operator based on the immigration rate and emigration rate to obtain new habitats;

[0036] (4) Execute the mutation operator to obtain a new habitat;

[0037] (5) Execute a local search strategy, which includes three local search operators, and execute each local search operator to obtain a new habitat;

[0038] (6) Determine whether the termination conditions of the pre-scheduling stage or the dynamic scheduling stage are met. If the termination conditions are met, output the optimal solution, i.e. the optimal pre-scheduling scheme or the dynamic scheduling scheme; otherwise, proceed to step (2) to continue iterating.

[0039] Preferably, the method of using a two-dimensional unequal-length encoding to represent each habitat in the population includes:

[0040] Let a habitat contain path selection sequence information and job sequence information. In the representation of the habitat, the first dimension is encoded for the path selection sequence information. The length of the first dimension is the total number of jobs in the remanufacturing workshop, and the value in the first dimension is the candidate path index selected by each job from its candidate path set.

[0041] The second dimension encodes the job sequence information. The length of the second dimension is the total number of operations in all jobs. The value in the second dimension is the index of each job. The order in which the same value appears is the order in which the corresponding job operations are executed. Based on the path selection sequence information, the machine index corresponding to each value in the job sequence information is obtained to form the corresponding machine sequence.

[0042] Preferably, the calculation of the immigration and emigration rates for each habitat using a sinusoidal migration model includes:

[0043]

[0044]

[0045] In the formula, λ i and μ i Let I represent the immigration rate and emigration rate of habitat i, respectively. max and E max S represents the maximum immigration rate and the maximum emigration rate, respectively. i S represents the population size in habitat i. max This indicates the maximum population size.

[0046] Preferably, the migration operator includes:

[0047] Randomly divide all assignments into two non-empty subsets to obtain the first assignment set and the second assignment set;

[0048] For the first dimension of the habitat, the fitness index variable corresponding to the location in the first job set in the new habitat is copied to the new habitat while keeping its location unchanged; the fitness index variable corresponding to the location in the second job set in the new habitat is copied to the new habitat while keeping its location unchanged.

[0049] For the second dimension of habitat, the fitness index variables of the operations that move into the habitat and belong to the first set of operations are copied to the new habitat while keeping their positions unchanged; the fitness index variables of the operations that move out of the habitat and belong to the second set of operations are copied to the new habitat while keeping their order unchanged.

[0050] Preferably, the mutation operator includes:

[0051] For the first dimension of the habitat, several fitness index variables are randomly selected and replaced with the indices of other candidate paths corresponding to the task in turn; if there are no other candidate paths for the task, this operation is not performed.

[0052] For the second dimension of the habitat, update the second dimension based on the modified first dimension of the habitat. If the length of the candidate path after replacement in the first dimension is the same as the length of the candidate path before replacement, no operation is performed. If the length of the candidate path after replacement in the first dimension is greater than the length of the candidate path before replacement, add a new job index at the end of the second dimension. If the length of the candidate path after replacement in the first dimension is less than the length of the candidate path before replacement, delete the job index at the redundant position in the second dimension.

[0053] Preferably, the three local search operators in the local search strategy are as follows:

[0054] The first local search operator: Traverse the first half of the job sequence information in the habitat. If the job arrival time of the traversed position is 0, then traverse the next position; otherwise, randomly insert the fitness index variable of that position into the second half of the job sequence information. After traversal, if no operation is performed, randomly select two fitness index variables in the second half of the job sequence information and perform a swap operation.

[0055] The second local search operator: randomly select a segment of fitness index variables from the job sequence information, randomly arrange the segment of fitness index variables, and then put them back in their original positions;

[0056] The third local search operator: randomly select two fitness index variables from the job sequence information and perform a swap operation.

[0057] Preferably, the step of establishing a dynamic scheduling objective function to minimize efficiency and robustness metrics includes:

[0058]

[0059]

[0060]

[0061]

[0062]

[0063]

[0064]

[0065]

[0066] In the formula, f2 is the dynamic scheduling objective function, ω1 and ω2 are the weights of the efficiency index and the robustness index, respectively, and satisfy ω1 + ω2 = 1, EI max and EI min RI represents the maximum and minimum values ​​of the efficiency index, respectively. max and RI min These represent the maximum and minimum values ​​of the robustness index, respectively, while EI represents the current efficiency index. The maximum completion time during the dynamic scheduling phase is RI, which is the current robustness metric. For machine M in scenario c during the dynamic scheduling phase k Perform operation End time, For machine M in scenario c during the dynamic scheduling phase k Perform operation The start time, For machine M in scenario c during the dynamic scheduling phase k' Perform operation End time, For machine M in scenario c during the dynamic scheduling phase k Perform operation The end time, c = 1, 2, ..., N, i = 1, 2, ..., I, k = 1, 2, ..., K, r = 1, 2, ..., R i .

[0067] This invention provides a robust optimization-based dynamic scheduling method for remanufacturing workshops. Addressing the issues of multiple uncertainties and the impact of disturbance events in remanufacturing workshops, the remanufacturing scheduling process is divided into a pre-scheduling stage and a dynamic scheduling stage. The pre-scheduling stage uses a discrete scenario set to describe the multiple uncertainties in the remanufacturing workshop and employs a robust optimization method to construct a mathematical model. The dynamic scheduling stage designs a hybrid rescheduling strategy to avoid the efficiency reduction of the remanufacturing system caused by disturbance events. Attached Figure Description

[0068] Figure 1 This is an example diagram of the optimized scheduling of the remanufacturing workshop according to the present invention;

[0069] Figure 2 This is a flowchart of a dynamic scheduling method for a remanufacturing workshop based on robust optimization according to the present invention.

[0070] Figure 3 This is a flowchart of the EBBO algorithm executed during the pre-scheduling phase of this invention;

[0071] Figure 4 This is an example diagram representing the habitat of the present invention;

[0072] Figure 5 This is an example diagram illustrating the application of the migration operator to the habitat according to the present invention;

[0073] Figure 6 This is an example diagram illustrating the application of the mutation operator to the habitat according to the present invention;

[0074] Figure 7 This is an example diagram illustrating the application of a local search operator to operation sequence information in habitats according to the present invention.

[0075] Figure 8 This is a flowchart of the hybrid rescheduling strategy executed during the dynamic scheduling phase of the present invention.

[0076] Figure 9 This is a graph showing the iterative convergence results of the EBBO algorithm and three other baseline algorithms in the experiments of this invention.

[0077] Figure 10 The figure shows the performance comparison results of the EBBO algorithm with three other baseline algorithms in the experiment of this invention. Detailed Implementation

[0078] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0079] 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 this invention pertains. The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the invention.

[0080] To overcome the limitations of existing dynamic scheduling schemes for remanufacturing shops, this invention proposes a novel dynamic scheduling method for remanufacturing shops based on robust optimization. This method is considered as a RO-RSDS (Robust Optimization-based Remanufacturing Shop Dynamic Scheduling) model. The entire remanufacturing scheduling process is divided into a pre-scheduling phase and a dynamic scheduling phase after a disturbance event occurs. The model is based on the following assumptions: all machines are available initially; processing can only begin after a job arrives, and there is no priority between jobs; all start-up time, setup time, and transportation time are ignored.

[0081] First, in the pre-scheduling phase, a discrete scenario set is used to describe the uncertainties in job arrival and processing times in the remanufacturing workshop. A robust optimization method is used to construct a mathematical model, aiming to find a stable solution that performs well under all possible scenarios. The pre-scheduling scheme is obtained by minimizing the completion time of the scheduling scheme and the difference in completion time under different scenarios. Second, once the remanufacturing process begins, if a disturbance event occurs, it will trigger the dynamic scheduling phase. In the dynamic scheduling phase, a novel hybrid rescheduling strategy is adopted, with efficiency and robustness as optimization objectives to obtain the final dynamic scheduling scheme, thereby addressing the problem of reduced efficiency in the remanufacturing system caused by disturbance events.

[0082] To clearly illustrate the RO-RSDS model, Figure 1 An example of optimized scheduling in a remanufacturing workshop is shown. Figure 1 The left side represents the pre-scheduling phase, which uses a discrete set of scenarios to describe the uncertainties in product arrival and processing times. In the example, assume two crankshafts and one gear need remanufacturing, denoted as jobs J1, J2, and J3, respectively, and four machines M1, M2, M3, and M4. The candidate path set for J1 is {M1→M2→M4, M3→M2→M1, M4→M3}, for J2 it is {M1→M4, M3→M1}, and for J3 it is {M3→M2, M2→M3, M4→M1}. N scenarios are used to describe the uncertain arrival and processing times for all jobs.

[0083] Assume all jobs choose path 1 in any scenario. In scenario 1, J1 arrives at time 0 and recovers to a new state after three operations: pyrolysis, polishing, and cleaning, denoted as operation O. 11 O 12 and O 13 The processing times are 6, 4, and 8 respectively; the arrival time of J2 is 10, and it recovers to a new state after two operations: polishing and cleaning, which are represented as operations O. 21 and O 22 The processing times are 2 and 5 respectively; the arrival time of J3 is 0, and it recovers to a new state after two operations: grinding and cleaning, which are represented as operation O respectively. 31 and O 32 The processing times are 7 and 3 respectively. In scenario n, the arrival time of J1 is 0, and the processing times are 5, 3, and 9 respectively; the arrival time of J2 is 0, and the processing times are 4 and 5 respectively; the arrival time of J3 is 6, and the processing times are 9 and 3 respectively. In scenario N, the arrival time of J1 is 2, and the processing times are 4, 6, and 9 respectively; the arrival time of J2 is 0, and the processing times are 3 and 5 respectively; the arrival time of J3 is 0, and the processing times are 8 and 2 respectively. In the dynamic scheduling phase, assuming the actual scenario is n, machine M3 fails at time 10, and the time required to restore normal operation is 4. After the failure, the unfinished operation O of machine M3 31 The rightward movement, and the operations affected by the fault event, are represented by gray diagonal stripes in the diagram.

[0084] like Figure 2 As shown, in the pre-scheduling stage, a discrete scenario set is used to describe the uncertainty of arrival time and processing time in the remanufacturing process. A robust optimization method is used to construct a mathematical model, and the robust optimization objective is to minimize the completion time of the scheduling scheme and the difference in completion time under different scenarios, so as to obtain a stable solution that performs well under different scenarios. The robust optimization objective function proposed in this embodiment is shown in Equation (1), and the maximum completion time in the pre-scheduling stage is obtained by Equations (2)-(7).

[0085]

[0086]

[0087]

[0088]

[0089]

[0090]

[0091]

[0092] In the formula, minf1 is the robust optimization objective function, N is the total number of scenes in the discrete scene set, and p n Let n be the probability of scenario n occurring. p represents the maximum completion time of the pre-scheduling phase in scenario n. n' Let n' be the probability of scenario n' occurring. R represents the maximum completion time during the pre-scheduling phase in scenario n'. I is the total number of jobs in the remanufacturing shop, and K is the total number of machines in the remanufacturing shop. i For the i-th assignment J i The total number of candidate paths, For the i-th assignment J i The total number of operations on the r-th candidate path. Given a binary variable, if on the k-th machine M k Execute the i-th job J i The r-th candidate path The j-th operation So otherwise, For machine M in scenario n during the pre-scheduling phase k Perform operation End time, For machine M in scenario n' during the pre-scheduling phase k Perform operation The end time. For machine M in scenario n during the pre-scheduling phase k Perform operation The start time, For machine M in scenario n' during the pre-scheduling phase k Perform operation The start time. For machine M in scenario n k Perform operation Processing time, For machine M in scenario n' k Perform operation Processing time.

[0093] AT in For scenario n, the task J i The arrival time, where j is the operation index. For binary variables, if the operation It is machine M k The first operation performed on, then otherwise, For a binary variable, if on the k'th machine M k' Execute the i-th job J i The r-th candidate path The (j-1)th operation So otherwise, For machine M in scenario n during the pre-scheduling phase k' Perform operation The end time. If it is a binary variable, then in machine M k Perform operation Adjacent and prior to operation So otherwise, If it is a binary variable, then in machine M k Execute the i'th job J i' The r'th candidate path The j'th operation So otherwise, For machine M in scenario n during the pre-scheduling phase k Execute the i'th job J i' The r-th candidate path The j'th operation The end time. AT in' Assignment J under scenario n' i Arrival time, For machine M in scenario n' during the pre-scheduling phase k' Perform operation End time, For machine M in scenario n' during the pre-scheduling phase k Execute the i'th job J i' The r-th candidate path The j'th operation The end time.

[0094] Furthermore, the constraints are established as shown in formulas (8)-(11):

[0095] Ensure that each job can only select one candidate path:

[0096]

[0097] Ensure that each machine can only perform one operation at a time:

[0098]

[0099] Ensure the start time on the machine is feasible:

[0100]

[0101] Ensure the end time on the machine is feasible:

[0102]

[0103] In the formula, If the assignment J is a binary variable, then... i If we choose the r-th candidate path, then... otherwise, M is a predefined constant, usually a very large number; n' is the scene index, n' = 1, 2, ..., N; n is the scene index, n = 1, 2, ..., N; i is the job index, i = 1, 2, ..., I; k is the machine index, k = 1, 2, ..., K; r is the candidate path index, r = 1, 2, ..., R. i s is the stage index, s=1 is the pre-scheduled stage, and s=2 is the dynamic scheduling stage.

[0104] The RO-RSDS model proposed in this invention is a typical NP-hard problem. Biogeography-based optimization (BBO) algorithm, as an intelligent optimization algorithm, solves NP-hard problems by simulating the migration process of species between habitats.

[0105] In the BBO algorithm, the Habitat Suitability Index (HSI) is used to evaluate the quality of each solution (i.e., habitat). A higher HSI indicates better performance, and vice versa. Suitability Index Variables (SIVs) are a set of factors that influence the quality of a solution.

[0106] The migration and mutation operators are the core of the BBO algorithm. The migration operator is a probabilistic operator that facilitates information exchange between different habitats. The immigration rate λ decreases as the number of species increases, while the emigration rate μ increases with the increase in the number of species. The mutation operator is also a probabilistic operator used to simulate habitat changes caused by sudden events in nature. Each habitat will change its SIV (Species Indicator Variance) according to a certain probability.

[0107] To address the problems of insufficient population diversity and premature convergence in the basic BBO algorithm, this embodiment makes three improvements to the basic BBO algorithm. The improved BBO algorithm serves as an Extended Biogeography-Based Optimization (EBBO) algorithm: (1) A new two-dimensional variable-length encoding scheme is designed to effectively represent the solution; (2) A sinusoidal migration model is introduced, and new migration operators and mutation operators are used to guide the population to migrate efficiently; (3) A local search strategy is proposed to improve population diversity and accelerate the convergence speed of the algorithm.

[0108] like Figure 3 As shown, the EBBO algorithm is used to output a pre-scheduling scheme during the pre-scheduling phase, including the following steps:

[0109] (1) Initialize the population and use a two-dimensional unequal length encoding method to represent each habitat in the population.

[0110] In the two-dimensional unequal-length encoding method, a habitat contains Route Selection Sequence (RSS) information and Job Sequence (JS) information. In the habitat representation, the first dimension encodes the RSS information, with a length equal to the total number of jobs in the remanufacturing workshop. The values ​​in the first dimension are the candidate path indices selected by each job from its candidate path set. The second dimension encodes the Job Sequence information, with a length equal to the total number of operations across all jobs. The values ​​in the second dimension are the job indices, and the order in which identical values ​​appear indicates the order in which the corresponding job performs its operations. Based on the RSS information, the machine index corresponding to each value in the Job Sequence information is obtained, forming the corresponding machine sequence.

[0111] based on Figure 1 The example provided in this embodiment illustrates a two-dimensional unequal-length encoding method. Figure 4As shown, the first dimension of the habitat information encodes the RSS information, with a length equal to the total number of jobs, and the value being the path index selected by each job from its candidate path set. For example, a value of 1 at the first position of the RSS information indicates that job J1 selected path 1, i.e., "M1→M2→M4"; a value of 1 at the second position indicates that job J2 selected path 1, i.e., "M1→M4". The second dimension encodes the JS information, with a length equal to the sum of the number of operations for all jobs, and the value being the index of each job. The order in which the values ​​appear indicates the order in which the corresponding jobs perform their operations. Based on the information about the job path selection in the two-dimensional unequal-length encoding scheme, the corresponding machine sequence can be further obtained. For example, from the RSS information above, we know that job J2 selected path 1 (i.e., "M1→M4"). Therefore, when the value "2" appears for the first time at the first position of the JS information, it indicates that the first operation of job J2 needs to be performed at that position, i.e., the machine sequence at that position is M1. When the value "2" appears for the second time at the fifth position of the JS information, it indicates that the second operation of job J2 needs to be performed at that position, i.e., the machine sequence at that position is M4. Following this logic, the machine sequence for all positions of the JS information can be obtained as "M1→M3→M1→M2→M4→M2→M4". Based on this, and combined with the arrival time of the job, the Gantt chart for scenario n can be obtained.

[0112] (2) The fitness index of each habitat is calculated based on the robust optimization objective function, and the immigration rate and emigration rate of each habitat are calculated using the sinusoidal migration model.

[0113] Compared with the traditional linear migration model, the sinusoidal migration model is more in line with natural laws and performs better. Therefore, this embodiment introduces the sinusoidal migration model to calculate the immigration rate and immigration rate in the EBBO algorithm, and the calculation formulas are (12) and (13) respectively:

[0114]

[0115]

[0116] In the formula, λ i and μ i Let I represent the immigration rate and emigration rate of habitat i, respectively. max and E max S represents the maximum immigration rate and the maximum emigration rate, respectively. i S represents the population size in habitat i. max This indicates the maximum population size.

[0117] (3) The migration operator is executed based on the immigration rate and the emigration rate to obtain new habitats.

[0118] (3.1) Randomly divide all assignments into two non-empty subsets to obtain the first assignment set and the second assignment set.

[0119] (3.2) For the first dimension of the habitat, the fitness index variable whose position in the new habitat corresponds to the first job set is copied to the new habitat while keeping its position unchanged; the fitness index variable whose position in the new habitat corresponds to the second job set is copied to the new habitat while keeping its position unchanged.

[0120] (3.3) For the second dimension of the habitat, the fitness index variables of the job indexes of the job moving into the habitat that belong to the first job set are copied to the new habitat, while keeping their positions unchanged; the fitness index variables of the job indexes of the job moving out of the habitat that belong to the second job set are copied to the new habitat, while keeping their order unchanged.

[0121] like Figure 5 As shown, if the first job set contains job indices 2, 4, 6 and the second job set contains job indices 1, 3, 5, and when the migration operator is executed on the RSS information, if the RSS information of the migration into the habitat is 1, 1, 2, 3, 1, 2 and the RSS information of the migration out of the habitat is 2, 1, 1, 1, 2, 1, then the 1, 3, 2 at positions 2, 4, 6 of the migration into the habitat is copied to positions 2, 4, 6 of the new habitat, and the 2, 1, 2 at positions 1, 3, 5 of the migration out of the habitat is copied to positions 1, 3, 5 of the new habitat. When executing the migration operator on the JS information, if the JS information for the new habitat is 1,5,4,2,4,6,3,1,2,2,5,3 and the JS information for the new habitat is 6,5,1,1,3,6,1,6,4,2,2,4,5, then the values ​​2,4,6 for the new habitat are copied to the same position in the new habitat, and the values ​​1,3,5 for the new habitat are filled into the new habitat in the same order.

[0122] (4) Execute the mutation operator to obtain a new habitat.

[0123] (4.1) For the first dimension of the habitat, randomly select several fitness index variables and replace them with other candidate path indices corresponding to the operation in turn; if there are no other candidate paths for the operation, this operation is not performed.

[0124] (4.2) For the second dimension of the habitat, update the second dimension based on the modified first dimension of the habitat. If the length of the candidate path after replacement in the first dimension is the same as the length of the candidate path before replacement, no operation is performed. If the length of the candidate path after replacement in the first dimension is greater than the length of the candidate path before replacement, add the new job index at the end of the second dimension. If the length of the candidate path after replacement in the first dimension is less than the length of the candidate path before replacement, delete the job index at the redundant position in the second dimension.

[0125] like Figure 6As shown, when performing the mutation operator on the RSS information, the RSS information of the habitat before mutation is 1, 1, 2, 3, 1, 2. The values ​​at positions 2 and 4 are randomly selected. The value 1 at position 2 is mutated to 2, and the value 3 at position 4 is mutated to 1. Therefore, the RSS information of the habitat after mutation is 1, 2, 2, 1, 1, 2. Then, the second dimension is updated according to the mutated first dimension. When candidate path 1 at position 2 of the first dimension is replaced by candidate path 2, the length of the replaced candidate path becomes shorter, so the job index 2 at the corresponding redundant position 10 is deleted. When candidate path 3 at position 4 of the first dimension is replaced by candidate path 1, the length of the replaced candidate path becomes longer, so the newly added job index 4 is added to the end.

[0126] (5) Execute a local search strategy, which includes three local search operators, and execute each local search operator to obtain a new habitat.

[0127] Considering that the order of the job index in JS information directly affects the quality of the solution, this embodiment proposes a local search strategy that includes three local search operators.

[0128] The first local search operator: Iterates through the first half of the job sequence information in the habitat. If the job arrival time at a traversed location is 0, iterates to the next location; otherwise, it randomly inserts the fitness index variable of that location into the last half of the job sequence information. After traversal, if no operation is performed, it randomly selects two fitness index variables from the last half of the job sequence information and performs a swap operation. For example... Figure 7 As shown in (a), for the JS information in the habitat as 1,5,4,2,4,6,3,1,2,2,5,3, the job indices 4 and 4 are obtained by traversing and randomly inserting them to get the new JS information in the habitat as 1,5,2,6,3,1,2,4,2,5,4,3.

[0129] The second local search operator: randomly selects a segment of fitness index variables from the job sequence information, randomly rearranges this segment of fitness index variables, and then returns it to its original position. For example... Figure 7 As shown in (b), for the JS information in the habitat as 1,5,4,2,4,6,3,1,2,2,5,3, a segment including the job index 2,4,6,3,1 is randomly selected and randomly arranged to obtain 4,3,2,1,6. Thus, the JS information in the new habitat is 1,5,4,4,3,2,1,6,2,2,5,3.

[0130] The third local search operator: randomly selects two fitness index variables from the job sequence information and performs a swap operation. For example... Figure 7As shown in (c), for the JS information in the habitat as 1,5,4,2,4,6,3,1,2,2,5,3, the operation index 5 of position 2 and the action index 2 of position 9 are randomly selected for exchange operation, resulting in the JS information in the new habitat as 1,2,4,2,4,6,3,1,5,2,5,3.

[0131] (6) Determine whether the termination condition of the pre-scheduling stage is met. If the termination condition is met, output the optimal solution, i.e. the optimal pre-scheduling scheme; otherwise, proceed to step (2) to continue iterating.

[0132] During the dynamic scheduling phase, if a disturbance event (such as machine failure) occurs, the remanufacturing system needs to determine the final dynamic scheduling scheme based on the pre-scheduling scheme and the disturbance event information, while ensuring scheduling efficiency and minimizing performance differences with the pre-scheduling scheme. This embodiment uses an efficiency index to evaluate the scheduling efficiency of the dynamic scheduling scheme, measured by the maximum completion time. Simultaneously, a robustness index is used to evaluate the performance difference between the dynamic scheduling scheme and the pre-scheduling scheme, measured by the performance deviation between the two schemes.

[0133] Currently, commonly used rescheduling strategies can be divided into the following three types: (1) Job shifting left or right rescheduling strategy, which means that when a disturbance event occurs, the start time of unfinished operations is advanced or postponed by a certain time while keeping the machine operation sequence unchanged. The advantage of this strategy is that it responds quickly and is conducive to maintaining system stability. (2) Local rescheduling strategy, which means that only operations directly or indirectly affected by the disturbance event are rescheduled. (3) Full rescheduling strategy, which means that the pre-scheduling plan is not considered, and the rescheduling plan is solved based on the resource status after the disturbance event occurs in the workshop and specific performance indicators. This strategy has better performance when dealing with disturbance events such as machine failures.

[0134] To quickly respond to disturbances such as machine failures and better maintain system stability, this embodiment combines the right-shift rescheduling strategy and the full rescheduling strategy, proposing, for example... Figure 8 The hybrid rescheduling strategy shown is described in detail below:

[0135] During the dynamic scheduling phase, if no disturbance event occurs, the remanufacturing workshop is dynamically scheduled according to the pre-scheduling plan. If a disturbance event occurs, the pre-scheduling plan is used as the input plan (denoted as Sol0), and the job right-shift rescheduling strategy is executed to obtain the dynamic scheduling plan after the job right shift (denoted as Sol1). If the obtained dynamic scheduling plan Sol1 is equal to or does not dominate the input plan Sol0, the dynamic scheduling plan Sol1 is output as the final dynamic scheduling plan and the process ends. Otherwise, a dynamic scheduling objective function is established by minimizing the efficiency index and robustness index, and the BBO algorithm (specifically the EBBO algorithm in this embodiment) is used to output the dynamic scheduling plan and the process ends. That is, the EBBO algorithm is used to calculate the fitness value with the dynamic scheduling objective function and execute the full rescheduling strategy to obtain a new scheduling plan, denoted as Sol2, and Sol2 is output as the final dynamic scheduling plan.

[0136] Unlike the pre-scheduling phase, the remanufacturing system has a clearly defined actual remanufacturing scenario in the dynamic scheduling phase. This embodiment assumes the actual remanufacturing scenario in the dynamic scheduling phase is c, where c ∈ {1, 2, ..., N}, and the scheduling objective is to minimize the Effectiveness Indicator (EI) and Robustness Indicator (RI). The maximum completion time TT in the dynamic scheduling phase is... c 2 It can be calculated by formulas (17), (18) and (21), and constraints (19) and (20) need to be satisfied to ensure that the start time and end time on the machine are feasible.

[0137]

[0138] EI=TT c 2 (15)

[0139]

[0140]

[0141]

[0142]

[0143]

[0144]

[0145] In the formula, f2 is the dynamic scheduling objective function, ω1 and ω2 are the weights of the efficiency index and the robustness index, respectively, and satisfy ω1 + ω2 = 1. EI max and EI minRI represents the maximum and minimum values ​​of multiple efficiency indicators in the current population, respectively. max and RI min These represent the maximum and minimum robustness indices for multiple habitats within the current population, respectively. EI represents the current efficiency index. RI represents the maximum completion time during the dynamic scheduling phase, and RI is the current robustness metric. For machine M in scenario c during the dynamic scheduling phase k Perform operation End time, For machine M in scenario c during the dynamic scheduling phase k Perform operation The start time. For machine M in scenario c during the dynamic scheduling phase k' Perform operation End time, For machine M in scenario c during the dynamic scheduling phase k Perform operation The end time.

[0146] The algorithm involved in the hybrid rescheduling strategy executed during the dynamic scheduling phase in this embodiment is also the EBBO algorithm, and the execution process is as follows:

[0147] (1) Initialize the population and use a two-dimensional unequal length encoding method to represent each habitat in the population.

[0148] (2) The fitness index value of each habitat is calculated based on the dynamic scheduling objective function, and the immigration rate and emigration rate of each habitat are calculated using a sinusoidal migration model.

[0149] (3) The migration operator is executed based on the immigration rate and the emigration rate to obtain new habitats.

[0150] (4) Execute the mutation operator to obtain a new habitat.

[0151] (5) Execute the local search strategy, which includes three local search operators. Execute each local search operator to obtain a new habitat.

[0152] (6) Determine whether the termination condition of the dynamic scheduling stage is met. If the termination condition is met, output the optimal solution, i.e. the optimal dynamic scheduling scheme; otherwise, proceed to step (2) to continue iterating.

[0153] It should be noted that the specific limitations of the EBBO algorithm executed during the dynamic scheduling phase can be found in the limitations of the EBBO algorithm during the pre-scheduling phase, which will not be repeated here.

[0154] The following experiments further illustrate the superiority of the robust optimization-based dynamic scheduling method for remanufacturing workshops proposed in this invention, as well as the effectiveness of the hybrid rescheduling strategy proposed in this invention.

[0155] Two sets of sensitivity experiments and two sets of performance simulation experiments were designed. First, the EBBO algorithm was compared with three baseline algorithms to select algorithm parameters and comprehensively evaluate algorithm performance. The baseline algorithms included the Improved Genetic Algorithm (IGA), Discrete Particle Swarm Optimization (DPSO), and Modified Biogeographical Optimization (MBBO). Second, the performance of the hybrid rescheduling strategy and the full rescheduling strategy was compared. The Non-dominated Sorting Genetic Algorithm-II (NSGA-II) was used to solve the dynamic scheduling scheme after implementing the full rescheduling strategy. All experiments were implemented using Python and run on a computer with a 64-bit Windows 10 operating system, an Intel(R) core 3.10GHz processor, and 16GB of memory.

[0156] (1) Experimental Design

[0157] To simulate a real remanufacturing environment, the specific values ​​used in this experiment are as follows: Number of candidate paths R i The value is [1, 4], and the path length is... The value is [1, 6], and the arrival time is AT. in The value is [0, 20] hours, representing the processing time. The value is [2, 8] hours, representing the time point of machine failure. The fault recovery time is set to [0.1, 10.0] hours. Each simulation instance is named according to the number of jobs, machines, and scenarios; for example, "J30_M10_S10" indicates that the remanufacturing workshop has 30 jobs, 10 machines, and 10 scenarios. To reduce experimental error, all experiments are run independently 10 times, and the average value is taken as the final experimental result. Furthermore, the EBBO algorithm parameter maximum migration rate I... max and maximum migration rate E max All values ​​are set to 1, and the weights ω1 and ω2 are both set to 0.5.

[0158] (2) Sensitivity analysis

[0159] The sensitivity tests in this experiment were all performed on the "J20_M10_S10" simulation instance, with a population size of 30 for all algorithms. The first set of experiments compared the performance of the four algorithms at different iteration numbers. The experimental results are as follows: Figure 9 As shown, the EBBO algorithm converges faster and has a better fitness value than the other three baseline algorithms. Experimental results demonstrate that the EBBO algorithm has stronger search capabilities and faster convergence speed compared to the other three baseline algorithms. Figure 9 It can also be seen that after 280 iterations, the fitness values ​​of the solutions obtained by the four algorithms all tend to stabilize. Therefore, in subsequent experiments, the number of iterations for all algorithms was set to 280.

[0160] The second set of experiments compared the performance of the four algorithms under different population sizes. The experimental results are as follows: Figure 10 As shown, under different population sizes, the fitness values ​​obtained by the EBBO algorithm are superior to the other three baseline algorithms and are relatively stable. The IGA algorithm only has good fitness values ​​when the population size is 40, 55, 60, and 70; the DPSO algorithm only has good fitness values ​​when the population size is 40 and 65; and the MBBO algorithm only has relatively stable fitness values ​​when the population size is small. Considering that the simulation experiment needs to ensure a fair and effective comparison of the four algorithms and to be conducted with the lowest possible computational complexity, the population size for all algorithms will be set to 40 in subsequent experiments.

[0161] (3) Performance simulation analysis

[0162] The first set of performance simulation experiments comprehensively evaluated the performance of the four algorithms during the pre-scheduling phase. The experimental results are shown in Tables 1 and 2. Table 1 lists the best and average values ​​of the solutions obtained by the four algorithms. As can be seen from Table 1, the best and average values ​​of the solutions obtained by the EBBO algorithm are superior to the other three baseline algorithms, indicating that the EBBO algorithm can find a better scheduling scheme when solving the model in this paper compared to the other three baseline algorithms. Table 2 lists the standard deviation of the solutions obtained by the four algorithms and the average CPU computation time (marked as "computation time" in the table, in hours). As can be seen from Table 2, the standard deviation of the solutions obtained by the EBBO algorithm is superior to the other three baseline algorithms, indicating that the EBBO algorithm has more stable performance when solving the model in this paper. Furthermore, because the EBBO algorithm uses a local search strategy, its computational complexity is higher than the other three baseline algorithms, requiring more computation time. However, the best, average, and standard deviation of the solutions obtained by the EBBO algorithm are all superior to the other three baseline algorithms, and the increased computation time is within an acceptable range. In summary, the EBBO algorithm outperforms the other three baseline algorithms when solving the RO-RSDS model.

[0163] Table 1 shows the best and average solutions obtained by the four algorithms.

[0164]

[0165] Table 2 shows the standard deviation and average computation time of the solutions obtained by the four algorithms.

[0166]

[0167] Based on the experimental results obtained in the pre-scheduling phase, the second set of performance simulation experiments compared the performance of the hybrid rescheduling strategy and the full rescheduling strategy in the dynamic scheduling phase. Machine fault information and experimental results are shown in Table 3. To quickly respond to disturbance events, a computation time of 60 seconds was used as the iteration stopping condition in the dynamic scheduling phase. As can be seen from Table 3, the solutions obtained by executing the hybrid rescheduling strategy outperform those obtained by executing the full rescheduling strategy, indicating that the proposed hybrid rescheduling strategy can effectively balance the efficiency and robustness of the scheduling scheme and can quickly respond to disturbance events, demonstrating better practicality and efficiency.

[0168] Table 3. Machine fault information and experimental results obtained from executing two rescheduling strategies.

[0169]

[0170] This invention addresses the remanufacturing workshop scheduling problem under the influence of uncertainty and disturbance events, proposing a dynamic scheduling method for remanufacturing workshops based on robust optimization. Building upon this, an extended biogeographical optimization algorithm is proposed, employing a two-dimensional unequal-length encoding scheme to effectively represent solutions. A sinusoidal migration model is introduced, along with novel migration and mutation operators to guide efficient population migration. Furthermore, a local search strategy is proposed to enhance population diversity and accelerate algorithm convergence. Simulation results demonstrate that the proposed algorithm exhibits superior performance across different problem scales, and the proposed hybrid rescheduling strategy effectively balances efficiency and robustness while providing a rapid response to disturbance events.

[0171] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0172] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the appended claims.

Claims

1. A dynamic scheduling method for remanufacturing workshops based on robust optimization, characterized in that, The robust optimization-based dynamic scheduling method for the remanufacturing shop includes a pre-scheduling phase and a dynamic scheduling phase, wherein: In the pre-scheduling stage, a discrete scenario set is used to describe the arrival time and processing time of the operations in the remanufacturing workshop. A robust optimization objective function is established based on minimizing the completion time of the pre-scheduling scheme and the difference in completion time under different scenarios. A biogeographical optimization algorithm is used to output the pre-scheduling scheme. In the dynamic scheduling phase, if no disturbance event occurs, the remanufacturing workshop is dynamically scheduled according to the pre-scheduling plan; if a disturbance event occurs, the pre-scheduling plan is used as the input plan, and the job right-shift rescheduling strategy is executed to obtain a dynamic scheduling plan. If the obtained dynamic scheduling plan is equal to or does not dominate the input plan, the obtained dynamic scheduling plan is output and the process ends; otherwise, a dynamic scheduling objective function is established by minimizing the efficiency index and robustness index, and a biogeographical optimization algorithm is used to output the dynamic scheduling plan and the process ends. The robust optimization objective function is as follows: In the formula, minf1 is the robust optimization objective function, N is the total number of scenes in the discrete scene set, and p n Let n be the probability of scenario n occurring. p represents the maximum completion time of the pre-scheduling phase in scenario n. n' Let n' be the probability of scenario n' occurring. Let I be the maximum completion time in the pre-scheduling phase under scenario n', and let K be the total number of jobs in the remanufacturing shop, R be the total number of machines in the remanufacturing shop, and R be the maximum completion time in the pre-scheduling phase. i For the i-th assignment J i The total number of candidate paths, For the i-th assignment J i The total number of operations on the r-th candidate path, Given a binary variable, if on the k-th machine M k Execute the i-th job J i The r-th candidate path The j-th operation So otherwise, For machine M in scenario n during the pre-scheduling phase k Perform operation End time, For machine M in scenario n' during the pre-scheduling phase k Perform operation End time, For machine M in scenario n during the pre-scheduling phase k Perform operation The start time, For machine M in scenario n' during the pre-scheduling phase k Perform operation The start time, For machine M in scenario n k Perform operation Processing time, For machine M in scenario n' k Perform operation Processing time; AT in For scenario n, the task J i Arrival time, For binary variables, if the operation It is machine M k The first operation performed on, then otherwise, For a binary variable, if on the k'th machine M k' Execute the i-th job J i The r-th candidate path The (j-1)th operation So otherwise, For machine M in scenario n during the pre-scheduling phase k' Perform operation End time, If it is a binary variable, then in machine M k Perform operation Adjacent and prior to operation So otherwise, If it is a binary variable, then in machine M k Execute the i'th job J i' The r'th candidate path The j'th operation So otherwise, For machine M in scenario n during the pre-scheduling phase k Execute the i'th job J i' The r-th candidate path The j'th operation End time, AT in' Assignment J under scenario n' i Arrival time, For machine M in scenario n' during the pre-scheduling phase k' Perform operation End time, For machine M in scenario n' during the pre-scheduling phase k Execute the i'th job J i' The r-th candidate path The j'th operation The end time.

2. The dynamic scheduling method for remanufacturing workshops based on robust optimization as described in claim 1, characterized in that, The constraints of the robust optimization objective function are as follows: Ensure that each job can only select one candidate path: Ensure that each machine can only perform one operation at a time: Ensure the start time on the machine is feasible: Ensure the end time on the machine is feasible: In the formula, If the assignment J is a binary variable, then... i If we choose the r-th candidate path, then... otherwise, M is a predefined constant, n = 1, 2, ..., N, i = 1, 2, ..., I, k = 1, 2, ..., K, r = 1, 2, ..., R i .

3. The dynamic scheduling method for remanufacturing workshops based on robust optimization as described in claim 1, characterized in that, The execution process of the biogeographical optimization algorithm is as follows: (1) Initialize the population and use a two-dimensional unequal length encoding method to represent each habitat in the population; (2) Calculate the fitness index value of each habitat based on the robust optimization objective function or the dynamic scheduling objective function, and at the same time use the sinusoidal migration model to calculate the immigration rate and emigration rate of each habitat. (3) Execute the migration operator based on the immigration rate and emigration rate to obtain new habitats; (4) Execute the mutation operator to obtain a new habitat; (5) Execute a local search strategy, which includes three local search operators, and execute each local search operator to obtain a new habitat; (6) Determine whether the termination conditions of the pre-scheduling stage or the dynamic scheduling stage are met. If the termination conditions are met, output the optimal solution, i.e. the optimal pre-scheduling scheme or the dynamic scheduling scheme; otherwise, proceed to step (2) to continue iterating.

4. The dynamic scheduling method for remanufacturing workshops based on robust optimization as described in claim 3, characterized in that, The two-dimensional unequal-length encoding method used to represent each habitat in the population includes: Let a habitat contain path selection sequence information and job sequence information. In the representation of the habitat, the first dimension is encoded for the path selection sequence information. The length of the first dimension is the total number of jobs in the remanufacturing workshop, and the value in the first dimension is the candidate path index selected by each job from its candidate path set. The second dimension encodes the job sequence information. The length of the second dimension is the total number of operations in all jobs. The value in the second dimension is the index of each job. The order in which the same value appears is the order in which the corresponding job operations are executed. Based on the path selection sequence information, the machine index corresponding to each value in the job sequence information is obtained to form the corresponding machine sequence.

5. The dynamic scheduling method for remanufacturing workshops based on robust optimization as described in claim 4, characterized in that, The calculation of immigration and emigration rates for each habitat using a sinusoidal migration model includes: In the formula, λ i and μ i Let I represent the immigration rate and emigration rate of habitat i, respectively. max and E max S represents the maximum immigration rate and the maximum emigration rate, respectively. i S represents the population size in habitat i. max This indicates the maximum population size.

6. The dynamic scheduling method for remanufacturing workshops based on robust optimization as described in claim 4, characterized in that, The migration operator includes: Randomly divide all assignments into two non-empty subsets to obtain the first assignment set and the second assignment set; For the first dimension of the habitat, the fitness index variable corresponding to the location in the first job set in the new habitat is copied to the new habitat while keeping its location unchanged; the fitness index variable corresponding to the location in the second job set in the new habitat is copied to the new habitat while keeping its location unchanged. For the second dimension of habitat, the fitness index variables of the operations that move into the habitat and belong to the first set of operations are copied to the new habitat while keeping their positions unchanged; the fitness index variables of the operations that move out of the habitat and belong to the second set of operations are copied to the new habitat while keeping their order unchanged.

7. The dynamic scheduling method for remanufacturing workshops based on robust optimization as described in claim 4, characterized in that, The mutation operator includes: For the first dimension of the habitat, several fitness index variables are randomly selected and replaced with the indices of other candidate paths corresponding to the task in turn; if there are no other candidate paths for the task, this operation is not performed. For the second dimension of the habitat, update the second dimension based on the modified first dimension of the habitat. If the length of the candidate path after replacement in the first dimension is the same as the length of the candidate path before replacement, no operation is performed. If the length of the candidate path after replacement in the first dimension is greater than the length of the candidate path before replacement, add a new job index at the end of the second dimension. If the length of the candidate path after replacement in the first dimension is less than the length of the candidate path before replacement, delete the job index at the redundant position in the second dimension.

8. The dynamic scheduling method for remanufacturing workshops based on robust optimization as described in claim 4, characterized in that, The three local search operators in the local search strategy are as follows: The first local search operator: Traverse the first half of the job sequence information in the habitat. If the job arrival time of the traversed position is 0, then traverse the next position; otherwise, randomly insert the fitness index variable of that position into the second half of the job sequence information. After traversal, if no operation is performed, randomly select two fitness index variables in the second half of the job sequence information and perform a swap operation. The second local search operator: randomly select a segment of fitness index variables from the job sequence information, randomly arrange the segment of fitness index variables, and then put them back in their original positions; The third local search operator: randomly select two fitness index variables from the job sequence information and perform a swap operation.

9. The dynamic scheduling method for remanufacturing workshops based on robust optimization as described in claim 1, characterized in that, The establishment of the dynamic scheduling objective function by minimizing efficiency and robustness metrics includes: In the formula, f2 is the dynamic scheduling objective function, ω1 and ω2 are the weights of the efficiency index and the robustness index, respectively, and satisfy ω1 + ω2 = 1, EI max and EI min RI represents the maximum and minimum values ​​of the efficiency index, respectively. max and RI min These represent the maximum and minimum values ​​of the robustness index, respectively, while EI represents the current efficiency index. The maximum completion time during the dynamic scheduling phase is RI, which is the current robustness metric. For machine M in scenario c during the dynamic scheduling phase k Perform operation End time, For machine M in scenario c during the dynamic scheduling phase k Perform operation The start time, For machine M in scenario c during the dynamic scheduling phase k' Perform operation End time, For machine M in scenario c during the dynamic scheduling phase k Perform operation The end time, c = 1, 2, ..., N, i = 1, 2, ..., I, k = 1, 2, ..., K, r = 1, 2, ..., R i .

Images