CN116774657A - Dynamic scheduling method for remanufacturing workshop based on robust optimization - Google Patents
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Abstract
The invention discloses a remanufacturing workshop dynamic scheduling method based on robust optimization, which comprises a pre-scheduling stage and a dynamic scheduling stage, wherein in the pre-scheduling stage, discrete scene sets are adopted to describe the arrival time and the processing time of the operation in a remanufacturing workshop, a robust optimization objective function is established based on the difference between the finishing time of a minimized pre-scheduling scheme and the finishing time in different scenes, and a biological geography optimization algorithm is adopted to output the pre-scheduling scheme; in the dynamic scheduling stage, if a disturbance event occurs, taking a pre-scheduling scheme as an input scheme, executing a right-shift rescheduling strategy of the job to obtain a dynamic scheduling scheme, and if the dynamic scheduling scheme is equal to or not dominant to the input scheme, outputting the dynamic scheduling scheme; otherwise, a dynamic scheduling objective function is established by the minimized efficiency index and the robustness index, and a dynamic scheduling scheme is output by adopting a biophysical optimization algorithm. The invention considers the problems of multiple uncertainties and the influence of disturbance events, and obtains a better scheduling scheme.
Description
Technical Field
The invention belongs to the field of remanufacturing workshops, and particularly relates to a dynamic scheduling method of a remanufacturing workshop based on robust optimization.
Background
Remanufacturing is a green manufacturing mode which combines the recycling of waste materials and the recycling development of low carbon, and has been widely paid attention to by various communities. The remanufacturing of the waste products can save 35% -60% of cost, 60% of energy and 70% of materials and reduce 60% of carbon dioxide emission, and the selling price is only 30% -40% of that of the traditional products, so that good economic benefit and environmental benefit are brought to society. The large-scale and standardized development of the remanufacturing industry is not separated from the development of the remanufacturing workshop scheduling technology, so that the research on the remanufacturing workshop scheduling optimization problem has important theoretical and practical significance for pushing the remanufacturing industry.
The prior art was studied earlier mainly for scheduling strategies in remanufacturing plants. Later, some research turned to the impact of different remanufacturing system configurations on overall scheduling efficiency, such as one existing integrated remanufacturing system configuration including a product disassembly shop, a dedicated flow line rework line shop, and a reassembly shop, and using minimized finishing time as an optimization objective to determine the order of product processing at the three workshops. In addition, there have also been studies on remanufacturing system configurations including a disassembly shop, a remanufacturing shop, and a remanufacturing shop, using a non-dedicated flow remanufacturing line to treat waste products having a difference in quality. However, remanufacturing plants use waste products as raw materials and are subject to more uncertainty factors and disturbance events, such as uncertainty in quality, arrival time, processing path, etc. of the waste products, machine failure, etc. than conventional manufacturing plants.
In recent years, some research has begun focusing on remanufacturing shop scheduling optimization problems in uncertain environments, such as engine block remanufacturing shop scheduling problems with batch and parallel machines, using Petri nets to describe process time and path uncertainties. In addition, uncertainty of waste product quality and processing time in the remanufacturing process is described by researching the random number and the triangular fuzzy number, and a remanufacturing production scheduling fuzzy model is constructed. There are also some studies that use fuzzy optimization methods to construct a remanufacturing shop scheduling model, and use a double fuzzy theory to describe the uncertainty of machining time, cost and reliability in the remanufacturing process and the interaction between the uncertainties, and also consider the uncertainty of machining path selection. The method has the advantages that the remanufacturing workshop scheduling model based on the game relationship is built in the prior art, a plurality of remanufacturing lines are divided according to the uncertainty of the quality of the waste products, the flexibility and the practicability of the model are improved by adopting an interval due date setting method, and the practicability of the model is improved by setting sequence related adjustment time related to the quality of the waste products. Compared with fuzzy optimization and random optimization methods, the robust optimization method is more suitable for multiple uncertainty optimization problems of lack of historical data and difficulty in data prediction. None of the above studies, however, have modeled the problem of optimized dispatch of a remanufacturing shop with multiple uncertainties using a robust optimization method.
In addition, some research has been focused on robust optimization methods, such as a scene-based remanufacturing scheduling optimization method, by which remanufacturing scheduling problems in a determined environment are addressed. But ignores the impact of the disturbance event on the remanufacturing shop schedule.
Disclosure of Invention
The invention aims to provide a dynamic scheduling method for a remanufacturing workshop based on robust optimization, which considers the problems of multiple uncertainties and the influence of disturbance events and obtains a better scheduling scheme.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
a remanufacturing shop dynamic scheduling method based on robust optimization, comprising a pre-scheduling stage and a dynamic scheduling stage, wherein:
describing the arrival time and the processing time of the operation in a remanufacturing workshop by adopting a discrete scene set, establishing a robust optimization objective function based on the difference between the finishing time of a minimized pre-scheduling scheme and the finishing time in different scenes, and outputting the pre-scheduling scheme by adopting a biophysical optimization algorithm;
in the dynamic scheduling stage, if no disturbance event occurs, carrying out dynamic scheduling of a remanufacturing workshop according to a pre-scheduling scheme; if a disturbance event occurs, taking the pre-scheduling scheme as an input scheme, executing a right shift rescheduling strategy of the operation to obtain a dynamic scheduling scheme, and if the obtained dynamic scheduling scheme is equal to or not dominant to the input scheme, outputting the obtained dynamic scheduling scheme and ending; otherwise, a dynamic scheduling objective function is established by the minimized efficiency index and the robustness index, and a dynamic scheduling scheme is output by adopting a biophysical optimization algorithm and is ended.
The following provides several alternatives, but not as additional limitations to the above-described overall scheme, and only further additions or preferences, each of which may be individually combined for the above-described overall scheme, or may be combined among multiple alternatives, without technical or logical contradictions.
Preferably, the robust optimization objective function is as follows:
in minf 1 Optimizing the objective function for robustness, N is discreteTotal number of scenes, p n For the probability of occurrence of scene n,to pre-schedule the maximum completion time of the phase, p, under scenario n n' For the probability of occurrence of scene n +.>For the maximum finishing time of the pre-scheduling phase in scenario n', I is the total number of jobs in the remanufacturing plant, K is the total number of machines in the remanufacturing plant, R i For the ith job J i Is>For the ith job J i Total number of operations on the r-th candidate path, for example>Is a binary variable if at the kth machine M k Executing the ith job J i Is +.>J-th operation of (2)>Then->Otherwise, go (L)> For machine M in scene n of the prescheduling phase k Execute operation on->Ending time of->For machine M in scene n' of the prescheduling phase k Execute operation on->Ending time of->For machine M in scene n of the prescheduling phase k Execute operation on->Start time of->For machine M in scene n' of the prescheduling phase k Execute operation on->Start time of->For machine M under scene n k Execute operation on->Processing time of>Machine M under scene n k Execute operation on->Is not limited, and the processing time of the device is not limited;
AT in for job J under scene n i Is used for the time of arrival of (a), is a binary variable if operated onIs machine M k The first operation performed on, then +.>Otherwise, go (L)>Is a binary variable if machine M is at the kth' station k' Executing the ith job J i Is +.>J-1 th operation of (2)>ThenOtherwise, go (L)>For machine M in scene n of the prescheduling phase k' Execute operation on->Ending time of->As binary variables, if in machine M k Execute operation on->Adjacent and prior to operationThen->Otherwise, go (L)> As binary variables, if in machine M k Executing the ith job J i' R' th candidate route +.>J' th operation->Then->Otherwise, go (L)>For machine M in scene n of the prescheduling phase k Executing the ith job J i' Is the r-th candidate path AR of (2) i r ' J' th operation->End time of (a), AT in' For job J under scene n i Time of arrival of- >For machine M in scene n' of the prescheduling phase k' Execute operation on->Ending time of->For machine M in scene n' of the prescheduling phase k Executing the ith job J i' Is +.>J' th operation->End time of (2).
Preferably, the constraint condition of the robust optimization objective function is as follows:
ensuring that each job can only select one candidate path:
ensuring that each machine can only perform one operation at a time:
it is possible to ensure a start time on the machine:
ensuring an end time on the machine is feasible:
in the method, in the process of the invention,is a binary variable if job J i Is the r candidate path, then +.>Otherwise the first set of parameters is selected,m is a pre-determinedDefining constants, n=1, 2, …, N, i=1, 2, …, I, k=1, 2, …, K, r=1, 2, …, R i 。
Preferably, the execution process of the biophysical optimization algorithm is as follows:
(1) Initializing a population, and representing each habitat in the population by adopting a two-dimensional unequal length coding method;
(2) Calculating the fitness index value of each habitat according to the robust optimization objective function or the dynamic scheduling objective function, and simultaneously calculating the mobility and the mobility of each habitat by adopting a sine migration model;
(3) Executing a migration operator according to the mobility and the mobility to obtain a new habitat;
(4) Executing a mutation operator to obtain a new habitat;
(5) Executing a local search strategy, wherein the local search strategy comprises three local search operators, and executing each local search operator to obtain a new habitat;
(6) Judging whether the termination condition of the pre-scheduling stage or the dynamic scheduling stage is met, and if the termination condition is met, outputting an optimal solution, namely an optimal pre-scheduling scheme or dynamic scheduling scheme; otherwise, the step (2) is entered to continue iteration.
Preferably, the method for representing each habitat in the population by adopting a two-dimensional unequal length coding method comprises the following steps:
in the representation of the habitat, the first dimension codes the path selection sequence information, the length of the first dimension is the total number of the operations in the remanufacturing workshop, and the value in the first dimension is the candidate path index selected from the candidate path set of each operation;
the second dimension codes the operation sequence information, the length of the second dimension is the total number of operations of all the operations, the value in the second dimension is each operation index, the sequence of the same value is the sequence of the operation execution of the corresponding operation, and the machine index corresponding to each value in the operation sequence information is obtained according to the path selection sequence information to form a corresponding machine sequence.
Preferably, the calculating the mobility and the mobility of each habitat using the sinusoidal migration model includes:
wherein lambda is i Sum mu i Respectively representing the mobility and the mobility of habitat I, I max And E is max Respectively representing the maximum mobility and the maximum mobility, S i Representing the population number of habitat i, S max Representing the maximum population number.
Preferably, the migration operator includes:
randomly dividing all the jobs into two non-empty subsets to obtain a first job set and a second job set;
copying, for a first dimension of the habitat, the fitness index variable corresponding to the first set of jobs in the moved-in habitat to the new habitat, and maintaining its position unchanged; copying the fitness index variable corresponding to the second set of operations in the shifted-out habitat to the new habitat, and maintaining its position unchanged;
copying the adaptability index variable of the operation index which is moved into the habitat and belongs to the first operation set to a new habitat aiming at a second dimension of the habitat, and keeping the position of the new habitat unchanged; and copying the adaptability index variable of the job index which is moved out of the habitat and belongs to the second job set to the new habitat, and keeping the sequence of the adaptability index variable unchanged.
Preferably, the mutation operator includes:
Randomly selecting a plurality of fitness index variables aiming at a first dimension of a habitat, and sequentially replacing the fitness index variables with other candidate path indexes corresponding to the operation; if the operation has no other candidate paths, the operation is not executed;
updating the second dimension according to the mutated first dimension in the habitat aiming at the second dimension of the habitat, and if the lengths of the candidate paths after replacement and the candidate paths before replacement in the first dimension are the same, not executing the operation; if the length of the candidate path after the replacement in the first dimension is greater than the length of the candidate path before the replacement, adding a newly added operation index at the tail of the second dimension; and if the length of the candidate path after the replacement in the first dimension is smaller than the length of the candidate path before the replacement, deleting the operation index of the redundant position in the second dimension.
Preferably, three local search operators in the local search strategy are as follows:
first local search operator: traversing the first half of the operation sequence information in the habitat, and traversing the next position if the operation arrival time of the traversed position is 0 moment; otherwise, randomly inserting the fitness index variable of the position into the second half of the operation sequence information; after traversing, if no operation is executed, randomly selecting two fitness index variables from the second half of the operation sequence information to execute exchange operation;
The second local search operator: randomly selecting a section of fitness index variable on the operation sequence information, randomly arranging the section of fitness index variable, and then returning to the original position;
third local search operator: two fitness index variables are randomly selected on the job sequence information to perform the exchanging operation.
Preferably, the establishing the dynamic scheduling objective function with the minimized efficiency index and the robustness index includes:
wherein f 2 To dynamically schedule the objective function omega 1 And omega 2 Weights of efficiency index and robustness index respectively, and satisfies omega 1 +ω 2 ＝1，EI max And EI min Respectively representing the maximum and minimum values of the efficiency index, RI max And RI min Respectively represent the maximum value and the minimum value of the robustness index, EI is the current efficiency index,for the maximum completion time of the dynamic scheduling phase, RI is the current robustness index,/-for>For machine M in scenario c of dynamic scheduling phase k Execute operation on->Ending time of->To dynamically adjustMachine M under scene c of degree phase k Execute operation on->Start time of->For machine M in scenario c of dynamic scheduling phase k' Execute operation on->Ending time of->For machine M in scenario c of dynamic scheduling phase k Execute operation on- >C=1, 2, …, N, i=1, 2, …, I, k=1, 2, …, K, r=1, 2, …, R i 。
The invention provides a remanufacturing workshop dynamic scheduling method based on robust optimization, which aims at the problems of multiple uncertainty and disturbance event influence of a remanufacturing workshop and divides the remanufacturing scheduling process into a pre-scheduling stage and a dynamic scheduling stage. The pre-scheduling stage uses a set of discrete scenarios to describe multiple uncertainties in the remanufacturing shop and uses a robust optimization method to construct the mathematical model. The dynamic scheduling stage designs a hybrid rescheduling strategy to avoid the problem of reduced remanufacturing system efficiency caused by disturbance events.
Drawings
FIG. 1 is an exemplary diagram of a remanufacturing plant optimization schedule of the present invention;
FIG. 2 is a flow chart of a method for dynamic scheduling in a remanufacturing plant based on robust optimization in accordance with the present invention;
FIG. 3 is a flow chart of the present invention executing the EBBO algorithm during a prescheduling phase;
FIG. 4 is an exemplary diagram of a habitat representation of the present invention;
FIG. 5 is an exemplary diagram of the present invention performing migration operators on habitats;
FIG. 6 is an exemplary diagram of the present invention performing a mutation operator on habitats;
FIG. 7 is an exemplary diagram of the present invention performing a local search operator on job sequence information in habitats;
FIG. 8 is a flow chart of a hybrid rescheduling strategy performed in the dynamic scheduling phase of the present invention;
FIG. 9 is a graph of iterative convergence results of the EBBO algorithm and the other three baseline algorithms in the experiment of the present invention;
FIG. 10 is a graph showing the performance of the EBBO algorithm in the experiments of the present invention compared to the other three baseline algorithms.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Unless defined otherwise, 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 belongs. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention.
In order to overcome the limitation of the dynamic scheduling scheme of the remanufacturing workshop in the prior art, the invention provides a novel dynamic scheduling method of the remanufacturing workshop based on robust optimization, which is regarded as an RO-RSDS (Robust Optimization-based Remanufacturing Shop Dynamic Scheduling) model, and the whole remanufacturing scheduling process is divided into a pre-scheduling stage and a dynamic scheduling stage after a disturbance event occurs. Of course, the model needs to be built based on the following assumptions: all machines are available at the beginning; after the operation arrives, the processing can be started, and no priority exists between the operations; all start-up times, adjustment times and transport times are ignored.
First, in the pre-scheduling stage, the uncertainty of the job arrival time and the processing time in the remanufacturing shop is described by using a discrete scene set, a mathematical model is constructed by using a robust optimization method, so as to find stable solutions which perform well in all possible scenes, and the pre-scheduling scheme is obtained by taking the difference between the finishing time of the minimized scheduling scheme and the finishing time in different scenes as an optimization target. And secondly, after the remanufacturing process starts, if a disturbance event occurs, triggering the remanufacturing process to enter a dynamic scheduling stage, adopting a new hybrid rescheduling strategy in the dynamic scheduling stage, and obtaining a final dynamic scheduling scheme by taking efficiency and robustness indexes as optimization targets so as to solve the problem of reduced remanufacturing system efficiency caused by the disturbance event.
To clearly illustrate the RO-RSDS model, FIG. 1 shows one example of remanufacturing shop optimization scheduling. On the left side of fig. 1 is a pre-scheduling stage, employing a set of discrete scenes to describe uncertainty in product arrival time and process time. In the example, it is assumed that two crankshafts and one gear are to be remanufactured, denoted as job J 1 、J 2 And J 3 There are 4 machines M 1 、M 2 、M 3 And M 4 。J 1 Is { M } set of candidate paths 1 →M 2 →M 4 ,M 3 →M 2 →M 1 ,M 4 →M 3 }，J 2 Is { M } set of candidate paths 1 →M 4 ,M 3 →M 1 }，J 3 Is { M } set of candidate paths 3 →M 2 ,M 2 →M 3 ,M 4 →M 1 N scenes are used to describe the uncertain arrival time and processing time of all jobs.
It is assumed that all jobs select the 1 st path in any scene. In scenario 1, J 1 Is 0, and is restored to a new state by three operations of pyrolysis, polishing and cleaning, respectively denoted as operation O 11 、O 12 And O 13 The processing time is 6, 4 and 8 respectively; j (J) 2 Is the arrival time of (a)10, recovering to new state after polishing and cleaning, respectively denoted as operation O 21 And O 22 The processing time is 2 and 5 respectively; j (J) 3 Is 0, and is restored to a new state by two operations of sanding and cleaning, respectively denoted as operation O 31 And O 32 The processing times were 7 and 3, respectively. In scene n, J 1 The arrival time of (2) is 0, and the processing time is 5, 3 and 9 respectively; j (J) 2 The arrival time of (2) is 0, and the processing time is 4 and 5 respectively; j (J) 3 The arrival time of (2) was 6 and the processing times were 9 and 3, respectively. In scenario N, J 1 The arrival time of (2) and the processing time of (4), 6 and 9 respectively; j (J) 2 The arrival time of (2) is 0, and the processing time is 3 and 5 respectively; j (J) 3 The arrival time of (2) was 0 and the processing times were 8 and 2, respectively. In the dynamic scheduling stage, assuming that the actual scene is n, machine M 3 At time 10, a fault occurs, and the time required for restoring the normal operation state is 4. When a fault occurs, machine M 3 Incomplete operation O 31 To the right, the operation affected by the fault event is represented in the figure using grey diagonal lines.
As shown in fig. 2, in the pre-scheduling stage, the uncertainty of the arrival time and the processing time in the remanufacturing process is described by using a discrete scene set, a mathematical model is constructed by using a robust optimization method, and the difference between the completion time of the minimum scheduling scheme and the completion time in different scenes is used as a robust optimization target, so that a stable solution which is well represented in the different scenes is obtained. The present embodiment proposes that the robust optimization objective function is as shown in equation (1), and the maximum completion time of the prescheduling stage is obtained by equations (2) - (7).
In minf 1 For robust optimization objective function, N is the total number of discrete scene sets, p n For the probability of occurrence of scene n,to pre-schedule the maximum completion time of the phase, p, under scenario n n' For the probability of occurrence of scene n +.>For the maximum finishing time of the prescheduling phase under the scene n'. I is the total number of operations in the remanufacturing workshop, and K is the total number of machines in the remanufacturing workshop. R is R i For the ith job J i Is >For the ith job J i Total number of operations on the r-th candidate path. />Is a binary variable if at the kth machine M k Executing the ith job J i Is +.>J-th operation of (2)>Then->Otherwise, go (L)> For machine M in scene n of the prescheduling phase k Execute operation on->Ending time of->For machine M in scene n' of the prescheduling phase k Execute operation on->End time of (2). />For machine M in scene n of the prescheduling phase k Execute operation on->Start time of->For machine M in scene n' of the prescheduling phase k Execute operation on->Is a start time of (c). />For machine M under scene n k Execute operation on->Processing time of>Machine M under scene n k Execute operation on->Is not limited, and the processing time of the same is not limited.
AT in For job J under scene n i J is the operation index, is a binary variable, if the operation->Is machine M k The first operation performed on, then +.>Otherwise, go (L)> Is a binary variable if machine M is at the kth' station k' Executing the ith job J i Is +.>J-1 th operation of (2)Then->Otherwise, go (L)> For machine M in scene n of the prescheduling phase k' Execute operation on->End time of (2). />As binary variables, if in machine M k Execute operation on- >Adjacent and prior to operation->Then->Otherwise, go (L)> As binary variables, if in machine M k Executing the ith job J i' R' th candidate route +.>J' th operation->Then->Otherwise, go (L)> For machine M in scene n of the prescheduling phase k Executing the ith job J i' Is +.>J' th operation->End time of (2). AT (automatic Transmission) in' For job J under scene n i Time of arrival of->For machine M in scene n' of the prescheduling phase k' Execute operation on->Ending time of->For machine M in scene n' of the prescheduling phase k Executing the ith job J i' Is +.>J' th operation->End time of (2).
Further, constraint conditions are established as shown in formulas (8) - (11):
ensuring that each job can only select one candidate path:
ensuring that each machine can only perform one operation at a time:
it is possible to ensure a start time on the machine:
ensuring an end time on the machine is feasible:
in the method, in the process of the invention,is a binary variable if job J i Is the r candidate path, then +.>Otherwise the first set of parameters is selected,m is a predefined constant, typically a large number, N 'is the scene index, N' =1, 2, …, 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 a phase index, s=1 is a pre-scheduling phase, and s=2 is a dynamic scheduling phase.
The RO-RSDS model proposed by the present invention is a typical NP-hard problem. The biophysical optimization (BBO) algorithm is used as an intelligent optimization algorithm to solve the NP-hard problem by simulating the migration process of species between habitats.
In the BBO algorithm, habitat fitness index (Habitat Suitability Index, HSI) is used to evaluate the merit of each solution (i.e., habitat). The higher the HSI of the solution, the better the performance of the solution, and conversely, the worse. Fitness index variables (Suitability Index Variables, SIVs) are a set of factors that affect the quality of a solution.
The migration operator and the mutation operator are cores of the BBO algorithm, the migration operator is a probability operator, information interaction between different habitats is facilitated, the mobility lambda is reduced along with the increase of the number of species, and the mobility mu is increased along with the increase of the number of species. Mutation operator is also a probability operator used for simulating the change of habitat caused by emergency in nature, and each habitat can change SIV according to a certain probability.
In order to solve the problems of insufficient population diversity, premature convergence and the like of a basic BBO algorithm, the three aspects of improvement are carried out on the basic BBO algorithm, and the improved BBO algorithm is used as an extended biological geography optimization (Extended Biogeography-Based Optimization, EBBO) algorithm: (1) A new two-dimensional unequal length coding scheme is designed to effectively represent the solution; (2) Introducing a sinusoidal migration model, and guiding a population to carry out efficient migration by adopting a new migration operator and a new mutation operator; (3) A local search strategy is proposed to increase the diversity of the population and speed up the convergence of the algorithm.
As shown in fig. 3, the EBBO algorithm is used to output the prescheduling scheme in the prescheduling stage, comprising the steps of:
(1) Initializing a population, and representing each habitat in the population by adopting a two-dimensional unequal length coding method.
In the two-dimensional unequal length encoding method, when a habitat contains route selection Sequence (Route Selection Sequence, RSS) information and Job Sequence (JS) information, in the representation of the habitat, the first dimension is encoded for the route selection Sequence information, the length of the first dimension is the total number of jobs in the remanufacturing shop, and the value in the first dimension is the candidate route index selected from the candidate route set for each Job. The second dimension codes the operation sequence information, the length of the second dimension is the total number of operations of all the operations, the value in the second dimension is each operation index, the sequence of the same value is the sequence of the operation execution of the corresponding operation, and the machine index corresponding to each value in the operation sequence information is obtained according to the path selection sequence information to form a corresponding machine sequence.
Based on the example in fig. 1, the present embodiment provides a two-dimensional unequal length encoding method, schematically shown in fig. 4, where the first dimension of habitat encodes RSS information with a length equal to the total number of jobs, and a value is a path index selected from its candidate path set for each job. For example, the value of the first position of the RSS information is 1, indicating job J 1 Path 1, i.e. "M", is selected 1 →M 2 →M 4 "; the second position has a value of 1, indicating job J 2 Path 1, i.e. "M", is selected 1 →M 4 ". The second dimension encodes JS information with a length equal to the sum of the operands of all jobs, a value being the index of each job, the order in which the values appear being the order in which the operations are performed for the corresponding job. According to the information of the operation selection path in the two-dimensional unequal length coding scheme, a corresponding machine sequence can be further obtained. For example, as is clear from the RSS information, job J 2 Path 1 (i.e. "M" is selected 1 →M 4 ") so that the value" 2 "indicates that the position needs to execute job J when the first position of JS information appears for the first time 2 The first operation of (a) that is, the machine sequence of the position is M 1 When the value of "2" appears for the second time at the fifth position of the JS information, it indicates that the position needs to execute the job J 2 The second operation of (a) that is, the machine sequence of the position is M 4 . Similarly, the machine sequence for obtaining JS information at all positions is' M 1 →M 3 →M 1 →M 2 →M 4 →M 2 →M 4 ". On this basis, the Gantt chart of scene n can be obtained by combining the arrival time of the operation.
(2) And calculating the fitness index value of each habitat according to the robust optimization objective function, and simultaneously calculating the mobility and the mobility of each habitat by adopting a sine migration model.
Compared with the traditional linear migration model, the sinusoidal migration model is more in line with the natural law and better in performance. Therefore, in this embodiment, a sinusoidal migration model is introduced to calculate the mobility and the migration rate in the EBBO algorithm, and the calculation formulas are formulas (12) and (13), respectively:
wherein lambda is i Sum mu i Respectively representing the mobility and the mobility of habitat I, I max And E is max Respectively representing the maximum mobility and the maximum mobility, S i Representing the population number of habitat i, S max Representing the maximum population number.
(3) And executing the migration operator according to the mobility and the mobility to obtain a new habitat.
(3.1) randomly dividing all jobs into two non-empty subsets, resulting in a first set of jobs and a second set of jobs.
(3.2) for a first dimension of the habitat, copying the fitness index variable corresponding to the first set of jobs in the moved-in habitat to the new habitat and maintaining its position unchanged; the fitness index variable corresponding to the second set of jobs in the shifted-out habitat is copied to the new habitat and its position is kept unchanged.
(3.3) for a second dimension of the habitat, copying the fitness index variable of the job index belonging to the first set of jobs moved into the habitat to the new habitat and keeping its position unchanged; and copying the adaptability index variable of the job index which is moved out of the habitat and belongs to the second job set to the new habitat, and keeping the sequence of the adaptability index variable unchanged.
As shown in fig. 5, if the first job set includes job indexes 2,4,6, the second job set includes job indexes 1,3,5, and when a migration algorithm is executed on RSS information, if the RSS information of an immigrating habitat is 1,1,2,3,1,2 and the RSS information of an immigrating habitat is 2,1,1,1,2,1, 1,3,2 at the 2,4,6 position of the immigrating habitat is copied to the 2,4,6 position of the new habitat, and 2,1,2 at the 1,3,5 position of the immigrating habitat is copied to the 1,3,5 position of the new habitat. When the migration algorithm is executed on the JS information, if the JS information of the migrating habitat is 1,5,4,2,4,6,3,1,2,2,5,3 and the JS information of the migrating habitat is 6,5,1,1,3,6,1,6,4,2,2,4,5, the values 2,4,6 of the migrating habitat are copied to the same position of the new habitat, and the values 1,3,5 of the migrating habitat are filled in the new habitat in the same order.
(4) And executing a mutation operator to obtain a new habitat.
(4.1) randomly selecting a plurality of fitness index variables aiming at a first dimension of the habitat, and sequentially replacing the fitness index variables with other candidate path indexes corresponding to the operation; if the job has no other candidate paths, the operation is not performed.
(4.2) updating the second dimension of the habitat according to the mutated first dimension in the habitat, and if the lengths of the candidate paths after replacement and the candidate paths before replacement in the first dimension are the same, not executing the operation; if the length of the candidate path after the replacement in the first dimension is greater than the length of the candidate path before the replacement, adding a newly added operation index at the tail of the second dimension; and if the length of the candidate path after the replacement in the first dimension is smaller than the length of the candidate path before the replacement, deleting the operation index of the redundant position in the second dimension.
As shown in fig. 6, when a mutation algorithm is performed on RSS information, RSS information of a habitat before mutation is 1,1,2,3,1,2, values at positions 2 and 4 are randomly taken, a value 1 at position 2 is mutated to 2, a value 3 at position 4 is mutated to 1, so that RSS information of the habitat after mutation is 1,2,2,1,1,2, then a second dimension is updated according to a first dimension after mutation, when a candidate path 1 at the first dimension position 2 is replaced with a candidate path 2, the length of the candidate path after replacement becomes shorter, and a corresponding operation index 2 at an unnecessary position 10 is deleted; when the candidate path 3 in the first dimension position 4 is replaced with the candidate path 1, the length of the replaced candidate path becomes longer, and the newly added job index 4 is added at the end.
(5) And executing a local search strategy, wherein the local search strategy comprises three local search operators, and executing each local search operator to obtain a new habitat.
Considering that the job index order of the JS information directly affects the merits of the solution, the present embodiment proposes a local search strategy including three local search operators.
First local search operator: traversing the first half of the operation sequence information in the habitat, and traversing the next position if the operation arrival time of the traversed position is 0 moment; otherwise, randomly inserting the fitness index variable of the position into the second half of the operation sequence information; after the traversing is completed, if no operation is executed, two fitness index variables are randomly selected from the second half of the operation sequence information to execute the exchanging operation. As shown in fig. 7 (a), for JS information in the habitat of 1,5,4,2,4,6,3,1,2,2,5,3, the job indexes 4 and 4 are traversed, and JS information in the new habitat of 1,5,2,6,3,1,2,4,2,5,4,3 is obtained after random insertion.
The second local search operator: and randomly selecting a section of fitness index variable on the operation sequence information, and putting the section of fitness index variable back to the original position after randomly arranging the section of fitness index variable. As shown in fig. 7 (b), for the JS information in the habitat as 1,5,4,2,4,6,3,1,2,2,5,3, a section including the job index 2,4,6,3,1 is randomly selected, and the result is 4,3,2,1,6 after the random arrangement, and the JS information in the new habitat is 1,5,4,4,3,2,1,6,2,2,5,3.
Third local search operator: two fitness index variables are randomly selected on the job sequence information to perform the exchanging operation. As shown in fig. 7 (c), the job index 5 at the position 2 and the action index 2 at the position 9 are randomly selected for exchange operation for JS information 1,5,4,2,4,6,3,1,2,2,5,3 in the habitat, resulting in JS information 1,2,4,2,4,6,3,1,5,2,5,3 in the new habitat.
(6) Judging whether a pre-scheduling stage termination condition is met, and if so, outputting an optimal solution, namely an optimal pre-scheduling scheme; otherwise, the step (2) is entered to continue iteration.
In the dynamic scheduling stage, if a disturbance event (such as a machine fault) occurs, the remanufacturing system needs to determine a final dynamic scheduling scheme on the basis of the pre-scheduling scheme according to disturbance event information on the premise of ensuring scheduling efficiency and reducing performance difference between the pre-scheduling scheme and the pre-scheduling scheme. The present embodiment adopts an efficiency index to evaluate the scheduling efficiency of the dynamic scheduling scheme, measured in terms of maximum completion time. Meanwhile, the robustness index is adopted to evaluate the performance difference between the dynamic scheduling scheme and the pre-scheduling scheme, and the performance difference between the pre-scheduling scheme and the dynamic scheduling scheme is measured.
Currently, the commonly used rescheduling strategies can be divided into the following three types: (1) The left shift or right shift rescheduling strategy of the operation is that when a disturbance event occurs, the starting time of the unfinished operation is advanced or delayed for a certain time on the premise of keeping the operation sequence of the machine unchanged. The advantage of this strategy is that it responds quickly, which is beneficial to maintaining the stability of the system. (2) Local rescheduling strategies, i.e. rescheduling only operations that are directly or indirectly affected by a disturbance event. (3) And a complete rescheduling strategy, namely solving the rescheduling scheme based on a specific performance index only according to the resource state after the disturbance event in the workshop without considering the pre-scheduling scheme. This strategy has better performance in addressing such disturbance events as machine failures.
In order to quickly respond to disturbance events such as machine faults and better maintain system stability, the embodiment combines a right shift rescheduling strategy and a full rescheduling strategy, and proposes a hybrid rescheduling strategy as shown in fig. 8, which is specifically described as follows:
in the dynamic scheduling stage, if no disturbance event occurs, carrying out dynamic scheduling of a remanufacturing workshop according to a pre-scheduling scheme; if a disturbance event occurs, a pre-scheduling scheme is used as an input scheme (denoted as Sol 0 ) Executing the right shift rescheduling strategy to obtain a dynamic scheduling scheme (Sol) 1 ) If the obtained dynamic scheduling scheme Sol 1 And input scheme Sol 0 Equal or mutually exclusive, then the dynamic scheduling scheme Sol is output 1 As a final dynamic scheduling scheme and ending; otherwise, the dynamic scheduling objective function is established with the minimum efficiency index and the robustness index,outputting the dynamic scheduling scheme by adopting a BBO algorithm (particularly an EBBO algorithm of the embodiment) and ending, namely, executing a complete rescheduling strategy by calculating a fitness value by using a dynamic scheduling objective function through the EBBO algorithm to obtain a new scheduling scheme which is recorded as Sol 2 And outputs Sol 2 As a final dynamic scheduling scheme.
Unlike the pre-scheduling phase, the remanufacturing system has already clarified the actual remanufacturing scenario during the dynamic scheduling phase. The present embodiment assumes that the actual remanufacturing scenario of the dynamic scheduling phase is c, c e {1,2, …, N }, the scheduling objective is to minimize the efficiency index (Effectiveness Indicator, EI) and the robustness index (Robustness Indicator, RI). Maximum time to completion TT for dynamic scheduling phase c 2 Can be calculated from equations (17), (18) and (21) and the constraints (19) and (20) need to be satisfied to ensure that start and end times on the machine are viable.
EI＝TT c 2 (15)
Wherein f 2 To dynamically schedule the objective function omega 1 And omega 2 Weights of efficiency index and robustness index respectively, and satisfies omega 1 +ω 2 ＝1。EI max And EI min Respectively representing the maximum and minimum values of a plurality of efficiency indexes in the current population, RI max And RI min Respectively representing the maximum and minimum values of the robustness index for a plurality of habitats in the current population. EI is the current efficiency index of the device,for the maximum completion time of the dynamic scheduling phase, RI is the current robustness index. />For machine M in scenario c of dynamic scheduling phase k Execute operation on->Ending time of->For machine M in scenario c of dynamic scheduling phase k Execute operation on->Is a start time of (c). />For machine M in scenario c of dynamic scheduling phase k' Execute operation on->Ending time of->For machine M in scenario c of dynamic scheduling phase k Execute operation on->End time of (2).
The algorithm involved in the hybrid rescheduling strategy executed in the dynamic scheduling stage in this embodiment is also an EBBO algorithm, and the execution process is as follows:
(1) Initializing a population, and representing each habitat in the population by adopting a two-dimensional unequal length coding method.
(2) And calculating the fitness index value of each habitat according to the dynamic scheduling objective function, and simultaneously calculating the mobility and the mobility of each habitat by adopting a sine migration model.
(3) And executing the migration operator according to the mobility and the mobility to obtain a new habitat.
(4) And executing a mutation operator to obtain a new habitat.
(5) And executing a local search strategy, wherein the local search strategy comprises three local search operators, and executing each local search operator to obtain a new habitat.
(6) Judging whether the termination condition of the dynamic scheduling stage is met, and if the termination condition is met, outputting an optimal solution, namely an optimal dynamic scheduling scheme; otherwise, the step (2) is entered to continue iteration.
It should be noted that, for specific limitation of the EBBO algorithm executed in the dynamic scheduling stage, reference may be made to limitation of the EBBO algorithm in the pre-scheduling stage, and no detailed description is given here.
The superiority of the dynamic scheduling method for the remanufacturing workshop based on robust optimization and the effectiveness of the hybrid rescheduling strategy provided by the invention are further described through experiments.
Two sets of sensitivity experiments and two sets of performance simulation experiments were designed. First, the EBBO algorithm is used to compare with the three baseline algorithms to select algorithm parameters and to comprehensively evaluate algorithm performance. Among them, baseline algorithms include Modified genetic algorithms (Improved Genetic Algorithm, IGA), discrete particle swarm optimization algorithms (Discrete Particle Swarm Optimization, DPSO), and Modified biophysical optimization algorithms (MBBO). And secondly, comparing the performances of the mixed rescheduling strategy and the complete rescheduling strategy, and solving a dynamic scheduling scheme after the complete rescheduling strategy is executed by adopting a second generation Non-dominant ordering genetic algorithm (Non-dominated Sorting Genetic Algorithm-II, NSGA-II). All experiments were performed using Python programming and run on a computer with an operating system of 64-bit Windows 10, a processor of Intel (R) core 3.10GHz, and a memory of 16 GB.
(1) Design of experiment
In order to simulate the actual remanufacturing environment, the specific values of the experiment are as follows: number of candidate paths R i The value is [1,4 ]]Path lengthThe value is [1,6 ]]Time of arrival AT in The value is 0,20]Hour, processing time->The value is [2,8 ]]Hour, machine failure time point takes on the value +.>Fault recovery time value of [0.1,10.0 ]]Hours. Each simulation instance is named according to the number of jobs, the number of machines, and the number of scenarios, e.g., "J30_M10_S10" represents 30 jobs, 10 machines, and 10 scenarios for a remanufacturing plant. To reduce experimental error, all experiments were run 10 times independently and then their average was taken as the final experimental result. Furthermore, the EBBO algorithm parameter maximum mobility I max And maximum mobility E max All set to 1, weight ω 1 And omega 2 Are set to 0.5.
(2) Sensitivity analysis
The sensitivity experiments of this experiment were all performed on the "j20_m10_s10" simulation example, with the population of all algorithms set to 30. The first set of experiments compares the performance of the four algorithms at different iterations. The experimental results are shown in fig. 9, and it can be seen that the EBBO algorithm converges more rapidly than the other three baseline algorithms, and the fitness value of the solution is better. Experimental results show that the EBBO algorithm has stronger searching capability and faster convergence speed compared with other three baseline algorithms. It can also be seen from fig. 9 that the fitness values of the solutions obtained by the four algorithms all tend to stabilize after 280 iterations. Therefore, the number of iterations of all algorithms was set to 280 in the subsequent experiments.
The second set of experiments compares the performance of the four algorithms at different cluster sizes. The experimental results are shown in fig. 10, and it can be seen that the fitness values of the solutions obtained by the EBBO algorithm are better than those obtained by the other three baseline algorithms and are relatively stable at different population sizes. IGA algorithms only have good fitness values at population sizes 40, 55, 60 and 70, DPSO algorithms only have good fitness values at population sizes 40 and 65, and MBBO algorithms only obtain solutions with relatively smooth fitness values at small-scale populations. Considering that simulation experiments need to ensure that four algorithms are fairly and effectively compared and are performed with low computational complexity as much as possible, in subsequent experiments the population number of all algorithms is set to 40.
(3) Performance simulation analysis
The performance of the four algorithms performed during the pre-scheduling stage was evaluated comprehensively by the first set of performance simulation experiments, the experimental results of which 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 solution obtained by the EBBO algorithm are better than the other three baseline algorithms, indicating that the EBBO algorithm can find a better scheduling scheme when solving the model herein than the other three baseline algorithms. Table 2 lists the standard deviation of the solutions obtained by the four algorithms and the CPU average calculation time (labeled "calculation time" in the table, in hours). As can be seen from table 2, the standard deviation of the solution obtained by the EBBO algorithm is better than that of the other three baseline algorithms, indicating that the performance of the EBBO algorithm is more stable when solving the model herein. In addition, the EBBO algorithm adopts a local search strategy, so that the calculation complexity is higher and more calculation time is needed compared with other three baseline algorithms, but the best value, average value and standard deviation of the obtained solution are better than those of the other three baseline algorithms, and the increased calculation time is within an acceptable range. In conclusion, the EBBO algorithm performs better than the other three baseline algorithms in solving the RO-RSDS model.
Table 1 best and average values of solutions obtained by four algorithms
Table 2 standard deviation and average calculation time of solutions obtained by four algorithms
Based on the experimental results obtained in the pre-scheduling stage, the second set of performance simulation experiments compares the performance of the hybrid rescheduling strategy and the full rescheduling strategy in the dynamic scheduling stage, and the machine fault information and the experimental results are shown in table 3. In order to respond quickly to a disturbance event, the dynamic scheduling phase uses a calculation time of 60 seconds as an iteration stop condition. As can be seen from table 3, the solutions obtained by implementing the hybrid rescheduling strategy all dominate the solutions obtained by implementing the full rescheduling strategy, which shows that the proposed hybrid rescheduling strategy can effectively balance the efficiency and robustness of the scheduling scheme and can quickly respond to disturbance events, with better practicability and efficiency.
TABLE 3 machine fault information and experimental results obtained by implementing two rescheduling strategies
Aiming at the problem of remanufacturing workshop scheduling under the influence of uncertainty and disturbance events, the invention provides a remanufacturing workshop dynamic scheduling method based on robust optimization. On the basis, an extended biological geography optimization algorithm is provided, a two-dimensional unequal length coding scheme is designed to effectively represent scheme solutions, a sinusoidal migration model is introduced, a new migration operator and a new mutation operator are adopted to guide a population to carry out efficient migration, and a local search strategy is provided to improve diversity of the population and accelerate convergence speed of the algorithm. Finally, simulation experiment results show that the proposed algorithm has better performance when solving problems of different scales, and the proposed hybrid rescheduling strategy can effectively balance the efficiency and robustness of a scheduling scheme and can quickly respond to disturbance events.
The technical features of the above-described embodiments may be arbitrarily combined, and all possible combinations of the technical features in the above-described embodiments are not described for brevity of description, however, as long as there is no contradiction between the combinations of the technical features, they should be considered as the scope of the description.
The above examples merely represent a few embodiments of the present invention, which are described in more detail and are not to be construed as limiting the scope of the invention. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the invention, which are all within the scope of the invention. Accordingly, the scope of the invention should be assessed as that of the appended claims.
Claims (10)
1. The remanufacturing workshop dynamic scheduling method based on the robust optimization is characterized by comprising a pre-scheduling stage and a dynamic scheduling stage, wherein:
describing the arrival time and the processing time of the operation in a remanufacturing workshop by adopting a discrete scene set, establishing a robust optimization objective function based on the difference between the finishing time of a minimized pre-scheduling scheme and the finishing time in different scenes, and outputting the pre-scheduling scheme by adopting a biophysical optimization algorithm;
In the dynamic scheduling stage, if no disturbance event occurs, carrying out dynamic scheduling of a remanufacturing workshop according to a pre-scheduling scheme; if a disturbance event occurs, taking the pre-scheduling scheme as an input scheme, executing a right shift rescheduling strategy of the operation to obtain a dynamic scheduling scheme, and if the obtained dynamic scheduling scheme is equal to or not dominant to the input scheme, outputting the obtained dynamic scheduling scheme and ending; otherwise, a dynamic scheduling objective function is established by the minimized efficiency index and the robustness index, and a dynamic scheduling scheme is output by adopting a biophysical optimization algorithm and is ended.
2. The remanufacturing shop dynamic scheduling method based on robust optimization of claim 1, wherein the robust optimization objective function is as follows:
in the formula, min f 1 Optimizing objective function for robustness, N is total scene in discrete scene setNumber p n For the probability of occurrence of scene n,to pre-schedule the maximum completion time of the phase, p, under scenario n n' For the probability of occurrence of scene n +.>For the maximum finishing time of the pre-scheduling phase in scenario n', I is the total number of jobs in the remanufacturing plant, K is the total number of machines in the remanufacturing plant, R i For the ith job J i Is >For the ith job J i Total number of operations on the r-th candidate path, for example>Is a binary variable if at the kth machine M k Executing the ith job J i Is +.>J-th operation of (2)>Then->Otherwise, go (L)>For machine M in scene n of the prescheduling phase k Execute operation on->Ending time of->For machine M in scene n' of the prescheduling phase k Execute operation on->Ending time of->For machine M in scene n of the prescheduling phase k Execute operation on->Start time of->For machine M in scene n' of the prescheduling phase k Execute operation on->Start time of->For machine M under scene n k Execute operation on->Processing time of>Machine M under scene n k Execute operation on->Is not limited, and the processing time of the device is not limited;
AT in for job J under scene n i Is used for the time of arrival of (a),is a binary variable, if the operation->Is machine M k The first operation performed on, then +.>Otherwise, go (L)>Is a binary variable if machine M is at the kth' station k' Executing the ith job J i Is +.>J-1 th operation of (2)>ThenOtherwise, go (L)>For machine M in scene n of the prescheduling phase k' Executing operations onEnding time of->As binary variables, if in machine M k Execute operation on->Adjacent and prior to operation- >Then->Otherwise, go (L)> As binary variables, if in machine M k Executing the ith job J i' R' th candidate route +.>J' th operation->Then->Otherwise, go (L)>For machine M in scene n of the prescheduling phase k Executing the ith job J i' Is +.>J' th operation of (2)End time of (a), AT in' For job J under scene n i Time of arrival of->For machine M in scene n' of the prescheduling phase k' Execute operation on->Ending time of->For machine M in scene n' of the prescheduling phase k Executing the ith job J i' Is +.>J' th operation->End time of (2).
3. The remanufacturing shop dynamic scheduling method based on robust optimization of claim 2, wherein the constraint condition of the robust optimization objective function is as follows:
ensuring that each job can only select one candidate path:
ensuring that each machine can only perform one operation at a time:
it is possible to ensure a start time on the machine:
ensuring an end time on the machine is feasible:
in the method, in the process of the invention,is a binary variable if job J i Is the r candidate path, then +.>Otherwise, go (L)>M is a predefined constant, n=1, 2, …, N, i=1, 2, …, I, k=1, 2, …, K, r=1, 2, …, R i 。
4. The robust optimization-based remanufacturing shop dynamic scheduling method of claim 1, wherein the biophysical optimization algorithm is performed as follows:
(1) Initializing a population, and representing each habitat in the population by adopting a two-dimensional unequal length coding method;
(2) Calculating the fitness index value of each habitat according to the robust optimization objective function or the dynamic scheduling objective function, and simultaneously calculating the mobility and the mobility of each habitat by adopting a sine migration model;
(3) Executing a migration operator according to the mobility and the mobility to obtain a new habitat;
(4) Executing a mutation operator to obtain a new habitat;
(5) Executing a local search strategy, wherein the local search strategy comprises three local search operators, and executing each local search operator to obtain a new habitat;
(6) Judging whether the termination condition of the pre-scheduling stage or the dynamic scheduling stage is met, and if the termination condition is met, outputting an optimal solution, namely an optimal pre-scheduling scheme or dynamic scheduling scheme; otherwise, the step (2) is entered to continue iteration.
5. The dynamic scheduling method for remanufacturing workshops based on robust optimization of claim 4, wherein the representing each habitat in the population using a two-dimensional unequal length encoding method comprises:
In the representation of the habitat, the first dimension codes the path selection sequence information, the length of the first dimension is the total number of the operations in the remanufacturing workshop, and the value in the first dimension is the candidate path index selected from the candidate path set of each operation;
the second dimension codes the operation sequence information, the length of the second dimension is the total number of operations of all the operations, the value in the second dimension is each operation index, the sequence of the same value is the sequence of the operation execution of the corresponding operation, and the machine index corresponding to each value in the operation sequence information is obtained according to the path selection sequence information to form a corresponding machine sequence.
6. The robust optimization-based remanufacturing shop dynamic scheduling method of claim 5, wherein the calculating the mobility and the mobility of each habitat using the sinusoidal migration model comprises:
wherein lambda is i Sum mu i Respectively representing the mobility and the mobility of habitat I, I max And E is max Respectively representing the maximum mobility and the maximum mobility, S i Representing the population number of habitat i, S max Representing the maximum population number.
7. The robust optimization based remanufacturing shop dynamic scheduling method of claim 5, wherein the migration operator comprises:
Randomly dividing all the jobs into two non-empty subsets to obtain a first job set and a second job set;
copying, for a first dimension of the habitat, the fitness index variable corresponding to the first set of jobs in the moved-in habitat to the new habitat, and maintaining its position unchanged; copying the fitness index variable corresponding to the second set of operations in the shifted-out habitat to the new habitat, and maintaining its position unchanged;
copying the adaptability index variable of the operation index which is moved into the habitat and belongs to the first operation set to a new habitat aiming at a second dimension of the habitat, and keeping the position of the new habitat unchanged; and copying the adaptability index variable of the job index which is moved out of the habitat and belongs to the second job set to the new habitat, and keeping the sequence of the adaptability index variable unchanged.
8. The robust optimization-based remanufacturing shop dynamic scheduling method of claim 5, wherein the mutation operator comprises:
randomly selecting a plurality of fitness index variables aiming at a first dimension of a habitat, and sequentially replacing the fitness index variables with other candidate path indexes corresponding to the operation; if the operation has no other candidate paths, the operation is not executed;
updating the second dimension according to the mutated first dimension in the habitat aiming at the second dimension of the habitat, and if the lengths of the candidate paths after replacement and the candidate paths before replacement in the first dimension are the same, not executing the operation; if the length of the candidate path after the replacement in the first dimension is greater than the length of the candidate path before the replacement, adding a newly added operation index at the tail of the second dimension; and if the length of the candidate path after the replacement in the first dimension is smaller than the length of the candidate path before the replacement, deleting the operation index of the redundant position in the second dimension.
9. The robust optimization based remanufacturing shop dynamic scheduling method of claim 5, wherein three local search operators in the local search strategy are as follows:
first local search operator: traversing the first half of the operation sequence information in the habitat, and traversing the next position if the operation arrival time of the traversed position is 0 moment; otherwise, randomly inserting the fitness index variable of the position into the second half of the operation sequence information; after traversing, if no operation is executed, randomly selecting two fitness index variables from the second half of the operation sequence information to execute exchange operation;
the second local search operator: randomly selecting a section of fitness index variable on the operation sequence information, randomly arranging the section of fitness index variable, and then returning to the original position;
third local search operator: two fitness index variables are randomly selected on the job sequence information to perform the exchanging operation.
10. The robust optimization-based remanufacturing shop dynamic scheduling method of claim 2, wherein the establishing the dynamic scheduling objective function with the minimized efficiency index and the robust index comprises:
EI＝TT c 2
Wherein f 2 To dynamically schedule the objective function omega 1 And omega 2 Weights of efficiency index and robustness index respectively, and satisfies omega 1 +ω 2 ＝1，EI max And EI min Respectively representing the maximum and minimum values of the efficiency index, RI max And RI min Respectively representing the maximum value and the minimum value of the robustness index, wherein EI is the current efficiency index, TT c 2 For the maximum completion time of the dynamic scheduling phase, RI is the current robustness index,for machine M in scenario c of dynamic scheduling phase k Execute operation on->Ending time of->For machine M in scenario c of dynamic scheduling phase k Execute operation on->Start time of->For machine M in scenario c of dynamic scheduling phase k' Execute operation on->Ending time of->For machine M in scenario c of dynamic scheduling phase k Execute operation on->C=1, 2, …, N, i=1, 2, …, I, k=1, 2, …, K, r=1, 2, …, R i 。
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| CN117434909A (en) * | 2023-12-18 | 2024-01-23 | 华侨大学 | Intermittent chemical system Petri network model predictive control method |
| CN117434909B (en) * | 2023-12-18 | 2024-03-12 | 华侨大学 | Intermittent chemical system Petri network model predictive control method |
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