CN111382915B - Flexible job shop scheduling method for co-fusion AGVs - Google Patents
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Abstract
The invention relates to a flexible job shop scheduling method of a co-fusion AGV, which establishes a flexible job scheduling mathematical model containing AGV transport; initializing parameters, and coding each individual in the population to generate a coding sequence; and obtaining the neighborhood code of each individual through intersection, mutation and sequence value exchange, and replacing the individual neighborhood code in the corresponding mutated population if the fitness value of the individual neighborhood code is smaller than that of the individual in the mutated population. The three-layer coding strategy of the procedure, the machine and the AGV sequence is used, so that the relation among the workpiece, the processing machine and the AGV can be effectively mapped; the self-adaptive weight factors dynamically adjust the crossover and mutation probability, so that the stability is good; the local searching capability of the variable neighborhood searching introduced with the strategy based on the mobile and exchange procedures is strong.
Description
Technical Field
The invention relates to the technical field of workshop job scheduling, in particular to a flexible job workshop scheduling method of a co-fusion AGV.
Background
The interconnection intercommunication is realized gradually to digital workshop equipment, AGVs are widely applied to workshop material handling with the characteristics of flexibility and intelligence, the algorithm research of traditional flexible job shop scheduling problem (Flexible job shop scheduling problem, FJSP) does not consider the material handling time, in discrete manufacturing production workshops, the integrated scheduling of AGVs collaborative production operation is realized, and the production efficiency can be effectively improved and the cost is reduced. The problem of the co-fusion scheduling of the AGVs and the flexible job shops not only needs to consider the processing procedure and the selection of processing machines, but also the handling cost of processed materials among the machines and the selection of the AGVs, is a reinforced version of the typical combination optimization problem, and cannot accurately solve the polynomial time optimal solution. In recent years, the use of intelligent algorithms to solve the problems becomes a mainstream solution, the genetic algorithm becomes a basic stone for researching and scheduling problems by using strong global searching capability and population parallel searching capability, and the particle swarm algorithm, simulated annealing algorithm, neighborhood searching and other algorithms are researched and improved by a plurality of students and have good effects.
The genetic algorithm can continuously optimize the performance of the solution through operations such as crossing, mutation, selection and the like, has stronger global searching capability, but in practical application, each parameter setting of the genetic algorithm often depends on experience, and the algorithm can not be ensured to converge to the global optimal solution under general conditions, so that the application field of the algorithm has certain limitation, and the genetic algorithm has the problems of easy sinking into the local optimal solution, low local searching efficiency and the like.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a flexible job shop scheduling method of a co-fusion AGV, which solves the problems that a genetic algorithm is easy to sink into a local optimal solution and the local searching efficiency is low.
The technical scheme adopted by the invention for achieving the purpose is as follows:
A flexible job shop scheduling method of a co-fusion AGV comprises the following steps:
step 1: establishing a flexible operation scheduling mathematical model containing AGV carrying;
Step 2: initializing parameters, and coding each individual in the population to generate a coding sequence;
step 3: arbitrarily selecting two individuals, crossing the coding sequences of the individuals until the number of the selected individuals reaches the number of the individuals in the population, and obtaining the crossed population;
step 4: carrying out mutation operation on individuals in the crossed population according to the initial mutation probability to obtain a mutated population;
step 5: solving a key working procedure set of each individual in the mutated population, and exchanging the last two sequence values of the key working procedure set of each individual to obtain a neighborhood code of each individual;
Step 6: and calculating the fitness value of the individuals in the mutated population and the fitness value of the individual neighborhood codes through a target evaluation function, comparing the fitness value of the individuals in the mutated population with the fitness value of the individual neighborhood codes, and if the fitness value of the individual neighborhood codes is smaller than the fitness value of the individuals in the mutated population, replacing the individuals in the corresponding mutated population with the individual neighborhood codes, and traversing the whole mutated population.
The flexible operation scheduling mathematical model containing AGV carrying is as follows:
Jj:{J1,J2,......,Jn}
Mi:{M0,M1,M2,……,Mm}
Ad:{A1,A2,……,AW}
Wherein J j is the processed workpieces in the workshop, and n is the number of the processed workpieces; m i is the number of processing machines in the workshop; a d is AGVs in a workshop, and w is the number of the AGVs;
in the workpiece machining process, constraint equations of a machined workpiece, a machining machine and an AGV are as follows:
cjk≤sj(k+1)
cjk≥sjk+qijk×yijk
qijk+sjk≤shl+E-E×rijkhl
cjk-sj(k+1)≤E-E×rijkhl
sjk+qijk≤atiw+rtijkw
Wherein c jk represents the processing completion time s jk of the kth process of the jth workpiece, y ijk is 0 or 1, 1 is selected when the kth process of the jth workpiece is selected to be processed on machine i, otherwise the variable value is 0, E represents a sufficiently large positive integer, q ijk represents the processing time of the kth process of the jth workpiece on machine i, s hl represents the first process of the jth workpiece, r ijkhl is 0 or 1, 1 is selected when the kth process of the jth workpiece is processed on machine i than the first process of the jth workpiece, and 0, at iw represents the start time of the W AGV at the current position to machine i, rt ijkw represents the time taken for the W AGV to reach the machine i processing the kth process of the jth workpiece from the current position;
the objective evaluation function is:
wherein Wt j represents the completion time of the last process of each workpiece j, the maximum process completion time is the maximum completion time of all the workpieces, and the target evaluation function is to obtain the minimum maximum completion time in the group coding sequence.
The parameters include: the number of workpieces n, the number of processing machines m, the number of AGVs w, the initial population size P, the number of population iterations G, the initial crossover probability P c and the initial variation probability P m.
The coding sequence consists of a plurality of sequence values, wherein each sequence value represents the serial number of the workpiece processing machine, the serial number of the workpiece or the serial number of the AGV, the sequence values with the same meaning are continuous, and the sequence value groups representing the workpiece processing machine, the sequence value groups representing the working procedure and the sequence value groups representing the AGV have the same sequence value number.
The mutation operation is carried out on individuals in the crossed population according to the initial mutation probability, and the method comprises the following steps:
Judging whether the current variation probability of the individuals in the crossed population is smaller than the initial variation probability, if so, exchanging any two sequence values in the coding sequence of the individuals, otherwise, keeping the current coding sequence of the individuals.
The working procedure set of each individual in the mutated population is as follows:
Or:{O1,O2,......,Ov}
the key process set solving constraint equation of each individual in the mutated population is as follows:
CE(r)＝SE(r)+p(r)
CL(r)＝SL(r)+p(r)
SE(r)＝max{CE[PJ(r)],CE[PM(r)]}
CL(r)＝min{SL[SJ(r)],SL[SM(r)]}
d(r)＝SL(r)-SE(r)
Wherein O r represents the r-th node process, SE (r) represents the earliest start time of O r, SL (r) represents the latest start time of O r, CE (r) represents the earliest finish time of O r, CL (r) represents the latest finish time of O r, p (r) represents the processing time of O r, PJ (r) represents the previous process with the same workpiece as process O r, SJ (r) represents the next process with the same workpiece as O r, PM (r) represents the previous process with the same processing machine as process O r, SM (r) represents the next process with the same processing machine as process O r, and O r is the key process if the value of the time difference d (r) of O r is 0.
The code sequence generation adopts three strategy modes, and weight is distributed for each strategy mode according to the proportion; the three strategy modes are respectively as follows: a workpiece processing machine maximum utilization priority strategy, an AGV maximum utilization priority strategy, and a random generation strategy.
The maximum utilization rate priority strategy of the workpiece processing machine is as follows:
firstly, setting an array, wherein the length of the array is equal to the number of the machines, the sequence of the array sequentially corresponds to the sequence of the processing machines, and the value on each bit of the array corresponds to the processing time on the corresponding machine; randomly selecting one workpiece in the workpiece set, starting from the first working procedure, adding the processing time of the selectable processing machine of the current working procedure with the time corresponding to the array, at the moment, not updating the array, selecting the shortest time from the array as the processing machine of the current working procedure, updating the array, namely adding the processing time of the selected processing machine to the corresponding position of the array, and the like until the processing machines of all working procedures of the current workpiece are selected, randomly selecting one workpiece from the rest of the workpiece set to perform the same operation until the working procedures of all the workpieces are selected.
The AGV maximum utilization priority policy is:
Firstly, setting an array S w, wherein the length of the array S w is equal to the number w of AGVs, the sequence of the array S w sequentially corresponds to the sequence of the AGVs, the value on each position of the array S w corresponds to the carrying time of the corresponding AGVs, then setting an array LP w, and the value in the array LP w sequentially corresponds to the current position of the machine where the AGVs are positioned; AGV carrying time is calculated through the current position value of AGVs in the array LP w and the serial number of the processing machine with the purpose of the process, a set of to-be-processed processes is traversed, W processes with the shortest time from the AGVs to the processing machine are selected, the selected W AGV carrying times are added with the value of the array S w, the array S w is updated, meanwhile, the serial number value of the processing machine with the purpose of the selected W AGVs is used for updating the array LP w, and the like, the W shortest carrying time processes are selected from the rest set of to-be-processed processes to carry out the operations until all to-be-processed processes are selected.
The invention has the following beneficial effects and advantages:
1. The three-layer coding strategy of the procedure, the machine and the AGV sequence is used, so that the relation among the workpiece, the processing machine and the AGV can be effectively mapped;
2. The self-adaptive weight factor of the invention dynamically adjusts the crossover and variation probability, and has better stability;
3. the invention has strong local searching capability for the variable neighborhood searching introduced based on the mobile and exchange procedure strategies.
Drawings
FIG. 1 is a flow chart of an algorithm of the present invention;
FIG. 2 is a diagram of an example of the encoding of the present algorithm;
FIG. 3 is a diagram of an example of machine selection uniform cross;
FIG. 4 is a diagram of an example process code crossover;
FIG. 5 is a diagram of an example of neighborhood de-encoding generation.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
In order that the above objects, features and advantages of the invention will be readily understood, a more particular description of the invention will be rendered by reference to the appended drawings. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. The invention may be embodied in many other forms than described herein and similarly modified by those skilled in the art without departing from the spirit or scope of the invention, which is therefore not limited to the specific embodiments disclosed below.
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 in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention.
Fig. 1 is a flowchart of the algorithm of the present invention.
Step 1, establishing a flexible operation scheduling mathematical model containing AGV carrying;
The FJSP problem with AGV handling is an extension of the conventional FJSP problem, requiring not only the order of the machining processes and the allocation of the set of available machines for each process to be determined, but also the handling schedule of the workpieces by the AGV to be considered. It can be generally described that the workshop has n workpieces J j:{J1,J2,......,Jn, each workpiece needs to select a corresponding working procedure processing machine in M machines M i:{M0,M1,M2,......,Mm, the workpieces are stored in a stereo warehouse, w AGVs a d:{A1,A2,......,AW are required to be conveyed to the corresponding machines during processing, and after all working procedures are finished, the workpieces are returned to the stereo warehouse by the AGVs. The objective evaluation functions required by the machine, the workpiece, the AGV and the like in the workpiece processing process are as follows:
Constraint equations such as equations (2) - (6)
cjk≤sj(k+1) (2)
cjk≥sjk+qijk×yijk (3)
qijk+sjk≤shl+E-E×rijkhl (4)
cjk-sj(l+1)≤E-E×rijkh(l+1) (5)
sjk+qijk≤atiw+rtijkw (6)
Where c jk represents the processing completion time s jk of the kth process of the jth workpiece, y ijk is a value of 0 or 1, when the kth process of the jth workpiece selects to process 1 on machine i, otherwise the variable value is 0, E represents a sufficiently large positive integer, q ijk represents the processing time of the kth process of the jth workpiece on machine i, s hl represents the first process of the jth workpiece, r ijkhl is a value of 0 or 1, when the kth process of the jth workpiece on machine i is processed before the first process of the jth workpiece, the variable value is 1, otherwise the variable value is 0, at iw represents the starting time of the W AGV at the current position to machine i, and rt ijkw represents the time taken for the W AGV to reach the machine i processing the kth process of the jth workpiece from the position.
Equations (2) and (3) represent constraint of workpiece processing sequence, the maximum processing time cannot be smaller than any workpiece finishing time, and the starting time of a certain working procedure of a workpiece cannot exceed the workpiece finishing time. The expressions (4) and (5) show that only one process can be performed at a time on the same machine, wherein E represents a sufficiently large positive integer. Equation (6) shows that the AGV must wait for the work piece to finish the previous process before it can start to transport the current work piece.
And step 2, setting initial parameters such as population number, variation probability and the like according to experimental environment and rules.
And step 3, taking the machine utilization rate into initial consideration, generating an initial code by adopting an initialization mode combining the maximum utilization rate priority of the machine, the maximum utilization rate priority of the AGV in the work procedure and the random generation, wherein the ratio of the three initialization modes is 0.4:0.4:0.2. According to the invention, the initial population mode is combined by the heuristic strategy and the random mode, so that the quality of the initial solution is higher;
And 4, selecting individuals in a tournament selection (tournament selection) mode, randomly selecting d genes from the parent population at each time, solving the fitness f (i) according to a fitness calculation function, storing the individuals with higher fitness into the cross pool population, and repeating the operation until the number of the genes in the selection pool meets the requirement.
Step 5 randomly generating an integer r in the interval [1, Z 0 ], copying the genes corresponding to the parent chromosomes P 1 and P 2 into the offspring C 1 and C 2, and finally copying the genes remained in the parent into the offspring.
And 6, adopting a dynamic mutation strategy, wherein a mutation probability solving formula is as follows:
pm＝pmax-(pmax-pmin)×gn÷gnmax (7)
Pm represents the current variation probability, gn represents the current program iteration number, gnmax represents the maximum iteration number. The machine coding adopts single-point mutation, and the process coding adopts exchange mutation strategy.
Step 7, in a mobile procedure neighborhood structure, calculating a corresponding key procedure set { O 1,O2,...,On } in the workshop scheduling by solving a key path, randomly selecting a key procedure v from the procedure set, and inserting v into the chromosome to obtain a neighborhood solution; and obtaining a new neighborhood solution by exchanging two processes of end-to-end connection of non-identical workpiece processes in the key process sub-blocks in the process block exchange neighborhood structure.
And step 8, when the algorithm reaches the maximum operation algebra, turning to step 5, otherwise, turning to the next step.
And 9, outputting an optimal scheduling solution corresponding to the optimal finishing time.
The invention can rapidly screen the feature matching result, and has important significance for image optimization processing.
Examples:
An example of a3 x 4FJSP problem is shown in table 1, where the data represents the time it takes for the process to work on the corresponding machine, and the transfer time between machines for the AGV is shown in table 2.
Table 1 3X 4FJSP problem example
TABLE 2AGV handling time
Setting various initial parameters according to the table.
The FJSP problems including AGV conveying consist of three sub-problems including machine selection, procedure sorting and AGV sequence coding, a proper machine is selected for each procedure according to constraints such as different machining time and idle conditions, then the procedures of workpieces are sorted, finally an AGV conveying sequence is generated according to procedure codes in a uniform distribution mode, and the machining sequence and time are determined. The final code structure is shown in fig. 2, the number of the machine selection code indicates which machine in the workable machines corresponds to the work piece process, the process sequence code corresponds to each process for all work pieces, each bit of the gene represents the number of the work piece to be processed, the position where it appears relatively represents which process corresponds to the work piece, and the serial number of the AGV code indicates the serial number of the trolley by taking the serial number of two AGVs as an example.
And calculating the fitness of the initial solution, and carrying out the selection reservation operation on the excellent individuals.
Different machine coding and process coding strategies are adopted in coding crossover, uniform crossover (uniform crossover, UX) operation is adopted in machine selection coding, an integer r is randomly generated in an interval [1, Z 0 ], then the corresponding genes of parent chromosomes P 1 and P 2 are copied into offspring C 1 and C 2, finally the remaining genes of the parent are copied into offspring, and the uniform crossover of machine selection is shown in figure 3. The crossover of the process coding part adopts a preferential operation method and a POX cross-mixing mode, the workpiece set is randomly divided into two parts, genes corresponding to the workpiece sets of P 1 and P 2 are copied into offspring C 1 and C 2, genes not contained in the workpiece set are copied into C 2 and C 1, and the process coding crossover is shown in figure 4.
And determining the mutation probability according to the current iteration times, adopting single-point mutation for machine coding, and adopting an exchange mutation strategy for process coding.
The neighborhood structure is exchanged by the variable neighborhood process block as shown in fig. 5, and a new neighborhood solution is obtained by exchanging two processes of the non-identical workpiece process end-to-end in the critical process sub-block.
Repeating the operation, and ending when the algorithm reaches the maximum iteration times.
And outputting the optimal scheduling result solution set.
Claims (3)
1. A flexible job shop scheduling method of a co-fusion AGV is characterized by comprising the following steps:
Step 1: establishing a flexible operation scheduling mathematical model containing AGV carrying; the flexible operation scheduling mathematical model containing AGV carrying is as follows:
Jj:{J1,J2,……,Jn}
Mi:{M0,M1,M2,……,Mm}
Ad:{A1,A2,……,AW}
Wherein J j is the processed workpieces in the workshop, and n is the number of the processed workpieces; m i is the number of processing machines in the workshop; a d is AGVs in a workshop, and w is the number of the AGVs;
in the workpiece machining process, constraint equations of a machined workpiece, a machining machine and an AGV are as follows:
cjk≤sj(k+1)
cjk≥sjk+qijk×yijk
qijk+sjk≤shl+E-E×rijkhl
cjk-sj(k+1)≤E-E×rijkhl
sjk+qijk≤atiw+rtijkw
Wherein c jk represents the processing completion time of the kth process of the jth workpiece, s jk represents the processing start time of the kth process of the jth workpiece, y ijk is 0 or 1, 1 is taken when the kth process of the jth workpiece is selected to process on machine i, otherwise the variable value is 0, E represents a sufficiently large positive integer, q ijk represents the processing time of the kth process of the jth workpiece on machine i, s hl represents the processing start time of the first process of the jth workpiece, r ijkhl is 0 or 1, 1 is taken when the kth process of the jth workpiece on machine i is processed before the first process of the jth workpiece, and 0, at iw represents the start time of the jth AGV at the current position to machine i, rt ijkw represents the time taken for the kth AGV to reach the machine i for processing the kth process of the jth workpiece from the current position;
the objective evaluation function is:
Wherein Wt j represents the completion time of the last process of each workpiece j, the maximum process completion time is the maximum completion time of all the workpieces, and the target evaluation function is to obtain the minimum maximum completion time in the group coding sequence;
step 2: initializing parameters, and coding each individual in the population to generate a coding sequence; the code sequence generation adopts three strategy modes, and weight is distributed for each strategy mode according to the proportion; the three strategy modes are respectively as follows: a workpiece processing machine maximum utilization priority strategy, an AGV maximum utilization priority strategy and a random generation strategy;
The maximum utilization rate priority strategy of the workpiece processing machine is as follows: firstly, setting an array, wherein the length of the array is equal to the number of the machines, the sequence of the array sequentially corresponds to the sequence of the processing machines, and the value on each bit of the array corresponds to the processing time on the corresponding machine; randomly selecting one workpiece in the workpiece set, starting from the first working procedure, adding the processing time of the processing machine selected by the current working procedure with the time corresponding to the array, not updating the array at the moment, selecting the shortest time from the array as the processing machine of the current working procedure, updating the array, namely adding the processing time of the selected processing machine to the corresponding position of the array, and the like until the processing machines of all working procedures of the current workpiece are selected, randomly selecting one workpiece from the rest of the workpiece set to perform the same operation until the working procedures of all the workpieces are selected;
The AGV maximum utilization priority policy is: firstly, setting an array S w, wherein the length of the array S w is equal to the number w of AGVs, the sequence of the array S w sequentially corresponds to the sequence of the AGVs, the value on each position of the array S w corresponds to the carrying time of the corresponding AGVs, then setting an array LP w, and the value in the array LP w sequentially corresponds to the current position of the machine where the AGVs are positioned; calculating AGV carrying time through the current position value of the AGV in the array LP w and the sequence number of the processing machine of the procedure purpose, traversing the procedure set to be processed, selecting W procedures from the AGV carrying the workpiece to the processing machine with the shortest time, adding the selected W AGV carrying times with the value of the array S w, updating the array S w, simultaneously updating the array LP w by using the sequence number value of the selected W AGV carrying destination machines, and the like, and selecting the W shortest carrying time procedures from the rest procedure set to be processed to carry out the operation until all the procedures to be processed are selected;
Step 3: arbitrarily selecting two individuals, crossing the coding sequences of the individuals until the number of the selected individuals reaches the number of the individuals in the population, and obtaining the crossed population; the coding sequence consists of a plurality of sequence values, wherein each sequence value represents the serial number of a workpiece processing machine, the serial number of a workpiece or the serial number of an AGV, the sequence values with the same meaning are continuous, and the sequence value groups representing the workpiece processing machine, the sequence value groups representing the working procedure and the sequence value groups representing the AGV have the same sequence value number;
Step 4: carrying out mutation operation on individuals in the crossed population according to the initial mutation probability to obtain a mutated population; the mutation operation is carried out on individuals in the crossed population according to the initial mutation probability, and the method comprises the following steps: judging whether the current variation probability of an individual in the crossed population is smaller than the initial variation probability, if so, exchanging any two sequence values in the coding sequence of the individual, otherwise, keeping the current coding sequence of the individual;
step 5: solving a key working procedure set of each individual in the mutated population, and exchanging the last two sequence values of the key working procedure set of each individual to obtain a neighborhood code of each individual;
Step 6: and calculating the fitness value of the individuals in the mutated population and the fitness value of the individual neighborhood codes through a target evaluation function, comparing the fitness value of the individuals in the mutated population with the fitness value of the individual neighborhood codes, and if the fitness value of the individual neighborhood codes is smaller than the fitness value of the individuals in the mutated population, replacing the individuals in the corresponding mutated population with the individual neighborhood codes, and traversing the whole mutated population.
2. The flexible job shop scheduling method of a co-fusion AGV according to claim 1, wherein: the parameters include: the number of workpieces n, the number of processing machines m, the number of AGVs w, the initial population size P, the number of population iterations G, the initial crossover probability P c and the initial variation probability P m.
3. The flexible job shop scheduling method of a co-fusion AGV according to claim 1, wherein: the working procedure set of each individual in the mutated population is as follows:
Or:{O1,O2,......,Ov}
the key process set solving constraint equation of each individual in the mutated population is as follows:
CE(r)＝SE(r)+p(r)
CL(r)＝SL(r)+p(r)
SE(r)＝max{CE[PJ(r)],CE[PM(r)]}
CL(r)＝min{SL[SJ(r)],SL[SM(r)]}
d(r)＝SL(r)-SE(r)
Wherein O r represents the r-th node process, SE (r) represents the earliest start time of O r, SL (r) represents the latest start time of O r, CE (r) represents the earliest finish time of O r, CL (r) represents the latest finish time of O r, p (r) represents the processing time of O r, PJ (r) represents the previous process with the same workpiece as process O r, SJ (r) represents the next process with the same workpiece as O r, PM (r) represents the previous process with the same processing machine as process O r, SM (r) represents the next process with the same processing machine as process O r, and O r is the key process if the value of the time difference d (r) of O r is 0.
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| CN112147960B (en) * | 2020-09-17 | 2022-07-26 | 武汉理工大学 | Optimized scheduling method and device for flexible manufacturing system |
| CN112633662A (en) * | 2020-12-17 | 2021-04-09 | 北京工业大学 | Encoding and decoding method for flexible job shop scheduling under limited transportation condition |
| CN112817319B (en) * | 2021-01-08 | 2021-10-15 | 唐旸 | AGV dispatching method and system and computer readable storage medium |
| CN114764663A (en) * | 2021-01-12 | 2022-07-19 | 佳禾智能科技股份有限公司 | GEP artificial intelligence scheduling method and device based on path and sequencing selection |
| CN113671910B (en) * | 2021-07-21 | 2022-09-27 | 华南理工大学 | Integrated multi-AGV flexible job shop scheduling method, device and medium |
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