CN113762811A - Method and system for solving non-stalled Job Shop scheduling problem considering overtime - Google Patents
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Abstract
The invention discloses a method and a system for solving a non-stalled Job Shop scheduling problem in consideration of overtime, wherein the method comprises the following steps: carrying out population initialization of a genetic algorithm; carrying out fitness evaluation on each chromosome by adopting a multi-stage decoding strategy with a reconstruction rule; judging whether an iteration termination condition is met, if so, outputting an optimal solution and finishing the operation; if not, inputting the optimal solution generated by the current iteration into a simulated annealing algorithm for local search optimization; based on the optimal solution of the simulated annealing algorithm, carrying out selection operation, cross operation and mutation operation of genetic operators in the current population to generate a next generation population; and evaluating the fitness of the next generation population, performing iterative operation until an iteration termination condition is met, and outputting a global optimal solution. The invention applies a multi-stage decoding method combined with a reconstruction rule and a population initialization method based on a scheduling rule to an improved genetic simulation annealing algorithm, and can obtain a feasible solution of smaller total advance and overtime cost under the condition of no lag constraint.
Description
Technical Field
The invention belongs to the technical field of intelligent manufacturing, and particularly relates to a method and a system for solving a non-pull-off Job Shop scheduling problem considering overtime.
Background
The Job Shop scheduling problem is a typical manufacturing system scheduling problem, and order-oriented production is one of the current major production models as the customer's personalized demand increases and the requirement for low-cost operation by the manufacturing enterprise.
Meeting lead time is an important goal in the pursuit of production operations for order-oriented manufacturing systems. If the order is in a late stage, the reputation of the enterprise is influenced, and the penalty cost of the late stage can be caused. Therefore, the corresponding scheduling problem also typically has a minimum stall as an optimization objective. Due to the exogenously and fluctuating nature of orders, and the endogenously and relative stability of manufacturing resources, optimal scheduling cannot guarantee that the lead time requirements are always met. In addition, in an actual manufacturing system, time is generally divided into regular working time and rest time, and when an order task is tight in the system, in order to ensure that the order is not delayed, overtime is generally utilized to expand production capacity.
In the existing research, the research considering overtime and non-pull-off period simultaneously is very few, but the situation is common in the actual manufacturing enterprises. Because the problem belongs to the problem of NP difficulty, approximate algorithms such as genetic algorithm, tabu search algorithm, simulated annealing algorithm and the like are mostly adopted in the solving algorithm. However, due to the addition of the no-stall constraint, the problem is prone to produce illegal solutions during the solution process.
Disclosure of Invention
In view of the above, the invention provides a method and a system for solving a problem of non-stall Job Shop scheduling considering overtime, which are used for solving the problem that illegal solutions are easy to generate under the constraint of considering overtime and non-stall simultaneously.
The invention discloses a method for solving a non-stalled Job Shop scheduling problem considering overtime, which comprises the following steps:
s1, carrying out chromosome coding based on the workpiece number, and carrying out population initialization of a genetic algorithm by adopting an initialization method based on a scheduling rule;
s2, taking the minimum total advanced completion cost and total overtime cost as a target function, and adopting a multi-stage decoding strategy with a reconstruction rule to evaluate the fitness of each chromosome;
s3, judging whether an iteration termination condition is met, if so, outputting an optimal solution and finishing the operation; if not, inputting the optimal solution generated by the current iteration into the simulated annealing algorithm for local search optimization, and outputting the optimal solution of the simulated annealing algorithm;
s4, based on the optimal solution of the simulated annealing algorithm, carrying out selection operation, crossover operation and mutation operation of genetic operators in the current population to generate a next generation population;
and S5, returning to the step S2 to evaluate the fitness of the next generation of population, performing iterative operation until an iteration termination condition is met, and outputting a global optimal solution.
Preferably, in step S1, the initializing the population by the genetic algorithm specifically includes:
four initial solutions are generated through four scheduling rules of shortest processing time first, smallest remaining time first, longest remaining time first and most priority of remaining time relative to total time respectively;
respectively generating a plurality of other solutions by a random gene exchange method based on the four initial solutions, and combining the plurality of other solutions with the four initial solutions to serve as N1 initial solutions generated by the scheduling rule;
generating N2 initial solutions by a random method;
combining N1 and N2 to be used as an initial population, and completing population initialization.
Preferably, in step S3, the formula with the minimum total lead completion cost and total shift cost as the objective function is:
wherein the content of the first and second substances,
nthe total number of the workpieces is,
workpieceiThe total pre-completion inventory cost of (c),C i as a workpieceiThe time-out time of (a) is,d i as a workpieceiThe time of delivery of the product is,C e unit time cost for completion in advance;
as a workpieceiThe total overtime cost of (c) is,C o in order to achieve the cost of overtime unit time,
as a workpieceiTo (1) ajThe overtime time of the working procedure is shortened,n i as a workpieceiTotal number of steps.
Preferably, in step S3, the fitness evaluation of each chromosome using the multi-stage decoding strategy with the reconstruction rule specifically includes:
s21, greedy insertion strategy: circularly scanning genes on the chromosome, advancing the start time of all working procedures to complete all workpieces before the delivery date, starting a reconstruction rule to randomly generate a chromosome if the current chromosome cannot ensure that all workpieces are completed before the delivery date, executing a greedy insertion strategy again until a non-delay scheduling result is obtained, ensuring the feasibility of solution, and transferring to the step S22;
s22, right shift strategy: on the basis of feasible solution, circularly scanning corresponding processes on each machine, moving the start time of all the processes backwards, reducing the time for completion in advance, calculating the fitness once after scanning the processes on all the machines for each round, and executing the step S23 when the fitness value of the current iteration and the next iteration is not changed any more;
s23, escape strategy: and circularly scanning corresponding processes on each machine, moving the processes in the overtime interval left/right to ensure that the overtime duration is shortest, calculating the fitness once after scanning the processes on all the machines in one round, and finishing decoding when the fitness of the current iteration and the next iteration does not change any more to obtain the fitness of each chromosome.
Preferably, the step S21 specifically includes:
s21-1) is providedlIndicates the sequence number of the locus,Lthe total length of the chromosome;mthe machine serial number is shown to indicate,Mthe number of the switchboard is;
s21-2) orderl= 1, let all machines idle;
s21-3) get the firstlGenes at the individual loci, and the corresponding steps and man-hours required for processing the genestMachine thereformAnd the earliest start time of the corresponding process relative to the previous processt 0 ；
S21-4) taking machinemA scheduled sequence of processes is added and the machine is acquiredmEnd time of last processt m (ii) a If it is nott 0 ≥t m Then it is firstlThe process corresponding to the gene at each gene position is carried out in a machinemGo up fromt 0 Starting processing at any moment; otherwise, fromt 0 Starting to traverse the machine from time to timemThe scheduled working procedures are carried out, if the idle time between the two working procedures is more thantThen will belPutting the working procedures corresponding to the genes on each gene position into the idle time interval for processing;
s21-5) ifl<LLet us orderl=l+1, go to step S21-3), otherwise, go to step S21-6);
s21-6) calculating a fitness value, and turning to the step S22 if the scheduling result is non-lingering scheduling; otherwise, triggering the reconstruction rule to reinitialize a chromosome, and turning to step S21-2).
Preferably, the step S22 specifically includes:
s22-1) is providedmThe machine serial number is shown to indicate,Mthe number of the total machines is the number of the machines,o m as a machinemThe process number of the above process sequence number,n m as a machinemThe number of the above steps;
s22-2) orderm = 1，o m = n m ；
S22-3) obtaining Processo m Corresponding information, including time of start-up/completionThe start time of the next procedure and the delivery date of the corresponding workpiece;
s22-4) working procedure for calculating work-piece delivery date and subsequent working procedure start timeo m The start-up time of (1) is moved backwards by a long time;
s22-5) execution procedureo m Move right operation and update procedureo m Start-up and completion times;
s22-6) ifo m >0, ordero m = o m 1, turning to step S22-3, otherwise, turning to step S22-7;
s22-7) ifm < MLet us orderm= m + 1，o m =n m Go to step S22-3, otherwise, go to step S22-8;
s22-8) calculating the fitness value of the current iterationF 1' remember the fitness value of the last iteration to beF 1If, ifF 1=F 1If yes, go to step S23; otherwise, it ordersF 1=F 1', turn S22-2).
Preferably, the step S23 specifically includes:
s23-1) is providedmThe machine serial number is shown to indicate,Mthe number of the total machines is the number of the machines,o m as a machinemThe process number of the above process sequence number,n m for each machinemThe number of the above steps;
s23-2) orderm= 1，o m =n m ；
S23-3) obtainingo m And the information corresponding to the working procedure comprises start/finish time, start/finish time of the previous/next working procedure and delivery date of the corresponding workpiece, and whether the working procedure is in the overtime time period or not is judged. If so, go to S23-4), otherwise go to S23-6);
s23-4) working procedure of start/finish time calculation combining with work delivery date and front/back working procedureso m The shift-in time after the forward shift and the backward shift of the start time is the shift distance of the shift-in time;
s23-5) execution procedureo m Moving the operation to the left/right, and updating the start time and the completion time of the corresponding working procedure;
s23-6) ifo m >0, ordero m = o m -1, go to step S23-3), otherwise go to step S23-7);
s23-7) ifm < MLet us orderm= m + 1，o m =n m Go to step S23-3), otherwise, go to step S23-8);
s23-8) calculating the fitness value of the current iterationF 2' remember the fitness value of the last iteration to beF 2If, ifF 2=F 2If yes, decoding is finished; otherwise, it ordersF 2=F 2', go to step S23-2).
The second aspect of the invention discloses a system for solving the problem of non-stalled Job Shop scheduling considering overtime, which comprises:
an initialization module: the method is used for carrying out chromosome coding based on workpiece numbers and carrying out population initialization of a genetic algorithm by adopting an initialization method based on a scheduling rule;
a fitness evaluation module: taking the minimum total advanced completion cost and total shift cost as a target function, and adopting a multi-stage decoding strategy with a reconstruction rule to evaluate the fitness of each chromosome;
a simulated annealing optimization module: judging whether an iteration termination condition is met, if so, outputting an optimal solution and finishing the operation; if not, inputting the optimal solution generated by the current iteration into the simulated annealing algorithm for local search optimization, and outputting the optimal solution of the simulated annealing algorithm;
a genetic operator operation module: based on the optimal solution of the simulated annealing algorithm, carrying out selection operation, cross operation and mutation operation of genetic operators in the current population to generate a next generation population;
an iterative operation module: and the system is used for returning to the fitness evaluation module to evaluate the fitness of the next generation of population, performing iterative operation until an iteration termination condition is met, and outputting a global optimal solution.
In a third aspect of the present invention, an electronic device is disclosed, comprising: at least one processor, at least one memory, a communication interface, and a bus;
the processor, the memory and the communication interface complete mutual communication through the bus;
the memory stores program instructions executable by the processor, which program instructions are invoked by the processor to implement the method according to the first aspect of the invention.
In a fourth aspect of the invention, a computer-readable storage medium is disclosed, which stores computer instructions for causing a computer to implement the method according to the first aspect of the invention.
Compared with the prior art, the invention has the following beneficial effects:
1) the invention provides a population initialization method based on the combination of a scheduling rule and a random method, so as to enhance the feasibility under the constraint condition of no lag period.
2) When the chromosomes are decoded, a multi-stage decoding strategy with a reconstruction rule is adopted, and the start time of all the working procedures is advanced through a greedy insertion strategy, so that all the workpieces are finished before the delivery date, and a non-delay scheduling result is obtained; on the basis of feasible solution, a right shift strategy is adopted to consider whether the idle time of the machine is available or not, so that the start time of all the processes is shifted backwards, and the time for completion in advance is reduced; the escape strategy moves the process in the overtime interval left/right, so that the overtime duration is shortest, more feasible solutions can be obtained more quickly, and a scheduling result with a better adaptability value can be obtained.
3) The invention combines a genetic algorithm and a simulated annealing algorithm, combines a population initialization method based on a scheduling rule and a multi-stage decoding method based on a reconstruction rule to be used in the improved genetic simulated annealing algorithm, inputs the optimal solution generated by each iteration of the genetic algorithm into the simulated annealing algorithm for further searching and optimizing, and combines the global searching capability of the genetic algorithm and the local searching capability of the simulated annealing to enhance the comprehensive searching capability of the algorithm, thereby obtaining smaller total advance and overtime.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of a method for solving the problem of non-stalled Job Shop scheduling considering overtime according to the present invention;
FIG. 2 is an example of chromosomal encoding according to the invention;
FIG. 3 is a schematic diagram of a greedy insertion strategy according to the present invention;
FIG. 4 is a schematic diagram of the right shift strategy of the present invention;
FIG. 5 is a schematic diagram of an escape strategy according to the present invention;
fig. 6 is a diagram illustrating a scheduling result according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.
The invention provides a method for solving the problem of non-off-schedule Job Shop scheduling considering overtime aiming at the problem of NP difficulty of simultaneously considering overtime and non-off-schedule in the Job Shop scheduling problem, which not only can rapidly obtain near-optimal and feasible scheduling of the problem, but also can obtain smaller total advance and total overtime.
Referring to fig. 1, the invention discloses a method for solving a no-stall Job Shop scheduling problem considering overtime, which comprises the following steps:
and S1, carrying out chromosome coding based on the workpiece number, and carrying out population initialization of the genetic algorithm by adopting an initialization method based on a scheduling rule.
Since the invention needs to guarantee the constraint condition of no lag period, the initial species group has great influence on the subsequent solving process. Therefore, the invention provides a population initialization method based on the combination of a scheduling rule and a random method, taking the total generation of 100 initial solutions as an example, and the specific process is as follows:
four initial solutions are generated by four scheduling rules of Shortest Processing Time First (SPT), Shortest Remaining Time First (SRPT), longest Remaining Time First (LRPT) and Remaining Time relative to total Time most First (LRPT/TWK);
respectively generating 9 other solutions by a random gene exchange method based on the four initial solutions, and combining the other solutions with the four initial solutions to serve as N1 initial solutions generated by the scheduling rule, namely generating 40 initial solutions by the scheduling rule;
generating N2 initial solutions by a random method;
n1 and N2 are combined to be used as an initial population, population initialization is completed, and if N2=60 is taken, 100 initial solutions are generated in total.
The invention adopts a chromosome coding mode based on the number of a workpiece, namely the number on each gene position represents a workpiece, the number of times of the same number is shown as the next process of the workpiece, and FIG. 2 is a chromosome coding example of the invention.
And S2, taking the minimum total advanced completion cost and total overtime cost as an objective function, and adopting a multi-stage decoding strategy with a reconstruction rule to evaluate the fitness of each chromosome.
When the chromosome is decoded, each gene is decoded based on the general principle of conventional decoding from left to right, and whether the machine idle time is available or not is considered, and a better fitness value is obtained by moving left and right, so that more feasible solutions can be obtained more quickly, and a better scheduling result of the fitness value can be obtained. The invention takes the minimum of total advanced completion cost and total shift cost as a target function, and the formula is as follows:
wherein the content of the first and second substances,
nthe total number of the workpieces is,
workpieceiThe total pre-completion inventory cost of (c),C i as a workpieceiThe time-out time of (a) is,d i as a workpieceiThe time of delivery of the product is,C e unit time cost for completion in advance;
as a workpieceiThe total overtime cost of (c) is,C o in order to achieve the cost of overtime unit time,
as a workpieceiTo (1) ajThe overtime time of the working procedure is shortened,n i as a workpieceiTotal number of steps.
And then, taking the target function as a fitness function, and adopting a multi-stage decoding strategy with a reconstruction rule to evaluate the fitness of each chromosome.
The present invention proposes a multi-stage decoding strategy with reconstruction rules with three stages: the first stage is a greedy insertion strategy and is used for enabling the start time of all working procedures to move left (move forwards) as much as possible so that all workpieces are finished before the delivery date to ensure the feasibility of solution; the second stage is a right shift strategy, which is used for shifting the start time of all the working procedures to the right (backward) as much as possible on the basis of a feasible solution so as to reduce the time for completion in advance; and the third stage is an escape strategy and is used for moving the working procedure in the overtime interval left/right to minimize the overtime time as much as possible. And after the three stages are executed, calculating to obtain a final fitness value.
The fitness evaluation of each chromosome by adopting the multi-stage decoding strategy with the reconstruction rule specifically comprises the following steps:
s21, greedy insertion strategy: and circularly scanning genes on the chromosome, advancing the start time of all the working procedures, completing all the workpieces before the delivery date until a non-delay scheduling result is obtained, ensuring the feasibility of the solution, and transferring to the step S22.
The step S21 specifically includes the following sub-steps:
s21-1) is providedlIndicates the sequence number of the locus,Lthe total length of the chromosome;mthe machine serial number is shown to indicate,Mthe number of the switchboard is;
s21-2) orderl= 1, let all machines idle;
s21-3) get the firstlGenes at the individual loci, and the corresponding steps and man-hours required for processing the genestMachine thereformAnd the earliest start time of the corresponding process relative to the previous processt 0 ；
S21-4) taking machinemA scheduled sequence of processes is added and the machine is acquiredmEnd time of last processt m (ii) a If it is nott 0 ≥t m Then it is firstlThe process corresponding to the gene at each gene position is carried out in a machinemGo up from t 0 Starting processing at any moment; otherwise, fromt 0 Starting to traverse the machine from time to timemThe scheduled working procedures are carried out, if the idle time between the two working procedures is more thantThen will belPutting the working procedures corresponding to the genes on each gene position into the idle time interval for processing;
s21-5) ifl<LLet us orderl=l+1, go to step S21-3), otherwise, go to step S21-6);
s21-6) calculating a fitness value, and turning to the step S22 if the scheduling result is non-lingering scheduling; otherwise, triggering the reconstruction rule to reinitialize a chromosome, and turning to step S21-2).
S22, right shift strategy: on the basis of feasible solution, the corresponding working procedures on each machine are scanned circularly, the working time of all the working procedures is moved backwards, the time for completion in advance is reduced, after each round of working procedures on all the machines are scanned, the fitness is calculated once, and when the fitness value of the current iteration and the next iteration is not changed any more, the step S23 is executed.
The step S22 specifically includes the following sub-steps:
s22-1) is providedmThe machine serial number is shown to indicate,Mthe number of the total machines is the number of the machines,o m as a machinemThe process number of the above process sequence number,n m as a machinemThe number of the above steps;
s22-2) orderm = 1，o m = n m ；
S22-3) obtaining Processo m Corresponding information comprises start-up/completion time, start-up time of a subsequent procedure and delivery date of a corresponding workpiece;
s22-4) working procedure for calculating work-piece delivery date and subsequent working procedure start timeo m The start-up time of (1) is moved backwards by a long time;
s22-5) execution procedureo m Move right operation and update procedureo m Start-up and completion times;
s22-6) ifo m >0, ordero m = o m -1, go to step S22-3), otherwise go to step S22-7);
s22-7) ifm < MLet us orderm= m + 1，o m =n m Go to step S22-3), otherwise, go to step S22-8);
s22-8) calculating the fitness value of the current iterationF 1' remember the fitness value of the last iteration to beF 1If, ifF 1=F 1If yes, go to step S23; otherwise, it ordersF 1=F 1', turn S22-2).
S23, escape strategy: and circularly scanning corresponding processes on each machine, moving the processes in the overtime interval left/right to ensure that the overtime duration is shortest, calculating the fitness once after scanning the processes on all the machines in one round, and finishing decoding when the fitness of the current iteration and the next iteration does not change any more to obtain the fitness of each chromosome.
The step S23 specifically includes the following sub-steps:
s23-1) is providedmThe machine serial number is shown to indicate,Mthe number of the total machines is the number of the machines,o m as a machinemThe process number of the above process sequence number,n m for each machinemThe number of the above steps;
s23-2) orderm= 1，o m =n m ；
S23-3) obtaining information corresponding to the working procedure, including start/finish time, start/finish time of the previous/next working procedure and delivery date of the corresponding workpiece, judging the working procedureo m Whether in an overtime period. If so, go to S23-4), otherwise go to S23-6);
s23-4) working procedure of start/finish time calculation combining with work delivery date and front/back working procedureso m The shift-in time after the forward shift and the backward shift of the start time is the shift distance of the shift-in time;
s23-5) execution procedureo m Moving the operation to the left/right, and updating the start time and the completion time of the corresponding working procedure;
s23-6) ifo m >0, ordero m = o m -1, go to step S23-3), otherwise go to step S23-7);
s23-7) ifm < MLet us orderm= m + 1，o m =n m Go to step S23-3), otherwise, go to step S23-8);
s23-8) calculating the fitness value of the current iterationF 2' remember the fitness value of the last iteration to beF 2If, ifF 2=F 2If yes, decoding is finished; otherwise, it ordersF 2=F 2', go to step S23-2).
S3, judging whether an iteration termination condition is met, if so, outputting an optimal solution and finishing the operation; if not, inputting the optimal solution generated by the current iteration into the simulated annealing algorithm for local search optimization, and outputting the optimal solution of the simulated annealing algorithm.
In order to enhance the searching capability of the algorithm, the genetic algorithm and the simulated annealing algorithm are combined, the deficiency of the local searching capability of the genetic algorithm is made up through the stronger local searching capability of the simulated annealing algorithm, the balance of local searching and global searching is realized, and the optimal solution of the current iteration is further optimized.
And S4, performing selection operation, cross operation and mutation operation of genetic operators in the current population based on the optimal solution of the simulated annealing algorithm to generate a next generation population.
Specifically, the selection, crossing and mutation operations are respectively carried out in a way of championship selection, a POX (vacancy operation cross) operator and single-point gene interchange, the maximum iteration number is used as a termination criterion of the algorithm, and an optimal solution storage strategy is adopted in the algorithm operation process.
And S5, returning to the step S2 to evaluate the fitness of the next generation of population, performing iterative operation until an iteration termination condition is met, and outputting a global optimal solution.
Specifically, after the next generation population is generated, the process returns to the step S2, the process of the steps S2-S5 is repeated, iteration is performed circularly until an iteration termination condition is met, and a global optimal solution is output as a final scheduling result.
The invention provides a non-off-time Job Shop scheduling problem solving method considering overtime aiming at the problems encountered in actual production and the current situation of the existing research, and aims to improve the quality and speed of problem solving and minimize the total advance and overtime cost. The quality of the initial population is improved by an initialization method based on a scheduling rule; using a multi-stage decoding strategy with reconstruction rules to quickly obtain a feasible solution to the problem with a better objective function value; the genetic simulated annealing algorithm is provided by combining the global search capability of the genetic algorithm and the local search capability of simulated annealing, so that the smaller total advance and overtime cost can be obtained under the condition of no delay.
The implementation and technical effects of the invention will be described below with reference to specific examples, taking the chromosome code of fig. 2 as an example, for a total of 4 workpieces corresponding to two machines M1、M2The abscissa represents the processing time, which is dimensionless time, and the ordinate represents the different processing machines, fig. 3 is a schematic diagram of a greedy insertion strategy, fig. 4 is a schematic diagram of a right-shift strategy, fig. 5 is a schematic diagram of an escape strategy, where t1-t2Indicates the overtime time interval, d1~d4Respectively corresponding to the delivery date of 4 workpieces,O i,j respectively representing the scheduling results of the jth process of the ith workpiece. Firstly, ensuring that all workpieces are finished in a delivery date through a greedy insertion strategy, realizing non-delay scheduling and obtaining a scheduling result of the graph 3; on the basis of non-delay scheduling, executing the right shift operation of the working procedure through a right shift strategy to shift the start time of the working procedure backwards so as to minimize the completion time in advance and obtain the scheduling result of the graph 4; and finally, executing left/right shift operation of the working procedure through an escape strategy, and updating the start time and the completion time of the corresponding working procedure to make the overtime time shortest, thereby obtaining the scheduling result of the graph 5.
FIG. 6 is a Gantt chart of a final scheduling result obtained by solving the improved benchmarking problem FT06 by using the overtime-considered non-stalled Job Shop scheduling problem solving method of the present invention according to one embodiment, where the abscissa is processing time, the ordinate represents different processing machines, and there are 6 workpieces corresponding to 6 machines M1~M6Wherein d is1~d6Respectively corresponding to the delivery date of 6 workpieces,O i,j the scheduling results respectively represent the scheduling results of the jth procedure of the ith workpiece, the time intervals 16-24 and 40-48 on the abscissa are overtime time intervals, and as can be seen from the analysis of fig. 6, the scheduling results obtain the scheduling results with the minimum delay-free period, total advance time/cost and total overtime/cost, and the scheduling results are more in line with the actual production requirements.
Corresponding to the embodiment of the method, the invention also discloses a system for solving the problem of non-stalled Job Shop scheduling considering overtime, which comprises the following steps:
an initialization module: the method is used for carrying out chromosome coding based on workpiece numbers and carrying out population initialization of a genetic algorithm by adopting an initialization method based on a scheduling rule;
a fitness evaluation module: taking the minimum total advanced completion cost and total shift cost as a target function, and adopting a multi-stage decoding strategy with a reconstruction rule to evaluate the fitness of each chromosome;
a simulated annealing optimization module: judging whether an iteration termination condition is met, if so, outputting an optimal solution and finishing the operation; if not, inputting the optimal solution generated by the current iteration into the simulated annealing algorithm for local search optimization, and outputting the optimal solution of the simulated annealing algorithm;
a genetic operator operation module: based on the optimal solution of the simulated annealing algorithm, carrying out selection operation, cross operation and mutation operation of genetic operators in the current population to generate a next generation population;
an iterative operation module: and the system is used for returning to the fitness evaluation module to evaluate the fitness of the next generation of population, performing iterative operation until an iteration termination condition is met, and outputting a global optimal solution.
The present invention also discloses an electronic device, comprising: at least one processor, at least one memory, a communication interface, and a bus; the processor, the memory and the communication interface complete mutual communication through the bus; the memory stores program instructions executable by the processor, which invokes the program instructions to implement the methods of the invention described above.
The invention also discloses a computer readable storage medium which stores computer instructions for causing the computer to implement all or part of the steps of the method of the embodiment of the invention. The storage medium includes: u disk, removable hard disk, ROM, RAM, magnetic disk or optical disk, etc.
The above-described system embodiments are merely illustrative, wherein the units described as separate parts may or may not be physically separate, and the parts shown as units may or may not be physical units, i.e. may be distributed over a plurality of network units. Without creative labor, a person skilled in the art can select some or all of the modules according to actual needs to achieve the purpose of the solution of the embodiment.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (10)
1. A method for solving a non-stalled Job Shop scheduling problem considering overtime comprises the following steps:
s1, carrying out chromosome coding based on the workpiece number, and carrying out population initialization of a genetic algorithm by adopting an initialization method based on a scheduling rule;
s2, taking the minimum total advanced completion cost and total overtime cost as a target function, and adopting a multi-stage decoding strategy with a reconstruction rule to evaluate the fitness of each chromosome;
s3, judging whether an iteration termination condition is met, if so, outputting an optimal solution and finishing the operation; if not, inputting the optimal solution generated by the current iteration into the simulated annealing algorithm for local search optimization, and outputting the optimal solution of the simulated annealing algorithm;
s4, based on the optimal solution of the simulated annealing algorithm, carrying out selection operation, crossover operation and mutation operation of genetic operators in the current population to generate a next generation population;
and S5, returning to the step S2 to evaluate the fitness of the next generation of population, performing iterative operation until an iteration termination condition is met, and outputting a global optimal solution.
2. The method for solving the problem of the non-stalled Job Shop scheduling problem considering overtime according to claim 1, wherein the initializing population of the genetic algorithm by using the scheduling rule-based initialization method in step S1 specifically comprises:
four initial solutions are generated through four scheduling rules of shortest processing time first, smallest remaining time first, longest remaining time first and most priority of remaining time relative to total time respectively;
respectively generating a plurality of other solutions by a random gene exchange method based on the four initial solutions, and combining the plurality of other solutions with the four initial solutions to serve as N1 initial solutions generated by the scheduling rule;
generating N2 initial solutions by a random method;
combining N1 and N2 to be used as an initial population, and completing population initialization.
3. The method for solving the no-stall Job Shop scheduling problem considering overtime according to claim 1, wherein in step S2, the formula with the minimum total early completion cost and total overtime cost as an objective function is as follows:
wherein the content of the first and second substances,
nthe total number of the workpieces is,
workpieceiThe total pre-completion inventory cost of (c),C i as a workpieceiThe time-out time of (a) is,d i as a workpieceiThe time of delivery of the product is,C e unit time cost for completion in advance;
as a workpieceiThe total overtime cost of (c) is,C o in order to achieve the cost of overtime unit time,
as a workpieceiTo (1) ajThe overtime time of the working procedure is shortened,n i as a workpieceiTotal number of steps.
4. The method for solving the non-stalled Job Shop scheduling problem considering overtime according to claim 1, wherein the step S2 of performing fitness evaluation on each chromosome by using a multi-stage decoding strategy with reconstruction rules specifically comprises:
s21, greedy insertion strategy: circularly scanning genes on the chromosome, advancing the start time of all working procedures to complete all workpieces before the delivery date, starting a reconstruction rule to randomly generate a chromosome if the current chromosome cannot ensure that all workpieces are completed before the delivery date, executing a greedy insertion strategy again until a non-delay scheduling result is obtained, ensuring the feasibility of solution, and transferring to the step S22;
s22, right shift strategy: on the basis of feasible solution, circularly scanning corresponding processes on each machine, moving the start time of all the processes backwards, reducing the time for completion in advance, calculating the fitness once after scanning the processes on all the machines for each round, and executing the step S23 when the fitness value of the current iteration and the next iteration is not changed any more;
s23, escape strategy: and circularly scanning corresponding processes on each machine, moving the processes in the overtime interval left/right to ensure that the overtime duration is shortest, calculating the fitness once after scanning the processes on all the machines in one round, and finishing decoding when the fitness of the current iteration and the next iteration does not change any more to obtain the fitness of each chromosome.
5. The method for solving the no-stall Job Shop scheduling problem in consideration of overtime according to claim 4, wherein the step S21 specifically includes:
s21-1) is providedlIndicates the sequence number of the locus,Lthe total length of the chromosome;mthe machine serial number is shown to indicate,Mthe number of the switchboard is;
s21-2) orderl= 1, let all machines idleUsing;
s21-3) get the firstlGenes at the individual loci, and the corresponding steps and man-hours required for processing the genestMachine thereformAnd the earliest start time of the corresponding process relative to the previous processt 0 ；
S21-4) taking machinemA scheduled sequence of processes is added and the machine is acquiredmEnd time of last processt m (ii) a If it is nott 0 ≥t m Then it is firstlThe process corresponding to the gene at each gene position is carried out in a machinemGo up fromt 0 Starting processing at any moment; otherwise, fromt 0 Starting to traverse the machine from time to timemThe scheduled working procedures are carried out, if the idle time between the two working procedures is more thantThen will belPutting the working procedures corresponding to the genes on each gene position into the idle time interval for processing;
s21-5) ifl<LLet us orderl=l+1, go to step S21-3), otherwise, go to step S21-6);
s21-6) calculating a fitness value, and turning to the step S22 if the scheduling result is non-lingering scheduling; otherwise, triggering the reconstruction rule to reinitialize a chromosome, and turning to step S21-2).
6. The method for solving the no-stall Job Shop scheduling problem in consideration of overtime according to claim 5, wherein the step S22 specifically includes:
s22-1) is providedmThe machine serial number is shown to indicate,Mthe number of the total machines is the number of the machines,o m as a machinemThe process number of the above process sequence number,n m as a machinemThe number of the above steps;
s22-2) orderm = 1，o m = n m ；
S22-3) obtaining Processo m Corresponding information comprises start-up/completion time, start-up time of a subsequent procedure and delivery date of a corresponding workpiece;
s22-4) delivery date and back track of combined workpieceWorking procedure start time calculation working procedureo m The start-up time of (1) is moved backwards by a long time;
s22-5) execution procedureo m Move right operation and update procedureo m Start-up and completion times;
s22-6) ifo m >0, ordero m = o m -1, go to step S22-3), otherwise go to step S22-7);
s22-7) ifm < MLet us orderm= m + 1，o m =n m Go to step S22-3), otherwise, go to step S22-8);
s22-8) calculating the fitness value of the current iterationF 1' remember the fitness value of the last iteration to beF 1If, ifF 1=F 1If yes, go to step S23; otherwise, it ordersF 1=F 1', turn S22-2).
7. The method for solving the no-stall Job Shop scheduling problem considering overtime according to claim 6, wherein the step S23 specifically includes:
s23-1) is providedmThe machine serial number is shown to indicate,Mthe number of the total machines is the number of the machines,o m as a machinemThe process number of the above process sequence number,n m for each machinemThe number of the above steps;
s23-2) orderm= 1，o m =n m ；
S23-3) obtaining information corresponding to the working procedure, including start/finish time, start/finish time of the previous/next working procedure and delivery date of the corresponding workpiece, judging the working procedureo m Whether in an overtime period; if so, go to S23-4), otherwise go to S23-6);
s23-4) working procedure of start/finish time calculation combining with work delivery date and front/back working procedureso m The shift distance of shift time is takenSeparating;
s23-5) execution procedureo m Moving the operation to the left/right, and updating the start time and the completion time of the corresponding working procedure;
s23-6) ifo m >0, ordero m = o m -1, go to step S23-3), otherwise go to step S23-7);
s23-7) ifm < MLet us orderm= m + 1，o m =n m Go to step S23-3), otherwise, go to step S23-8);
s23-8) calculating the fitness value of the current iterationF 2' remember the fitness value of the last iteration to beF 2If, ifF 2=F 2If yes, decoding is finished; otherwise, it ordersF 2=F 2', go to step S23-2).
8. A system for solving a no-stall Job Shop scheduling problem in view of overtime, the system comprising:
an initialization module: the method is used for carrying out chromosome coding based on workpiece numbers and carrying out population initialization of a genetic algorithm by adopting an initialization method based on a scheduling rule;
a fitness evaluation module: taking the minimum total advanced completion cost and total shift cost as a target function, and adopting a multi-stage decoding strategy with a reconstruction rule to evaluate the fitness of each chromosome;
a simulated annealing optimization module: judging whether an iteration termination condition is met, if so, outputting an optimal solution and finishing the operation; if not, inputting the optimal solution generated by the current iteration into the simulated annealing algorithm for local search optimization, and outputting the optimal solution of the simulated annealing algorithm;
a genetic operator operation module: based on the optimal solution of the simulated annealing algorithm, carrying out selection operation, cross operation and mutation operation of genetic operators in the current population to generate a next generation population;
an iterative operation module: and the system is used for returning to the fitness evaluation module to evaluate the fitness of the next generation of population, performing iterative operation until an iteration termination condition is met, and outputting a global optimal solution.
9. An electronic device, comprising: at least one processor, at least one memory, a communication interface, and a bus;
the processor, the memory and the communication interface complete mutual communication through the bus;
the memory stores program instructions executable by the processor, the processor invoking the program instructions to implement the method of any one of claims 1-7.
10. A computer-readable storage medium storing computer instructions for causing a computer to implement the method of any one of claims 1 to 7.
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