CN106611288A - Improved solving algorithm for flexible flow shop scheduling problem - Google Patents
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Abstract
The invention provides an improved solving algorithm for a flexible flow shop scheduling problem. Particle velocity and position correlation operators are redefined. A coding matrix and a decoding matrix are introduced to represent the relationship among workpiece, machine and scheduling. In order to improve the initial group quality of the improved discrete particle swarm algorithm for the flexible flow shop scheduling problem, a shortest time decomposition policy algorithm based on an NEH algorithm is proposed for the first time by analyzing the relationship between initial machine selection and total completion time of scheduling. The improved discrete particle swarm algorithm is used for global optimization. The algorithm has the advantages that the quality of the initial solution of a particle population is improved; and the time for particles to find the optimal solution is shortened; and an inertial weighting method with exponential decrease is used to effectively avoid the premature convergence of the particles and enhance the early global search ability of the particles.
Description
Technical field
The present invention relates to solving job shop scheduling problem field.
Background technology
Flexible Flow Shop Scheduling (Flexible Flow Shop Scheduling Problem, FFSP) is big
The most frequently used simplified model of amount actual production line scheduling problem, is the important combinatorial optimization problem of a class, has become first system
Make the key of engineering practice.FFSP has proven to a np hard problem, is the problem that academia pays close attention to jointly with engineering circles.
Therefore, the research to FFSP has important theory significance and using value.
Solving the main method of FFSP at present has genetic algorithm, particle cluster algorithm, Immune Clonal Selection Algorithm # ant group algorithms
Deng, there is method to produce initial population using structure type heuristic method algorithm, and carry out global search with reference to genetic algorithm；Also adopt
Flexible Flow Shop Scheduling is solved with genetic algorithm and flexible for mixed constraints using particle swarm optimization algorithm
Flow Shop Scheduling is solved；Expand initial using the method for the random order for generating all process steps order and machine
The space of solution, mainly solves machine choice result and depends on work.But machine choice is not accounted for the scheduling result that sorts
Affect.
FFSP can be described as：Workpiece set J={ J to be processed1, J2... Ji... Jn, (n for workpiece number, i
∈ [1, n]), collection of machines is M={ M1, M2... Mj... Mm(j ∈ [1, m]),Wherein λ represents process number,
SjTotal number of machines on jth procedure is represented, m is machine quantity.Each workpiece needs (the m platforms in m parallel scheduler subsystem
On machine) selection one is processed, and meet following constraints：
1) each workpiece can be processed on different machines；
2) each workpiece cannot interrupt once processing；
3) every machine MjSimultaneously a workpiece J can only be processedi, each workpiece JiSimultaneously can only be by a machine MjProcessing；
4) time of workpiece and traveling time were included in process time；
5) allow to exist between operation to wait, it is allowed to which machine leaves unused when workpiece is not reached.
The optimization aim of FFSP is the processing sequence that find out this workpiece so as to which total complete time is minimum.Below
Provide the computational methods for calculating workpiece total complete time：
In formula：
For the completion date of last completion workpiece on i-th machine；CmaxFor the completion date of last completion workpiece,
The total time sorted.The optimality criterion of FFSP is that the value of total processing charges is minimum, and the target of scheduling is to solve for n task
Optimum processing sequence, make total complete time CmaxMinimum, to reach the demand, the invention provides a kind of improved flexibility
The derivation algorithm of Flow Shop Scheduling.
The content of the invention
For the deficiency that above-mentioned literature research achievement is present, the invention provides a kind of improved flexible Flow Shop scheduling
The derivation algorithm of problem.
In order to solve above-mentioned deficiency, the present invention is achieved by the following technical solutions：
Step 1：FSSP algorithms are defined and flow process
Step 2:：The relational operator of particle rapidity and position is redefined, selects total with scheduling by analyzing initial machine
The relation of completion date, proposes first a kind of most short used time decomposition strategy algorithm based on NEH algorithms
Step 3：Introduce encoder matrix and decoding matrix to represent the relation between workpiece, machine and scheduling
Step 4：Global optimization is carried out using discrete particle cluster algorithm is improved
Present invention has the advantages that：
The advantage of this algorithm is the quality that improve particle populations initial solution, shortens the time that particle finds optimal solution；
Simultaneously using the inertia weight mode exponentially successively decreased, particle Premature Convergence is effectively prevented from, enhances the overall situation of particle early stage
Search capability.
Description of the drawings
The general frame of the FFSP of accompanying drawing 1
Accompanying drawing 2 solves the algorithm flow of FFSP
Specific embodiment
Step 1：FSSP algorithms are defined and flow process, and it is described in detail below：
Step 1.1) definition of FSSP algorithms
1) constant series：The position of particle is X, and the operative position of constant series (i, j) exchanges in X i-th element and j-th
Element.
2) addition operatorThe constant series of latter speed are added to the constant series of previous speed or position
The end of list.For example：AssumeSo
3) subtraction operatorSubtraction operation deducts individual body position or the particle of particle for the globally optimal solution of particle
Individual optimal solution position deducts particle body position, is as a result constant series.For example:Hypothesis A=(3,1,2,4,5,6), B=
(1,2,4,3,6,5), due to A (1)=B (4)=3, first turnaround sequence is just (Isosorbide-5-Nitrae), that is to say, that subtraction result first
It is 4 on individual position, by that analogy, then
4) multiplication operatorMultiplication operation takes advantage of speed and Studying factors c for inertia weight ω (ω ∈ R)1、c2(c2∈
R speed) is taken advantage of, the result of computing is respectively with ω, c1、c2For the speed that probability retains particle.
Step 1.2) FFSP algorithm flows
Including particle populations scale, inertia weight factor ω, Studying factors c1、c2, piece count n, machine quantity m, storage
Work pieces process matrix J obNumber, workpiece association battle array JobRJob, workpiece total elapsed time Totaltime, maximum iteration time T
Step 2：The relational operator of particle rapidity and position is redefined, selects total with scheduling complete by analyzing initial machine
Relation between man-hour, proposes first a kind of most short used time decomposition strategy algorithm based on NEH algorithms, and its concrete calculating process is such as
Under：
The size of FFSP scheduling completion dates depends on the processing sequence of operation on the processing machine and machine of workpiece selection,
Therefore the quality for improving particle populations initial solution is particularly important.Improve initial solution quality can shorten solve FSSP time and
Strengthen the performance that particle finds optimal solution.According to workpiece, total elapsed time carries out descending arrangement to workpiece on machine, then successively
Take out workpiece and be iterated insertion operation.Here, most short used time decomposition strategy thought：By workpiece, total elapsed time is pressed on machine
Decomposed according to every procedure, descending arrangement is carried out according to total time of each workpiece on every procedure, according to every procedure
Contrasted with adjacency total time and sorted, until complete to all workpiece descending sorts.Wherein, adjacency is defined such as
Under：
Pro=min ETCR (i, j) (i ∈ { 1,2 ..., SubTask }, j ∈ { 1,2 ..., M }
Represent the degree of closeness between two procedures process time, adjacency is less show closer to.The most short used time decomposes
Policing algorithm step：
Step 2.1) priority level list S={ 1,2 ..., M } is set, whereinP is process number,
sumpiFor the machine number of the i-th procedure, M is the number of total machine；Simultaneously the copy pcopy of setting process number, makes pcopy
=p；Adjacency Pro is set；Counter t=1；The setting m=M of priority；
Step 2.2) in pth copy procedure, according to the total time that workpiece is processed on machine, descending is carried out to workpiece
Arrangement, obtains collating sequence seq；
Step 2.3) priority list S is arranged according to seq：To t and t+1 two procedures in seq, compare the difference of numerical value,
If greater than Pro, then the priority of plurality is set to m, then arranges m=m-1；Otherwise, before comparing the two procedures
One procedure, until obtaining comparative result；
Step 2.4) judge whether t is equal to M：If it is, the priority of t procedures is set to minimum 1,5 are gone to step；
Otherwise, 3 are gone to step；
Step 2.5) output priority list S；
Step 2.6) machine chain is generated according to regular S dynamic randoms.
Step 3：Introduce encoder matrix and decoding matrix to represent the relation between workpiece, machine and scheduling, its is concrete
Calculating process is as follows：
The coding of step 3.1 particle and decoding
The coded system of particle had both affected the search capability of particle, and the diversity of population is affected again.This method coded system
It is using Indirect encod, code length is adoptedWherein JNiRepresent the operation quantity of i-th workpiece.This coded system
Benefit be that an encoding scheme correspond to a scheduling strategy.Coding represents that wherein P represents process number with vector ECJ (P)；
Decoding matrix represents that wherein M represents collection of machines, and J represents set of tasks, and P represents operation set, B tables with DCJ (M, J, P, N)
Show the piece count for processing corresponding machine.Work as m=3, during J=3, particle ECJ=(2,3,3,1,1,1,3,2,2,2) is
A kind of feasible coding strategy.ECJ (1)=2 represents that the 1st procedure of the 1st workpiece is processed on machine 2, ECJ (4)=1 table
Show that the 1st of the 2nd workpiece processes to operation on machine 1, by that analogy.After given particle encoding scheme, needs are decoded
Operation：To mark off in whole subtasks of correspondence machining, and with reference to workpiece incidence matrix JobSubJob, solved
The result of code is stored enter in decoding matrix.
Step 4：Global optimization is carried out using discrete particle cluster algorithm is improved, its detailed process is as follows：
Global optimization is carried out by inertia weight adjustment.
Inertia weight ω is a critically important parameter in algorithm, and it balances the ability of searching optimum of particle and local is visited
Suo Nengli.Larger inertia weight can strengthen the global search capability of particle, and less inertia weight can improve the office of particle
Portion's exploring ability.In order to be able to make algorithm more comprehensively be searched in the early stage, calculate public using the inertia weight for exponentially successively decreasing
Formula, is shown below：
α=ωmax-ωmin
In formula：ωmaxAnd ωminFor the maximum and minimum of a value of inertia weight, Iter is current iteration number of times, maxIter
For maximum iteration time.
Claims (4)
1. a kind of derivation algorithm of improved flexible Flow Shop Scheduling, the present invention relates to solving job shop scheduling problem field, its
It is characterized in that, comprises the steps：
Step 1：FSSP algorithms are defined and flow process, and it is described in detail below：
Step 1.1）FSSP algorithms are defined
1）Constant series：The position of particle be X, constant series（I, j）Operative position exchange X in i-th element and j-th element
2）Addition operator：The constant series of latter speed are added to the constant series list of previous speed or position
End, for example：Assume, then
3）Subtraction operator:Subtraction operation deducts individual body position or the particle individuality of particle for the globally optimal solution of particle
Optimal solution position deducts particle body position, is as a result constant series, for example:Assume A=（3,1,2,4,5,6）, B=（1,2,4,
3,6,5）, due to A（1）=B（4）=3, first turnaround sequence be just（1,4）, that is to say, that subtraction result is on first position
4, by that analogy, then
4）Multiplication operator：Multiplication operation is inertia weightTake advantage of speed and Studying factors、
Take advantage of speed, the result of computing be respectively with、、For the speed that probability retains particle
Step 1.2）FFSP algorithm flows
Including particle populations scale, the inertia weight factor, Studying factors、, piece count n, machine quantity m, storage
Work pieces process matrix J obNumber, workpiece association battle array JobRJob, workpiece total elapsed time Totaltime, maximum iteration time
T
Step 2:：The relational operator of particle rapidity and position is redefined, is selected and the total completion of scheduling by analyzing initial machine
The relation of time, proposes first a kind of most short used time decomposition strategy algorithm based on NEH algorithms
Step 3：Introduce encoder matrix and decoding matrix to represent the relation between workpiece, machine and scheduling
Step 4：Global optimization is carried out using discrete particle cluster algorithm is improved.
2., according to the derivation algorithm of a kind of improved flexible Flow Shop Scheduling described in claim 1, it is characterized in that,
Concrete calculating process in the above step 2 is as follows：
Step 2：The relational operator of particle rapidity and position is redefined, is selected and scheduling total complete man-hour by analyzing initial machine
Between relation, a kind of most short used time decomposition strategy algorithm based on NEH algorithms is proposed first, its concrete calculating process is as follows：
The size of FFSP scheduling completion dates depends on the processing sequence of operation on the processing machine and machine of workpiece selection, therefore
The quality for improving particle populations initial solution is particularly important, and improving the quality of initial solution can shorten the time and enhancing for solving FSSP
Particle finds the performance of optimal solution, and according to workpiece, total elapsed time carries out descending arrangement to workpiece on machine, then takes out successively
Workpiece is iterated insertion operation, here, most short used time decomposition strategy thought：By workpiece on machine total elapsed time according to every
Procedure is decomposed, and descending arrangement is carried out according to total time of each workpiece on every procedure, according to the total of every procedure
Time is contrasted with adjacency and is sorted, until all workpiece descending sorts are completed, wherein, adjacency is defined as follows：
The degree of closeness between two procedures process time is represented, adjacency is less to be shown closer to most short used time decomposition strategy
Algorithm steps：
Step 2.1）Priority level list is set, wherein
, p is process number,For the machine number of the i-th procedure, M is the number of total machine；Together
When setting process number copy pcopy, make pcopy=p；Adjacency Pro is set；Counter t=1；The setting m=M of priority；
Step 2.2）In pth copy procedure, according to the total time that workpiece is processed on machine, descending row is carried out to workpiece
Row, obtain collating sequence seq；
Step 2.3）Priority list S is arranged according to seq：To t and t+1 two procedures in seq, compare the difference of numerical value, if
More than Pro, then the priority of plurality is set to m, then arranges m=m-1；Otherwise, compare the two procedures first one
Operation, until obtaining comparative result；
Step 2.4）Judge whether t is equal to M：If it is, the priority of t procedures is set to minimum 1,5 are gone to step；It is no
Then, 3 are gone to step；
Step 2.5）Output priority list S；
Step 2.6）Machine chain is generated according to regular S dynamic randoms.
3., according to the derivation algorithm of a kind of improved flexible Flow Shop Scheduling described in claim 1, it is characterized in that,
Concrete calculating process in the above step 3 is as follows：
Step 3：Introduce encoder matrix and decoding matrix to represent the relation between workpiece, machine and scheduling, its concrete calculating
Process is as follows：
The coding of step 3.1 particle and decoding
The coded system of particle had both affected the search capability of particle, affected the diversity of population, this method coded system to adopt again
Using Indirect encod, code length is, whereinRepresent the operation quantity of i-th workpiece, this coded system
Benefit be that an encoding scheme correspond to a scheduling strategy, coding vector ECJ（P）Represent, wherein P represents process number；
Decoding matrix represents that wherein M represents collection of machines, and J represents set of tasks, and P represents operation set, B tables with DCJ (M, J, P, N)
Show the piece count for processing corresponding machine, work as m=3, during J=3, particle ECJ=（2,3,3,1,1,1,3,2,2,2,）As one
Plant feasible coding strategy, ECJ（1）1st procedure of=2 the 1st workpiece of expression is processed on machine 2,Represent that the 1st of the 2nd workpiece processes to operation on machine 1, by that analogy, give particle coding staff
After case, need to carry out decoding operate：To mark off in whole subtasks of correspondence machining, and with reference to workpiece incidence matrix
JobSubJob, the result for decoding it is stored enter in decoding matrix.
4., according to the derivation algorithm of a kind of improved flexible Flow Shop Scheduling described in claim 1, it is characterized in that,
Concrete calculating process in the above step 4 is as follows：
Step 4：Global optimization is carried out using discrete particle cluster algorithm is improved, its detailed process is as follows：
Global optimization is carried out by inertia weight adjustment
Inertia weightIt is a critically important parameter in algorithm, it balances the ability of searching optimum of particle and energy is explored in local
Power, larger inertia weight can strengthen the global search capability of particle, and the local that less inertia weight can improve particle is visited
Suo Nengli, in order to be able to make algorithm more comprehensively be searched in the early stage, adopts the inertia weight computing formula exponentially successively decreased, such as
Shown in following formula：
In formula：WithFor the maximum and minimum of a value of inertia weight, Iter is current iteration number of times, and maxIter is
Maximum iteration time.
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| CN107506866A (en) * | 2017-08-31 | 2017-12-22 | 景德镇陶瓷大学 | A kind of how tactful particle group optimizing method and system for solving permutation flow shop scheduling |
| CN109034633A (en) * | 2018-08-04 | 2018-12-18 | 郑州航空工业管理学院 | Improved adaptive GA-IAGA solves the flexible job shop scheduling method with traveling time |
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| CN111007823A (en) * | 2019-12-25 | 2020-04-14 | 北京理工大学 | Flexible job shop dynamic scheduling method and device |
| WO2022012267A1 (en) * | 2020-07-17 | 2022-01-20 | 北京理工大学 | Collaboration method for multiple machining robots in hardware flexible production workshop |
| CN113805545B (en) * | 2021-09-14 | 2023-03-21 | 大连理工大学 | Flexible flow shop combined scheduling rule generation method considering batch processing |
| CN113805545A (en) * | 2021-09-14 | 2021-12-17 | 大连理工大学 | Flexible flow shop combined scheduling rule generation method considering batch processing |
| CN115826537A (en) * | 2023-01-29 | 2023-03-21 | 广东省科学院智能制造研究所 | Flexible scheduling method for multi-robot production line |
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Application publication date: 20170503 |