CN109784603A - A method of flexible job shop scheduling is solved based on mixing whale group algorithm - Google Patents
A method of flexible job shop scheduling is solved based on mixing whale group algorithm Download PDFInfo
- Publication number
- CN109784603A CN109784603A CN201811359927.9A CN201811359927A CN109784603A CN 109784603 A CN109784603 A CN 109784603A CN 201811359927 A CN201811359927 A CN 201811359927A CN 109784603 A CN109784603 A CN 109784603A
- Authority
- CN
- China
- Prior art keywords
- scheduling
- value
- workpiece
- egk
- whale
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 238000000034 method Methods 0.000 title claims abstract description 87
- 241000283153 Cetacea Species 0.000 title claims abstract description 57
- 230000008569 process Effects 0.000 claims abstract description 40
- 238000012163 sequencing technique Methods 0.000 claims abstract description 21
- 238000005457 optimization Methods 0.000 claims abstract description 12
- 230000007246 mechanism Effects 0.000 claims abstract description 9
- 230000009466 transformation Effects 0.000 claims abstract description 7
- 230000003044 adaptive effect Effects 0.000 claims abstract description 5
- 238000013507 mapping Methods 0.000 claims abstract description 5
- 230000000875 corresponding effect Effects 0.000 claims description 27
- 238000006243 chemical reaction Methods 0.000 claims description 15
- 230000006870 function Effects 0.000 claims description 15
- 238000012545 processing Methods 0.000 claims description 12
- 238000004519 manufacturing process Methods 0.000 claims description 8
- 230000001174 ascending effect Effects 0.000 claims description 6
- 238000003754 machining Methods 0.000 claims description 5
- 238000004364 calculation method Methods 0.000 claims description 4
- 230000000694 effects Effects 0.000 claims description 4
- 230000008859 change Effects 0.000 claims description 3
- 238000009826 distribution Methods 0.000 claims description 3
- 230000002045 lasting effect Effects 0.000 claims description 3
- 230000008707 rearrangement Effects 0.000 claims description 3
- 230000002068 genetic effect Effects 0.000 description 4
- 241000282461 Canis lupus Species 0.000 description 3
- 230000008901 benefit Effects 0.000 description 3
- 238000012795 verification Methods 0.000 description 3
- 238000011160 research Methods 0.000 description 2
- 238000012360 testing method Methods 0.000 description 2
- 238000004458 analytical method Methods 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
- 210000000349 chromosome Anatomy 0.000 description 1
- 230000007812 deficiency Effects 0.000 description 1
- 238000013461 design Methods 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 239000011159 matrix material Substances 0.000 description 1
- 230000035772 mutation Effects 0.000 description 1
- 230000035699 permeability Effects 0.000 description 1
- 238000010845 search algorithm Methods 0.000 description 1
- 238000000926 separation method Methods 0.000 description 1
- 239000002356 single layer Substances 0.000 description 1
- 241000894007 species Species 0.000 description 1
- 238000003860 storage Methods 0.000 description 1
Abstract
The invention discloses a kind of methods for solving flexible job shop scheduling based on mixing whale group algorithm, and the coding mode for defining flexible job shop scheduling first is two-part random code, then carry out Mapping and Converting using transformation mechanism；Defining fitness function and it is most short to solve total elapsed time is optimization aim；Then whale group algorithm is used, to the parameter and whale initialization of population in Flexible Job-shop Scheduling Problems, it is initially divided into the sequencing schemes of random generation process and preferably machine assignment scheme corresponding with Operation Sequencing scheme is generated using the hereditary variation mode of improved adaptive GA-IAGA, and then generate preferably initial population；The fitness value for calculating each scheduling scheme is found and retains best scheduling solution；Optimal scheduling solution and its corresponding fitness function value are finally exported, as required optimal scheduling scheme, the present invention solves the problems, such as that the solving precision shown in existing Flexible Job-shop Scheduling Problems is not high, convergence rate is slower.
Description
Technical field
The invention belongs to flexible job shop scheduling technical fields, and in particular to one kind is solved based on mixing whale group algorithm
The method of flexible job shop scheduling.
Background technique
Flexible Job-shop Scheduling Problems (Flexible Job-shop Scheduling Problem, FJSP) are as biography
The extension form for job-shop scheduling problem of uniting increases the select permeability of flexible workpiece machining path, and the difficulty solved is more
Greatly, a kind of combinatorial optimization problem with NP difficulty characteristic also is had proved to be closer in production reality.For asking for the problem
Solution, various intelligent algorithms are its main means at present, also become the research hotspot in current production scheduling field.
In the prior art, processing sequence FJSP associated with the time started passes through the study to separation graph model, design
A kind of field embodies the tabu search algorithm of reconciliation spatial diversity, and demonstrates algorithm by the test of standard example
Superiority；Based on discrete harmonious searching algorithm for solving the method for minimizes Maximal Makespan FJSP efficiently to sort,
Mixing grey wolf optimization algorithm is improved, Advanced group species dynamic, backward learning initialization population and optimum individual variation etc. three is passed through
A aspect improves operation to algorithm, and is emulated to standard example, the results showed that, improved mixing grey wolf optimization
Algorithm can effectively jump out local optimum, find better solution, and result robustness is stronger.Pass through employing multicolor sets theory
Middle circuit Boolean matrix constructs the multiple constraint model and single layer genetic coding mode of Flexible Job-shop Scheduling Problems, makes GA
The search range of algorithm is reduced, and the room and time complexity of chromosome is effectively reduced, and then is improved algorithm and asked
Solve the speed and precision of FJSP problem.Mixed type grey wolf optimization algorithm (HGWO), using two-part individual UVR exposure mode realize from
The continuous programming code of scheduling solution is dissipated, and strengthens the local search ability of algorithm using neighborhood search strategy is become, while introducing heredity
The intersection and mutation operation of algorithm enhance the diversity of population, by imitating Flexible Job-shop Scheduling Problems standard example
True test, the results showed that the algorithm can efficiently avoid precocity, improve solving speed and precision.Using quantum computational theory
Improved whale optimization algorithm (WOA), and job-shop scheduling problem being solved using it, it was demonstrated that the convergence of algorithm
Property and correctness, and job-shop scheduling problem belongs to discrete scheduling problem, and improved whale algorithm is mainly by even
Continuous whale individual position vector is iterated operation to realize solution and optimizing, and the prior art does not provide between the two
Specific conversion process.Therefore, one of the hot spot that production scheduling problems are still manufacturing field research is solved using New Algorithm.
WSA is proposed by the inspiration of guidance is mutually exchanged using ultrasonic wave between individual during whale predation predation
The new meta-heuristic algorithm of one kind.WSA is with its special iterative manner, it was demonstrated that it solves the superior of combinatorial optimization problem
Property.But it should use it to solve discrete class problem, first have to solve the mutual conversion between solution and individual position vector and ask
Topic, therefore, herein by the classical base for solving to mutually convert between scheduling problem solution and individual position vector of shifting to new management mechanisms of introducing
It on plinth, is solved using the algorithm come this classical combinatorial optimization problems to FJSP, and by embodiment solution and to score
Analysis carrys out the superiority of verification algorithm, to explore the new approach of a solution FJSP.
Summary of the invention
The object of the present invention is to provide a kind of method for solving flexible job shop scheduling based on mixing whale group algorithm, solutions
Having determined, the solving precision shown in Flexible Job-shop Scheduling Problems existing in the prior art is not high, convergence rate is slower
Problem.
The technical scheme adopted by the invention is that a kind of solve flexible job shop scheduling based on mixing whale group algorithm
Method is specifically implemented according to the following steps:
Step 1, the coding mode for defining flexible job shop scheduling are two-part random code, then use interpreter
System carries out Mapping and Converting；
Step 2 defines fitness function, most short for optimization aim to solve total elapsed time；
Step 3, using whale group algorithm, in Flexible Job-shop Scheduling Problems parameter and whale population it is initial
Change, first bound ε, the strength of sound source ρ to location variable element individual in whale group algorithm0, current iteration number t, maximum
The number of iterations M parameter is set；Initialization of population is divided into two steps and carries out, the sequencing schemes of the random generation process of the first step, the
Two steps generate preferably machine assignment scheme corresponding with Operation Sequencing scheme using the hereditary variation mode of improved adaptive GA-IAGA,
And then generate preferably initial population；
Step 4, the fitness value for calculating each scheduling scheme, find and retain best scheduling solution S*；
The optimal scheduling solution S of step 5, output*And its corresponding fitness function value, S*As required optimal scheduling scheme.
The features of the present invention also characterized in that
Interpreter fixture body follows the steps below to implement in step 1:
A, conversion of the scheduling scheme to a body position:
I) machine choice: serial number is concentrated to be converted into individual position vector element value in the optional machine of process according to the following formula:
X (i)=[2m/ (s (i) -1)] (n (i) -1)-m, s (i) ≠ 1
Wherein: x (i) indicates i-th of element of individual position vector；S (i) indicates that element i corresponds to what process can choose
Machine number；N (i) ∈ [1, s (i)] indicates selected serial number of the machine inside optional machine collection.If s (i)=1, x (i)
Any value in [- m, m].
Ii) Operation Sequencing: firstly generating one group of random number in [- m, m], and by ascending order arrangement ROV rule be each with
Machine number assigns a unique ROV value, makes the corresponding process of each ROV value, then according to the coded sequence of process to ROV value
It is reset, the sequence of random number corresponding to the ROV value after rearrangement is the value of each element in individual position vector.
B, conversion of the individual position vector to scheduling scheme:
I) machine choice: executing according to the inverse operation of formula of the scheduling scheme into the conversion of a body position in a, by
This obtains the number of machine:
Ii) Operation Sequencing: make the process sequence and position in corresponding one unique coding of each element number first
Then element carries out ascending order arrangement to position element according to ROV rule, ROV value corresponding element at this time numbers and then constructs work
Sequence sequencing schemes；
Step 2 is specifically implemented according to the following steps:
The problem of step 2.1, flexible job shop scheduling, model FJSP was described as follows:
Assuming that M is the quantity of process equipment, N is workpiece to be processed quantity, and P is process number, and I is the set of all devices；
IegThe available devices set of the g procedure of workpiece e is represented,JeFor the process number of workpiece e, x is all workpiece
Process sequence, SegkIndicate the g procedure of workpiece e at the beginning of processing on equipment k；EegkFor the g procedure of workpiece e
Process finishing time on equipment k；TegkFor lasting process time of the g procedure on equipment k of workpiece e, and k ∈ Ieg
Then there is Eegk=Segk+Tegk；EpIndicate the completion date of finishing operation；MS indicates the last completion date of all workpiece；
When the jth procedure of workpiece i and the g procedure of workpiece e execute on the same device, if process j is prior to work
When sequence g is processed, Qijeg=1, otherwise Qijeg=0；If the g procedure of workpiece e is processed on lathe k, Xegk=1, otherwise Xegk
=0；
If certain FJSP shares the possible processing sequence of S kind, it is desirable that shortest Machining Sequencing of total activity duration is first sought every
A processing sequence x (x ∈ { 1 ..., S }) the corresponding activity duration；Obviously, the completion date of last manufacturing procedure is in sequence x
The last completion date of all workpiece:
MS=Ep (1)
Step 2.2 sets objective function F (x) are as follows:
F (x)=min (MSx )=min ((Ep)x) (2)
Wherein, x=1 ..., S；Qijeg=1；
S.T.Segk-Ee(g-1)n≥0 (3)
E=1 ..., N；G=1 ..., Je；Xegk=1, Xe(g-1)n=1
Segk-Eijk≥0 (4)
E=1 ..., N；G=1 ..., Je；Xijk=1, Xegk=1, Qijeg=1.
Step 4 is specifically implemented according to the following steps:
Step 4.1 is iterated operation using formula (5), specific as follows
In formula:WithI-th of element of X is respectively referred in the position of t step and t+1 step iteration；
Refer to i-th of element of Y in the position of t step iteration；
dX,YRefer to the distance between X and Y；
Indicate that 0 arrivesBetween the random number that generates, wherein the value of attenuation coefficient η with
The dimension of objective function, domain are related to peak Distribution feature；
Scheduling solution is converted to whale individual position vector using transformation mechanism, and retains S by step 4.2*Corresponding
Body X*；
Step 4.3 is iterated operation using formula (5), judges whether the termination condition for meeting algorithm, if not satisfied,
T=t+1 is then enabled, step 4.3.1~step 4.3.7 is repeated；If satisfaction thens follow the steps 5, specific as follows:
Step 4.3.1, the distance between two whales calculation method is defined；
Step 4.3.2, to each whaleFind more excellent and nearest individual；If there is no then remaining stationary；
Step 4.3.3, all fitness values are found to be greater thanIndividual, such as
Step 4.3.4, each fitness value is calculated to be greater thanIndividualWithThe distance between D1,D2,
D3；
Step 4.3.5, to D1,D2,D3Sequence selects individual corresponding to minimum valueAsIt is more excellent and nearest
Individual；
Step 4.3.6, willWithValue and initialization parameter bring into iterative formula (5) update each individual
Position vector
Step 4.3.7, conversion regime of the individual position vector to scheduling scheme is executed, it is right to generate all individuals after updating
The scheduling scheme answered, return step 4.2.
ρ in step 4.10Take empirical value 2.
In step 4.1, the initial value of attenuation coefficient η determines as follows:
Firstly, enabling
I.e.
dmaxRefer in possible maximum distance between two whales in region of search,
Wherein, n is the dimension of objective function,WithThe lower limit and the upper limit of i-th of variable are respectively indicated, therefore, η=-
20·ln(0.25)/dmax。
The invention has the advantages that being passed through based on the method that mixing whale group algorithm solves flexible job shop scheduling
Transformation mechanism realizes the mutual conversion between FJSP scheduling solution and whale individual position vector, and then utilizes the stronger part WSA
And ability of searching optimum, and the advantage in terms of maintaining population diversity, it is solved to be iterated, to improve the solution of FJSP
Accuracy and speed.
Detailed description of the invention
Fig. 1, which is that the present invention is a kind of, solves whale group calculation in the method for flexible job shop scheduling based on mixing whale group algorithm
The flow chart of method solution FJSP；
Fig. 2, which is that the present invention is a kind of, solves embodiment 1 in the method for flexible job shop scheduling based on mixing whale group algorithm
WSA evolution convergence curve；
Fig. 3, which is that the present invention is a kind of, solves embodiment 1 in the method for flexible job shop scheduling based on mixing whale group algorithm
Scheduling result Gantt chart；
Fig. 4, which is that the present invention is a kind of, solves embodiment in the method for flexible job shop scheduling based on mixing whale group algorithm
2WSA evolution convergence curve；
Fig. 5, which is that the present invention is a kind of, solves embodiment in the method for flexible job shop scheduling based on mixing whale group algorithm
3WSA evolution convergence curve.
Specific embodiment
The following describes the present invention in detail with reference to the accompanying drawings and specific embodiments.
A kind of method that flexible job shop scheduling is solved based on mixing whale group algorithm of the present invention, as shown in Fig. 1, tool
Body follows the steps below to implement:
Step 1, the coding mode for defining flexible job shop scheduling are two-part random code, then use interpreter
System carries out Mapping and Converting, wherein transformation mechanism is specifically implemented according to the following steps:
A, conversion of the scheduling scheme to a body position:
I) machine choice: serial number is concentrated to be converted into individual position vector element value in the optional machine of process according to the following formula:
X (i)=[2m/ (s (i) -1)] (n (i) -1)-m, s (i) ≠ 1
Wherein: x (i) indicates i-th of element of individual position vector；S (i) indicates that element i corresponds to what process can choose
Machine number；N (i) ∈ [1, s (i)] indicates selected serial number of the machine inside optional machine collection.If s (i)=1, x (i)
Any value in [- m, m].
Ii) Operation Sequencing: firstly generating one group of random number in [- m, m], and by ascending order arrangement ROV rule be each with
Machine number assigns a unique ROV value, makes the corresponding process of each ROV value, then according to the coded sequence of process to ROV value
It is reset, the sequence of random number corresponding to the ROV value after rearrangement is the value of each element in individual position vector.
B, conversion of the individual position vector to scheduling scheme:
I) machine choice: executing according to the inverse operation of formula of the scheduling scheme into the conversion of a body position in a, by
This obtains the number of machine:
Ii) Operation Sequencing: make the process sequence and position in corresponding one unique coding of each element number first
Then element carries out ascending order arrangement to position element according to ROV rule, ROV value corresponding element at this time numbers and then constructs work
Sequence sequencing schemes；
Step 2 defines fitness function, most short for optimization aim to solve total elapsed time, specifically according to the following steps
Implement:
The problem of step 2.1, flexible job shop scheduling, model FJSP was described as follows:
Assuming that M is the quantity of process equipment, N is workpiece to be processed quantity, and P is process number, and I is the set of all devices；
IegThe available devices set of the g procedure of workpiece e is represented,JeFor the process number of workpiece e, x is adding for all workpiece
Work order, SegkIndicate the g procedure of workpiece e at the beginning of processing on equipment k；EegkG procedure for workpiece e exists
Process finishing time on equipment k；TegkFor lasting process time of the g procedure on equipment k of workpiece e, and k ∈ IegThen
There is Eegk=Segk+Tegk；EpIndicate the completion date of finishing operation；MS indicates the last completion date of all workpiece；
When the jth procedure of workpiece i and the g procedure of workpiece e execute on the same device, if process j is prior to work
When sequence g is processed, Qijeg=1, otherwise Qijeg=0；If the g procedure of workpiece e is processed on lathe k, Xegk=1, otherwise Xegk
=0；
If certain FJSP shares the possible processing sequence of S kind, it is desirable that shortest Machining Sequencing of total activity duration is first sought every
A processing sequence x (x ∈ { 1 ..., S }) the corresponding activity duration；Obviously, the completion date of last manufacturing procedure is in sequence x
The last completion date of all workpiece:
MS=Ep (1)
Step 2.2 sets objective function F (x) are as follows:
F (x)=min (MSx )=min ((Ep)x) (2)
Wherein, x=1 ..., S；Qijeg=1；
S.T.Segk-Ee(g-1)n≥0 (3)
E=1 ..., N；G=1 ..., Je；Xegk=1, Xe(g-1)n=1
Segk-Eijk≥0 (4)
E=1 ..., N；G=1 ..., Je；Xijk=1, Xegk=1, Qijeg=1；
Step 3, using whale group algorithm, in Flexible Job-shop Scheduling Problems parameter and whale population it is initial
Change, first bound ε, the strength of sound source ρ to location variable element individual in whale group algorithm0, current iteration number t, maximum
The number of iterations M parameter is set；Initialization of population is divided into two steps and carries out, the sequencing schemes of the random generation process of the first step, the
Two steps generate preferably machine assignment scheme corresponding with Operation Sequencing scheme using the hereditary variation mode of improved adaptive GA-IAGA,
And then generate preferably initial population；
Step 4, the fitness value for calculating each scheduling scheme, find and retain best scheduling solution S*, specifically according to following
Step is implemented:
Step 4.1 is iterated operation using formula (5), specific as follows
In formula:WithI-th of element of X is respectively referred in the position of t step and t+1 step iteration；
Refer to i-th of element of Y in the position of t step iteration；
dX,YRefer to the distance between X and Y；
Indicate that 0 arrivesBetween the random number that generates, wherein the value of attenuation coefficient η with
The dimension of objective function, domain are related to peak Distribution feature；
Scheduling solution is converted to whale individual position vector using transformation mechanism, and retains S by step 4.2*Corresponding
Body X*；
Step 4.3 is iterated operation using formula (5), judges whether the termination condition for meeting algorithm, if not satisfied,
T=t+1 is then enabled, step 4.3.1~step 4.3.7 is repeated；If satisfaction thens follow the steps 5, specific as follows:
Step 4.3.1, the distance between two whales calculation method is defined；
Step 4.3.2, to each whaleFind more excellent and nearest individual；If there is no then remaining stationary；
Step 4.3.3, all fitness values are found to be greater thanIndividual, such as
Step 4.3.4, each fitness value is calculated to be greater thanIndividualWithThe distance between D1,D2,
D3；
Step 4.3.5, to D1,D2,D3Sequence selects individual corresponding to minimum valueAsIt is more excellent and nearest
Individual；
Step 4.3.6, willWithValue and initialization parameter bring into iterative formula (5) update each individual
Position vector
Step 4.3.7, conversion regime of the individual position vector to scheduling scheme is executed, it is right to generate all individuals after updating
The scheduling scheme answered, return step 4.2；
ρ in step 4.10Take empirical value 2；
In step 4.1, the initial value of attenuation coefficient η determines as follows:
Firstly, enabling
I.e.
dmaxRefer in possible maximum distance between two whales in region of search,
Wherein, n is the dimension of objective function,WithThe lower limit and the upper limit of i-th of variable are respectively indicated, therefore, η=-
20·ln(0.25)/dmax；
The optimal scheduling solution S of step 5, output*And its corresponding fitness function value, S*As required optimal scheduling scheme.
A kind of method for solving flexible job shop scheduling based on mixing whale group algorithm of the present invention, is asked to verify WSA
The feasibility of Flexible Job-shop Scheduling Problems is solved, emulation experiment carried out to three embodiments respectively with it herein, and with
Other intelligent algorithms compare and analyze.Simulated environment are as follows: use MATILAB2016a, be configured to CPU frequency 1.9GHz,
It is carried out in the environment of AMD A10-7300 Radeon R6 processor, 10 operating system of Windows.
Embodiment 1
The FJSP that example 1 is 3 × 6, processing tasks information is as shown in table 1, and the parameter setting of whale group algorithm is as follows: kind
Group's scale is 50, and whale individual position vector dimension is 30, ρ0It is set as 2, dmax=32.86, attenuation coefficient η takes 0, and maximum changes
Generation number M is 400:
1 example of table, 1 processing tasks information table
Machine assignment and Operation Sequencing are encoded using the two-part coding based on random by key, then individual position vector
Length be 30, and each element any value in [- 3,3] generates 30 random numbers using computer, and according to one
Fixed sequential storage, as shown in table 2, wherein OPijIndicate the jth procedure of workpiece i:
The individual position vector figure of table 2
For embodiment 1, it is solved its WSA evolution convergence curve as shown in Fig. 2, being calculated by this whale group known to Fig. 2
Method can converge to quickly 134 from 144, it is as shown in Figure 3 to correspond to scheduling result Gantt chart at 35 generation.
Embodiment 2
For further verification algorithm feasibility and superiority, select document [1] (Fu Weiping, Liu Dongmei, Lai Chunwei,
Wang Wen solves multi items flexibility scheduling problem [J] computer integrated manufacturing system based on the improved adaptive GA-IAGA of polychromatic sets,
2011,17 (05): 1004-1010.) in example 2 emulated, specific machining information is shown in document [1], whale group algorithm
Parameter setting is as follows: population scale 100, and whale individual position vector dimension is 108, ρ in example 10It is set as 2, dmax=
It is 200 that 104.96, attenuation coefficient η, which take 0, maximum number of iterations M,.Its WSA evolution convergence curve is obtained as shown in figure 4, obtaining optimal
Solution is 121 minutes, by the WSA evolution convergence curve of Fig. 4 and the evolution curve comparison of example 2 it is found that this whale group algorithm can be
When 32 generation, 121 soon are converged to from 150, in contrast, the speed solved is obviously very fast.
Embodiment 3
For compare more fully hereinafter with verification algorithm effect, choose 8 inside the Kacem benchmark problem of job shop scheduling problem
× 8 embodiments are solved, and are calculated 20 times.The parameter setting of whale group algorithm is as follows: population scale 100, whale position
Setting vector dimension is 54, ρ0It is set as 2, dmaxIt is 200 that=117.57, attenuation coefficient η, which take 0, maximum number of iterations M, embodiment 3
WSA evolution convergence curve it is as shown in Figure 5.Table 3 be whale group algorithm by acquired results and evolution algorithm, MS master-slave genetic algorithm,
The solving result comparison of multistage genetic algorithm, ant group algorithm:
Each algorithm solving result comparison of 3 Kacem of table, 8 × 8 benchmark problem
| Method name | Optimal value | Figure of merit number | Convergence in mean algebra | The convergence in mean time/min |
| Evolution algorithm | 15 | 1 | ||
| MS master-slave genetic algorithm | 19 | 2 | 200 | 41.8 |
| Multistage algorithm | 15 | |||
| Ant-genetic algorithm | 14 | 2 | 53 | 8.7 |
| Whale group algorithm | 14 | 3 | 35 | 7.6 |
Deficiency in terms of the solving precision and speed that show for traditional algorithm when solving FJSP, the present invention is with new
Meta-heuristic algorithm WSA FJSP is solved, by using two-part coding mode and introduce transformation mechanism and establish
Mutual mapping between scheduling problem solution and whale individual position vector, then solves FJSP using WSA, and emulation is real
Example is applied the result shows that WSA has certain superiority in terms of solving FJSP, the special iterative formula of the algorithm is found more excellent
And nearest iterative manner, certain advantage is shown when solving Combinatorial Optimization class problem.
Claims (6)
1. it is a kind of based on mixing whale group algorithm solve flexible job shop scheduling method, which is characterized in that specifically according to
Lower step is implemented:
Step 1, define flexible job shop scheduling coding mode be two-part random code, then using change the mechanism into
Row Mapping and Converting；
Step 2 defines fitness function, most short for optimization aim to solve total elapsed time；
Step 3, using whale group algorithm, it is first to the parameter and whale initialization of population in Flexible Job-shop Scheduling Problems
First to bound ε, the strength of sound source ρ of location variable element individual in whale group algorithm0, current iteration number t, greatest iteration time
Number M parameter is set；Initialization of population is divided into the progress of two steps, and the sequencing schemes of the random generation process of the first step, second step is adopted
Preferably machine assignment scheme corresponding with Operation Sequencing scheme is generated with the hereditary variation mode of improved adaptive GA-IAGA, and then is produced
Raw preferably initial population；
Step 4, the fitness value for calculating each scheduling scheme, find and retain best scheduling solution S*；
The optimal scheduling solution S of step 5, output*And its corresponding fitness function value, S*As required optimal scheduling scheme.
2. a kind of method that flexible job shop scheduling is solved based on mixing whale group algorithm according to claim 1,
It is characterized in that, interpreter fixture body follows the steps below to implement in the step 1:
A, conversion of the scheduling scheme to a body position:
I) machine choice: serial number is concentrated to be converted into individual position vector element value in the optional machine of process according to the following formula:
X (i)=[2m/ (s (i) -1)] (n (i) -1)-m, s (i) ≠ 1
Wherein: x (i) indicates i-th of element of individual position vector；S (i) indicates that element i corresponds to the machine that process can choose
Number；N (i) ∈ [1, s (i)] indicates selected serial number of the machine inside optional machine collection.If s (i)=1, x (i) [-
M, m] in any value.
Ii) Operation Sequencing: firstly generating one group of random number in [- m, m], and is each random number by ascending order arrangement ROV rule
A unique ROV value is assigned, makes the corresponding process of each ROV value, then ROV value is carried out according to the coded sequence of process
It resets, the sequence of random number corresponding to the ROV value after rearrangement is the value of each element in individual position vector.
B, conversion of the individual position vector to scheduling scheme:
I) it machine choice: executes according to the inverse operation of formula of the scheduling scheme into the conversion of a body position in a, thus obtains
Obtain the number of machine:
Ii) Operation Sequencing: making the process sequence and position element in corresponding one unique coding of each element number first,
Then ascending order arrangement is carried out to position element according to ROV rule, ROV value corresponding element at this time numbers and then constructs Operation Sequencing
Scheme；
3. a kind of method that flexible job shop scheduling is solved based on mixing whale group algorithm according to claim 2,
It is characterized in that, the step 2 is specifically implemented according to the following steps:
The problem of step 2.1, flexible job shop scheduling, model FJSP was described as follows:
Assuming that M is the quantity of process equipment, N is workpiece to be processed quantity, and P is process number, and I is the set of all devices；IegGeneration
The available devices set of the g procedure of table workpiece e,JeFor the process number of workpiece e, x is the processing time of all workpiece
Sequence, SegkIndicate the g procedure of workpiece e at the beginning of processing on equipment k；EegkFor workpiece e g procedure in equipment
Process finishing time on k；TegkFor lasting process time of the g procedure on equipment k of workpiece e, and k ∈ IegThen there is Eegk
=Segk+Tegk；EpIndicate the completion date of finishing operation；MS indicates the last completion date of all workpiece；
When the jth procedure of workpiece i and the g procedure of workpiece e execute on the same device, if process j adds prior to process g
Working hour, Qijeg=1, otherwise Qijeg=0；If the g procedure of workpiece e is processed on lathe k, Xegk=1, otherwise Xegk=0；
If certain FJSP shares the possible processing sequence of S kind, it is desirable that shortest Machining Sequencing of total activity duration first seeks each add
Work sequence x (x ∈ { 1 ..., S }) the corresponding activity duration；Obviously, the completion date of last manufacturing procedure is i.e. all in sequence x
The last completion date of workpiece:
MS=Ep (1)
Step 2.2 sets objective function F (x) are as follows:
F (x)=min (MSx )=min ((Ep)x) (2)
Wherein, x=1 ..., S；Qijeg=1；
S.T.Segk-Ee(g-1)n≥0 (3)
E=1 ..., N；G=1 ..., Je；Xegk=1, Xe(g-1)n=1
Segk-Eijk≥0 (4)
E=1 ..., N；G=1 ..., Je；Xijk=1, Xegk=1, Qijeg=1.
4. a kind of method that flexible job shop scheduling is solved based on mixing whale group algorithm according to claim 3,
It is characterized in that, the step 4 is specifically implemented according to the following steps:
Step 4.1 is iterated operation using formula (5), specific as follows
In formula:WithI-th of element of X is respectively referred in the position of t step and t+1 step iteration；
Refer to i-th of element of Y in the position of t step iteration；
dX,YRefer to the distance between X and Y；
Indicate that 0 arrivesBetween the random number that generates, wherein the value and target of attenuation coefficient η
The dimension of function, domain are related to peak Distribution feature；
Scheduling solution is converted to whale individual position vector using transformation mechanism, and retains S by step 4.2*Corresponding individual X*；
Step 4.3 is iterated operation using formula (5), judges whether the termination condition for meeting algorithm, if not satisfied, then enabling t
=t+1 repeats step 4.3.1~step 4.3.7；If satisfaction thens follow the steps 5, specific as follows:
Step 4.3.1, the distance between two whales calculation method is defined；
Step 4.3.2, to each whaleFind more excellent and nearest individual；If there is no then remaining stationary；
Step 4.3.3, all fitness values are found to be greater thanIndividual, such as
Step 4.3.4, each fitness value is calculated to be greater thanIndividualWithThe distance between D1,D2,D3；
Step 4.3.5, to D1,D2,D3Sequence selects the smallest such as D3, then D3Corresponding individualAsIt is " more excellent and most
Individual closely "；
Step 4.3.6, willWithValue and initialization parameter bring into iterative formula (5) update each body position to
Amount
Step 4.3.7, conversion regime of the individual position vector to scheduling scheme is executed, it is corresponding to generate all individuals after updating
Scheduling scheme, return step 4.2.
5. a kind of method that flexible job shop scheduling is solved based on mixing whale group algorithm according to claim 4,
It is characterized in that, ρ in the step 4.10Take empirical value 2.
6. a kind of method that flexible job shop scheduling is solved based on mixing whale group algorithm according to claim 5,
It is characterized in that, in the step 4.1, the initial value of attenuation coefficient η determines as follows:
Firstly, enabling
I.e.
dmaxRefer in possible maximum distance between two whales in region of search,
Wherein, n is the dimension of objective function,WithRespectively indicate the lower limit and the upper limit of i-th of variable, therefore, η=- 20
ln(0.25)/dmax。
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201811359927.9A CN109784603B (en) | 2018-11-15 | 2018-11-15 | Method for solving flexible job shop scheduling based on mixed whale swarm algorithm |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201811359927.9A CN109784603B (en) | 2018-11-15 | 2018-11-15 | Method for solving flexible job shop scheduling based on mixed whale swarm algorithm |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN109784603A true CN109784603A (en) | 2019-05-21 |
| CN109784603B CN109784603B (en) | 2024-02-02 |
Family
ID=66496457
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201811359927.9A Active CN109784603B (en) | 2018-11-15 | 2018-11-15 | Method for solving flexible job shop scheduling based on mixed whale swarm algorithm |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN109784603B (en) |
Cited By (12)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110425084A (en) * | 2019-08-09 | 2019-11-08 | 湘电风能有限公司 | A kind of whale group PID independent pitch control method of large-scale wind electricity unit |
| CN110490372A (en) * | 2019-07-26 | 2019-11-22 | 华中农业大学 | A kind of mixed distribution formula evolvement method solving extensive Job-Shop Scheduling Problem |
| CN110543151A (en) * | 2019-08-12 | 2019-12-06 | 陕西科技大学 | Method for solving workshop energy-saving scheduling problem based on improved NSGA-II |
| CN110632907A (en) * | 2019-10-30 | 2019-12-31 | 山东师范大学 | Scheduling optimization method and system for distributed assembly type replacement flow shop |
| CN110782085A (en) * | 2019-10-23 | 2020-02-11 | 武汉晨曦芸峰科技有限公司 | Casting production scheduling method and system |
| CN111598297A (en) * | 2020-04-15 | 2020-08-28 | 浙江工业大学 | Flexible job shop scheduling machine selection method based on residual process maximum value optimization |
| CN111967654A (en) * | 2020-07-27 | 2020-11-20 | 西安工程大学 | Method for solving flexible job shop scheduling based on hybrid genetic algorithm |
| CN112016746A (en) * | 2020-08-26 | 2020-12-01 | 广东电网有限责任公司广州供电局 | Dispatching method and device for power generation car, computer equipment and storage medium |
| CN112783172A (en) * | 2020-12-31 | 2021-05-11 | 重庆大学 | AGV and machine integrated scheduling method based on discrete whale optimization algorithm |
| CN113408951A (en) * | 2021-07-16 | 2021-09-17 | 山东大学 | Optimal flexible scheduling method and system based on dynamic information accumulated lion group |
| CN114692345A (en) * | 2022-06-02 | 2022-07-01 | 河南科技学院 | Intelligent scheduling method for crane boom production |
| CN115438879A (en) * | 2022-05-09 | 2022-12-06 | 国网浙江省电力有限公司 | Improved hybrid algorithm-based electric vehicle charging station location and volume selection method and device |
Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20080235065A1 (en) * | 2005-12-06 | 2008-09-25 | International Business Machines Corporation | Methods and Apparatus for Implementing a Flexible Multi-User Advance Reservation System Where Reservation Requests are Specified in Terms of Multiple Options and Where Each Option Has an Associated Business Value |
| CN104880949A (en) * | 2015-05-27 | 2015-09-02 | 江南大学 | Method of acquiring workpiece-processing optimal scheduling based on improved chicken flock algorithm |
| CN105096004A (en) * | 2015-08-18 | 2015-11-25 | 中水东北勘测设计研究有限责任公司 | Real-time scheduling method for reservoir group water supply and transfer system |
| CN105929690A (en) * | 2016-04-29 | 2016-09-07 | 南京信息工程大学 | Flexible workshop robustness scheduling method based on decomposition multi-target evolution algorithm |
| WO2016169286A1 (en) * | 2015-04-20 | 2016-10-27 | 海安县申菱电器制造有限公司 | Workshop layout method for discrete manufacturing system |
| CN106610654A (en) * | 2015-12-29 | 2017-05-03 | 四川用联信息技术有限公司 | Improved genetic algorithm for flexible workshop scheduling |
| US20170323274A1 (en) * | 2016-05-06 | 2017-11-09 | General Electric Company | Controlling aircraft operations and aircraft engine components assignment |
| CN108776461A (en) * | 2018-05-21 | 2018-11-09 | 北京石油化工学院 | A kind of flexible job shop scheduling method and system |
-
2018
- 2018-11-15 CN CN201811359927.9A patent/CN109784603B/en active Active
Patent Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20080235065A1 (en) * | 2005-12-06 | 2008-09-25 | International Business Machines Corporation | Methods and Apparatus for Implementing a Flexible Multi-User Advance Reservation System Where Reservation Requests are Specified in Terms of Multiple Options and Where Each Option Has an Associated Business Value |
| WO2016169286A1 (en) * | 2015-04-20 | 2016-10-27 | 海安县申菱电器制造有限公司 | Workshop layout method for discrete manufacturing system |
| CN104880949A (en) * | 2015-05-27 | 2015-09-02 | 江南大学 | Method of acquiring workpiece-processing optimal scheduling based on improved chicken flock algorithm |
| CN105096004A (en) * | 2015-08-18 | 2015-11-25 | 中水东北勘测设计研究有限责任公司 | Real-time scheduling method for reservoir group water supply and transfer system |
| CN106610654A (en) * | 2015-12-29 | 2017-05-03 | 四川用联信息技术有限公司 | Improved genetic algorithm for flexible workshop scheduling |
| CN105929690A (en) * | 2016-04-29 | 2016-09-07 | 南京信息工程大学 | Flexible workshop robustness scheduling method based on decomposition multi-target evolution algorithm |
| US20170323274A1 (en) * | 2016-05-06 | 2017-11-09 | General Electric Company | Controlling aircraft operations and aircraft engine components assignment |
| CN108776461A (en) * | 2018-05-21 | 2018-11-09 | 北京石油化工学院 | A kind of flexible job shop scheduling method and system |
Non-Patent Citations (4)
| Title |
|---|
| YUAN YUAN 等: "A hybrid harmony search algorithm for the flexible job shop scheduling problem", 《APPLIED SOFT COMPUTING》 * |
| 姜天华: "混合灰狼优化算法求解柔性作业车间调度问题", 《控制与决策》 * |
| 徐云琴 等: "具有行为效应的含AGV柔性车间调度研究", 《计算机应用研究》 * |
| 曾冰 等: "改进鲸鱼群算法及其在炼钢连铸调度中的应用", 《郑州大学学报(工学版)》 * |
Cited By (19)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110490372A (en) * | 2019-07-26 | 2019-11-22 | 华中农业大学 | A kind of mixed distribution formula evolvement method solving extensive Job-Shop Scheduling Problem |
| CN110490372B (en) * | 2019-07-26 | 2022-03-01 | 华中农业大学 | Mixed distributed evolution method for solving large-scale workshop operation scheduling problem |
| CN110425084B (en) * | 2019-08-09 | 2020-09-22 | 湘电风能有限公司 | Whale swarm PID (proportion integration differentiation) independent pitch control method of large wind turbine generator |
| CN110425084A (en) * | 2019-08-09 | 2019-11-08 | 湘电风能有限公司 | A kind of whale group PID independent pitch control method of large-scale wind electricity unit |
| CN110543151A (en) * | 2019-08-12 | 2019-12-06 | 陕西科技大学 | Method for solving workshop energy-saving scheduling problem based on improved NSGA-II |
| CN110782085B (en) * | 2019-10-23 | 2022-03-29 | 武汉晨曦芸峰科技有限公司 | Casting production scheduling method and system |
| CN110782085A (en) * | 2019-10-23 | 2020-02-11 | 武汉晨曦芸峰科技有限公司 | Casting production scheduling method and system |
| CN110632907A (en) * | 2019-10-30 | 2019-12-31 | 山东师范大学 | Scheduling optimization method and system for distributed assembly type replacement flow shop |
| CN111598297A (en) * | 2020-04-15 | 2020-08-28 | 浙江工业大学 | Flexible job shop scheduling machine selection method based on residual process maximum value optimization |
| CN111598297B (en) * | 2020-04-15 | 2023-04-07 | 浙江工业大学 | Flexible job shop scheduling machine selection method based on residual process maximum value optimization |
| CN111967654A (en) * | 2020-07-27 | 2020-11-20 | 西安工程大学 | Method for solving flexible job shop scheduling based on hybrid genetic algorithm |
| CN112016746A (en) * | 2020-08-26 | 2020-12-01 | 广东电网有限责任公司广州供电局 | Dispatching method and device for power generation car, computer equipment and storage medium |
| CN112783172A (en) * | 2020-12-31 | 2021-05-11 | 重庆大学 | AGV and machine integrated scheduling method based on discrete whale optimization algorithm |
| CN112783172B (en) * | 2020-12-31 | 2023-03-31 | 重庆大学 | AGV and machine integrated scheduling method based on discrete whale optimization algorithm |
| CN113408951B (en) * | 2021-07-16 | 2022-08-12 | 山东大学 | Optimal flexible scheduling method and system based on dynamic information accumulated lion group |
| CN113408951A (en) * | 2021-07-16 | 2021-09-17 | 山东大学 | Optimal flexible scheduling method and system based on dynamic information accumulated lion group |
| CN115438879A (en) * | 2022-05-09 | 2022-12-06 | 国网浙江省电力有限公司 | Improved hybrid algorithm-based electric vehicle charging station location and volume selection method and device |
| CN115438879B (en) * | 2022-05-09 | 2023-02-17 | 国网浙江省电力有限公司 | Improved hybrid algorithm-based electric vehicle charging station location and volume selection method and device |
| CN114692345A (en) * | 2022-06-02 | 2022-07-01 | 河南科技学院 | Intelligent scheduling method for crane boom production |
Also Published As
| Publication number | Publication date |
|---|---|
| CN109784603B (en) | 2024-02-02 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN109784603A (en) | A method of flexible job shop scheduling is solved based on mixing whale group algorithm | |
| CN109886588B (en) | Method for solving flexible job shop scheduling based on improved whale algorithm | |
| CN109886589A (en) | A method of low-carbon Job-Shop is solved based on whale optimization algorithm is improved | |
| Diwold et al. | Performance evaluation of artificial bee colony optimization and new selection schemes | |
| Cao et al. | Assembly planning using a novel immune approach | |
| CN108320057A (en) | A kind of flexible job shop scheduling method based on restricted stable pairing strategy | |
| CN108734202A (en) | A kind of Fault Diagnosis for HV Circuit Breakers method based on improved BP | |
| CN104516785B (en) | A kind of cloud computing resources dispatch system and method | |
| CN110059015A (en) | Evolution of Population multiple target priorities of test cases sort method | |
| CN106611231A (en) | Hybrid particle swarm tabu search algorithm for solving job-shop scheduling problem | |
| CN110531716A (en) | The method for solving low-carbon Job-Shop problem based on discrete whale algorithm | |
| CN108832615A (en) | A kind of reconstruction method of power distribution network and system based on improvement binary particle swarm algorithm | |
| CN112434779B (en) | Improved ant colony algorithm-based tight coupling task allocation method | |
| CN106611378A (en) | Priority encoding-based hybrid genetic algorithm for solving job-shop scheduling problem | |
| CN111369000A (en) | High-dimensional multi-target evolution method based on decomposition | |
| CN109784604A (en) | A kind of flexible job shop manufacturing recourses distribution method based on whale algorithm | |
| CN108399105B (en) | Software and hardware partitioning method based on improved brainstorming algorithm | |
| CN116985146B (en) | Robot parallel disassembly planning method for retired electronic products | |
| CN114021934A (en) | Method for solving workshop energy-saving scheduling problem based on improved SPEA2 | |
| CN110989538B (en) | Closed-loop scheduling optimization method for complex production process | |
| Carvalho et al. | Multi-objective Flexible Job-Shop scheduling problem with DIPSO: More diversity, greater efficiency | |
| CN109472366A (en) | A kind of coding-decoding method and device of machine learning model | |
| CN115438877A (en) | Multi-objective distributed flexible workshop scheduling optimization method based on gray wolf algorithm | |
| Liu | Investigation of particle swarm optimization for job shop scheduling problem | |
| CN114648232A (en) | Cloud resource flexible job scheduling method based on improved chimpanzee optimization algorithm |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |