CN109146136A - A method of first kind assembly line balancing problem is solved based on immune genetic algorithm - Google Patents
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Abstract
A method of first kind assembly line balancing problem is solved based on immune genetic algorithm, the method define a function ψ (), and the individual in population to be made to meet assembly precedence relations constraint, and give the constraint condition and objective function of first kind assembly line balancing problem, it finally constructs immune genetic algorithm and solves first kind assembly line balancing problem, this method includes the definition of function ψ (), constraint condition, objective function, immune genetic algorithm；Wherein immune genetic algorithm includes: setup parameter, initialization, Population Regeneration, updates data base, termination condition verifying and result output.The present invention combines Artificial Immune Algorithm and genetic algorithm, establishes a kind of better hybrid algorithm of comprehensive performance, can be used for solving first kind assembly line balancing problem, such as solving APXV9R20B antenna mount line balance problem.
Description
Technical field
The present invention relates to a kind of methods for solving first kind assembly line balancing problem based on immune genetic algorithm.
Background technique
For assembly line as a kind of important manufacture system, it is the beginning efficiently produced.It is most heavy in the design of assembly line
It wants, it is crucial that assembly line balancing problem.In order to solve product first kind assembly line balancing problem, especially APXV9R20B
Antenna mount line balance problem, this patent devise a kind of immune genetic algorithm.
Since Ford was established in 1913 first automobile assembly line, line balancing problem just generates therewith, still
Until this problem in 1954 is just by Bryton in its Master's thesis " Balancing of a continuous production
Line " in formally propose.So far, the method for solving the problems, such as this mainly has: optimal method (exact method), heuristic side
Method and artificial intelligence approach.
Bowman solves assembly line balancing problem using two independent linear programming models, and operand is very big, with reality
Border situation differs greatly.Calleja etc. proposes a kind of MILP model solution AWALBP.Wherein, to minimize assembly beat as mesh
Scalar functions.The result shows that the length of workpiece is longer, solution will be more difficult；For large-scale problem, workpiece can only be obtained
Optimal solution of the length within 25 units；For small/medium-scale, Workpiece length can be obtained in 25~40 units
Within optimal solution.Ozcan proposes that a kind of mixed integer programming of the linear segmented of chance constraint solves bilateral random assembling line
Equilibrium problem.Sample result shows, which is effective, and be in terms of bilateral random assembling line balance Study on Problems first
Piece article.Bautista etc. proposes that a kind of dynamic programming algorithm based on heuristic rule solves I class assembly line balancing problem.
269 examples are chosen from the document published, and are solved using proposed algorithm.The result shows that there is 267
Example can obtain better solution, another example also obtains optimal solution, can not only solve to an example.Wu Erfei etc.
It is proposed that a kind of branch-bound algorithm solves two-sided assembly line equilibrium problem.The algorithm is using task based access control, single step, depth-first
Method scans for, and branch node search order is controlled using a series of heuristic rules, dominates rule, lower bound with node
Rule, maximum cushioning time rule etc. delimit branch node, to quickly find optimal solution.Numerical results show the calculation
Method has preferable performance.
Although optimal method can obtain the optimal solution of problem to be asked, due to its a large amount of mathematical computations and reality
Border production line the complex nature of the problem and reduce the practicality, the problem of it may be only available for smaller calculation scale.
Jackson uses enumerative technique to solve first kind assembly line balancing problem for the first time.He theoretically proves, this method one
Surely optimal solution can be obtained, and is better than complete enumerative technique.But with the increase of Solve problems scale, when the solution of this method
Between it is time-consuming huge.Amen proposes that two kinds of new heuristics solve the assembly line balancing problem towards cost.A kind of preferential rule
Then it is called " cost of idleness optimal varied "；Another more complicated method is called " sliding problem window ", and this method can not only be used
In the solution of assembly line balancing problem, and it can be used for some other solution with dominance relation problem.Chen etc. is adopted
The U-shaped assembly line balancing problem with parallel workstation is studied with heuristic.The result shows that the algorithm executes
Speed quickly, while also being predicted: if asked using the algorithm the U-shaped assembly line balancing problem for not having parallel workstation
Solution then has about 50% probability to obtain optimal solution.Fazlollahtabar etc. proposes a kind of heuristic side based on RPW algorithm
Method studies random assembling line balance problem, meanwhile, also develop normal distribution method and Monte Carlo simulation approach.Example knot
Fruit shows compared with normal distribution method, proposed algorithm and more effective with Monte Carlo simulation approach.Su etc. is used and is based on
The two-phase heuristic algorithm of Petri network solves E class mixed-model assembly line equilibrium problem.Example shows for extensive problem,
Either in the precision aspect of solution, in terms of the efficiency being also to solve for, which can realize preferable effect.
In recent years, the intelligent algorithms such as genetic algorithm, ant group algorithm, particle swarm algorithm are constantly applied to assembly line
In the solution research of equilibrium problem, preferable effect is achieved.Yu etc. proposes that a kind of self-adapted genetic algorithm solves ALB problem.
The result shows that the algorithm has faster convergence rate compared with traditional heuristic.Mutlu etc. proposes a kind of iteration
Genetic algorithm solves employee's distribution and equilibrium problem on assembly line.The problem of by seeing periodical to 32 disclosures, solves, hair
Now wherein there are 26 problems that can obtain new optimum solution or identical optimum solution.In addition, the algorithm can be asked in shorter
Solve the solution scheme that extensive problem is obtained in the time.McMullen etc. using ant colony optimization for solving have parallel workstation with
Machine mixed-model assembly line equilibrium problem.The result shows that ant group algorithm has better performance compared with heuristic.Zhang etc.
It is proposed that a kind of ant colony clone algorithm is solved to minimize assembly beat as the two-sided assembly line equilibrium problem of objective function.Utilize ant
Group's clone's search strategy and heuristic task distribution rule generate the feasible solution of problem, ant colony clone algorithm control problem optimal solution
Search process.Example proves the validity of the algorithm.Hamta etc. proposes a kind of Hybrid Particle Swarm to multiple target assembly line
Equilibrium problem is studied.The result shows that proposed algorithm is not only solving quality compared with multi-objective evolutionary algorithm
Aspect is more excellent, and in terms of solving the time also faster.
However, be directed to first kind assembly line balancing problem complexity, each algorithm all show itself advantage and
Defect all suffers from time performance and optimizes the double challenge of performance.Different method for solving be combined with each other, and have complementary advantages, are
A current new trend.
The method of the present invention combines genetic algorithm and immune algorithm, both algorithm advantages can be combined by establishing one kind
And overcome the hybrid algorithm of self-defect, and the hybrid algorithm is applied to the solution of APXV9R20B antenna mount line balance, it takes
Obtained preferable result.
Summary of the invention
Its of the invention purpose, which is that provide, a kind of solves first kind assembly line balancing problem based on immune genetic algorithm
Method solves due to its a large amount of mathematical computations and actual production line the complex nature of the problem and reduces the practicality, it
The problem of may be only available for smaller calculation scale.
It adopts the technical scheme that achieve the above object, one kind solving first kind assembly line based on immune genetic algorithm
The method of equilibrium problem, method includes the following steps:
1) definition of function ψ ():
A*, meet:
(1) if Then switching matrixAIn With Position；
(2) if Then matrixAIn With Position remains unchanged；
Wherein,
nRepresent the total number of fittage；MatrixAIn it is any column representnA fully intermeshing；
2) constraint condition includes:
One assembling work element can only be assigned in a work station
Wherein,kIndicate the serial number of mounting work station,MIndicate the sum of mounting work station,iIndicate the serial number of assembling work element；
Assemble priority constraint relationship constraint
Wherein,jIndicate the serial number of assembling work element；
Assembly beat constraint (that is, the assembly time at any operative station is not greater than assembly beat)
Wherein,NIndicate the set of assembling work element,t i Indicate theiThe assembly time of a operation element,CIndicate assembly beat；
The value range of variable
3) objective function:
Wherein,f 1It indicates to minimize work station number,f 2It indicates to minimize Smoothness Index,w 1Withw 2Indicate weight coefficient；
The minimum work station number is
Wherein, mIndicate the serial number of mounting work station；
The minimum Smoothness Index is
Wherein, ST k Indicate thekThe assembly time of a mounting work station；
Therefore, the calculation formula of objective function are as follows:
| (1) |
4) immune genetic algorithm:
Step 1: setup parameter
(1) PS: population scale；
(2)P c : crossover probability；
(3) P m : mutation probability；
(4) P i : immunity inoculation probability；
(5) : similarity threshold, ；
Step 2: initialization:
It is random to generatePSA initial individuals, thisPSA initial individuals are denoted as matrixA, and operate on it, make to meet A*；
Step 3: Population Regeneration:
(1) crossover operation:
It enables , wherein Expression is greater than or equal toxMinimum positive integer；Such as
FruitM 1For odd number, thenM 1←M 1-1；
Firstly, fromtFor populationA (t)In randomly selectM 1Individual building matrix ；Then, from In with
Machine chooses two individuals and executes crossover operation, and principle is as shown in Figure 1, the matrix after crossover operation is denoted as ；Most
Afterwards, right It executes Operation, and enable ；
(2) mutation operation:
It enables ；Firstly, fromtFor populationA (t)In randomly selectM 2Individual structure
Build matrix ；Then, right In it is all individual carry out mutation operations, principle as shown in Fig. 2, by variation
Matrix after operation is denoted as ；Finally, right It executes Operation, and enable ；
(3) immunity inoculation operates:
It enables ,P g Represent the vaccine inoculation in data base.Firstly, fromtFor populationA (t)
In randomly selectM 3Individual building matrix ；Then, right In it is all individual andP g Crossover operation is carried out,
Principle is as shown in Figure 1, the matrix after crossover operation is denoted as ；Finally, right It executes
Operation, and enable ；
(4) antibody existence expectation selection:
It enables ,In own
The existence of individual it is expected according to formulaIt is calculated, and ascending order arrangement is carried out to result, before selectionPSEach and every one
Body constitutes next-generation populationA (t+1)；
Wherein,
Wherein, Indicate antibodyuAnd antibodyv?jGenic value on the gene of position is equal, i.e. antibodyu
And antibodyvWith allelej；
Indicate antibodyuAnd antibodyvTotal number with allele；
Step 4: data base is updated:
MatrixA (t+1)In ownMThe objective function of individual is calculated according to formula (1), and with minimum target function
Individual be denoted as ；If , then ；Otherwise, ；
Step 5: termination condition verifying:
As long as terminating iteration in general, algorithm meets any one in following three conditions；
(1) fitness of optimum individual reaches given threshold value；
(2) fitness of optimum individual and the fitness of group no longer rise；
(3) the number of iterations reaches preset algebra；
Wherein, stop condition of the alternative condition (2) as algorithm, i.e., in the iterative process of algorithm, once optimum individual is suitable
Response and group's fitness no longer rise, then stop iteration, enter step six；Otherwise, it is transferred to step 3；
Step 6: result output:
Export best assembly line balancing result.
Beneficial effect
The present invention has the following advantages that compared with prior art.
It is an advantage of the invention that solve due to its a large amount of mathematical computations and actual production line the complex nature of the problem and
The practicality is reduced, the problem of it may be only available for smaller calculation scale, this method combines genetic algorithm and immune algorithm
Get up, both algorithm advantages can be combined and overcome the hybrid algorithm of self-defect by establishing one kind, and the hybrid algorithm is answered
For the solution of APXV9R20B antenna mount line balance, yield good result.
Detailed description of the invention
Below in conjunction with attached drawing, the invention will be further described.
Fig. 1 is the crossover operation schematic diagram of immune genetic algorithm in the invention patent；
Fig. 2 is the mutation operation schematic diagram of immune genetic algorithm in the invention patent；
Fig. 3 is the operational flowchart of immune genetic algorithm in the invention patent.
Specific embodiment
With reference to the accompanying drawing, the present invention is further illustrated.
A method of first kind assembly line balancing problem, as shown in Figure 1-Figure 3, the party are solved based on immune genetic algorithm
Method the following steps are included:
1) definition of function ψ ():
A*, meet:
(1) if Then switching matrixAIn With Position；
(2) if Then matrixAIn With Position remains unchanged；
Wherein,
nRepresent the total number of fittage；MatrixAIn it is any column representnA fully intermeshing；
2) constraint condition includes:
One assembling work element can only be assigned in a work station
Wherein,kIndicate the serial number of mounting work station,MIndicate the sum of mounting work station,iIndicate the serial number of assembling work element；
Assemble priority constraint relationship constraint
Wherein,jIndicate the serial number of assembling work element；
Assembly beat constraint (that is, the assembly time at any operative station is not greater than assembly beat)
Wherein,NIndicate the set of assembling work element,t i Indicate theiThe assembly time of a operation element,CIndicate assembly beat；
The value range of variable
3) objective function:
Wherein,f 1It indicates to minimize work station number,f 2It indicates to minimize Smoothness Index,w 1Withw 2Indicate weight coefficient；
The minimum work station number is
Wherein, mIndicate the serial number of mounting work station；
The minimum Smoothness Index is
Wherein, ST k Indicate thekThe assembly time of a mounting work station；
Therefore, the calculation formula of objective function are as follows:
| (1) |
4) immune genetic algorithm:
Step 1: setup parameter
(1) PS: population scale；
(2)P c : crossover probability；
(3) P m : mutation probability；
(4) P i : immunity inoculation probability；
(5) : similarity threshold, ；
Step 2: initialization:
It is random to generatePSA initial individuals, thisPSA initial individuals are denoted as matrixA, and operate on it, make to meet A*；
Step 3: Population Regeneration:
(1) crossover operation:
It enables , wherein Expression is greater than or equal toxMinimum positive integer；Such as
FruitM 1For odd number, thenM 1←M 1-1；
Firstly, fromtFor populationA (t)In randomly selectM 1Individual building matrix ；Then, from In with
Machine chooses two individuals and executes crossover operation, and principle is as shown in Figure 1, the matrix after crossover operation is denoted as ；Most
Afterwards, right It executes Operation, and enable ；
(2) mutation operation:
It enables ；Firstly, fromtFor populationA (t)In randomly selectM 2Individual structure
Build matrix ；Then, right In it is all individual carry out mutation operations, principle as shown in Fig. 2, by variation
Matrix after operation is denoted as ；Finally, right It executes Operation,
And it enables ；
(3) immunity inoculation operates:
It enables ,P g Represent the vaccine inoculation in data base.Firstly, fromtFor populationA (t)
In randomly selectM 3Individual building matrix ；Then, right In it is all individual andP g Crossover operation is carried out,
Principle is as shown in Figure 1, the matrix after crossover operation is denoted as ；Finally, right It executes
Operation, and enable ；
(4) antibody existence expectation selection:
It enables ,In own
The existence of individual it is expected according to formulaIt is calculated, and ascending order arrangement is carried out to result, before selectionPSIt is a
Individual constitutes next-generation populationA (t+1)；
Wherein,
Wherein, Indicate antibodyuAnd antibodyv?jGenic value on the gene of position is equal, i.e. antibodyu
And antibodyvWith allelej；
Indicate antibodyuAnd antibodyvTotal number with allele；
Step 4: data base is updated:
MatrixA (t+1)In ownMThe objective function of individual is calculated according to formula (1), and with minimum target function
Individual be denoted as ；If , then ；Otherwise, ；
Step 5: termination condition verifying:
As long as terminating iteration in general, algorithm meets any one in following three conditions；
(1) fitness of optimum individual reaches given threshold value；
(2) fitness of optimum individual and the fitness of group no longer rise；
(3) the number of iterations reaches preset algebra；
Wherein, stop condition of the alternative condition (2) as algorithm, i.e., in the iterative process of algorithm, once optimum individual is suitable
Response and group's fitness no longer rise, then stop iteration, enter step six；Otherwise, it is transferred to step 3；
Step 6: result output:
Its flow chart for exporting best assembly line balancing result is as shown in Figure 3.
Application verification is done to the algorithm now in conjunction with example
Table 1 is the information of APXV9R20B antenna mount
The information of 1 APXV9R20B antenna mount of table
| Task sequence Number | Task description | It is directly subsequent Task | When operation Between/second |
| 1 | Put the chassis on the assembly line and clean | 2,3,5,6,7 | 3.4 |
| 2 | Install the high frequency oscillator | 10 | 6.96 |
| 3 | Install the wall components | 4,8 | 5.29 |
| 4 | Install the input cable components | 9 | 2.58 |
| 5 | Install the high frequency isolation | 28 | 12.13 |
| 6 | Install the low frequency isolation | 28 | 3.9 |
| 7 | Install the high frequency isolation block | 28 | 4.2 |
| 8 | Install low frequency oscillator | 9 | 10.46 |
| 9 | low frequency cable wiring | 11,14,15 | 6.12 |
| 10 | High frequency cable wiring | 12,13 | 10 |
| 11 | Install low frequency ground plate | 16 | 12.59 |
| 12 | The high frequency oscillator cable welding to the oscillator | 17 | 21.8 |
| 13 | Install high frequency ground plate | 18 | 12.98 |
| 14 | Install the low frequency oscillator cable in place | 16 | 9.29 |
| 15 | Install low frequency switching | 16 | 4.38 |
| 16 | Low frequency cable welding and cleaning | 19,21 | 28.89 |
| 17 | Install the high frequency oscillator cable in place | 20 | 8.43 |
| 18 | The high frequency cable welding and cleaning | 20 | 22.66 |
| 19 | Place the low frequency phase shifter components | 23 | 1.76 |
| 20 | Place the high frequency phase shifter components | 22,24 | 1.63 |
| 21 | Install low frequency flat | 23 | 6.14 |
| 22 | Install high frequency flat | 25 | 4.97 |
| 23 | Low frequency plate welding | 25 | 26.90 |
| 24 | High frequency plate welding | 25 | 33.43 |
| 25 | Install phase shift | 26,27 | 11.63 |
| 26 | Fixed the guide box and the front panel | 28 | 5.23 |
| 27 | The support installation | 28 | 3.07 |
| 28 | Install support | 7.37 |
Table 2 is the solving result using this patent immune genetic algorithm.
2 solving result of table
| Mounting work station serial number | Task-set | Assembly time/second |
| 1 | 1,2,3,8,10 | 36.11 |
| 2 | 4,5,12 | 36.51 |
| 3 | 13,9,14,15 | 32.77 |
| 4 | 18,11 | 35.25 |
| 5 | 16,21,19 | 36.79 |
| 6 | 17,20,23 | 36.96 |
| 7 | 7,24 | 37.63 |
| 8 | 6,22,25,26,27,28 | 36.17 |
According to table 2, the balanced ratio of APXV9R20B antenna mount line are as follows: =93.81%。
Claims (1)
1. a kind of method for solving first kind assembly line balancing problem based on immune genetic algorithm, which is characterized in that this method packet
Include following steps:
1) definition of function ψ ():
A*, meet:
(1) if Then switching matrixAIn With Position；
(2) if Then matrixAIn With Position remains unchanged；
Wherein,
nRepresent the total number of fittage；MatrixAIn it is any column representnA fully intermeshing；
2) constraint condition includes:
One assembling work element can only be assigned in a work station
Wherein,kIndicate the serial number of mounting work station,MIndicate the sum of mounting work station,iIndicate the serial number of assembling work element；
Assemble priority constraint relationship constraint
Wherein,jIndicate the serial number of assembling work element；
Assembly beat constraint (that is, the assembly time at any operative station is not greater than assembly beat)
Wherein,NIndicate the set of assembling work element,t i Indicate theiThe assembly time of a operation element,CIndicate assembly beat；
The value range of variable
3) objective function:
Wherein,f 1It indicates to minimize work station number,f 2It indicates to minimize Smoothness Index,w 1Withw 2Indicate weight coefficient；
The minimum work station number is
Wherein, mIndicate the serial number of mounting work station；
The minimum Smoothness Index is
Wherein, ST k Indicate thekThe assembly time of a mounting work station；
Therefore, the calculation formula of objective function are as follows:
4) immune genetic algorithm:
Step 1: setup parameter
(1) PS: population scale；
(2)P c : crossover probability；
(3) P m : mutation probability；
(4) P i : immunity inoculation probability；
(5) : similarity threshold, ；
Step 2: initialization:
It is random to generatePSA initial individuals, thisPSA initial individuals are denoted as matrixA, and operate on it, make to meet A*；
Step 3: Population Regeneration:
(1) crossover operation:
It enables , wherein Expression is greater than or equal toxMinimum positive integer；Such as
FruitM 1For odd number, thenM 1←M 1-1；
Firstly, fromtFor populationA (t)In randomly selectM 1Individual building matrix ；Then, from In it is random
It chooses two individuals and executes crossover operation, principle is as shown in Figure 1, the matrix after crossover operation is denoted as ；Finally,
It is right It executes Operation, and enable ；
(2) mutation operation:
It enables ；Firstly, fromtFor populationA (t)In randomly selectM 2Individual building
Matrix ；Then, right In it is all individual carry out mutation operations, principle as shown in Fig. 2, by variation behaviour
Matrix after work is denoted as ；Finally, right It executes Operation, and enable ；
(3) immunity inoculation operates:
It enables ,P g Represent the vaccine inoculation in data base；Firstly, fromtFor populationA (t)
In randomly selectM 3Individual building matrix ；Then, right In it is all individual andP g Crossover operation is carried out,
Principle is as shown in Figure 1, the matrix after crossover operation is denoted as ；Finally, right It executes
Operation, and enable ；
(4) antibody existence expectation selection:
It enables ,In ownThe existence of individual it is expected according to formulaIt is calculated, and result is carried out
Ascending order arrangement, before selectionPSIndividual constitutes next-generation populationA (t+1)；
Wherein,
Wherein, Indicate antibodyuAnd antibodyv?jGenic value on the gene of position is equal, i.e. antibodyu
And antibodyvWith allelej；
Indicate antibodyuAnd antibodyvTotal number with allele；
Step 4: data base is updated:
MatrixA (t+1)In ownMThe objective function of individual is calculated according to formula (1), and with minimum target function
Individual is denoted as ；If , then ；Otherwise, ；
Step 5: termination condition verifying:
As long as terminating iteration in general, algorithm meets any one in following three conditions；
(1) fitness of optimum individual reaches given threshold value；
(2) fitness of optimum individual and the fitness of group no longer rise；
(3) the number of iterations reaches preset algebra；
Wherein, stop condition of the alternative condition (2) as algorithm, i.e., in the iterative process of algorithm, once optimum individual is suitable
Response and group's fitness no longer rise, then stop iteration, enter step six；Otherwise, it is transferred to step 3；
Step 6: result output:
Export best assembly line balancing result.
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