a grouping genetic algorithm for heuristically solving the cell formation problem
DESCRIPTION
A Grouping Genetic Algorithm for heuristically solving the cell formation problem. Teerawut Tunnukij Christian Hicks. Components of GAs Problems of the classical GAs for solving the cell formation problem. Goal. Performance & benefits of the proposed GGA. - PowerPoint PPT PresentationTRANSCRIPT
Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne
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Teerawut Tunnukij
Christian Hicks
Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne
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Road Map
Facilities layout design
Facilities layout design
Start
GT/CMGT/CM
Clustering methods
Clustering methods
Benefits of GT/CM to facilities layout design
• General problems of clustering methods
• Suitable methods for the solutions
GAsGAs
• Components of GAs• Problems of the classical GAs for solving the cell formation problem
GGAsGGAs
Developed GGA
Developed GGA
General structure & components of the developed GGA
Comparisons & performance
Comparisons & performance
Performance & benefits of the proposed GGA
Goal
Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne
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Select machines for each operation and specify operation sequences
The facilities layout design
Layout DesignLayout Design
Transportation System Design Transportation System Design
Job AssignmentJob Assignment
Cell FormationCell Formation Group machines into cells
Assign cells within plants and machines within cells
Design aisle structure and select material handling equipment
Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne
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Group Technology & Cellular Manufacturing
Clustering Methods
Manufacturing cells
Manufacturing cells
have been used for identifying
Based upon
Group Technology
A philosophy that aims to exploit similarities and achieve efficiencies by grouping.
GT has been applied to manufacturing systems known as Cellular Manufacturing (CM).
Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne
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Manufacturing Layout
Process (Functional) Layout
Process (Functional) Layout Group (Cellular) LayoutGroup (Cellular) Layout
Like resources placed togetherResources to produce like products placed together
T T T
MM M T
M
SG CG CG
SG
D D D
D
T T T CG CG
T T T SG SG
M M D D D
M M D D D
A cluster or cell
Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne
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The benefits of CM
Cellular Manufacturing
Cellular Manufacturing
Main benefits
• Reduced throughput time
• Reduced work in progress
• Improved material flows
Others• Reduced inventory
• Improved use of space
• Improved team work
• Reduced waste
• Increased flexibility
Reduced Manufacturing
Costs
Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne
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Clustering Methods
A large number of clustering methods
have been developed
A large number of clustering methods
have been developed
Part family grouping
Part family grouping
Machine grouping
Machine grouping
Machine-part grouping
Machine-part grouping
Can be classified into
Form part families and then group machines into cells.
Form machine cells based upon similarities in part routing and then allocate parts to cells.
Form part families and machine cells simultaneously.
Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne
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Clustering Methods
Part family groupingPart family grouping Machine groupingMachine grouping
Machine-part groupingMachine-part grouping
Classification & Coding
Similarity coefficient-based Methods
Graph theoretic
Machine-Part incidencematrix-based Methods
• Most of these methods have exploited the machine-part matrix as the initial information to identify potential manufacturing cells.
Mathematical Programming-based Methods
HeuristicMethods
Meta-heuristicMethods
Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne
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A machine-part incidence matrix
1 2 3 4 5 61 1 1 12 1 1 1 13 1 1 14 1 1 1 1
1 3 6 2 4 52 1 1 1 11 1 1 14 1 1 1 13 1 1 1
(a) the original matrix (b) a rearranged matrix into block-diagonal forms
Exceptional elements
Parts Parts
Ma
ch
ine
s
Ma
ch
ine
s
Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne
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General problems of clustering methods
Conventional methods do not always produce a desirable solution.
Conventional methods do not always produce a desirable solution.
There are many ‘exceptional elements’ (machines & parts that cannot be assigned to cells).
There are many ‘exceptional elements’ (machines & parts that cannot be assigned to cells).
The cell formation problem has been shown to be a non-deterministic polynomial (NP) complete problem.
The cell formation problem has been shown to be a non-deterministic polynomial (NP) complete problem.
Meta-heuristic methods
Meta-heuristic methods
• Good methods for the solution
• SA, TS, GAs
Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne
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Genetic Algorithms (GAs)
• GAs are one of the meta-heuristic algorithms. They are stochastic search techniques for approximating optimal solutions within complex search spaces.
• The technique is based upon the mechanics of natural genetics and selection.
• The basic idea derived from an analogy with biological evolution, in which the fitness of individual determines its ability to survive and reproduce, known as ‘the survival of the fittest’.
Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne
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GAs: The main components
GAsGAs
1. Genetic representation1. Genetic representation
2. Method for generating the initial population
2. Method for generating the initial population
3. Evaluation function3. Evaluation function
4. Reproduction selection scheme
4. Reproduction selection scheme
5. Genetic operators5. Genetic operators
6. Mechanism for creating successive generations
6. Mechanism for creating successive generations
7. Stopping Criteria7. Stopping Criteria
8. GA parameter settings8. GA parameter settings
Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne
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GAs: The cell formation problem
• Venugopal and Narendran (1992) were the first researchers to apply GAs to the cell formation problem.
1 2 3 4 5 61 1 2 3 2 1
6 parts (or machines)
Cell number Chromosome:Cell 1: 1,2,6Cell 2: 3,5Cell 3: 4
The general chromosome representation
The general chromosome representation
A potential solution
Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne
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GAs: The problem of the classical GAs
• The standard gene encoding scheme includes significant redundancy when representing a grouping problem (Falkenauer 1998)
A B A C
C A C B
1 2 1 3
3 1 3 2
All chromosomes represent the same solution
All chromosomes represent the same solution
This repetition problem• increases the size of the
search space;• reduces the effectiveness
of the GAs.
Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne
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Grouping Genetic Algorithms (GGAs)
• The GGA, introduced by Falkenauer (1998), is a specialised GA tool that has been adapted to suit and handle the structure of grouping problems.
• The GGA differs from the classical GAs in two important aspects:1. The special gene encoding scheme;2. The special genetic operators.
• De Lit et al. (2000) first applied the GGA to solve the cell formation problem with the fixed maximum cell size.
Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne
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The developed GGA: The general structure
StartEncodeGenes
GeneratePopulation
Population Genetic Operation
Parent 1
Crossover operation
Parent 2
Offspring 1
Offspring 2
Parent 1 Offspring 1
Mutation operation
Chromosome
Repair Process
Check & remove empty cells
Check no. of cells 2≤C≤min(M-1,P-1)
Check & replace duplicate cell no.
Check & relocate unassigned parts
& machines
Evaluate Fitness
Grouping efficacy
Roulette Wheel
Stop
Terminate?
Number of generation
Yes
No
Chromosome selection
Create population for the next generation
Randomly combine genes with a repair process
Integer representing a cell number
Chromosome
Chromosome
Random selection
1 2 3 4
4.1
56
7
Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne
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The analysis of performance
A simple CFP A simple CFP
1 2 3 4 5 6 7 81 1 1 12 1 1 1 1 13 1 1 1 1 14 1 1 15 1 1 1
1 4 7 2 3 5 6 81 1 1 14 1 1 15 1 1 12 1 1 1 1 13 1 1 1 1 1
(a) The 5x8 original matrix
(b) The 5x8 matrix after clustered
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
1 3 5 7 9 11 13 15 17 19
Generation
Fit
nes
s
Best Fitness Avg. Fitness
0.0
0.2
0.4
0.6
0.8
1.0
1 3 5 7 9 11 13 15 17 19
Generation
Fit
nes
s
Best Fitness Avg. Fitness
the performance of the GGA proposed by Yasuda, et al. (2005)
the performance of the developed GGA
Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne
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Data set Size ZODIAC GRAFICS Cheng & others’ GA
CF-GGA Yasuda and others’ GGA
Developed GGA
CR1 24×40 100.00 100.00 100.00 100.00 100.00 100.00
CR2 24×40 85.11 85.11 85.11 85.11 85.11 85.11
CR3 24×40 73.03 NA 73.03 NA 73.03 73.51
CR4 24×40 73.51 73.51 NA 73.29 73.51 73.51
CR5 24×40 20.42 43.27 49.37 48.98 48.98 53.21
CR6 24×40 18.23 44.51 44.67 46.81 45.00 46.04
CR7 24×40 17.61 41.61 42.50 44.14 41.90 43.66
KN1 16×43 53.76 54.39 53.89 53.70 55.43 56.88
The analysis of performance
Comparisons of five clustering algorithms Comparisons of five clustering algorithms
• CR1-CR7 obtained from Chandrasekharan and Rajagopalan (1989)• KN1 obtained from King and Nakornchai (1982)
Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne
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The analysis of performance
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
100.00
CR1 CR2 CR3 CR4 CR5 CR6 CR7 KN1
ZODIAC
GRAFICS
Cheng & others’ GA
CF-GGA
Yasuda and others’ GGA
Developed GGA
Gro
up
ing
eff
ica
cy
Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne
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Conclusions
• The developed GGA including a repair process was developed for solving the CFP without the predetermination of the No. of manufacturing cells and the No. of machines within the cell.
• The developed GGA was applied to well-known data sets from the literature and was compared to other methods. The results show the developed GGA is effective, performs very well, and outperforms other selected methods in most cases.
• The designed parameter experiment suggests that the large no. of population size have more chance to obtain the better solution, and using the range 0.6-0.7 for probability of crossover and the range 0.2-0.3 for probability of mutation tends to produce the better solution.
Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne
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Further Work
• Develop the proposed GGA to be able to consider important parameters such as operation sequences and others.
• Apply the developed GGA to a data set obtained from a collaborating company.
Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne
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Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne
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References
Aytug, H., Khouja, M. and Vergara, F. E., 2003, Use of genetic algorithms to solve production and operations management problems: A review, International Journal of Production Research, 41(17), 3955-4009.
Brown, E. C. and Sumichrast, R. T., 2001, CF-GGA: A grouping genetic algorithm for the cell formation problem, International Journal of Production Research, 39(16), 3651-3669.
Chandrasekharan, M. P. and Rajagopalan, R., 1989, GROUPABILITY: An analysis of the properties of binary data matrices for group technology, International Journal of Production Research, 27(6), 1035-1052.
Cheng, C. H., Gupta, Y. P., Lee, W. H. and Wong, K. F., 1998, TSP-based heuristic for forming machine groups and part families, International Journal of Production Research, 36(5), 1325-1337.
De Lit, P., Falkenauer, E. and Delchambre, A., 2000, Grouping genetic algorithms: An efficient method to solve the cell formation problem, Mathematics and Computers in Simulation, 51(3-4), 257-271.
Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne
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References
Dimopoulos, C. and Zalzala, A. M. S., 2000, Recent developments in evolutionary computation for manufacturing optimization: Problems, solutions, and comparisons, IEEE Transactions on Evolutionary Computation, 4(2), 93-113.
Falkenauer, E., 1998, Genetic Algorithms and Grouping Problems (New York: John Wiley & Sons).
Gallagher, C. C. and Knight, W. A., 1973, Group Technology (London: Gutterworth).
Gallagher, C. C. and Knight, W. A., 1986, Group Technology Production Methods in Manufacture (New York: Wiley).
Hyer, N. L. and Wemmerlov, U., 1984, Group Technology and Productivity, Harvard Business Review, 62(4), 140-149.
King, J. R. and Nakornchai, V., 1982, Machine-Component Group Formation in Group Technology - Review and Extension, International Journal of Production Research, 20(2), 117-133.
Kumar, C. S. and Chandrasekharan, M. P., 1990, Grouping Efficacy - a Quantitative Criterion for Goodness of Block Diagonal Forms of Binary Matrices in Group Technology, International Journal of Production Research, 28(2), 233-243.
Mr T. Tunnukij & Dr. C. Hicks, University of Newcastle upon Tyne
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References
Srinivasan, G. and Narendran, T. T., 1991, GRAFICS. A nonhierarchical clustering algorithm for group technology, International Journal of Production Research, 29(3), 463-478.
Venugopal, V. and Narendran, T. T., 1992, Genetic algorithm approach to the machine-component grouping problem with multiple objectives, Computers & Industrial Engineering, 22(4), 469-480.
Wemmerlov, U. and Hyer, N. L., 1989, Cellular manufacturing in the US industry: a survey of users, International Journal of Production Research, 27(9), 1511-1530.
Wu, Y., 1999, Computer aided design of cellular manufacturing layout, Ph.D. Thesis, School of Engineering and Applied Science, University of Durham.
Yasuda, K., Hu, L. and Yin, Y., 2005, A grouping genetic algorithm for the multi-objective cell formation problem, International Journal of Production Research, 43(4), 829-853.