A Grouping Genetic Algorithm

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A Grouping Genetic Algorithm for heuristically
solving the cell formation problem
Teerawut Tunnukij Christian Hicks
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Road Map
Comparisons performance
Developed GGA
Clustering methods
GGAs
GAs
GT/CM
Facilities layout design
Start
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The facilities layout design
Select machines for each operation and specify
operation sequences
Job Assignment
Cell Formation
Group machines into cells
Layout Design
Assign cells within plants and machines within
cells
Transportation System Design
Design aisle structure and select material
handling equipment
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Group Technology Cellular Manufacturing
Clustering Methods
A philosophy that aims to exploit similarities
and achieve efficiencies by grouping.
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Manufacturing Layout
Process (Functional) Layout
Group (Cellular) Layout
A cluster or cell
Like resources placed together
Resources to produce like products placed together
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Cellular Manufacturing (CM)
The parts that have similar processing
requirements and/or geometrical shapes.
Cellular Manufacturing
The machines that are required for the
manufacture of each part family.
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The benefits of CM

• 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

Cellular Manufacturing
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Clustering Methods
Form part families and then group machines into
cells.
A large number of clustering methods have been
developed
Form machine cells based upon similarities in
part routing and then allocate parts to cells.
Form part families and machine cells
simultaneously.
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Clustering Methods
Part family grouping
Machine grouping
Similarity coefficient- based Methods
Classification Coding
Graph theoretic
Mathematical Programming- based Methods
Heuristic Methods
Meta-heuristic Methods
Machine-part grouping
Machine-Part incidence matrix-based Methods

• Most of these methods have exploited the
  machine-part matrix as the initial information to
  identify potential manufacturing cells.

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A machine-part incidence matrix
Exceptional elements
Parts
Parts
Machines
Machines
(a) the original matrix
(b) a rearranged matrix into block-diagonal forms
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General problems of clustering methods
Conventional methods do not always produce a
desirable solution.
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.
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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.

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GAs The main components
1. Genetic representation
5. Genetic operators
2. Method for generating the initial population
6. Mechanism for creating successive generations
GAs
3. Evaluation function
7. Stopping Criteria
4. Reproduction selection scheme
8. GA parameter settings
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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.

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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)

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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 aspects1. The special gene encoding
  scheme2. 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.

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The developed GGA The general structure
1
2
4
3
Encode Genes
Generate Population
Population
Start
Chromosome
Random selection
Randomly combine genes with a repair process
Integer representing a cell number
Chromosome
Stop
Create population for the next generation
Number of generation
Yes
Terminate?
No
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Chromosome
4.1
Chromosome selection
6
5
Roulette Wheel
Evaluate Fitness Grouping efficacy
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The developed GGA Genetic representation
6 parts
4 machines
Cell section
Cell number
Chromosome Cell 1 p1,p2,p6 m3 Cell 2
p3,p5 m2,m4 Cell 3 p4 m1
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The developed GGA Generating the initial
population

• The initial population of chromosomes is
  generated randomly with a repair process that
  rectifies empty cells.
• Each cell must contain at least one part and one
  machine.
• Wichmann and Hills seed-based random number
  generator was adapted for generating random
  numbers in the developed GGA, with a very large
  period of 2.78x1013.
• The developed GGA can solve the CFP without the
  predetermination of the No. of manufacturing
  cells and the No. of machines within the cell.

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The developed GGA Genetic operators
Falknauers crossover
Injection point
Select crossover points
Injection
Remove the empty cell
Relocate unassigned components by the replacement
heuristic
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The developed GGA Genetic operators
Elimination mutation
Eliminating cell
Select a cell number
Elimination
Relocate unassigned components by the replacement
heuristic
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The developed GGA Repair process
Check remove empty cells
Replace duplicate cell numbers
3
1
Each cell must contain at least one part one
machine
The duplicate cell no. is replaced with a new
cell no.
Check the number of cells
Relocate unassigned components
2
4

• 2Cmin(M-1,P-1)
• Clt2 a new cell no. will be inserted to the cell
  section
• Cgtmin(M-1,P-1) a cell(s) will be randomly
  selected and eliminated.

• The replacement heuristic utilises the
  information in the given machine-part matrix to
  place
• unassigned parts in the existing cell that
  contains the most machine(s) it needs by
  examining the column j
• unassigned machines in the existing cell that
  contains the most part(s) that needs it by
  examining the row i.

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The developed GGA Evaluation criteria
Grouping efficacy (?)
where e the total number of operations (number
of 1s in the matrix) e0 the number of 1s in the
off-diagonal blocks ev the number of voids in
the diagonal blocks.
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The analysis of performance
A simple CFP
(a) The 5x8 original matrix
(b) The 5x8 matrix after clustered
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The analysis of performance
Comparisons of five clustering algorithms

• CR1-CR7 obtained from Chandrasekharan and
  Rajagopalan (1989)
• KN1 obtained from King and Nakornchai (1982)

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The analysis of performance
Grouping efficacy
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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.

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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.

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Thank you
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References
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31
References
Dimopoulos, C. and Zalzala, A. M. S., 2000,
Recent developments in evolutionary computation
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References
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