© C.Hicks, University of Newcastle

IGLS04/1

Determining optimum Genetic Algorithm parameters for designing manufacturing

facilities in the capital goods industry

Dr Christian HicksUniversity of Newcastle upon Tyne

http://www.staff.ncl.ac.uk/chris.hicks/presindex.htm

© C.Hicks, University of Newcastle

IGLS04/2

Layout literature

Two main themes:

• Facilities layout problem (FLP)

• Group Technology / Cellular Manufacturing

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IGLS04/3

Facilities Layout Problem

“The determination of the relative locations for, and the allocation of available space among a number of workstations” (Azadivar and Wang, 2000).

• Block layouts represent resources as rectangles

• FLP formulated as: quadratic set covering problem, mixed integer programming problem and a graph theoretic problem.

• The FLP involves the solution of inefficient NP-complete algorithms. The longest time for solution increases exponentially with problem size.

• A lot of research based upon small or theoretical situations.

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IGLS04/4

Cellular Manufacturing

• Clusters of dissimilar machines are placed close together

• Manufacturing cells design steps:– Job assignment; – cell formation; – layout of cells within plant; – Layout of machines within cells– Transportation system design

• 3 approaches to cell formation: part family grouping, machine grouping and machine-part grouping.

• Cell formation and the layout problems are both NP-complete problems.

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IGLS04/5

Cellular Manufacturing• CM can reduce set-up and flow times,

transfer batch sizes and WIP.However:• 8/9 simulation studies found that

functional layouts performed better than CM in terms of a range of evaluation criteria

• 14/15 empirical studies revealed CM produced significant operational benefits.

Possible explanation:• CM facilitates teamworking and

provides a starting point for JIT. This may explain the difference in results obtained by research based upon simulation and empirical studies.

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IGLS04/6

GA Procedure

• Use GAs to create sequences of machines.

• Apply a placement algorithm to generate layout.

• Measure total direct or rectilinear distance to evaluate the layout.

Two approaches:• Algorithm can treat layouts as a single

facilities layout problem, or it can treat them as a hierarchical set of cell problems.

• The approach supports both FLP and CM.

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IGLS04/7

Genetic Algorithm

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IGLS04/8

Company level

Factory level1,0,0,0 2,0,0,0 3,0,0,0

1,1,0,0

1,1,1,0 1,1,2,0

0,0,0,0

2,3,0,0

1,1,

1,1

1,1,

1,2

1,1,

1,3

2,3,

1,1

2,3,

1,2

2,3,

1,3

Department level

Cell level

Machine level

Genetic representation

1,2,3,1 1,3,1,2 1,1,3,1 1,2,3,3

Factory digit

Departmental digit

Cell digit

Machine digit

Chromosome for single area

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IGLS04/9

Genetic representation

1111 1112 1121 1123 1122 1mn1 1mn2

1mn1 1mn2

1111 1112

1111 1123 1122

Chromosome

Area 1

Area 2

Area mn

Resource 1110

Resource 1120

Resource 1510

1110 1120

Resource 1100

Subc

hrom

osom

esSu

bchr

omos

omes

Chromosome with hierarchical constraints

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IGLS04/10

Placement Algorithm

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IGLS04/11

Case Study

• 52 Machine tools• 3408 complex components• 734 part types• Complex product structures• Total distance travelled

– Direct distance 232Km

– Rectilinear distance 642Km

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IGLS04/12

Random generation

Total Rectinear Distance Travelled for Randomly Generated Layouts (Hierarchy of Areas)

0

100000

200000

300000

400000

500000

600000

700000

800000

100 500 1000 5000 10000 20000 50000

Number of random layouts generated

Mean

Minimum

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IGLS04/13

Experimental Design

Factor Levels

Layout type Single cell, multiple cells

Population size 50, 250, 500

Probability of crossover

0.3, 0.6, 0.9

Probability of mutation

0.02, 0.1, 0.18

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IGLS04/14

Total Rectilinear Distance Travelled vs. Generation(multiple areas)

0

100000

200000

300000

400000

500000

600000

700000

800000

1 11 21 31 41 51 61 71 81 91 101 111 121 131

Generation

Mean

Minimum

GA ParametersPopulation 250Crossover 90%Mutation 10%

Tot

al r

ectil

inea

r di

stan

ce tr

avel

led

(m)

Hierarchy of areas

The number of generations was the only significant factor.

Best configuration

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IGLS04/15

Single area

Significant factors:• Population size• Probability of crossover• Number of generations

Total rectilinear distance travelled vs generation (single area)

0

100000

200000

300000

400000

500000

600000

700000

800000

1 11 21 31 41 51 61 71 81 91 101

111

121

131

141

151

161

171

181

191

201

211

221

231

Generation

Mean

Minimum

GA ParametersPopulation 500Crossover 60%Mutation 10%

Tot

al r

ectil

inea

r di

stan

ce tr

avel

led

(m)

Best configuration

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IGLS04/16

Conclusions

• Developed a GA tool that can treat layouts as a single area or a hierarchy of cell layout problems.

• GA tool significantly better than random search

• GA worked better with unconstrained single area problems. In this case, population size, probability of crossover and number of generations were significant factors.

• With the hierarchy of cells approach only the number of generations was significant. Quality of layout influenced by initial allocation of machines to cells.