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## Parallel Evolutionary

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### Parallel Evolutionary Multi-Criterion Optimization for Block Layout Problems Shinya Watanabe Tomoyuki Hiroyasu Mitsunori Miki Intelligent Systems Design Laboratory – PowerPoint PPT presentation

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Title: Parallel Evolutionary

1
Parallel Evolutionary Multi-Criterion
Optimization for Block Layout Problems
? Shinya Watanabe Tomoyuki Hiroyasu Mitsunori Miki
Intelligent Systems Design Laboratory, Doshisha
University,Japan
2
Background (1)
?EMO
Evolutionary Multi-criterion Optimizations
(Ex. VEGA,MOGA,NPGAetc)
• Some of EMO can derive the good pareto optimum
solutions.
• EMO need high calculation cost.
• Evolutionary algorithms have potential
parallelism.
• PC Cluster Systems become very popular.

3
Background (2)
?Parallel EMO Algorithms
• Some parallel models for EMO are proposed
• There are few studies for the validity on
parallel model.
• Divided Range Multi-Objective Genetic Algorithms
(DRMOGA)
• it is applied to some test functions and it is
found that this model is effective model for
continuous multi-objective problems.

Purpose
The purpose of this study is to find the
effectiveness of DRMOGA.
4
Multi-Criterion Optimization Problems(1)
?Multi-Criterion Optimization Problems (MOPs)
In the optimization problems, when there are
several objective functions, the problems are
called multi-objective or multi-criterion
problems.
Design variables
Xx1, x2, . , xn
Objective function
Ff1(x), f2(x), , fm(x)
Constraints
Gi(x)lt0 ( i 1, 2, , k)
5
Multi-objective GA (1)
Multi-objective GA
Like single objective GA , genetic operations
such as evaluation, selection, crossover, and
mutation, are repeated.
1st generation
5th generation
10th generation
30th generation
Pareto optimal solutions
50th generation
6
DGA model
• Distributed GAs
• A population is divided into subpopulations
(islands)
• SGA is performed on each subpopulation
• Migration is performed for some generations
• Exchange of individuals

7
Divided Range Multi-Objective GA(1)
1st The individuals are sorted by the values of
focused objective function. 2nd The N/m
individuals are chosen in sequence. 3rd SGA
is performed on each sub population. 4th After
some generations, the step is returned to first
Step
8
Formulation of Block Layout Problems
Block Layout Problems with Floor
Constraints (Sirai 1999)
Objects
Block Packing method
3
4
6
1
7
f2Total Area S
where nnumber of blocks cij flow from
block i to block j dij distance from block i
to block j
5
2
9
Numerical Example
• Application models
• SGA , DGA , DRMOGA
• Layout problems
• 13, 27blocks
• Parameter

GA parameter
value
Number of individuals
100 (total 1600)
crossover rate
1.0
mutation rate
0.05
migration interval (resorted interval)
20
20
migration rate
0.2
terminal condition
300generation
10
Cluster system for calculation
Spec. of Cluster (16 nodes)
Processor Pentium?(Deschutes) Clock
400MHz Processors 1 16 Main memory
128Mbytes 16 Network Fast Ethernet
(100Mbps) Communication TCP/IP, MPICH
1.1.2 OS Linux 2.2.10 Compiler gcc
(egcs-2.91.61)
11
Results of 13 Blocks case
13
Real weak pareto solutions
DGA
DRMOGA
12
Results of 13 Blocks case (SGA)
13
Local optimum solutions
Real weak pareto solutions
13
Results of 27 Blocks case
27
A
B
DRMOGA
DGA
14
27
(f_1, f_2) (38446, 49920)
(f_1, f_2) (42739, 43264)
A
B
15
Results
• Most of the solutions were weak-pareto
solutions.
• SGA, DGA and DRMOGA are applied to the layout
problems
• There are small difference between the results of
three methods.
• When results of DRMOGA compared with those of
DGA, there isnt big advantage.
• SGA sometimes could not find the real weak
pareto solutions.

16
Results
Division 1
(x)
2
f
Division 2
f
(x)
1
(x)
2
f
The individuals cant be divided into two
division by the value of the focused objective
function(f2(x)).
Cant exchange individuals enough.
f
(x)
1
17
Conclusion
• The DRMOGA was applied to discrete problems The
block layout problems.
• The test problems didnt have definitely pareto
solutions.
• The searching ability of DGA and DRMOGA were
almost same in numerical examples.
• The mechanism of DRMOGA didnt work effectively
in these problems.
• SGA may be caught by local minimum.

18
?????????
?????????
?????????
???????
?????????
???????
?????
???
??
19
Divided Range Multi-Objective GA(2)
DGA( Island model)

DRMOGA

20
Results of 10 Blocks case (DRMOGA)
A
Local optimum set
B
Real weak pareto set
21
A
B
22
Results of 10 Blocks case
DGA
SGA
23
• Why are the results in this presentation
different from the results in the paper?
• In first, we selected GA parameters with no
consideration. But we investigated more suitable
GA parameters, and in this presentation, we
used new GA parameters. Thats why this results
Is different from results in paper.
• What do you aim in this presentation?
• Main purpose in this study is to investigate the
effectiveness of DRMOGA for Block layout
problems. To my regret, this problem isnt
suitable for multi-criterion problems and we
cant get good results.
• How do you think about meaning of this
presentation?
• In other discrete problem, the effectiveness of
DRMOGA hasnt been researched yet. And I think
that in the problem that has obviously
trade-off relationships, DRMOGA will get good
results. Because in that problems , the
characteristics of DRMOGA can work effectively.

24
Multi-objective GA (2)
Squire EMO
• VEGA Schaffer (1985)
• VEGAPareto optimum individuals Tamaki (1995)
• Ranking Goldberg (1989)
• MOGA Fonseca (1993)
• Non Pareto optimum Elimination Kobayashi (1996)
• Ranking sharing Srinvas (1994)
• Others

25
(f_1, f_2) (838544, 14238)
13
(f_1, f_2) (879179, 13560)
26
Configuration of GA
• Expression of solutions
• Genetic operations

27
Calculation Time
Calculation time(sec)
method
Case
1.08E03
SGA
DGA
1.73E01
13blocks
2.02E01
DRMOGA
1.37E03
SGA
27blocks
5.28E01
DGA
DRMOGA
5.61E01
28
Results of 27 Blocks case
27
SGA