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Distributed Genetic Algorithms
with a New Sharing Approach in
Multiobjective Optimization
Problems
Tomoyuki HIROYASU
Mitsunori MIKI
Sinya WATANABE
Doshisha University
Kyoto, Japan
1. Introduction
Introduction (No.1)
Genetic Algorithms
Multiobjective Optimization
Problems
The Pareto optimum solutions
Need a lot of iterations
Need a large memory
Many objects
Real world problem
Parallel Processing
Introduction (No.2)
High performance
Commodity hardware
Low cost
PC Clusters
Introduction (No.3)
Evaluation fitness
Makinen, et. al.，Parallel CFD96, (1996)
Crossover, selection
Rowe, et. al.，2NWGA, (1996)
Population
Hiyane, No. 9 Automatic system symposium(1997)
Distributed Genetic Algorithms
Introduction (No. 4)
Distributed Genetic Algorithms
Hiyane (1997) concluded that DGAs are the
powerful tool for MOPs.
The diversity of solutions becomes low
Sharing to total population
Aim of this study
Preliminary study of parallel genetic algorithms
Introduced simple algorithms of Distributed
Genetic Algorithm with sharing for total population
Effects of sharing in distributed genetic algorithms
Single processor
2. Distributed Genetic
Algorithms with Sharing
Distributed Genetic Algorithms
island
Genetic operations in each island
Migration interval
Migration
rate population
Migration
Divide
into sub populations
Distributed Genetic Algorithms
with Sharing
F1
Genetic operations in each island
F2
migration
divide
gather
Total
sharing
population
populations
into
from
islands
islands
Divide
population
into
islands
Evaluation methods
•The number of solutions
•Error
•Cover rate of solutions
•Coefficient of variation
Evaluation method (Error)
d1
d2
d3
d4

n
E=
i=1
di
N
2
Evaluation method (Cover rate)
Min
Max
F1
F2
Evaluation method
(Coefficient of variation)
1) Count the number of solutions in
the certain radius for each solution
2) Derive the coefficient of variation of
the numbers
F1
3) Derive the average
4) It shows the diversity of
the solutions ( 1.0 is the
best)
F2
3. Numerical Examples
Test Function
Objective function
fi = – xi
g j = –x j
Constraints
i = 1,2, n
j = 1,2, ,n
g n+k = xk – 6
k = 1,2,

g 2n + 1 = 1 – x1 x2
In this study, we used 4 objectives.
xn
,n
Test functions
-6
-5
-4
-3
-2
-1
-1
2 objectives
-2
-3
0
-2
-4
-4
-6
0
-5
-0.5
-6
-1
3 objectives
-1.5
0
-2
-4
-6
Coding
Design variables → real values
keep good heredity
phenotype ｘ
x={1.23, 34.2, 4.23, 8.29}
=
genotype X
X={1.23, 34.2, 4.23, 8.29}
Parameters
parameter
value
initial population size
1000
crossover rate
1.0
mutation rate
0.0
migration rate
0.1
migration interval
2
island number
10
Effect of distribution
number of
coefficient generations
of variation
calculation
solutions
error
cover
ratio
1 island
1980
0.191
0.856
2.46
6
194.9
10 islands
2690
0.196
0.853
3.10
6
34.3
Terminal condition = function call (1000)
time [sec]
Termination condition= number of function call
number of
error
solutions
cover
ratio
DGA
3888
0.171
0.855
DGA with
sharing
3079
0.153
0.855
calculation
coefficient generations
time [sec]
of variation
4.11
3.10
8.7
91.0
10.1
563.1
Termination condition= calculation time
number of
solutions
error
DGA
3422
0.182
DGA with
sharing
1581
0.226
cover
ratio
0.856
0.847
coefficient of
variation
3.65
2.15
generations
function
call
7.8
18998
3.0
4985
Errors
0.12
0.11
Error
0.1
0.09
0.08
0.07
0.06
0.05
0.000
DGA
0.025
0.050
0.075
0.100
Sleep time
0.125
DGA with sharing
Cover ratio
0.950
Cover ratio
0.925
0.900
0.875
DGA
0.850
0.000
0.025
0.050
0.075
0.100
Sleep time
0.125
DGA with sharing
Hybrid sharing method
total sharing
divide population into
small islands
genetic operation in
each island
migration
gather populations
from islands
sharing in each island
Results of hybrid method
number of
error
solutions
cover
ratio
coefficient
of variation
generations
Calculation
Time [sec]
DGA
3888
0.171
0.855
4.11
8.7
91.0
DGA with
sharing
3079
0.153
0.855
3.10
10.1
563.1
Hybrid
sharing
2922
0.183
0.858
10.0
275.5
2.43
4. Conclusions
Conclusions
Distributed genetic algorithm is good method for parallel
processing but it reduces the diversity of solutions.
To increase the diversity of solutions, the sharing is necessary
even in distributed genetic algorithm.
DGA with sharing to total population
The proposed approach increase the diversity and the accuracy of
solutions
The proposed approach is especially useful when it takes much
time to evaluate objective functions
Another approach where the sharing is performed in islands and in
total population is proposed and this approach reduces the
calculation time and makes some increase in the diversity while
the accuracy of the solutions is decreased.
Conclusions (future work)
Applying to another test functions
Larger problems, something from real applications
Parallel processing
Sorting in parallel
Crossover

n+1
GPi
2
C =G +  N(0,  i )
i=1
GPi
G
Constraints
Feasible region
c1
c2
p1
c3