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Figure 5. Fitness and strength calculation method
of SPEA2 (Cha2008)
Hybrid SP2-IRR GA
The SP2-IRR GA (Cha 2008; Cha et al. 2011a) is
proposed through the integration of an advanced
selection method (i.e., SPEA2) and dynamic search
encoding policy (i.e., IRR GA). The developed
algorithm is shown in Figure 6. This algorithm is
also characterized as mainly 4 steps:
1. Initialization of population (
P
0
) and archive
(
E
o
) by randomly generated binary numbers
(i.e., 0 and 1)
2. Evaluation of each binary of the population
P
0
for the first generation or
P
t
for the t-th
generation)
3. Non-dominated sorting based on SPEA2
algorithm using fitness values of current
population and previous archive set (
E
t
)
4. Genetic operation to generate child popula-
tion for the next generation.
a first step to calculate the row fitness, the strength
values of the current population and archive set
are calculated. The strength value of an individual
is the number of individuals that is dominated in
the current and archived population. With these
defined strength values, the row fitness value is
determined by adding the strength values of its
dominators in the archive and current population
(Zitzler et al 2001).
One difference in the SPEA2 mechanism is a
truncation operator. The truncation operator is
performed to sustain the archive set size. In case
the archive size is smaller than the defined size,
the number of shortage individual is coped from
the current population to archive. In case the ar-
chive size is bigger than the defined size, the
individual that has the minimum distance to an-
other individual is chosen for removal, but if there
are several individuals with the same minimum
distance, the tie is broken by considering the
second smallest distances.
For the third step the strength values are cal-
culated by
S i
and
{
( )
=
j j P
∈ + ∧
E
i
j
t
t
∑
R i
=
S j
. And density estimation is
( )
( )
j P E j
∈ + ∧
i
t
t
carried to get final fitness by summing
R
( )
and
D
( )
for each individual. All non-dominated
individuals in
P
t
and
E
t
to
E
t
+1
. If the size of
the
E
t
+1
is bigger than predefined size of archive,
truncation operation is carried out to cut out and
sustain the size of archive, and if it is smaller than
the predefined size of archive, the archive is filled
with best dominated individuals of
P
t
and
E
t
.
By tournament selection, the new
P
t
+1
is filled.
For the fourth step the general genetic operator
is carried out to create new parent population
P
t
+
(
)
.
1
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