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n
f
o
r
th
e
lan
g
u
a
g
e.
T
h
is
p
ap
er
p
r
esen
ts
a
GI
alg
o
r
ith
m
co
m
b
i
n
es
w
it
h
t
h
e
g
e
n
eti
c
alg
o
r
ith
m
(
G
A
)
,
w
h
ic
h
h
as
a
p
o
w
er
f
u
l
g
lo
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ex
p
lo
r
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ca
p
ab
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y
.
A
P
D
A
s
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m
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lato
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h
as
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m
p
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m
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th
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co
m
p
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tati
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t
t
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r
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eth
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f
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th
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p
ar
s
in
g
th
at
r
es
u
lt
s
in
ter
m
s
o
f
ac
ce
p
ta
n
ce
o
r
r
ej
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tio
n
o
f
th
e
s
tr
in
g
.
T
h
e
p
r
o
ce
d
u
r
e
f
o
r
th
e
P
D
A
s
i
m
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lato
r
h
as
b
ee
n
i
m
p
le
m
e
n
ted
an
d
e
x
p
la
in
ed
w
i
th
th
e
h
elp
o
f
e
x
a
m
p
les.
T
h
e
au
th
o
r
h
a
s
i
m
p
le
m
e
n
ted
t
w
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p
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t
cr
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ased
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y
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cr
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s
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d
i
n
v
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ted
m
u
tat
io
n
w
i
th
r
an
d
o
m
o
f
f
s
p
r
i
n
g
th
e
n
ap
p
lie
d
„
XO
R
‟
o
p
er
atio
n
f
o
r
t
h
e
r
e
p
r
o
d
u
ctio
n
.
T
h
e
r
ep
r
o
d
u
ctio
n
o
p
er
ato
r
s
em
p
lo
y
ed
in
tr
o
d
u
ce
s
d
iv
er
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it
y
i
n
t
h
e
p
o
p
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latio
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elp
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GI
G
A
to
ex
p
lo
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th
e
s
ea
r
ch
s
p
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ad
eq
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atel
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e
au
th
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r
h
a
s
co
m
p
ar
ed
t
h
e
p
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f
o
r
m
an
ce
o
f
th
e
p
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o
p
o
s
ed
GI
GA
w
it
h
t
h
r
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ex
i
s
ti
n
g
al
g
o
r
ith
m
s
n
a
m
el
y
cla
s
s
ical
g
en
et
ic
alg
o
r
ith
m
(
C
G
A
)
[
3
8
]
,
r
an
d
o
m
o
f
f
s
p
r
in
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g
en
er
atio
n
g
e
n
etic
alg
o
r
it
h
m
(
R
OGG
A
)
[
3
6
]
an
d
cr
o
w
d
i
n
g
alg
o
r
ith
m
[
3
7
]
.
T
h
e
co
m
p
ar
ativ
e
r
es
u
lts
lead
to
a
co
n
clu
s
i
o
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I
GA
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tp
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ese
s
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o
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ith
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s
.
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h
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r
est
o
f
th
e
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
w
s
:
Sectio
n
2
r
ev
ie
w
s
th
e
r
elate
d
r
esear
c
h
es
o
n
GI
p
r
o
b
lem
.
Sectio
n
3
p
r
esen
t
s
t
h
e
C
FG
in
d
u
ctio
n
ap
p
r
o
ac
h
u
s
i
n
g
G
A
ad
ap
ted
in
t
h
i
s
p
ap
er
.
T
h
is
s
ec
tio
n
s
h
o
w
s
th
e
c
h
r
o
m
o
s
o
m
e
s
tr
u
c
t
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r
in
g
,
f
it
n
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s
f
u
n
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a
n
d
r
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r
o
d
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ctio
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o
p
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th
at
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v
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lo
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r
C
F
G
in
d
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io
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s
h
o
w
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p
u
s
h
d
o
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a
u
to
m
ata
s
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m
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la
to
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t
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v
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io
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et
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d
s
i
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co
r
p
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ated
f
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th
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er
if
ica
tio
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u
r
p
o
s
e.
T
h
e
ex
p
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im
e
n
tal
s
et
u
p
,
r
esu
lt
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d
d
is
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s
s
i
o
n
o
n
r
esu
lt
s
ar
e
g
iv
en
i
n
Sectio
n
5
.
Sectio
n
6
co
n
clu
d
e
s
th
e
p
ap
er
an
d
ass
es
s
es t
h
e
f
u
t
u
r
e
p
er
s
p
ec
tiv
es.
2.
RE
L
AT
E
D
WO
RK
Go
ld
[
1
8
]
p
r
o
p
o
s
ed
th
e
f
ir
s
t
l
ea
r
n
in
g
m
o
d
el
to
ad
d
r
ess
“
I
s
th
e
in
fo
r
ma
tio
n
s
u
fficien
t
to
d
etermin
e
w
h
ich
o
f
th
e
p
o
s
s
ib
le
la
n
g
u
a
g
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u
n
kn
o
w
n
la
n
g
u
a
g
e?
”,
b
u
t
it
w
a
s
s
u
f
f
er
ed
b
ec
au
s
e
s
u
f
f
icie
n
t
in
f
o
r
m
atio
n
ab
o
u
t
t
h
e
id
en
ti
f
i
ca
tio
n
o
f
co
r
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ec
t
g
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a
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ar
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n
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t
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x
is
t.
T
o
ad
d
r
ess
th
e
is
s
u
e
o
f
[
1
8
]
,
An
g
lu
i
n
[
1
9
]
p
r
o
p
o
s
ed
tell
tales.
A
lt
h
o
u
g
h
,
Go
ld
[
1
8
]
laid
th
e
f
o
u
n
d
atio
n
o
f
lear
n
i
n
g
m
o
d
el
,
b
u
t
B
u
n
k
e
a
n
d
A
lb
er
to
[
2
0
]
p
r
o
p
o
s
ed
t
h
e
f
ir
s
t
u
s
ab
le
lear
n
in
g
m
o
d
el
also
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f
f
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ce
it
w
a
s
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n
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le
to
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ea
l
w
it
h
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ati
v
e
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ata,
w
as
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f
it
f
o
r
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ata,
d
o
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itab
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f
o
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t
h
er
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o
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d
f
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a
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th
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T
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q
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o
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el,
al
s
o
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ef
er
r
ed
as
an
o
r
ac
le
w
a
s
p
r
o
p
o
s
ed
in
[
2
1
]
is
a
s
u
p
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v
i
s
ed
lear
n
in
g
m
o
d
el
i
n
w
h
ich
a
n
o
r
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le
k
n
o
w
s
th
e
a
n
s
w
er
.
I
t
w
as
f
o
u
n
d
ca
p
ab
le
in
an
s
w
er
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n
g
a
p
ar
ticu
lar
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y
p
e
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f
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n
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ce
s
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te
m
,
b
u
t
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m
p
le
m
e
n
ti
n
g
a
n
o
r
ac
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is
a
m
at
ter
o
f
co
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ce
r
n
,
w
h
ic
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n
ee
d
s
v
as
t
in
f
o
r
m
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,
h
en
ce
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s
s
co
m
m
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l
y
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s
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,
w
h
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s
Go
ld
‟
s
m
o
d
el
is
m
o
r
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p
o
p
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lar
.
Valian
t
[
2
2
]
co
m
b
i
n
ed
th
e
b
est
f
ea
t
u
r
es
o
f
[
1
8
]
an
d
[
2
1
]
an
d
p
r
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ted
p
r
o
b
a
b
ly
ap
p
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m
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P
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lear
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P
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f
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d
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to
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1
102
1)
P
A
C
lear
n
i
n
g
ass
u
m
es
th
a
t
t
h
e
in
f
er
en
ce
al
g
o
r
it
h
m
m
u
s
t
le
ar
n
in
p
o
l
y
n
o
m
ial
ti
m
e
u
n
d
er
all
d
is
tr
ib
u
tio
n
,
b
u
t th
i
s
b
eliev
e
s
is
to
o
s
tr
in
g
i
n
r
ea
lit
y
.
2)
P
A
C
lear
n
in
g
is
n
o
t
f
it
f
o
r
n
e
g
ati
v
e
an
d
NP
h
ar
d
eq
u
i
v
alen
ce
r
esu
lts
.
A
m
o
d
i
f
ied
v
er
s
io
n
o
f
P
A
C
m
o
d
el
w
a
s
p
r
esen
t i
n
[
2
3
]
in
w
h
ic
h
s
i
m
p
licit
y
w
as
m
ea
s
u
r
ed
u
s
i
n
g
Ko
l
m
o
g
o
r
o
v
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m
p
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x
it
y
.
I
n
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in
f
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p
r
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s
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ak
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tio
n
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r
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m
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t.
W
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ar
d
[
2
4
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s
h
o
w
ed
th
e
i
m
p
ac
t
o
f
d
if
f
er
en
t
g
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a
m
m
a
r
r
ep
r
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tatio
n
.
T
h
e
ex
p
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im
en
tal
r
esu
l
ts
p
r
esen
ted
t
h
a
t
th
e
ev
o
l
u
tio
n
ar
y
alg
o
r
ith
m
(
E
A
)
u
s
i
n
g
s
ta
n
d
ar
d
co
n
te
x
t
f
r
ee
g
r
a
m
m
ar
(
C
FG)
(
B
ac
k
u
s
Nau
r
Fo
r
m
(
B
NF)
)
o
u
tp
er
f
o
r
m
ed
o
t
h
er
s
[
2
4
]
.
T
h
an
ar
u
k
an
d
Ok
u
m
ar
u
[
2
5
]
class
if
ied
GI
in
to
th
r
ee
ca
teg
o
r
ies:
s
u
p
er
v
i
s
ed
,
s
em
i
-
s
u
p
er
v
i
s
ed
an
d
u
n
s
u
p
er
v
is
ed
.
J
av
ed
et.
al
[
2
6
]
p
r
o
p
o
s
ed
a
g
en
etic
p
r
o
g
r
am
m
in
g
(
GP
)
b
ased
ap
p
r
o
ac
h
to
lear
n
th
e
C
FG.
T
h
e
w
o
r
k
p
r
esen
ted
in
[
2
6
]
w
a
s
th
e
ex
te
n
s
io
n
o
f
th
e
w
o
r
k
d
o
n
e
i
n
[
2
4
]
.
A
s
eq
u
e
n
tial
s
tr
u
ct
u
r
in
g
ap
p
r
o
ac
h
w
a
s
p
r
o
p
o
s
ed
in
[
2
8
]
th
at
p
e
r
f
o
r
m
co
d
in
g
an
d
d
ec
o
d
in
g
o
f
b
in
ar
y
co
d
ed
ch
r
o
m
o
s
o
m
es
in
to
ter
m
in
al
s
an
d
n
o
n
-
ter
m
in
al
s
a
n
d
v
ice
-
v
er
s
a.
A
G
A
b
ased
C
F
G
i
n
d
u
ctio
n
l
i
b
r
ar
y
w
a
s
p
r
o
p
o
s
ed
in
[
2
8
,
2
9
]
.
A
ca
s
e
s
t
u
d
y
o
n
GI
w
a
s
p
r
o
p
o
s
ed
in
[
2
7
]
in
cl
u
d
es
t
h
e
b
asic
s
o
f
G
A
in
w
h
i
ch
s
i
m
p
le
cr
o
s
s
o
v
er
(
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n
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1
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3.
2
.
F
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e
lar
g
el
y
d
ep
en
d
s
u
p
o
n
t
h
e
ac
ce
p
tan
c
e
(
r
ej
ec
tio
n
)
o
f
th
e
p
o
s
itiv
e
an
d
n
eg
at
iv
e
s
a
m
p
le
s
tr
i
n
g
s
.
T
h
e
f
itn
es
s
v
al
u
e
in
cr
ea
s
e
f
o
r
ac
ce
p
tin
g
p
o
s
iti
v
e
(
A
P
)
an
d
r
ej
ec
tin
g
n
eg
at
iv
e
(
R
N)
s
a
m
p
le,
w
h
er
ea
s
it
d
ec
r
ea
s
es
f
o
r
ac
ce
p
tin
g
n
e
g
ati
v
e
(
A
N)
a
n
d
r
ej
ec
tin
g
p
o
s
iti
v
e
(
R
P
)
s
am
p
le.
T
h
e
p
r
o
b
lem
s
p
e
cif
ic
f
ac
to
r
(
s
)
also
p
lay
s
a
s
ig
n
i
f
ican
t
r
o
le
in
G
A
‟
s
p
er
f
o
r
m
a
n
ce
.
I
n
ca
s
e
o
f
GI
,
p
r
o
d
u
ctio
n
r
u
le
len
g
t
h
(
P
R
)
is
an
i
m
p
o
r
tan
t f
ac
to
r
,
h
a
s
b
ee
n
co
n
s
id
er
ed
in
th
e
f
it
n
es
s
ca
lc
u
latio
n
.
E
q
u
atio
n
(
1
)
h
as b
ee
n
ap
p
lied
to
ca
lcu
late
t
h
e
f
i
tn
e
s
s
o
f
a
n
in
d
i
v
id
u
a
l.
*
(
(
)
(
)
)
(
2
*
)
F
i
t
n
e
s
s
C
A
P
R
N
A
N
R
P
C
P
R
(
1
)
T
h
e
f
o
llo
w
i
n
g
co
n
v
e
n
tio
n
h
as
b
ee
n
f
o
llo
w
ed
f
o
r
th
e
s
elec
tio
n
o
f
t
h
e
b
est
g
r
a
m
m
ar
r
u
les:
“A
g
r
a
m
m
ar
t
h
at
ac
ce
p
t
s
all
t
h
e
p
o
s
iti
v
e
s
tr
i
n
g
s
a
n
d
r
ej
ec
ts
th
e
e
n
tire
n
eg
ati
v
e
s
tr
in
g
f
r
o
m
s
et
o
f
tr
ain
i
n
g
d
at
a
w
it
h
m
in
i
m
u
m
n
u
m
b
er
o
f
p
r
o
d
u
ctio
n
r
u
le
s
”
.
T
h
e
v
a
lu
e
o
f
co
n
s
ta
n
t
(
C
=
1
0
)
is
f
o
u
n
d
s
u
f
f
icie
n
t
to
ac
co
m
m
o
d
ate
g
r
a
m
m
ar
r
u
les
b
lo
ck
s
p
r
esen
t i
n
th
e
s
y
m
b
o
lic
ch
r
o
m
o
s
o
m
e.
3.
3
.
Repro
du
ct
io
n O
pera
t
o
r
s
T
h
e
GA‟
s
p
er
f
o
r
m
a
n
ce
lar
g
e
l
y
d
ep
en
d
s
o
n
t
h
e
t
w
o
m
o
s
t
co
m
m
o
n
l
y
u
s
ed
g
en
etic
o
p
e
r
ato
r
s
ar
e
cr
o
s
s
o
v
er
an
d
m
u
tatio
n
.
T
h
e
o
p
er
ato
r
s
‟
cr
o
s
s
o
v
er
an
d
m
u
tatio
n
p
la
y
a
s
i
g
n
i
f
ican
t
r
o
l
e
in
th
e
p
o
p
u
lat
io
n
d
iv
er
s
it
y
m
a
n
a
g
e
m
e
n
t a
n
d
th
e
r
ef
o
r
e
i
m
p
r
o
v
es t
h
e
co
n
v
er
g
en
ce
s
p
ee
d
.
A
v
ar
iatio
n
o
f
t
w
o
p
o
in
t
cr
o
s
s
o
v
er
b
ased
o
n
th
e
c
y
clic
cr
o
s
s
o
v
er
h
as
b
ee
n
i
n
co
r
p
o
r
ated
to
p
er
f
o
r
m
th
e
cr
o
s
s
o
v
er
o
p
er
atio
n
.
T
h
e
in
v
er
ted
m
u
ta
tio
n
m
et
h
o
d
h
as
b
ee
n
ap
p
lied
w
it
h
r
an
d
o
m
m
a
s
k
.
A
s
w
e
k
n
o
w
th
e
m
u
tatio
n
o
p
er
ato
r
in
tr
o
d
u
ce
s
d
iv
er
s
it
y
i
n
th
e
p
o
p
u
latio
n
h
e
l
p
s
to
k
ee
p
t
h
e
s
ea
r
c
h
p
r
o
ce
s
s
aliv
e.
R
a
n
d
o
m
m
as
k
is
u
s
e
f
u
l
in
ac
h
iev
i
n
g
th
e
d
iv
er
s
it
y
.
T
h
e
f
o
llo
w
i
n
g
co
n
v
e
n
tio
n
h
as
b
ee
n
ap
p
lied
:
“
s
i
m
p
ly
ap
p
l
y
“
XO
R
”
o
p
er
atio
n
b
et
w
ee
n
t
h
e
p
ar
e
n
t
s
tr
in
g
s
r
ec
eiv
ed
a
f
ter
cr
o
s
s
o
v
er
o
p
er
a
tio
n
a
n
d
t
h
e
r
an
d
o
m
o
f
f
s
p
r
in
g
”.
An
ex
a
m
p
le
f
o
r
b
o
th
cr
o
s
s
o
v
er
an
d
m
u
ta
tio
n
o
p
er
atio
n
s
h
av
e
b
ee
n
r
ep
r
esen
ted
in
Fi
g
u
r
e
3
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
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8938
IJ
-
AI
Vo
l.
6
,
No
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3
,
Sep
tem
b
er
2
0
1
7
:
10
0
–
11
1
104
.
P1
1
1
0
1
0
0
1
1
P
11
P
12
P
13
P2
0
0
1
0
1
1
1
0
P
21
P
22
P
23
OS1
1
0
1
0
1
1
1
1
P
22
P
13
P
11
OS2
0
1
0
1
1
0
0
0
P
12
P
23
P
21
(
a)
OS1
1
0
1
0
1
1
1
1
RM
1
0
1
0
1
0
1
0
OS1
=
OS1
XO
R
R
M
OS1
0
0
0
0
0
1
0
1
(
b
)
Fig
u
r
e
3
.
D
e
m
o
n
s
tr
atio
n
s
o
f
c
r
o
s
s
o
v
er
an
d
m
u
tatio
n
o
p
er
atio
n
s
.
(
a)
R
ep
r
esen
ti
n
g
th
e
t
w
o
p
o
in
t c
u
t c
r
o
s
s
o
v
er
b
ased
o
n
cy
c
lic
cr
o
s
s
o
v
er
.
(
b
)
I
n
v
er
ted
m
u
tatio
n
b
y
g
e
n
er
ati
n
g
r
a
n
d
o
m
m
a
s
k
(
R
M)
an
d
th
en
ap
p
l
y
in
g
XO
R
o
p
er
atio
n
.
3.
3
.
Ver
if
ica
t
io
n o
f
Rules
us
ing
P
DA
Si
m
u
la
t
o
r
T
h
is
s
ec
tio
n
e
x
p
lain
s
t
h
e
wo
r
k
in
g
o
f
p
u
s
h
d
o
w
n
a
u
to
m
a
ta
in
co
r
p
o
r
ated
d
u
r
in
g
C
FG
in
d
u
ctio
n
.
T
h
e
P
DA
s
i
m
u
lato
r
u
tili
ze
s
v
ar
io
u
s
m
et
h
o
d
s
f
o
r
th
e
v
er
i
f
i
ca
tio
n
p
u
r
p
o
s
e.
T
h
e
d
escr
ip
tio
n
o
f
ea
ch
m
et
h
o
d
u
s
ed
in
t
h
e
i
m
p
le
m
en
tat
io
n
o
f
P
DA
s
i
m
u
lato
r
is
o
u
tli
n
ed
b
e
lo
w
:
P
DA
_
S
imu
la
to
r
(
in
p
u
t_
S
tr
in
g
,
S
ta
ck
)
:
I
t
ac
ce
p
ts
in
p
u
t
s
tr
i
n
g
a
n
d
s
tac
k
a
s
an
i
n
p
u
t.
T
h
e
p
u
r
p
o
s
e
o
f
t
h
i
s
p
r
o
ce
d
u
r
e
is
to
s
i
m
u
late
t
h
e
o
v
er
all
w
o
r
k
in
g
.
I
t
u
s
es
to
p
o
f
s
tack
(
T
OS)
f
o
r
th
e
s
i
m
u
latio
n
p
u
r
p
o
s
e.
I
f
T
OS
=
i
n
p
u
t
s
y
m
b
o
l
=
$
,
i
n
d
icate
th
at
t
h
e
i
n
p
u
t
s
tr
i
n
g
i
s
a
cc
ep
ted
f
o
r
th
e
g
r
a
m
m
ar
.
I
f
T
OS
=
T
er
m
i
n
al
a
n
d
th
e
f
ir
s
t
s
y
m
b
o
l
m
atc
h
es
w
i
th
th
e
s
y
m
b
o
l
p
r
ese
n
t
at
T
OS,
th
en
b
o
th
th
e
s
y
m
b
o
ls
ar
e
r
e
m
o
v
ed
.
I
f
T
OS
=
n
o
n
-
ter
m
i
n
al
(
X)
,
t
h
e
n
i
n
s
u
c
h
s
it
u
atio
n
,
all
t
h
e
p
r
o
d
u
ctio
n
o
f
„
X
‟
r
ep
lace
t
h
e
T
OS
w
i
th
t
h
e
r
ig
h
t
s
id
e
o
f
t
h
e
p
r
o
d
u
ctio
n
r
u
le
an
d
ca
ll
t
h
e
P
DA
_
S
imu
la
to
r
(
)
r
ec
u
r
s
iv
el
y
.
I
n
ca
s
e
o
f
n
o
n
-
ac
ce
p
tan
ce
,
t
h
e
s
elec
ted
p
r
o
d
u
ctio
n
r
u
les r
ep
ea
t th
e
p
r
o
ce
s
s
f
o
r
an
o
th
er
p
r
o
d
u
ctio
n
th
at
s
tar
t
s
w
it
h
„
X
‟
.
g
et_
in
p
u
t (
T_
in
p
u
t
_
S
tr
in
g
)
:
I
t
s
i
m
p
l
y
r
etu
r
n
s
t
h
e
n
e
x
t te
r
m
i
n
al
p
r
esen
t in
t
h
e
i
n
p
u
t s
tr
in
g
.
g
et_
To
p
_
S
(
T_
S
ta
ck
)
:
R
etu
r
n
s
T
OS sy
m
b
o
l p
r
esen
t i
n
th
e
s
t
ac
k
.
r
emo
ve
_
fir
s
t_
in
p
u
t (
)
:
I
t is u
s
e
d
to
r
em
o
v
e
t
h
e
f
ir
s
t s
y
m
b
o
l o
f
th
e
i
n
p
u
t stri
n
g
.
r
emo
ve
_
TOP_
S
ta
ck
(
)
:
I
t is u
s
ed
to
r
em
o
v
e
T
OS ite
m
f
r
o
m
t
h
e
s
tac
k
.
co
p
y_
r
ig
h
t
(
T_
S
ta
ck
,
X
)
:
I
t
ac
ce
p
t
s
tack
an
d
p
r
o
d
u
ctio
n
r
u
les
as
an
in
p
u
t.
I
t
is
u
s
ed
to
r
ep
lace
th
e
T
OS
w
it
h
r
ig
h
t
s
id
e
o
f
th
e
p
r
o
d
u
ctio
n
r
u
l
e.
ve
r
ify_
s
tr
in
g
(
S
tr
in
g
s
tr
)
:
T
h
is
p
r
o
ce
d
u
r
e
is
ex
ec
u
ted
to
tak
e
th
e
d
ec
is
io
n
ab
o
u
t
th
e
ac
ce
p
tan
ce
o
r
r
e
j
ec
tio
n
o
f
th
e
in
p
u
t stri
n
g
“str”
T
h
e
p
r
o
ce
d
u
r
e
P
DA
_
S
imu
la
t
o
r
(
in
p
u
t_
S
tr
in
g
,
S
ta
ck
)
an
d
its
as
s
o
ciate
d
f
u
n
ctio
n
s
d
e
f
i
n
itio
n
s
ar
e
g
iv
e
n
b
elo
w
:
P
r
o
ce
d
ur
e:
P
DA
_
Sim
ula
to
r
(
inp
ut_
Str
i
ng
,
Sta
ck
)
B
eg
in
Set T
_
in
p
u
t_
Strin
g
=
i
n
p
u
t_
S
tr
in
g
Set T
_
Stack
=
Stack
Set X
=
g
et_
in
p
u
t(
)
Set S
=
g
et_
T
o
p
_
S(
)
I
f
s
tack
o
v
er
f
lo
w
(
)
th
e
n
r
etu
r
n
(
2
)
E
n
d
I
f
I
f
(
E
n
d
_
o
f
_
Strin
g
&
&
E
n
d
_
o
f
_
Stac
k
)
th
e
n
r
etu
r
n
(
1
)
E
n
d
I
f
I
f
(
S =
=
T
er
m
in
a
l &
&
X
=
=
S)
p
er
f
o
r
m
r
e
m
o
v
e_
f
ir
s
t_
in
p
u
t (
)
p
er
f
o
r
m
r
e
m
o
v
e_
T
OP
_
Stack
(
)
E
n
d
I
f
I
f
(
S =
=
n
o
n
-
ter
m
in
al)
t
h
en
Fo
r
all
p
r
o
d
u
ctio
n
r
u
les i
n
P
s
tar
tin
g
w
it
h
S
I
f
p
r
o
d
u
ctio
n
r
u
le
is
N
u
ll t
h
en
p
er
f
o
r
m
r
e
m
o
v
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a
s
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th
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g
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DA
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m
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lato
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ted
i
n
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ab
le
1
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2
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an
d
3
ar
e
f
o
r
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es
t
g
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m
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cc
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to
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r
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t
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r
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„
$
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n
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icate
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d
b
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tto
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t
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s
tac
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r
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ec
tiv
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y
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au
th
o
r
h
as
s
h
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n
b
est
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er
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L
1
t
h
r
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g
h
L
4
,
i
n
d
icate
s
t
h
at
th
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p
r
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ed
GI
GA
d
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lier
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h
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er
ted
m
u
tatio
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er
ato
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d
o
m
m
as
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XOR o
p
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f
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t d
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t
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s
o
n
;
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h
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au
t
h
o
r
h
as
co
m
p
ar
ed
th
e
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o
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ith
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w
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t
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g
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A
p
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av
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at
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g
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ce
.
4
.
4
.
St
a
t
is
t
ica
l A
na
ly
s
is
A
s
tati
s
tical
te
s
t
h
as
b
ee
n
p
er
f
o
r
m
ed
co
n
s
id
er
in
g
t
h
e
h
y
p
o
t
h
esi
s
:
“
th
ere
is
n
o
s
ig
n
ifica
n
t
d
iffer
en
ce
in
th
e
mea
n
o
f
s
a
mp
les
a
t
t
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e
5
%
leve
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o
f
co
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”.
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tal
1
5
s
a
m
p
les
h
a
v
e
b
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n
d
r
a
w
n
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r
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m
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h
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o
r
ith
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f
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r
th
e
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d
o
m
l
y
s
e
lecte
d
lan
g
u
a
g
e.
T
h
e
d
escr
ip
ti
v
e
an
a
l
y
s
is
is
d
ep
icted
in
T
ab
le
7
r
ep
r
esen
ts
t
h
e
m
i
n
i
m
u
m
,
m
a
x
i
m
u
m
a
n
d
av
e
r
ag
e
f
it
n
es
s
.
T
h
e
m
ai
n
A
NO
VA
r
es
u
lt
is
r
ep
r
esen
ted
in
T
ab
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6
.
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h
e
p
-
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0
.
0
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ll
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y
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o
th
e
s
is
.
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h
er
ef
o
r
e,
m
u
ltip
le
co
m
p
ar
is
o
n
te
s
ts
:
T
u
k
e
y
HS
D
test
h
a
s
b
ee
n
ad
ap
ted
.
T
h
e
r
esu
lt
s
o
f
T
u
k
e
y
HS
D
test
is
d
ep
icted
i
n
T
ab
le
8
in
d
icate
s
t
h
at
t
h
e
p
er
f
o
r
m
a
n
ce
o
f
t
h
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is
s
i
g
n
i
f
ica
n
tl
y
b
etter
t
h
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C
G
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a
n
d
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s
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n
ce
th
e
p
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e
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d
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0
5
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s
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r
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0
5
,
w
h
er
ea
s
th
e
p
r
o
p
o
s
ed
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GA
w
i
th
P
D
A
s
i
m
u
lato
r
p
er
f
o
r
m
b
etter
th
a
n
t
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e
cr
o
w
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in
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h
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.
Fig
u
r
e
4
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r
ap
h
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l
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d
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th
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ated
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t.
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A
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