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[
2
1
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28
1
.
4
.
G
lo
ba
l O
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iza
t
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Ma
th
e
m
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l
o
p
ti
m
iza
tio
n
is
m
i
n
i
m
izatio
n
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m
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x
i
m
izatio
n
o
f
a
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l
v
alu
ed
f
u
n
ctio
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b
y
s
elec
ti
n
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th
e
b
est
s
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f
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m
a
n
a
v
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ilab
le
s
et
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f
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s
o
lu
tio
n
s
[
3
2
]
.
I
n
th
e
ca
s
e
o
f
m
i
n
i
m
i
zin
g
a
r
ea
l
v
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ed
f
u
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ca
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co
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th
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m
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e
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m
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m
ize
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th
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f
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p
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f
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as f
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:
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m
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f
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co
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w
h
ich
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s
also
th
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g
lo
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i
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.
Hig
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ith
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v
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s
[
3
2
]
.
No
n
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co
n
v
ex
f
u
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s
o
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th
e
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th
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ta
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I
n
m
a
n
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in
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ta
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ce
s
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ti
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g
o
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m
s
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s
t
u
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k
in
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m
w
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u
t
co
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v
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i
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l
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n
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m
u
m
.
T
h
u
s
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n
l
y
g
o
o
d
lo
ca
l
m
in
i
m
u
m
ca
n
b
e
co
m
p
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ted
i
n
g
e
n
er
al.
Ho
w
e
v
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a
m
aj
o
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it
y
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f
i
m
p
o
r
tan
t
p
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s
in
e
n
g
in
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r
i
n
g
l
ik
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f
ilter
d
esi
g
n
in
v
o
l
v
e
n
o
n
-
co
n
v
ex
g
lo
b
al
o
p
tim
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n
.
He
n
ce
d
e
v
elo
p
m
en
t
o
f
h
e
u
r
is
tic
r
a
n
d
o
m
s
ea
r
ch
alg
o
r
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h
m
s
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n
s
p
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ed
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b
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o
lo
g
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li
k
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P
SO
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n
d
GA
w
h
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n
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m
p
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te
n
ea
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p
ti
m
al
s
o
l
u
tio
n
s
ar
e
o
f
in
ter
e
s
t
[
2
0
]
T
h
e
r
est
o
f
th
e
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
w
s
.
Sect
io
n
2
p
r
esen
ts
th
e
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v
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t
io
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o
f
t
h
e
tr
ain
in
g
alg
o
r
ith
m
s
a
n
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co
m
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ar
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t
h
e
v
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s
o
p
ti
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o
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it
h
m
s
u
s
ed
i
n
tr
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n
g
f
ee
d
f
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r
w
a
r
d
n
eu
r
al
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et
w
o
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k
s
.
Sectio
n
3
r
e
v
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w
s
th
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alg
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r
it
h
m
s
u
s
ed
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n
tr
ai
n
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n
g
r
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t
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et
w
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k
s
.
C
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cl
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s
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n
is
p
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n
ted
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ec
tio
n
5
.
2.
RE
VI
E
W
O
F
O
P
T
I
M
I
Z
A
T
I
O
N
AL
G
O
R
I
T
H
M
S USE
D
F
O
R
T
RAIN
I
N
G
F
E
E
DF
O
RWARD
NE
URA
L
N
E
T
WO
RK
S
T
r
ain
in
g
A
NN
s
u
s
in
g
b
ac
k
p
r
o
p
ag
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n
alg
o
r
it
h
m
h
ad
li
m
i
t
atio
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s
i
n
ter
m
s
o
f
o
v
er
f
it
tin
g
,
in
cr
ea
s
e
i
n
lear
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in
g
ti
m
e
w
ith
t
h
e
s
i
ze
o
f
th
e
tr
ain
in
g
d
ata,
an
d
m
o
s
t
i
m
p
o
r
tan
tl
y
t
h
e
r
is
k
o
f
g
etti
n
g
s
t
u
c
k
in
t
h
e
f
lat
r
eg
io
n
s
o
f
th
e
s
ea
r
ch
s
p
ac
e
th
er
eb
y
co
n
v
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g
in
g
to
a
lo
ca
l
m
in
i
m
u
m
a
n
d
n
o
t
f
i
n
d
in
g
th
e
g
l
o
b
al
m
i
n
i
m
u
m
[
1
]
.
T
h
er
ef
o
r
e,
b
io
l
o
g
icall
y
i
n
s
p
ir
ed
o
p
tim
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n
alg
o
r
it
h
m
s
li
k
e
Gen
et
ic
A
lg
o
r
it
h
m
(
G
A
)
an
d
P
ar
ticle
S
w
ar
m
Op
ti
m
izatio
n
(
P
SO)
w
er
e
u
s
e
d
to
tr
ain
A
NN
s
.
GA
is
i
n
s
p
ir
ed
b
y
n
at
u
r
al
e
v
o
lu
tio
n
a
n
d
ad
o
p
ts
th
e
p
r
in
cip
l
es
o
f
s
elec
tio
n
,
cr
o
s
s
o
v
er
an
d
m
u
tatio
n
[
2
4
]
.
I
t
is
s
to
ch
asti
c
an
d
d
er
iv
ati
v
e
f
r
ee
an
d
th
er
ef
o
r
e
ca
n
b
e
ap
p
lied
to
b
o
th
co
n
tin
u
o
u
s
an
d
d
is
cr
ete
o
p
tim
izatio
n
p
r
o
b
lem
s
.
I
n
[
2
]
[
2
3
]
th
e
a
u
th
o
r
s
h
a
v
e
u
s
ed
G
A
w
it
h
cr
o
s
s
o
v
er
to
ca
lc
u
late
th
e
w
ei
g
h
t
s
o
f
t
h
e
f
ee
d
f
o
r
w
ar
d
n
e
u
r
al
n
e
t
w
o
r
k
(
FNN)
.
He
h
a
s
d
e
m
o
n
s
tr
at
ed
in
h
is
w
o
r
k
[
3
]
th
at
G
A
o
u
tp
er
f
o
r
m
s
b
ac
k
p
r
o
p
ag
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n
alg
o
r
ith
m
.
T
r
ain
in
g
n
eu
r
al
n
et
w
o
r
k
s
w
ith
d
is
tr
ib
u
ted
GA
r
ei
n
f
o
r
ce
d
b
y
p
er
ce
p
tr
o
n
lear
n
in
g
r
u
le
w
a
s
p
r
o
p
o
s
ed
an
d
ap
p
lied
b
y
Olik
er
et
al
in
[
4
]
.
A
v
er
s
io
n
o
f
G
A
k
n
o
w
n
as
s
o
f
t
al
g
o
r
ith
m
i
s
co
m
b
in
ed
w
it
h
b
ac
k
p
r
o
p
o
g
atio
n
an
d
s
o
f
t
-
b
p
i
s
ap
p
lied
to
tr
ain
ANNs
i
n
[
1
9
]
b
y
A
d
a
w
y
e
t.a
l.
T
h
is
alg
o
r
i
th
m
o
b
tain
s
a
g
o
o
d
w
ei
g
h
t
v
ec
to
r
th
er
eb
y
r
ed
u
ci
n
g
t
h
e
er
r
o
r
o
f
t
h
e
o
u
tp
u
t.
T
h
e
p
ar
allel
v
er
s
io
n
o
f
G
A
h
as
b
e
en
u
s
ed
i
n
[
2
2
]
f
o
r
ti
m
e
s
er
ie
s
p
r
ed
ictio
n
.
P
SO
is
i
n
s
p
ir
ed
b
y
t
h
e
s
w
ar
m
b
eh
a
v
io
u
r
o
f
f
lo
ck
o
f
b
ir
d
s
o
r
s
ch
o
o
l
o
f
f
i
s
h
e
s
.
I
t
w
a
s
p
r
o
p
o
s
ed
b
y
Ken
n
ed
y
an
d
E
b
er
h
ar
t
in
[
5
]
an
d
h
as
b
ee
n
u
s
ed
f
o
r
tr
ain
in
g
n
e
u
r
al
n
e
t
w
o
r
k
s
b
y
G
u
d
is
e
an
d
Ven
a
y
a
g
a
m
o
o
r
th
y
i
n
[
6
]
.
T
h
e
p
er
f
o
r
m
an
ce
o
f
t
h
e
P
SO
al
g
o
r
ith
m
i
s
co
m
p
ar
ed
w
it
h
t
h
e
b
ac
k
p
r
o
p
o
g
atio
n
alg
o
r
ith
m
b
y
tr
ain
i
n
g
t
h
e
n
e
u
r
al
n
et
w
o
r
k
to
lear
n
a
n
o
n
li
n
ea
r
f
u
n
ctio
n
.
I
t
w
as
f
o
u
n
d
t
h
e
P
SO
w
as
f
a
s
ter
b
et
w
ee
n
th
e
t
w
o
alg
o
r
ith
m
s
t
o
lear
n
th
e
n
o
n
li
n
ea
r
f
u
n
ctio
n
as
it
r
eq
u
ir
ed
less
n
u
m
b
er
o
f
co
m
p
u
tatio
n
s
th
a
n
B
P
to
attain
th
e
s
a
m
e
er
r
o
r
g
o
al
[
6
]
.
P
SO a
lg
o
r
ith
m
its
el
f
h
a
s
ce
r
tain
li
m
it
s
in
ter
m
s
o
f
co
n
v
er
g
e
n
ce
,
p
r
ec
is
io
n
an
d
p
ar
am
e
ter
s
elec
tio
n
.
I
t
w
a
s
s
lo
w
er
d
u
r
in
g
t
h
e
f
i
n
al
s
tag
e
s
o
f
ev
o
l
u
tio
n
a
n
d
h
ad
lo
w
er
p
r
ec
is
io
n
.
T
h
er
ef
o
r
e,
C
h
en
e
t
al
i
n
[
3
1
]
p
r
o
p
o
s
ed
an
alg
o
r
ith
m
c
alled
A
r
ti
f
ic
ial
Fi
s
h
S
w
ar
m
A
l
g
o
r
ith
m
(
A
F
S
A
)
-
P
SO
p
ar
allel
h
y
b
r
id
ev
o
lu
tio
n
ar
y
a
lg
o
r
it
h
m
(
A
P
PHE)
f
o
r
tr
ain
i
n
g
F
NNs.
T
h
is
a
lg
o
r
ith
m
d
i
v
id
es
t
h
e
P
SO
p
o
p
u
latio
n
i
n
to
t
w
o
s
u
b
p
o
p
u
latio
n
s
.
P
SO
i
s
e
x
ec
u
ted
in
o
n
e
s
u
b
p
o
p
u
latio
n
an
d
AF
S
A
i
n
t
h
e
o
t
h
er
i
n
p
ar
allel.
T
h
e
b
est
s
o
lu
tio
n
o
f
b
o
th
th
e
s
u
b
p
o
p
u
latio
n
is
g
i
v
en
b
ac
k
to
t
h
e
s
w
ar
m
an
d
P
S
O
is
n
o
w
e
x
ec
u
ted
i
n
b
o
th
s
u
b
p
o
p
u
latio
n
s
.
T
h
e
al
g
o
r
ith
m
ter
m
i
n
ates
w
h
e
n
a
ter
m
i
n
atio
n
cr
iter
io
n
is
s
ati
s
f
ied
.
T
h
e
au
th
o
r
s
test
ed
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
-
AI
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N:
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A
r
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r
is
tic
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a
l o
p
timiz
a
tio
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b
a
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A
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(
D.
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in
e
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ess
ie
A
ma
li
)
29
th
e
p
er
f
o
r
m
a
n
ce
o
f
t
h
e
p
r
o
p
o
s
ed
A
P
P
HE
alg
o
r
ith
m
w
it
h
th
e
L
e
v
e
n
b
er
g
-
Ma
r
q
u
ar
d
t
B
ac
k
p
r
o
p
ag
atio
n
(
L
MB
P
)
alg
o
r
ith
m
b
y
tr
ai
n
i
n
g
th
e
n
e
u
r
al
n
et
w
o
r
k
i
n
ir
i
s
d
at
a
class
if
ica
tio
n
.
T
h
e
n
e
u
r
al
n
e
t
w
o
r
k
tr
ai
n
ed
u
s
i
n
g
th
e
A
P
P
HE
alg
o
r
ith
m
d
id
b
etter
th
a
n
L
MB
P
in
ter
m
s
o
f
f
aster
co
n
v
er
g
en
ce
to
t
h
e
g
lo
b
al
m
in
i
m
u
m
a
n
d
ac
cu
r
ac
y
o
f
t
h
e
r
es
u
lt.
H
y
b
r
id
alg
o
r
it
h
m
s
th
a
t
co
m
b
in
e
g
lo
b
al
o
p
ti
m
izatio
n
al
g
o
r
ith
m
a
n
d
lo
ca
l
s
ea
r
ch
al
g
o
r
ith
m
s
w
er
e
u
s
ed
to
tr
ain
A
NN
s
.
H
y
b
r
id
A
r
ti
f
icial
B
ee
C
o
lo
n
y
A
l
g
o
r
ith
m
t
h
at
co
m
b
i
n
es
th
e
A
r
ti
f
icial
B
ee
C
o
lo
n
y
alg
o
r
ith
m
(
A
B
C
)
an
d
th
e
L
e
v
en
b
er
g
-
Ma
r
q
u
ar
d
t
(
L
M)
is
u
s
ed
f
o
r
tr
ain
i
n
g
A
N
N
in
[
7
]
.
A
B
C
is
a
g
lo
b
al
o
p
tim
izatio
n
alg
o
r
it
h
m
an
d
f
i
n
d
s
t
h
e
g
lo
b
al
m
in
i
m
u
m
w
h
e
r
ea
s
L
M
is
u
s
ed
to
ex
p
lo
it
th
e
lo
ca
l
m
i
n
i
m
u
m
.
T
h
er
ef
o
r
e
a
h
y
b
r
id
alg
o
r
it
h
m
t
h
at
co
m
b
i
n
es
th
e
ex
p
lo
r
atio
n
ab
ilit
y
o
f
t
h
e
A
B
C
a
n
d
ex
p
lo
it
atio
n
ab
ilit
y
o
f
th
e
L
M
h
a
s
b
ee
n
p
r
o
p
o
s
ed
b
y
Oztu
r
k
i
n
[
7
]
.
T
h
e
h
y
b
r
id
alg
o
r
ith
m
p
er
f
o
r
m
s
b
etter
th
a
n
th
e
alg
o
r
ith
m
s
b
y
th
e
m
s
el
v
es.
A
m
o
d
i
f
ied
L
M
alg
o
r
ith
m
w
h
ich
ad
d
r
ess
ed
th
e
d
em
a
n
d
o
f
m
e
m
o
r
y
f
o
r
lar
g
e
j
ac
o
b
ian
s
an
d
th
e
n
ee
d
f
o
r
i
n
v
er
tin
g
t
h
e
lar
g
e
m
atr
ice
s
w
a
s
p
r
o
p
o
s
ed
b
y
W
ila
m
o
w
s
k
i
a
n
d
C
h
e
n
i
n
[
1
1
]
.
T
h
eir
p
r
o
p
o
s
ed
alg
o
r
ith
m
u
s
ed
a
n
e
w
p
er
f
o
r
m
i
n
g
in
d
e
x
w
h
ich
r
ed
u
ce
s
t
h
e
s
ize
o
f
t
h
e
m
atr
i
x
t
h
at
i
s
to
b
e
in
v
er
ted
t
h
er
eb
y
in
cr
ea
s
i
n
g
t
h
e
co
m
p
u
tatio
n
s
p
ee
d
.
Si
m
u
lated
an
n
ea
li
n
g
is
a
g
l
o
b
al
s
ea
r
ch
h
eu
r
i
s
tic
t
h
at
is
in
s
p
ir
ed
b
y
an
n
ea
li
n
g
i
n
m
etall
u
r
g
y
.
Me
tallu
r
g
y
is
a
p
h
y
s
ical
p
r
o
ce
s
s
o
f
h
ea
tin
g
m
etal
to
v
er
y
h
ig
h
te
m
p
er
at
u
r
es
a
n
d
t
h
en
co
o
lin
g
it
v
er
y
s
lo
w
l
y
.
T
h
is
h
elp
s
r
e
m
o
v
e
th
e
d
ef
ec
t
s
in
t
h
e
cr
y
s
tals
f
o
r
m
ed
.
Si
m
u
lated
an
n
ea
li
n
g
i
s
co
m
b
i
n
ed
w
ith
l
o
ca
l
g
r
ad
ie
n
t
s
ea
r
ch
alg
o
r
it
h
m
(
R
p
r
o
p
)
in
[
8
]
an
d
in
[
9
]
w
it
h
tab
u
s
e
ar
ch
to
tr
ain
A
NNs.
A
co
m
p
o
s
ite
s
q
u
ar
ed
er
r
o
r
alg
o
r
ith
m
w
as
p
r
o
p
o
s
ed
an
d
a
p
p
lied
to
tr
ain
A
N
Ns
b
y
Go
n
za
g
a
et
al.
i
n
[
1
1
]
.
I
n
t
h
is
alg
o
r
ith
m
th
e
f
ir
s
t
p
ar
t
o
f
tr
ain
i
n
g
u
s
es
t
h
e
li
n
ea
r
er
r
o
r
w
h
ile
th
e
s
ec
o
n
d
p
ar
t
u
s
es
th
e
n
o
n
li
n
ea
r
.
B
y
d
o
in
g
s
o
t
h
e
alg
o
r
ith
m
escap
es
th
e
s
u
b
o
p
ti
m
al
s
o
l
u
tio
n
s
an
d
c
o
n
v
er
g
e
s
to
th
e
o
p
ti
m
a
l so
lu
ti
o
n
f
as
ter
th
a
n
th
e
b
ac
k
p
r
o
p
o
g
atio
n
alg
o
r
it
h
m
.
A
n
o
v
el
a
n
t
al
g
o
r
ith
m
p
r
o
p
o
s
ed
Do
r
ig
o
in
[
2
8
]
is
u
s
ed
b
y
L
i
a
n
d
L
i
u
i
n
[
2
7
]
an
d
ap
p
lie
d
to
tr
ain
f
ee
d
f
o
r
w
ar
d
n
eu
r
al
n
et
f
o
r
ca
ll
ad
m
is
s
io
n
co
n
tr
o
l.
An
t
co
l
o
n
y
o
p
ti
m
izatio
n
(
AC
O)
is
a
g
lo
b
al
o
p
ti
m
izatio
n
alg
o
r
ith
m
t
h
at
is
i
n
s
p
ir
ed
b
y
t
h
e
s
w
ar
m
b
eh
a
v
io
u
r
o
f
a
n
ts
f
o
llo
w
i
n
g
a
p
at
h
s
ee
k
in
g
f
o
o
d
f
r
o
m
t
h
eir
co
lo
n
ies
[
2
8
]
.
T
h
e
an
ts
h
av
e
to
p
er
f
o
r
m
t
w
o
tas
k
s
.
Fir
s
t
t
h
e
y
h
a
v
e
to
s
elec
t
th
e
p
ath
w
h
ic
h
t
h
e
y
w
a
n
t
to
f
o
llo
w
a
n
d
s
ec
o
n
d
l
y
ad
j
u
s
t
th
e
ir
p
h
er
o
m
o
n
e
lev
el
alo
n
g
t
h
e
ch
o
s
e
n
p
ath
.
A
v
er
s
io
n
o
f
t
h
e
af
o
r
e
m
e
n
t
io
n
ed
AC
O
is
u
s
ed
f
o
r
tr
ain
i
n
g
a
n
eu
r
al
n
et
in
[
2
7
]
.
T
h
is
A
C
O
tr
ain
ed
n
e
u
r
al
n
et
w
o
r
k
p
er
f
o
r
m
ed
w
ell
w
h
en
co
m
p
ar
ed
to
B
P
h
o
w
ev
er
it
s
p
er
f
o
r
m
a
n
ce
d
eg
r
ad
es
w
it
h
t
h
e
i
n
cr
ea
s
e
i
n
t
h
e
n
u
m
b
er
o
f
i
n
p
u
ts
d
u
e
to
t
h
e
co
m
m
u
n
icatio
n
o
v
er
h
ea
d
.
Qu
a
n
tu
m
C
o
m
p
u
tin
g
w
it
h
o
p
ti
m
izat
io
n
al
g
o
r
ith
m
s
s
tar
ted
to
ev
o
lv
e.
Qu
a
n
t
u
m
in
s
p
ir
ed
GA
[
1
3
]
a
q
u
an
t
u
m
i
n
s
p
i
r
ed
p
ar
allel
GA
w
a
s
p
r
o
p
o
s
ed
in
[
1
4
]
.
A
Qu
a
n
tu
m
Sh
u
f
f
led
Fro
g
L
ea
p
in
g
A
l
g
o
r
ith
m
(
QSF
L
A
)
w
a
s
p
r
o
p
o
s
ed
an
d
u
s
ed
f
o
r
t
r
ain
in
g
ANNs
b
y
L
i
u
a
n
d
Z
h
an
g
i
n
[
1
5
]
.
T
h
is
alg
o
r
it
h
m
ef
f
icie
n
tl
y
s
o
l
v
ed
co
n
tin
u
o
u
s
o
p
ti
m
iza
tio
n
p
r
o
b
le
m
i
n
h
ig
h
d
i
m
en
s
io
n
al
s
p
ac
e
an
d
d
id
b
e
tter
th
an
t
h
e
B
P
alg
o
r
ith
m
i
n
ter
m
s
o
f
co
n
v
er
g
e
n
ce
a
n
d
ac
cu
r
ac
y
.
3.
RE
VI
E
W
O
F
O
P
T
I
M
I
Z
A
T
I
O
N
AL
G
O
R
I
T
H
M
S USE
D
F
O
R
T
RAIN
I
N
G
RE
CURR
E
NT
ARTI
F
I
CI
AL
N
E
URA
L
NE
T
WO
RK
S
B
r
ee
d
in
g
s
w
ar
m
a
lg
o
r
it
h
m
i
s
a
h
y
b
r
id
o
f
G
A
an
d
P
SO.
T
h
is
w
a
s
p
r
o
p
o
s
ed
b
y
Ma
tth
e
w
e
t
al
in
[
1
0
]
an
d
u
s
ed
it
to
tr
ain
in
g
o
f
A
NN
s
.
T
h
eir
alg
o
r
ith
m
u
s
e
s
th
e
cla
s
s
ical
P
SO
f
o
r
m
u
la
f
o
r
u
p
d
atin
g
t
h
e
v
elo
cit
y
a
n
d
th
e
p
o
s
it
io
n
s
o
f
t
h
e
p
ar
ticles,
an
d
u
s
es
t
h
e
s
elec
t
io
n
,
m
u
tat
i
o
n
an
d
cr
o
s
s
o
v
er
p
r
i
n
cip
les
f
r
o
m
G
A
.
I
n
ad
d
itio
n
th
e
a
u
th
o
r
s
h
a
v
e
also
i
n
tr
o
d
u
c
ed
a
p
ar
am
eter
ca
lled
t
h
e
b
r
ee
d
in
g
p
ar
a
m
e
ter
,
w
h
ic
h
d
eter
m
in
es
t
h
e
p
o
p
u
latio
n
s
ize
th
a
t
s
h
o
u
ld
u
n
d
er
g
o
b
r
ee
d
in
g
.
S
in
ce
b
r
ee
d
in
g
s
w
ar
m
s
al
g
o
r
it
h
m
w
as
a
g
e
n
er
al
p
o
p
u
lat
io
n
b
ased
alg
o
r
ith
m
,
w
h
en
i
t
w
as
u
s
ed
t
o
tr
ain
r
ec
u
r
r
en
t
n
eu
r
al
n
et
w
o
r
k
s
it
w
a
s
f
o
u
n
d
t
h
at
t
h
e
al
g
o
r
ith
m
w
as
ab
le
to
s
ca
le
b
etter
.
I
n
[
1
6
]
a
h
y
b
r
id
B
ay
e
s
ian
lear
n
i
n
g
m
et
h
o
d
w
h
i
ch
co
m
b
in
e
s
Ma
r
k
o
v
c
h
ai
n
Mo
n
te
C
ar
lo
m
et
h
o
d
s
w
it
h
f
u
zz
y
m
e
m
b
er
s
h
ip
f
u
n
c
ti
o
n
s
an
d
G
A
is
u
s
ed
b
y
Ko
ca
d
ag
li
f
o
r
tr
ai
n
in
g
B
a
y
e
s
ia
n
n
e
u
r
al
n
et
w
o
r
k
s
.
T
h
e
au
th
o
r
h
a
s
ad
d
r
ess
ed
th
e
p
r
o
b
le
m
s
o
f
co
m
p
le
x
it
y
i
n
ch
o
o
s
i
n
g
t
h
e
p
ar
a
m
eter
s
o
f
t
h
e
m
o
d
el,
th
e
tr
ain
i
n
g
ti
m
e
ass
o
ciate
d
w
it
h
th
e
B
a
y
esia
n
n
eu
r
al
n
et
w
o
r
k
s
.
He
ar
g
u
es
t
h
at
t
h
e
p
r
o
p
o
s
ed
h
y
b
r
id
m
o
d
el
ca
n
o
v
er
co
m
e
th
e
p
r
o
b
lem
s
f
ac
ed
w
it
h
n
o
r
m
a
l
tr
ain
i
n
g
al
g
o
r
ith
m
s
.
A
h
y
b
r
id
m
o
d
el
th
at
co
m
b
i
n
es
th
e
g
r
ad
ien
t
d
escen
t
a
n
d
m
eta
h
eu
r
i
s
tics
i
s
p
r
o
p
o
s
ed
an
d
u
s
ed
in
[
1
7
]
.
A
n
i
m
p
r
o
v
ed
v
er
s
io
n
o
f
P
SO
w
i
th
ti
m
e
v
ar
y
in
g
p
ar
a
m
eter
a
n
d
co
n
s
tr
ictio
n
h
elp
s
i
n
i
m
p
r
o
v
i
n
g
t
h
e
s
ea
r
c
h
ab
ilit
y
a
n
d
co
n
v
er
g
e
n
ce
.
I
n
o
r
d
er
to
p
r
ev
en
t
o
v
er
f
i
tti
n
g
a
cr
o
s
s
v
alid
atio
n
m
et
h
o
d
is
also
in
c
lu
d
ed
in
th
e
al
g
o
r
ith
m
.
A
v
ar
ian
t
o
f
P
SO
ca
lled
th
e
m
o
d
i
f
ied
b
in
ar
y
P
ar
ticle
S
w
ar
m
Op
ti
m
izatio
n
(
MP
SO)
w
as
p
r
o
p
o
s
ed
b
y
E
b
er
h
ar
t
f
o
r
b
in
ar
y
p
r
o
b
lem
s
[
2
1
]
.
T
h
is
v
er
s
io
n
o
f
P
SO
w
a
s
u
s
ed
to
tr
ai
n
r
ec
u
r
r
en
t
n
eu
r
al
n
et
w
o
r
k
s
i
n
[
2
9
]
f
o
r
d
ec
o
d
in
g
o
f
1
/n
r
ate
co
n
v
u
la
tio
n
al
co
d
es.
T
h
is
ap
p
r
o
ac
h
p
r
o
v
id
ed
lo
w
late
n
c
y
a
n
d
co
n
v
er
g
ed
to
a
g
lo
b
al
m
i
n
i
m
u
m
t
h
er
eb
y
m
a
k
i
n
g
it
m
o
r
e
p
r
ac
ticab
le.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8938
IJ
-
AI
6
,
No
.
1
,
Ma
r
ch
2
0
1
7
:
26
–
32
30
4.
DIS
C
U
S
SI
O
N
A
r
ev
ie
w
o
f
t
h
e
liter
atu
r
e
s
h
o
w
s
t
h
at
o
p
ti
m
izat
io
n
alg
o
r
it
h
m
s
ap
p
r
o
x
i
m
ate
n
o
n
li
n
ea
r
f
u
n
ctio
n
s
an
d
p
r
o
v
id
e
n
ea
r
ac
c
u
r
ate
s
o
l
u
tio
n
s
.
B
io
lo
g
ica
ll
y
i
n
s
p
ir
ed
o
p
tim
izatio
n
al
g
o
r
ith
m
s
li
k
e
G
A
,
P
SO,
A
C
O,
A
B
C
,
AFS
A
ar
e
s
to
ch
ast
ic
in
n
at
u
r
e.
T
h
is
h
elp
s
th
e
s
e
alg
o
r
it
h
m
s
ex
p
lo
r
e
th
e
s
ea
r
ch
s
p
ac
e
an
d
escap
e
f
r
o
m
lo
ca
l
m
i
n
i
m
a.
B
ac
k
p
r
o
p
o
g
atio
n
h
o
w
e
v
er
u
s
es
g
r
ad
ien
t
d
esce
n
t
an
d
m
i
g
h
t
g
et
s
t
u
c
k
in
t
h
e
lo
ca
l
m
i
n
i
m
u
m
.
L
iter
at
u
r
e
s
h
o
w
s
t
h
at
v
ar
ian
t
s
o
f
t
h
e
o
p
ti
m
izat
io
n
al
g
o
r
it
h
m
s
esp
ec
iall
y
h
y
b
r
id
al
g
o
r
ith
m
s
t
h
at
co
m
b
i
n
e
g
lo
b
al
an
d
lo
ca
l
s
ea
r
ch
h
e
u
r
is
tic
p
er
f
o
r
m
b
etter
th
a
n
t
h
e
al
g
o
r
ith
m
s
b
y
t
h
e
m
s
el
v
es.
T
h
ese
h
y
b
r
id
alg
o
r
it
h
m
s
p
er
f
o
r
m
ed
b
etter
th
a
n
th
e
al
g
o
r
ith
m
s
b
y
th
e
m
s
elv
e
s
in
ter
m
s
o
f
t
h
e
lear
n
in
g
r
ate,
ac
cu
r
ac
y
an
d
co
n
v
er
g
e
n
ce
.
B
ec
au
s
e
th
e
s
e
h
y
b
r
id
alg
o
r
ith
m
s
co
m
b
i
n
e
t
h
e
ex
p
lo
r
ato
r
y
a
b
ilit
y
o
f
t
h
e
g
lo
b
al
o
p
ti
m
izati
o
n
alg
o
r
ith
m
s
an
d
th
e
e
x
p
lo
itatio
n
ab
ilit
y
o
f
t
h
e
l
o
ca
l
s
ea
r
ch
a
lg
o
r
it
h
m
s
th
e
y
p
r
o
v
id
e
b
etter
r
es
u
lts
.
L
iter
atu
r
e
also
co
n
f
ir
m
s
t
h
at
h
y
b
r
id
al
g
o
r
ith
m
s
o
u
tp
er
f
o
r
m
t
h
e
al
g
o
r
it
h
m
s
b
y
t
h
e
m
s
elv
e
s
i
n
tr
ai
n
i
n
g
r
ec
u
r
r
en
t
n
e
u
r
al
n
et
w
o
r
k
s
.
Sh
o
w
n
in
T
ab
le
1
.
T
ab
le
1
C
o
m
p
ar
is
o
n
o
f
Glo
b
al
Op
ti
m
izatio
n
A
lg
o
r
it
h
m
s
A
N
N
T
r
a
i
n
i
n
g
A
l
g
o
r
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t
h
m
S
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c
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e
sse
s
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h
a
l
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e
n
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s
G
e
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t
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c
A
l
g
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r
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t
h
m
Ex
p
l
o
r
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s l
a
r
g
e
a
n
d
c
o
mp
l
e
x
se
a
r
c
h
s
p
a
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e
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l
o
w
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r
c
o
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v
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P
a
r
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w
a
r
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p
t
i
mi
z
a
t
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o
n
F
e
w
e
r
n
u
m
b
e
r
o
f
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t
a
t
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q
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e
d
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B
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b
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H
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F
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a
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p
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man
c
e
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r
a
d
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s w
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m
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n
n
e
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l
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c
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f
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l
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s
O
v
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f
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t
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n
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en
t
y
ea
r
s
n
o
v
el
h
e
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r
is
tic
g
lo
b
al
o
p
ti
m
izatio
n
a
lg
o
r
it
h
m
s
th
at
o
u
tp
er
f
o
r
m
c
u
r
r
en
t
s
tate
o
f
th
e
ar
t
o
p
tim
izatio
n
al
g
o
r
ith
m
s
h
av
e
b
ee
n
p
r
o
p
o
s
ed
[
3
2
]
.
I
n
th
e
ap
p
r
o
ac
h
p
r
o
p
o
s
ed
in
[
3
2
]
al
ter
n
ati
n
g
c
y
c
les
o
f
ex
p
lo
r
atio
n
a
n
d
ex
p
lo
itat
io
n
ar
e
u
s
ed
to
ac
h
iev
e
a
co
m
p
r
o
m
is
e
b
et
w
ee
n
ex
p
lo
r
atio
n
o
f
n
e
w
s
o
l
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tio
n
s
a
n
d
ex
p
lo
itatio
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o
f
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x
i
s
ti
n
g
s
o
l
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tio
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d
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at
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r
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co
n
v
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ce
to
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l
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i
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m
a.
Gr
ad
ien
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ased
alg
o
r
ith
m
s
li
k
e
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ac
k
p
r
o
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ati
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a
v
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te
n
d
en
c
y
to
g
et
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tu
c
k
i
n
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ca
l
m
i
n
i
m
a
lead
in
g
to
p
o
o
r
p
er
f
o
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m
an
ce
o
f
th
e
A
NN.
T
h
u
s
ap
p
licatio
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f
n
o
v
el
h
e
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r
is
tic
g
lo
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al
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ti
m
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alg
o
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it
h
m
s
li
k
e
th
e
Gala
ctic
S
w
ar
m
Op
ti
m
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n
(
GS
O)
alg
o
r
it
h
m
[
3
2
]
to
A
NN
tr
ai
n
i
n
g
is
o
f
in
ter
es
t.
C
o
m
ap
r
is
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d
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f
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t
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tic
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o
p
tim
izatio
n
a
lg
o
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it
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m
s
s
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c
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as
[
3
2
]
an
d
[
3
3
]
o
n
b
en
ch
m
ar
k
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NN
tr
ain
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g
p
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s
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ed
f
o
r
f
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tu
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e
w
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k
.
5.
CO
NCLU
SI
O
N
T
h
is
p
ap
er
r
ev
ie
w
s
th
e
g
lo
b
al
o
p
tim
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io
n
alg
o
r
it
h
m
s
u
s
ed
f
o
r
tr
ain
in
g
f
ee
d
f
o
r
w
ar
d
an
d
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ec
u
r
r
en
t
n
eu
r
al
n
e
w
o
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k
s
.
A
N
NS
a
n
d
m
o
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t
o
f
t
h
e
g
lo
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al
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m
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alg
o
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it
h
m
s
ar
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b
io
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ica
ll
y
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n
s
p
ir
ed
an
d
t
h
e
y
b
o
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r
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w
id
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f
r
o
m
th
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o
cia
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b
eh
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io
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an
d
b
io
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g
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s
tr
u
ctu
r
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h
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T
h
er
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y
it
ca
n
b
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p
o
s
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y
s
tated
th
at
tr
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n
i
n
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e
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ets
w
i
th
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io
lo
g
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n
s
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o
p
tim
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alg
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i
th
m
s
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ill
p
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id
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a
m
o
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co
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lear
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.
A
r
ev
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w
o
f
t
h
e
li
ter
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e
p
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d
u
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o
r
ith
m
s
,
h
y
b
r
id
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g
o
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m
s
w
h
ic
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co
m
b
i
n
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t
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g
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d
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l
o
p
ti
m
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al
g
o
r
ith
m
s
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tp
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f
o
r
m
t
h
e
alg
o
r
ith
m
s
b
y
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m
s
el
v
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m
s
o
f
f
as
ter
co
n
v
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e
n
ce
a
n
d
ac
cu
r
ac
y
o
f
t
h
e
o
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tp
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t.
I
n
r
ec
en
t
y
ea
r
s
n
o
v
el
h
eu
r
i
s
tic
g
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p
ti
m
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alg
o
r
ith
m
s
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h
at
o
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tp
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f
o
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m
c
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r
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en
t
s
tate
o
f
th
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ar
t
o
p
tim
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n
alg
o
r
ith
m
s
h
av
e
b
ee
n
p
r
o
p
o
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ed
.
T
h
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alg
o
r
ith
m
s
ca
n
b
e
co
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id
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f
o
r
A
N
N
tr
ain
i
n
g
i
n
t
h
e
f
u
t
u
r
e.
RE
F
E
R
E
NC
E
S
[1
]
M
G
o
ri,
A
T
e
si.
On
th
e
p
ro
b
lem
o
f
lo
c
a
l
m
in
im
a
in
b
a
c
k
p
ro
p
a
g
a
ti
o
n
.
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Pa
tt
e
rn
An
a
lys
is
a
n
d
M
a
c
h
in
e
In
telli
g
e
n
c
e
,
1
9
9
2
;
1
4
:
7
6
-
8
6
.
[2
]
D
W
h
it
e
le
y
.
Ap
p
lyin
g
Ge
n
e
ti
c
Al
g
o
rit
h
ms
t
o
Ne
u
ra
l
Ne
two
rk
s
L
e
a
rn
in
g
.
P
ro
c
e
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d
i
n
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s
o
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7
th
C
o
n
f
e
re
n
c
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o
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S
o
c
iety
o
f
A
rti
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In
telli
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e
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n
d
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im
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latio
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o
f
Be
h
a
v
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S
u
ss
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x
,
En
g
lan
d
:
P
it
m
a
n
P
u
b
li
s
h
in
g
.
1
9
8
9
;
1
3
7
-
1
4
4
.
[3
]
D
W
h
it
e
le
y
,
T
S
tark
w
e
a
th
e
r,
C
Bo
g
a
rt.
G
e
n
e
ti
c
A
l
g
o
rit
h
m
s
a
n
d
n
e
u
ra
l
Ne
tw
o
rk
s:
Op
ti
m
izi
n
g
C
o
n
n
e
c
ti
o
n
s
a
n
d
Co
n
n
e
c
ti
v
it
y
.
Pa
ra
ll
e
l
C
o
mp
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ti
n
g
,
1
9
9
0
;
1
4
:
3
4
7
-
3
6
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
-
AI
I
SS
N:
2252
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8938
A
r
ev
iew
o
f h
eu
r
is
tic
g
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a
l o
p
timiz
a
tio
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A
r
tifi
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l N
eu
r
a
l…
(
D.
Gera
ld
in
e
B
ess
ie
A
ma
li
)
31
[4
]
Olik
e
r,
S
,
e
t
a
l.
De
sig
n
a
rc
h
i
tec
tu
re
s
a
n
d
tr
a
in
i
n
g
o
f
n
e
u
ra
l
n
e
tw
o
rk
s
wit
h
a
d
istrib
u
ted
g
e
n
e
ti
c
a
lg
o
rit
h
m.
IE
EE
In
tern
a
ti
o
n
a
l
C
o
n
f
e
re
n
c
e
o
n
Ne
u
r
a
l
Ne
tw
o
rk
s.
1
9
9
3
;
1
:
1
9
9
-
2
0
2
.
[5
]
Ja
m
e
s
Ke
n
n
e
d
y
,
R
Eb
e
rh
a
rt.
Pa
rticle
swa
rm
o
p
ti
miza
ti
o
n
.
IEE
E
ln
tem
a
ti
o
n
a
l
Co
n
f
.
o
n
Nc
u
ra
l
Ne
tw
o
rk
s,
P
c
rth
,
Au
stra
li
a
.
1
9
9
5
;
4
:
1
9
4
2
-
1
9
4
8
.
[6
]
G
u
d
ise
,
V
e
n
a
y
a
g
a
m
o
o
rth
y
G
K.
Co
mp
a
ris
o
n
o
f
p
a
rticle
swa
rm
o
p
ti
miz
a
ti
o
n
a
n
d
b
a
c
k
p
ro
p
a
g
a
t
io
n
a
s
tra
i
n
in
g
a
lg
o
rith
ms
f
o
r n
e
u
ra
l
n
e
two
rk
s
.
P
ro
c
e
e
d
in
g
s o
f
th
e
2
0
0
3
IEE
E
in
S
w
a
r
m
In
telli
g
e
n
c
e
S
y
m
p
o
siu
m
,
2
0
0
3
:
1
1
0
-
1
1
7
.
[7
]
Oz
tu
rk
,
Ka
ra
b
o
g
a
.
Hy
b
rid
Arti
fi
c
ia
l
Bee
Co
lo
n
y
a
l
g
o
rit
h
m
f
o
r
n
e
u
ra
l
n
e
two
rk
tra
i
n
i
n
g
.
2
0
1
1
IE
EE
Co
n
g
re
ss
o
n
Ev
o
lu
ti
o
n
a
ry
Co
m
p
u
tatio
n
(CEC)
,
2
0
1
1
:
84
-
8
8
.
[8
]
N
T
r
e
a
d
g
o
ld
,
T
Ge
d
e
o
n
.
S
im
u
late
d
a
n
n
e
a
li
n
g
a
n
d
w
e
i
g
h
t
d
e
c
a
y
i
n
a
d
a
p
ti
v
e
lea
rn
in
g
:
th
e
sa
rp
ro
p
a
lg
o
rit
h
m
.
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Ne
u
ra
l
Ne
two
rk
s
,
1
9
9
8
;
9
:
6
6
2
–
6
6
8
.
[9
]
T
L
u
d
e
r
m
ir
e
t
a
l.
A
n
o
p
ti
m
iza
ti
o
n
m
e
th
o
d
o
l
o
g
y
f
o
r
n
e
u
ra
l
n
e
tw
o
r
k
we
ig
h
ts
a
n
d
a
rc
h
it
e
c
tu
re
s
.
IEE
E
T
ra
n
s
a
c
ti
o
n
s
o
n
Ne
u
ra
l
Ne
two
rk
s
,
2
0
0
6
;
1
7
(
5
):
1
4
5
2
–
1
4
6
0
.
[1
0
]
S
e
tt
les
M
e
t
a
l
.
Bre
e
d
in
g
sw
a
rm
s:
a
n
e
w
a
p
p
r
o
a
c
h
to
re
c
u
rr
e
n
t
n
e
u
ra
l
n
e
two
rk
tra
i
n
i
n
g
.
In
P
r
o
c
e
e
d
in
g
s
o
f
th
e
7
t
h
a
n
n
u
a
l
c
o
n
f
e
re
n
c
e
o
n
G
e
n
e
ti
c
a
n
d
e
v
o
lu
ti
o
n
a
ry
c
o
m
p
u
tatio
n
A
CM
,
2
0
0
5
;
1
8
5
-
1
9
2
.
[1
1
]
G
o
n
z
a
g
a
D
e
t
a
l.
Co
mp
o
site
sq
u
a
re
d
-
e
rr
o
r
a
lg
o
ri
th
m
f
o
r
tra
i
n
in
g
f
e
e
d
fo
rwa
rd
n
e
u
ra
l
n
e
two
rk
s
.
A
d
v
a
n
c
e
s
in
Dig
it
a
l
F
il
terin
g
a
n
d
S
ig
n
a
l
P
ro
c
e
ss
in
g
I
E
EE
S
y
m
p
o
siu
m
,
1
9
9
8
;
1
1
6
-
1
2
0
.
[1
2
]
W
il
a
m
o
w
sk
i
e
t
a
l.
Ef
fi
c
ien
t
a
lg
o
rith
m
fo
r
tra
i
n
in
g
n
e
u
r
a
l
n
e
two
r
k
s
wit
h
o
n
e
h
i
d
d
e
n
l
a
y
e
r
.
In
P
ro
c
.
IJCN
N
Ju
l
1
0
.
1
9
9
9
;
3
:
1
7
2
5
-
7
2
8
.
[1
3
]
Na
ra
y
a
n
a
n
A
.
M
o
o
re
M
.
Q
u
a
n
tu
m
-
in
sp
ire
d
g
e
n
e
ti
c
a
l
g
o
ri
th
ms
.
In
Ev
o
lu
ti
o
n
a
ry
Co
m
p
u
tatio
n
,
P
ro
c
e
e
d
in
g
s
o
f
IEE
E
In
tern
a
ti
o
n
a
l
C
o
n
f
e
re
n
c
e
,
1
9
9
6
:
61
-
6
6
.
[1
4
]
Ha
n
KH
e
t
a
l.
Pa
ra
ll
e
l
q
u
a
n
t
u
m
-
i
n
sp
ire
d
g
e
n
e
t
ic a
lg
o
rith
m f
o
r
c
o
mb
in
a
to
ri
a
l
o
p
ti
miza
t
io
n
p
ro
b
lem
.
In
Ev
o
lu
t
io
n
a
ry
Co
m
p
u
tatio
n
,
2
0
0
1
P
r
o
c
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e
d
in
g
s o
f
th
e
2
0
0
1
C
o
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g
re
ss
,
2
0
0
1
;
2
:
1
4
2
2
-
1
4
2
9
.
[1
5
]
L
iu
L
,
Zh
a
n
g
Q
.
T
ra
i
n
in
g
a
n
d
a
p
p
li
c
a
ti
o
n
o
f
p
r
o
c
e
ss
n
e
u
ra
l
n
e
two
rk
b
a
se
d
o
n
q
u
a
n
t
u
m
sh
u
ff
l
e
d
fro
g
lea
p
i
n
g
a
lg
o
rith
m
.
In
C
o
m
p
u
ter
S
c
i
e
n
c
e
a
n
d
Ne
tw
o
rk
T
e
c
h
n
o
lo
g
y
(ICC
S
NT
),
2
0
1
3
3
rd
I
n
tern
a
ti
o
n
a
l
C
o
n
f
e
re
n
c
e
.
2
0
1
3
:
829
-
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3
3
.
[1
6
]
Ko
c
a
d
a
ğ
lı
O
.
A
n
o
v
e
l
h
y
b
rid
lea
rn
in
g
a
lg
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rit
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m
f
o
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f
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2
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M
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G
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t
a
l.
Op
ti
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iza
ti
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n
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f
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a
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tu
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2
0
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3
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.
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4
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.
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5
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.
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6
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A
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L
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A
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3
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Ja
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s m
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