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h
e
r
ec
eiv
er
w
ill
ap
p
ly
an
ex
tr
ac
tio
n
tech
n
iq
u
e
o
n
s
teg
o
-
im
ag
e
f
o
r
th
at
p
u
r
p
o
s
e.
Via
tr
an
s
m
itti
n
g
a
s
teg
o
-
im
ag
e
f
r
o
m
th
e
s
en
d
er
to
th
e
r
ec
eiv
er
,
th
er
e
ar
e
m
an
y
u
n
au
th
o
r
ized
p
er
s
o
n
s
o
r
p
ar
ties
th
at
n
o
tice
a
s
teg
o
-
im
ag
e
b
u
t
w
ith
o
u
t
ex
tr
ac
tin
g
th
e
h
id
d
en
co
n
ten
ts
o
f
a
s
teg
o
-
im
ag
e
[
5
]
.
T
h
e
em
b
ed
d
in
g
tech
n
iq
u
es
ar
e
s
elec
ted
ac
co
r
d
in
g
to
ty
p
e
o
f
d
o
m
ain
,
th
e
ty
p
es
o
f
em
b
ed
d
in
g
d
o
m
ain
s
ar
e
s
p
atial
an
d
f
r
eq
u
en
cy
d
o
m
ain
s
.
T
h
e
ty
p
es
o
f
h
o
s
t
o
r
co
v
er
ar
e
tex
t,
au
d
io
,
im
ag
e
an
d
v
id
eo
[
6
]
.
T
h
e
s
p
atial
d
o
m
ain
is
u
s
ed
in
th
is
w
o
r
k
.
I
n
th
e
s
p
atial
d
o
m
ain
,
th
e
s
ec
r
et
m
ess
ag
e
is
em
b
ed
d
ed
in
th
e
s
p
ec
if
ied
p
o
s
itio
n
s
b
y
ad
d
in
g
o
r
r
ep
lacin
g
th
e
b
its
o
f
s
elec
ted
b
its
o
f
co
v
er
o
r
h
o
s
t
im
ag
e.
Gen
er
ally
,
th
e
ty
p
ical
ch
ar
ac
ter
is
tics
o
f
s
p
atial
d
o
m
ain
ar
e
all
m
eth
o
d
s
r
elate
d
to
th
is
d
o
m
ain
ar
e
v
er
y
ea
s
y
an
d
s
im
p
le
to
u
n
d
er
s
tan
d
,
th
e
ex
ec
u
tio
n
tim
e
i
s
lo
w
,
a
s
ec
r
et
m
ess
ag
e
is
ap
p
lied
to
th
e
p
ix
els
d
ir
ec
tly
w
ith
o
u
t
tr
an
s
f
o
r
m
in
g
an
o
r
ig
in
al
im
ag
e
an
d
f
in
ally
a
s
ec
r
et
m
ess
ag
e
is
em
b
ed
d
ed
in
th
e
r
eg
io
n
o
r
p
ar
t
o
f
h
o
s
t
o
r
co
v
er
im
ag
e
th
at
co
n
s
id
er
ed
as
r
ed
u
n
d
an
t
[
7
]
.
T
h
er
e
ar
e
m
an
y
tech
n
iq
u
es
r
elate
d
to
th
e
s
p
atial
d
o
m
ain
o
f
an
im
ag
e
s
teg
an
o
g
r
ap
h
y
s
u
ch
as
L
ea
s
t
Sig
n
if
ican
t
B
it
(
L
SB
)
an
d
Mo
s
t
Sig
n
if
ican
t
B
it
(
MSB
)
tech
n
iq
u
es.
T
h
e
L
SB
tech
n
iq
u
e
is
u
s
ed
in
th
e
ex
is
tin
g
p
ap
p
er
.
T
h
is
tech
n
iq
u
e
em
b
ed
s
s
ec
r
et
in
f
o
r
m
atio
n
in
th
e
least
s
ig
n
if
ican
t
b
it
o
f
s
elec
ted
p
i
x
els
o
f
th
e
h
o
s
t
im
ag
e.
So
,
it
ex
p
lo
its
th
e
p
o
in
t
w
h
ich
th
e
p
r
ec
is
io
n
in
s
ev
er
al
im
ag
e
f
o
r
m
ats
is
g
r
ea
ter
th
an
th
e
h
u
m
an
v
is
io
n
.
T
h
e
v
ar
iatio
n
s
o
f
im
ag
e
co
lo
r
s
ar
e
in
d
is
tin
g
u
is
h
ab
le
b
y
h
u
m
an
v
is
io
n
[
8
]
.
Fig
u
r
e
1
.
G
en
e
r
i
c
M
od
e
l
o
f
an
I
m
ag
e
Steg
an
o
g
r
ap
h
i
c
2.
T
H
E
R
E
L
A
T
E
D
AT
T
E
M
P
T
S
T
h
e
tech
n
iq
u
es
o
f
d
ata
h
id
in
g
ar
e
clas
s
i
f
ied
i
n
to
L
SB
s
u
b
s
ti
tu
tio
n
o
f
s
p
atial
d
o
m
ai
n
;
L
SB
is
s
i
m
ilar
to
m
a
n
y
m
e
th
o
d
s
as
P
ix
el
V
alu
e
Di
f
f
er
e
n
ci
n
g
(
P
VD)
.
T
h
e
p
r
in
cip
le
w
o
r
k
o
f
L
SB
s
u
b
s
tit
u
tio
n
m
et
h
o
d
is
r
ep
lacin
g
L
SB
’
s
o
f
p
ix
el
s
v
a
lu
es
w
i
th
in
i
m
a
g
e
t
h
at
co
n
s
i
d
er
ed
as
co
v
er
to
g
et
s
te
g
o
im
ag
e,
t
h
i
s
is
m
o
s
t
co
m
m
o
n
l
y
u
s
ed
.
Secr
et
b
it
s
o
f
s
en
s
iti
v
e
i
n
f
o
r
m
atio
n
ar
e
r
e
p
lace
d
w
it
h
i
n
L
SB
’
s
b
its
o
f
c
o
v
er
i
m
a
g
e.
W
h
en
r
esu
lt
o
f
m
atch
i
n
g
p
r
o
ce
s
s
is
n
o
t
o
b
tain
?
T
h
en
th
e
ad
d
in
g
o
r
s
u
b
tr
ac
tin
g
o
p
er
atio
n
s
f
o
r
v
alu
e
o
f
co
v
er
i
m
a
g
e
p
ix
el
ar
e
p
er
f
o
r
m
ed
f
o
r
o
n
e
r
a
n
d
o
m
l
y
.
T
h
e
co
r
e
w
o
r
k
o
f
P
V
D
b
ased
m
eth
o
d
s
is
co
m
p
u
tin
g
t
h
e
d
i
f
f
er
en
ce
o
f
t
w
o
p
ix
el
s
t
h
at
ar
e
co
n
s
ec
u
ti
v
e
to
s
p
ec
if
y
t
h
e
d
ep
th
o
f
e
m
b
ed
d
ed
b
its
.
C
h
an
g
et
al.
[
9
]
th
e
s
tr
ateg
y
o
f
d
y
n
a
m
ic
p
r
o
g
r
a
m
m
i
n
g
t
h
at
p
r
o
p
o
s
ed
is
p
ick
th
e
o
p
ti
m
al
o
r
b
est
v
ia
all
tab
les
o
f
s
u
b
s
t
itu
tio
n
ef
f
icie
n
tl
y
.
I
n
[
1
0
]
th
e
P
SO
is
u
s
ed
to
h
id
e
a
s
ec
r
et
in
f
o
r
m
at
io
n
o
r
m
e
s
s
a
g
e
in
an
i
m
a
g
e
b
ased
o
n
L
SB
an
d
in
[
1
1
]
an
im
ag
e
h
id
in
g
w
it
h
i
n
a
n
o
th
er
i
m
ag
e
u
s
i
n
g
L
S
B
tech
n
iq
u
e.
T
h
ese
m
et
h
o
d
s
b
ased
P
SO
alg
o
r
j
th
m
ar
e
b
etter
r
esu
lt
s
th
an
o
th
er
s
ta
n
d
ar
d
L
SB
tec
h
n
iq
u
e
s
.
T
h
e
tech
n
iq
u
e
t
h
at
u
s
es
d
y
n
a
m
ic
p
r
o
g
r
a
m
m
i
n
g
a
n
d
g
e
n
etic
al
g
o
r
ith
m
s
ar
e
b
ased
o
n
ef
f
ec
ts
t
h
at
co
n
s
id
er
ed
as
v
is
u
al
f
o
r
h
u
m
a
n
.
T
h
e
d
ata
h
id
in
g
tec
h
n
iq
u
es
o
f
s
p
atial
d
o
m
a
in
ar
e
p
r
o
d
u
cin
g
g
o
o
d
q
u
alit
y
s
te
g
o
im
ag
e
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
2
,
A
p
r
il 2
0
1
8
:
1
1
5
6
–
1168
1158
3.
RE
S
E
ARCH
M
E
T
H
O
D
3
.
1
.
P
a
rt
ica
le
Swa
r
m
O
pti
m
iza
t
i
o
n
Alg
o
rit
h
m
(
P
SO
)
I
n
1
9
9
5
,
b
y
Ken
n
ed
y
a
n
d
E
b
er
h
ar
t,
T
h
e
P
SO
w
a
s
i
n
tr
o
d
u
c
ed
[
1
2
]
.
T
h
e
m
o
d
el
o
f
P
SO
c
o
n
s
is
ts
o
f
m
an
y
p
ar
ticle
s
f
o
r
s
w
ar
m
,
At
t
h
e
b
eg
i
n
n
in
g
,
t
h
i
s
p
r
esen
t
s
’
N
’
n
u
m
b
er
o
f
p
ar
ticle
s
r
an
d
o
m
l
y
.
f
o
r
ea
c
h
p
ar
ticle
,
t
h
e
r
es
u
lt
o
f
a
n
o
b
j
ec
tiv
e
f
u
n
ctio
n
i
s
o
b
tain
ed
.
t
h
e
p
ar
ticle
an
d
its
g
r
o
u
p
o
f
t
h
e
f
l
y
in
g
v
elo
cit
y
ca
n
b
e
g
en
er
ated
to
n
e
x
t
g
en
er
atio
n
w
it
h
s
ee
k
i
n
g
s
ti
ll
to
g
et
b
etter
s
o
lu
tio
n
.
T
h
e
p
b
est
r
ep
r
e
d
en
ts
th
e
o
p
ti
m
al
v
al
u
e
o
b
tain
ed
v
ia
p
ar
ticle
an
d
t
h
e
g
b
est
r
ep
r
ed
en
ts
t
h
e
b
est
v
a
lu
e
o
b
tain
ed
a
m
o
n
g
all
t
h
e
p
ar
ticles
[
13
]
.
T
h
e
r
an
d
o
m
ca
n
d
id
ate
s
o
lu
tio
n
s
p
o
p
u
latio
n
is
in
i
tialized
.
f
o
r
s
ea
r
ch
in
g
a
n
e
w
s
o
lu
tio
n
s
,
t
h
e
y
m
u
s
t
m
o
v
e
i
n
an
iter
ativ
e
m
an
n
er
v
ia
th
e
d
-
d
i
m
en
s
io
n
s
s
ea
r
c
h
s
p
ac
e
o
f
p
r
o
b
lem
w
h
en
t
h
e
f
it
n
ess
f
u
n
c
tio
n
(
f
)
ca
n
co
m
p
u
ted
as
m
etr
ic
o
r
m
ea
s
u
r
e
f
o
r
q
u
ali
t
y
ass
es
s
m
en
t.
th
e
p
o
s
itio
n
-
v
ec
t
o
r
x
i
(
w
h
er
e
i
is
a
n
i
n
d
ex
f
o
r
p
ar
ticle)
is
u
s
ed
to
r
ep
r
esen
t
a
p
o
s
itio
n
s
s
i
n
ce
ea
c
h
p
ar
t
icle
h
as
a
p
o
s
itio
n
.
T
h
e
v
elo
cit
y
-
v
ec
to
r
v
i
is
u
s
ed
to
r
ep
r
esen
t
a
v
elo
cit
y
.
Fo
r
ea
ch
o
n
e
o
f
p
ar
ticle,
th
e
b
est
p
o
s
itio
n
i
s
r
e
m
e
m
b
er
ed
b
y
t
h
e
m
.
a
v
ec
to
r
i
-
th
,
w
it
h
its
d
-
d
i
m
e
n
s
io
n
al
v
alu
e
is
r
ep
r
esen
ted
as
p
b
est
(
p
id
)
.
T
h
e
b
est
p
o
s
itio
n
-
v
ec
to
r
is
s
to
r
ed
i
n
a
v
ec
to
r
i
-
t
h
,
an
d
i
ts
d
-
t
h
d
i
m
e
n
s
io
n
al
v
al
u
e
w
h
ic
h
is
r
ep
r
esen
ted
as
g
b
est
(
p
g
d
)
.
t r
ep
r
esen
ts
ti
m
e
iter
ati
o
n
,
E
q
u
atio
n
(
1
)
is
u
s
ed
to
d
eter
m
in
e
t
h
e
u
p
d
atin
g
o
r
m
o
d
if
y
in
g
t
h
e
v
elo
cit
y
(
v
id
)
f
r
o
m
th
e
o
ld
v
elo
cit
y
to
t
h
e
n
e
w
.
T
h
e
s
u
m
o
p
er
atio
n
o
f
t
h
e
p
r
ev
io
u
s
p
o
s
itio
n
an
d
th
e
n
e
w
v
elo
cit
y
is
u
s
ed
t
o
s
p
ec
if
y
a
n
e
w
p
o
s
itio
n
(
x
id
)
as sh
o
w
n
b
elo
w
i
n
E
q
u
atio
n
(
2
)
.
V(
id
+1
)
=
w
*
v
id
+
c1
*
r
1
*
(
p
g
d
-
x
id
)
+c
2
*
r
2
*
(
p
id
–
x
id
)
(
1
)
X(
id
+1
)
=
x
id
+
v
(
id
+1
)
(
2
)
W
h
er
e
i
f
r
o
m
1
to
N;
an
in
er
tia
w
ei
g
h
t
is
d
escr
ib
ed
as
w
,
r
1
an
d
r
2
ar
e
c
o
n
s
id
er
ed
as
r
an
d
o
m
n
u
m
b
er
s
,
to
m
ai
n
tai
n
th
e
d
iv
er
s
it
y
o
f
th
e
p
o
p
u
latio
n
,
th
ese
ar
e
u
s
ed
.
T
h
e
s
e
n
u
m
b
er
s
ar
e
d
is
tr
ib
u
ted
in
th
e
in
ter
v
al
[
0
,
1
]
o
f
th
e
d
-
t
h
d
i
m
e
n
s
io
n
f
o
r
th
e
i
-
t
h
p
ar
ticle.
c1
ac
ts
a
p
o
s
itiv
e
co
n
s
ta
n
t
n
u
m
b
er
,
th
i
s
co
n
s
ta
n
t
i
s
ca
lled
co
ef
f
icie
n
t
o
f
th
e
s
el
f
-
r
ec
o
g
n
itio
n
co
m
p
o
n
en
t;
c2
r
ep
r
ese
n
ts
a
p
o
s
itiv
e
co
n
s
ta
n
t
n
u
m
b
er
,
t
h
is
co
n
s
ta
n
t
is
ca
lled
co
ef
f
icie
n
t
o
f
t
h
e
s
o
cial
co
m
p
o
n
en
t.
Fro
m
eq
u
atio
n
(
2
)
,
a
p
ar
ticle
d
ec
id
es
w
h
er
e
to
m
o
v
e
f
r
o
m
c
u
r
r
en
t
p
o
s
itio
n
to
n
ex
t
p
o
s
itio
n
,
w
it
h
its
ex
p
er
ien
ce
,
it
s
a
v
es
th
e
m
e
m
o
r
y
o
f
th
e
b
est
p
ast
p
o
s
itio
n
,
an
d
th
e
m
o
s
t
s
u
cc
e
s
s
f
u
l
p
ar
ticle.
to
lea
d
th
e
p
ar
ticles
in
th
e
s
ea
r
ch
s
p
ac
e
ef
f
ec
ti
v
el
y
,
d
u
r
in
g
o
n
e
iter
atio
n
,
th
e
m
a
x
i
m
u
m
m
o
v
i
n
g
d
is
tan
ce
m
u
s
t
in
b
e
t
w
ee
n
th
e
m
a
x
i
m
u
m
v
elo
cit
y
[
−
v
m
ax
,
v
m
ax
]
.
T
h
e
s
tep
s
o
f
s
tan
d
ar
d
P
SO
alg
o
r
ith
m
ar
e
s
h
o
w
n
i
n
alg
o
r
it
h
m
(
1
)
[
1
4
]:
A
l
g
o
r
i
t
h
m
1
.
T
h
e
S
t
a
n
d
a
r
d
PSO
A
l
g
o
r
i
t
h
m
I/
P
:
P
a
r
a
me
t
e
r
s i
n
i
t
i
a
l
i
z
a
t
i
o
n
(
c
1
,
c
2
,
w
,
v
max
,
S
w
a
r
m_
S
i
z
e
,
M
a
x
_
I
t
e
r
,
r
1
,
r
2
)
.
O/
P
:
h
i
g
h
e
st
f
i
t
n
e
ss o
p
t
i
m
i
z
a
t
i
o
n
S
t
e
p
1
:
G
e
n
e
r
a
t
i
n
g
i
n
i
t
i
a
l
p
a
r
t
i
c
l
e
s a
n
d
v
e
l
o
c
i
t
i
e
s
r
a
n
d
o
ml
y
S
t
e
p
2
:
F
o
r
e
a
c
h
p
a
r
t
i
c
l
e
s
,
t
h
e
f
i
t
n
e
ss f
u
n
c
t
i
o
n
i
s
c
a
l
c
u
l
a
t
e
d
.
S
t
e
p
3
:
I
f
n
e
w
p
o
si
t
i
o
n
i
s
b
e
t
t
e
r
t
h
a
n
o
l
d
p
o
si
t
i
o
n
t
h
e
n
u
p
d
a
t
i
n
g
p
r
o
c
e
ss i
s
p
e
r
f
o
r
me
d
.
S
t
e
p
4
:
S
p
e
c
i
f
y
t
h
e
b
e
st
p
a
r
t
i
c
l
e
a
n
d
u
p
d
a
t
e
t
h
e
p
o
s
i
t
i
o
n
s
u
s
i
n
g
E
q
u
a
t
i
o
n
s (1
)
a
n
d
(
2
)
.
S
t
e
p
5
:
I
f
t
h
e
h
i
g
h
f
i
t
n
e
ss
i
s sa
t
i
sf
i
e
d
o
r
max
i
m
u
m
n
u
mb
e
r
o
f
i
t
e
r
a
t
i
o
n
s
h
a
s e
x
c
e
e
d
e
d
t
h
e
n
g
o
t
o
6
e
l
se
g
o
t
o
2
.
S
t
e
p
6
:
t
h
e
b
e
st
v
a
l
u
e
i
s St
o
r
e
d
t
h
e
n
e
x
i
t
.
3
.
2
.
Dev
elo
ped
P
SO
Alg
o
rit
h
m
W
ith
p
ar
ticle
s
w
ar
m
o
p
tim
izatio
n
(
P
SO)
,
th
e
p
r
o
b
lem
is
ad
d
r
ess
ed
u
s
in
g
s
w
ar
m
o
f
p
ar
ticles
w
h
ich
m
o
v
e
s
at
d
o
m
ain
o
f
s
ea
r
ch
s
p
ac
e
lo
o
k
in
g
f
o
r
b
est
s
o
lu
tio
n
.
E
ac
h
o
n
e
o
f
p
ar
ticles
h
as
p
o
s
itio
n
an
d
v
elo
city
.
T
h
e
p
ar
ticles
m
o
v
e
w
ith
in
th
e
s
ea
r
ch
s
p
ac
e
b
y
iter
ativ
el
y
u
p
d
atin
g
th
em
.
Fo
r
s
tr
ateg
ies
o
f
an
iter
atio
n
f
o
r
u
p
d
atin
g
,
tw
o
ch
o
ices
ar
e
f
o
u
n
d
;
s
y
n
ch
r
o
n
o
u
s
o
r
asy
n
ch
r
o
n
o
u
s
[
15
]
.
Usi
n
g
th
e
d
ev
elo
p
ed
P
SO
alg
o
r
ith
m
in
th
is
w
o
r
k
aim
s
to
s
ec
u
r
e
tr
an
s
m
itted
in
f
o
r
m
atio
n
th
at
s
en
t
b
y
s
en
d
er
v
ia
in
s
ec
u
r
e
co
m
m
u
n
icatio
n
ch
an
n
el
to
th
e
r
ec
eiv
er
.
T
h
e
im
p
o
r
tan
t
aim
o
f
th
e
p
r
o
p
o
s
ed
s
y
s
tem
is
to
p
r
o
v
id
e
s
ec
u
r
e
co
m
m
u
n
icatio
n
b
etw
ee
n
s
en
d
er
an
d
r
ec
eiv
er
.
So
,
an
o
p
tim
al
p
o
s
itio
n
s
in
th
e
s
ea
r
ch
s
p
ac
e
o
f
p
r
o
b
lem
ar
e
d
eter
m
in
ed
b
y
u
s
in
g
d
ev
elo
p
ed
P
SO
alg
o
r
ith
m
to
em
b
ed
a
s
ec
r
et
m
ess
ag
e
in
th
e
h
o
s
t
o
r
co
v
er
im
ag
e.
A
f
ter
d
eter
m
in
in
g
an
o
p
tim
al
s
o
lu
tio
n
s
in
th
e
h
o
s
t
o
r
co
v
er
im
ag
e
b
y
th
is
d
ev
elo
p
ed
alg
o
r
ith
m
,
w
h
er
e
s
tar
tin
g
p
o
in
t
o
f
p
ar
ticle
d
id
n
o
t
s
p
ec
if
y
in
th
e
P
SO
alg
o
r
ith
m
,
a
p
ar
ticle
s
o
m
etim
e
p
u
t
in
ce
n
ter
o
f
th
e
im
ag
e
o
r
p
u
t
r
an
d
o
m
ly
in
an
y
p
o
s
itio
n
o
f
th
e
s
ea
r
ch
s
p
ac
e.
T
h
e
n
ew
o
f
d
ev
elo
p
ed
P
SO
is
to
f
i
n
d
th
e
s
tar
tin
g
p
o
in
t.
th
e
h
o
s
t
o
r
co
v
er
im
ag
e
is
d
iv
id
ed
in
to
f
iv
e
p
ar
ts
as
f
o
llo
w
in
g
s
eq
u
en
ce
(
u
p
p
er
r
ig
h
t
p
ar
t,
u
p
p
er
lef
t
p
ar
t,
lo
w
er
lef
t
p
ar
t
,
lo
w
er
r
ig
h
t
p
ar
t
an
d
ce
n
ter
o
f
im
ag
e
p
ar
t)
.
T
h
e
s
tan
d
ar
d
P
SO
alg
o
r
ith
m
as
s
h
o
w
n
ab
o
v
e
in
alg
o
r
ith
m
(
1
)
i
s
p
er
f
o
r
m
ed
in
p
ar
allel
m
an
n
er
o
n
th
o
s
e
f
iv
e
p
ar
ts
.
Fo
r
all
lo
ca
tio
n
s
in
th
e
im
ag
e,
th
e
f
itn
ess
f
u
n
ctio
n
is
co
m
p
u
ted
th
r
o
u
g
h
ap
p
ly
in
g
s
o
m
e
s
tep
s
o
f
s
tatis
tical
ca
lcu
latio
n
s
s
u
ch
as
X
-
p
o
s
itio
n
,
Y
-
p
o
s
itio
n
,
Me
an
an
d
Var
ian
ce
.
T
h
e
2D
-
d
im
en
s
io
n
al
lo
ca
tio
n
s
ca
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
I
n
fo
r
ma
tio
n
Hid
in
g
u
s
in
g
LS
B
Tech
n
iq
u
e
B
a
s
ed
On
Dev
elo
p
ed
P
S
O
A
lg
o
r
ith
m
(
W
i
s
a
m
A
b
ed
S
h
u
ku
r
)
115
9
d
en
o
ted
b
y
X
-
p
o
s
itio
n
an
d
Y
-
p
o
s
itio
n
f
o
r
th
e
co
ef
f
icien
ts
in
th
e
im
ag
e.
Fo
r
ea
ch
s
p
ec
if
ied
p
o
s
itio
n
s
,
th
e
m
ea
n
is
co
m
p
u
ted
b
y
ap
p
ly
in
g
E
q
u
atio
n
(
3
)
w
h
ile
th
e
v
ar
ian
ce
is
ca
lcu
lated
b
y
ap
p
ly
in
g
E
q
u
atio
n
(
4
)
as
s
h
o
w
n
b
elo
w
.
M
Me
an
(
i)
=
(
∑
X
i(
j
)
)/
M
(
3
)
j
=1
M
Var
ian
ce
(
i)
=
(
∑(X
i(
j
)
-
m
ea
n
(
i)
)
2
)/
M
(
4
)
j
=1
w
h
er
e
:
x
i(
j
)
is
th
e
d
atu
m
i
n
s
p
ec
if
ic
p
o
s
itio
n
,
a
n
d
M
is
th
e
n
u
m
b
er
o
f
lo
ca
tio
n
s
.
A
ll
i
n
f
o
r
m
atio
n
th
a
t r
elate
d
f
o
r
ea
ch
b
ir
d
o
r
p
ar
ticle
ar
e
s
h
o
w
n
as
f
o
llo
w
in
g
:
1.
T
h
e
cu
r
r
en
t p
o
s
itio
n
f
itn
e
s
s
o
f
th
e
b
ir
d
o
r
p
ar
ticle
is
d
en
o
ted
b
y
f
(
x
)
.
2.
Fo
r
ea
ch
p
o
s
itio
n
in
t
h
e
s
ea
r
c
h
s
p
ac
e,
th
e
b
est f
it
n
es
s
is
d
en
o
ted
b
y
f
(
g
b
est).
3.
T
h
e
n
eig
h
b
o
r
s
f
(
x
)
b
est
f
itn
e
s
s
is
d
en
o
ted
b
y
f
(
x
b
es
t)
.
4.
T
h
e
cu
r
r
en
t p
o
s
itio
n
o
f
t
h
e
f
i
t
n
es
s
b
ir
d
o
r
p
ar
ticle
is
d
en
o
ted
b
y
L
x
.
5.
T
h
e
b
est f
itn
e
s
s
p
o
s
itio
n
i
n
t
h
e
s
e
ar
ch
s
p
ac
e
is
d
en
o
ted
b
y
L
g
b
est
.
6.
T
h
e
b
est f
itn
e
s
s
p
o
s
itio
n
o
f
th
e
n
eig
h
b
o
r
f
(
x
)
is
d
en
o
ted
b
y
L
x
b
est.
7.
T
h
e
co
g
n
iti
v
e
a
n
d
s
o
cial
p
ar
a
m
eter
s
ar
e
ca
lled
ac
ce
ler
atio
n
p
ar
a
m
eter
s
t
h
at
b
o
u
n
d
ed
b
et
w
ee
n
0
an
d
2
,
th
ese
p
ar
a
m
eter
s
ar
e
d
en
o
ted
b
y
α
,
β.
8.
T
h
e
r
an
d
o
m
n
u
m
b
er
s
d
is
tr
ib
u
t
ed
in
[
0
,
1
]
ar
e
d
en
o
ted
b
y
r
an
d
1
&
r
an
d
2
.
9.
T
h
e
m
a
x
i
m
u
m
n
u
m
b
er
o
f
iter
a
tio
n
is
d
en
o
ted
b
y
D.
E
ac
h
p
ar
ticle
m
o
v
es
in
th
e
m
u
lti
-
d
i
m
e
n
s
io
n
al
s
o
lu
tio
n
s
s
p
ac
e
w
it
h
d
i
f
f
er
e
n
t
s
p
ee
d
s
,
th
er
ef
o
r
e,
it
s
v
elo
cit
y
o
r
s
p
ee
d
is
ac
co
r
d
in
g
to
th
eir
m
o
v
in
g
.
Fo
r
ea
ch
p
o
s
itio
n
,
s
av
i
n
g
in
f
o
r
m
ati
o
n
o
f
its
p
r
ev
io
u
s
m
o
v
e
m
e
n
t
i
n
t
h
e
p
r
o
b
lem
s
p
a
ce
is
r
ec
o
r
d
ed
.
T
h
e
m
o
v
e
m
e
n
t
o
f
p
ar
ticle
is
in
f
l
u
en
ce
d
b
y
j
u
s
t
t
w
o
f
ac
to
r
s
,
t
h
e
f
ir
s
t
f
ac
to
r
is
t
h
e
lo
ca
l
b
est
s
o
lu
tio
n
a
n
d
th
e
s
ec
o
n
d
f
ac
to
r
is
th
e
g
lo
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al
b
est
s
o
l
u
tio
n
.
A
p
ar
ti
cle
u
p
d
ates
its
v
elo
cit
y
a
n
d
p
o
s
itio
n
if
i
t
ca
n
s
p
ec
if
y
in
g
a
b
est
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ca
tio
n
t
h
at
co
n
s
id
er
ed
as
b
etter
th
a
n
o
th
er
s
lo
ca
tio
n
s
w
h
ic
h
v
is
i
ted
p
r
ev
io
u
s
l
y
.
T
h
e
v
elo
cit
y
a
n
d
p
o
s
itio
n
u
p
d
atin
g
p
r
o
ce
s
s
is
p
er
f
o
r
m
ed
u
s
in
g
E
q
u
atio
n
(
5
)
an
d
E
q
u
atio
n
(
6
)
r
esp
ec
tiv
el
y
.
f
i(
t+1
)
=
f
(
x
)
+
α
r
an
d
1
(
L
g
b
e
s
t
-
L
x
)
+
β
r
an
d
2
(
L
x
b
est
–
L
x
)
(
5
)
L
x
i(
t+1
)
=L
x
+f
i(
t+1
)
(
6
)
W
ith
ea
ch
iter
atio
n
,
T
h
e
g
lo
b
al
b
est
lo
ca
tio
n
(
g
b
est)
is
co
m
p
ar
ed
to
th
e
f
iv
e
p
ar
ts
.
th
e
lo
ca
t
io
n
ac
ts
t
h
e
b
est
s
tar
tin
g
p
o
in
t
of
s
elec
ted
lo
ca
tio
n
s
w
h
en
t
h
e
g
b
est
i
s
eq
u
aled
.
T
h
is
is
co
n
s
id
er
ed
as
th
e
s
tar
t
p
o
in
t
o
f
th
e
P
SO
s
ea
r
ch
s
p
ac
e
w
h
ic
h
p
r
o
d
u
ce
s
t
h
e
b
est
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ca
tio
n
s
o
r
p
o
s
itio
n
s
.
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h
e
d
ev
elo
p
ed
P
SO
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g
o
r
ith
m
f
o
r
f
i
n
d
in
g
b
est
p
o
s
itio
n
is
s
h
o
w
n
i
n
al
g
o
r
ith
m
(
2
)
.
f
o
r
an
iter
atio
n
p
r
o
ce
s
s
o
f
t
h
e
al
g
o
r
it
h
m
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i
f
b
etter
s
o
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tio
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i
s
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ati
s
f
ied
,
th
en
th
e
g
lo
b
al
b
est
p
o
s
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an
d
th
e
b
est
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ca
l
p
o
s
itio
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ar
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m
o
d
if
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o
r
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ated
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h
is
p
r
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ce
s
s
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co
n
tin
u
o
u
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un
t
il
t
h
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eter
m
i
n
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n
u
m
b
er
o
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ter
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s
is
ex
h
a
u
s
ted
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n
t
h
is
w
o
r
k
,
T
h
e
n
u
m
b
er
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f
ite
r
at
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s
is
500
iter
ati
on
[
8
]
.
A
l
g
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r
i
t
h
m
2
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D
e
v
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p
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d
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g
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m
In
p
u
t
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2
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*
1
2
8
c
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r
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mag
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p
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t
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r
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a
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L
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p
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c
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t
p
u
t
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d
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n
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t
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p
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t
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t
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p
2
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si
t
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ss
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c
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t
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d
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si
n
g
E
q
u
a
t
i
n
(
3
)
a
n
d
E
q
u
a
t
i
o
n
(
4
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S
t
e
p
3
:
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o
r
t
h
e
se
l
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c
t
e
d
i
m
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d
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p
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g.
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f
t
h
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p
a
r
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i
c
l
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f
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t
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ss f (
x
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<
p
a
r
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l
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e
st
f
i
t
n
e
ss f (
x
b
e
st
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h
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n
f
(
x
b
e
st
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f
(
x
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a
n
d
L
x
b
e
st
=
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x
h.
I
f
f
(
x
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<
f
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b
e
s
t
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h
e
n
f
(
g
b
e
st
)
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f
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x
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a
n
d
L
(
g
b
e
st
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=
L
x
i.
U
p
d
a
t
e
Pa
r
t
i
c
l
e
v
e
l
o
c
i
t
y
u
si
n
g
E
q
u
a
t
i
o
n
(
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
2
,
A
p
r
il 2
0
1
8
:
1
1
5
6
–
1168
1160
P
a
r
t
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c
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p
o
s
i
t
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u
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n
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a
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o
n
(
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j
.
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f
L
1
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3
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4
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o
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3
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d
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t
e
p
4
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e
t
D
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1
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t
e
p
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a
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h
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c
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Eq
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a
t
i
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n
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3
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d
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q
u
a
t
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n
(
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n
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9
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A
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ss V
e
l
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c
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t
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t
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p
1
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v
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3.
Ste
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
I
n
fo
r
ma
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