I
nd
o
ne
s
ia
n J
o
urna
l o
f
E
lect
rica
l En
g
ineering
a
nd
Co
m
pu
t
er
Science
Vo
l.
3
9
,
No
.
1
,
Ju
ly
2
0
2
5
,
p
p
.
720
~
7
3
6
I
SS
N:
2
5
0
2
-
4
7
5
2
,
DOI
: 1
0
.
1
1
5
9
1
/ijeecs.v
3
9
.i
1
.
pp
720
-
7
3
6
720
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
ee
cs.ia
esco
r
e.
co
m
An ef
ficien
t
D
VH
O
P
loca
liza
tion a
lg
o
rithm bas
ed on
simula
ted
a
nnea
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f
o
r wir
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senso
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tw
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rk
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m
a
r
Arr
o
ub
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Da
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if
2
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chid Sa
a
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y
Driss
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ni
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i
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R
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)
,
F
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d
V
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p
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ma
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a
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c
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S
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LA
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TP,
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a
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Art
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I
nfo
AB
S
T
RAC
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A
r
ticle
his
to
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y:
R
ec
eiv
ed
Mar
19
,
2
0
2
4
R
ev
is
ed
Dec
18
,
2
0
2
4
Acc
ep
ted
Feb
27
,
2
0
2
5
In
th
e
las
t
d
e
c
a
d
e
,
th
e
re
se
a
rc
h
c
o
m
m
u
n
it
y
h
a
s
d
e
v
o
ted
sig
n
ifi
c
a
n
t
a
tt
e
n
ti
o
n
to
wire
les
s
se
n
so
r
n
e
two
r
k
s
(W
S
Ns
)
b
e
c
a
u
se
th
e
y
c
o
n
tri
b
u
te
p
o
siti
v
e
ly
t
o
so
m
e
c
rit
ica
l
issu
e
s
e
n
c
o
u
n
tere
d
i
n
n
a
t
u
re
a
n
d
e
v
e
n
in
in
d
u
str
y
.
On
th
e
o
th
e
r
h
a
n
d
,
lo
c
a
li
z
a
ti
o
n
is
o
n
e
o
f
t
h
e
m
o
st
imp
o
rta
n
t
p
a
rts
o
f
WS
N.
He
n
c
e
,
th
e
c
o
n
c
e
p
ti
o
n
o
f
a
n
e
fficie
n
t
m
e
th
o
d
o
f
lo
c
a
li
z
a
ti
o
n
h
a
s
b
e
c
o
m
e
a
h
o
t
re
se
a
rc
h
to
p
ic.
Las
tl
y
,
i
t
h
a
s
b
e
e
n
in
v
e
n
te
d
,
a
se
t
o
f
o
p
ti
m
a
l
p
o
siti
o
n
in
g
m
e
th
o
d
s
th
a
t
m
a
k
e
lo
c
a
te
a
n
o
d
e
with
lo
w
c
o
st
a
n
d
g
iv
e
p
re
c
ise
re
su
lt
s
.
In
o
u
r
c
o
n
tri
b
u
ti
o
n
,
we
in
v
e
stig
a
te
t
h
e
s
o
u
rc
e
o
f
imp
re
c
isio
n
i
n
t
h
e
d
istan
c
e
v
e
c
to
r
-
hop
(DV
HO
P
)
l
o
c
a
li
z
a
ti
o
n
a
l
g
o
r
it
h
m
.
Ho
we
v
e
r,
we
fo
u
n
d
th
e
la
st
ste
p
o
f
DV
HO
P
c
a
u
se
d
a
n
imp
re
c
isio
n
i
n
t
h
e
c
a
lcu
lati
o
n
.
C
o
n
se
q
u
e
n
tl
y
,
o
u
r
wo
r
k
wa
s
to
re
p
lac
e
th
is
ste
p
,
a
imi
n
g
t
o
re
a
c
h
sa
ti
sfa
c
to
ry
p
re
c
isio
n
.
F
o
r
th
a
t
p
u
r
p
o
se
,
we
c
re
a
ted
th
re
e
imp
ro
v
e
d
v
e
rsi
o
n
s
o
f
th
is
a
l
g
o
rit
h
m
b
y
a
d
o
p
ti
n
g
two
m
e
ta
-
h
e
u
risti
c
(sim
u
late
d
a
n
n
e
a
li
n
g
,
p
a
rti
c
le
sw
a
rm
o
p
ti
m
iza
ti
o
n
)
a
n
d
F
m
in
c
o
n
s
o
lv
e
r
d
e
d
ica
ted
t
o
o
p
ti
m
iza
ti
o
n
i
n
th
e
fiel
d
o
f
WS
N
n
o
d
e
lo
c
a
li
z
a
ti
o
n
.
Th
e
e
x
p
e
rime
n
tal
re
su
lt
s
o
b
tain
e
d
in
th
is
w
o
rk
p
ro
v
e
th
e
e
fficie
n
c
y
o
f
sim
u
late
d
a
n
n
e
a
li
n
g
(
SA
)
-
DV
HO
P
in
term
s
o
f
a
c
c
u
ra
c
y
.
F
u
rth
e
rm
o
re
,
th
e
e
n
h
a
n
c
e
d
a
lg
o
ri
th
m
o
u
tp
e
rfo
rm
s
it
s
o
p
p
o
n
e
n
ts
b
y
v
a
ry
in
g
th
e
p
e
rc
e
n
tag
e
o
f
a
n
c
h
o
rs an
d
th
e
n
u
m
b
e
r
o
f
n
o
d
e
s.
K
ey
w
o
r
d
s
:
DVHOP
L
o
ca
lizatio
n
Me
tah
eu
r
is
tic
alg
o
r
ith
m
s
Simu
lated
an
n
ea
lin
g
W
SN
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Om
ar
Ar
r
o
u
b
L
R
I
T
-
GSC
M
A
s
s
o
ciate
d
Un
it
to
C
NR
ST
(
UR
AC
2
9
)
,
FS
R
Mo
h
am
m
ed
V
-
A
g
d
al
Un
iv
e
r
s
ity
B
P 1
0
1
4
R
ab
at
Mo
r
o
cc
o
E
m
ail:
o
m
ar
_
ar
r
o
u
b
@
u
m
5
.
ac
.
m
a
1.
I
NT
RO
D
UCT
I
O
N
No
wad
ay
s
,
with
th
e
co
n
tin
u
o
u
s
d
ev
elo
p
m
e
n
t
o
f
m
icr
o
elec
tr
o
-
m
ec
h
an
ical
s
y
s
tem
s
(
ME
MS)
,
th
er
e
is
a
s
ig
n
if
ican
t
in
ter
est
b
y
r
esear
ch
er
s
in
wir
eless
s
en
s
o
r
n
e
two
r
k
(
W
SN
)
[
1
]
,
b
ec
au
s
e
th
e
latter
h
as
s
h
o
wn
ef
f
icien
cy
in
d
if
f
er
en
t
a
p
p
lic
atio
n
s
,
s
u
ch
as
m
ilit
ar
y
s
en
s
in
g
,
s
m
ar
t
e
n
v
ir
o
n
m
en
tal
[
2
]
,
v
eh
icu
la
r
ad
-
h
o
c
n
etwo
r
k
(
VANE
T
)
[
3
]
,
h
ea
lth
ca
r
e
[
4
]
,
ag
r
icu
ltu
r
e
[
5
]
,
in
d
u
s
tr
y
[
6
]
,
a
n
d
m
u
ltime
d
ia
[
7
]
.
H
o
wev
er
,
lo
ca
lizatio
n
is
an
im
p
o
r
tan
t
p
ar
t
o
f
W
SN.
I
n
d
ee
d
,
with
o
u
t
lo
ca
tio
n
'
s
in
f
o
r
m
atio
n
,
m
ess
ag
es
will
b
e
m
is
s
ed
.
F
o
r
ex
am
p
le,
u
s
in
g
W
SN
in
o
r
d
er
to
d
etec
t
th
e
f
ir
e
f
o
r
est.
I
n
d
ee
d
,
b
r
in
g
in
g
th
e
lo
ca
tio
n
in
f
o
r
m
atio
n
to
th
e
b
ase
s
tatio
n
ca
n
h
el
p
th
e
f
ir
e
f
ig
h
ter
r
ea
ct
r
ap
id
l
y
to
m
ak
e
th
e
n
ec
ess
ar
y
i
n
ter
v
e
n
tio
n
s
.
At
th
is
p
o
in
t,
th
e
co
m
m
o
n
l
y
u
s
ed
s
o
lu
tio
n
to
lo
ca
te
th
e
s
en
s
o
r
n
o
d
e
in
W
SN
is
th
e
g
lo
b
al
p
o
s
itio
n
in
g
s
y
s
te
m
(
GPS).
Per
h
a
p
s
,
th
is
p
o
s
itio
n
in
g
s
o
lu
tio
n
is
n
o
t
p
r
ac
ticab
le
in
all
ca
s
es
b
ec
au
s
e
GPS
ca
n
n
o
t
b
e
u
s
ed
in
in
d
o
o
r
ar
ea
s
.
B
esid
es
th
at,
it
co
n
s
u
m
es
a
l
o
t
o
f
en
er
g
y
.
I
n
o
r
d
er
to
m
itig
ate
t
h
e
two
is
s
u
es
ca
u
s
ed
b
y
GPS,
s
o
m
e
alter
n
ativ
e
s
o
lu
tio
n
s
h
av
e
b
ee
n
in
v
en
ted
to
t
h
e
lo
ca
lizatio
n
p
r
o
b
lem
,
in
wh
ich
we
eq
u
ip
ju
s
t
a
f
ew
s
en
s
o
r
n
o
d
es
wit
h
GPS
n
am
ed
an
ch
o
r
s
an
d
th
o
s
e
an
ch
o
r
s
h
elp
t
h
e
o
t
h
er
u
n
k
n
o
wn
n
o
d
es
b
e
awa
r
e
o
f
th
eir
p
o
s
itio
n
s
b
y
u
s
in
g
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
A
n
efficien
t D
V
HOP
lo
ca
liz
a
tio
n
a
lg
o
r
ith
m
b
a
s
ed
o
n
s
imu
la
ted
…
(
Oma
r
A
r
r
o
u
b
)
721
n
etwo
r
k
co
n
n
ec
tiv
ity
an
d
s
o
m
e
ad
d
itio
n
al
ca
lcu
latio
n
s
.
B
y
o
p
tin
g
f
o
r
alter
n
ativ
e
lo
ca
li
za
tio
n
s
o
lu
tio
n
s
,
we
av
o
id
th
e
h
ig
h
e
n
er
g
y
co
n
s
u
m
p
tio
n
o
f
th
e
lo
ca
lizatio
n
p
r
o
ce
s
s
.
T
h
e
lo
c
a
l
i
z
a
t
io
n
te
c
h
n
i
q
u
e
s
c
a
n
b
e
c
l
a
s
s
i
f
i
ed
i
n
to
t
wo
c
l
a
s
s
e
s
:
r
an
g
e
-
b
a
s
ed
a
n
d
r
a
n
g
e
-
f
r
e
e
t
e
c
h
n
iq
u
e
s
[
8
]
,
[
9
]
.
H
o
w
ev
er
,
r
a
n
g
e
-
f
r
e
e
m
e
t
h
o
d
s
a
r
e
b
a
s
e
d
o
n
t
h
e
co
n
n
e
c
t
iv
i
t
y
o
f
t
h
e
n
e
t
w
o
r
k
,
th
e
a
d
v
an
t
ag
e
s
o
f
th
o
s
e
m
e
t
h
o
d
s
t
h
a
t
t
h
ey
d
o
n
’
t
n
e
e
d
a
n
y
a
d
d
it
i
o
n
a
l
h
a
r
d
w
a
r
e
,
m
ak
i
n
g
th
em
m
o
r
e
e
f
f
i
c
i
en
t
i
n
t
e
r
m
s
o
f
l
o
w
c
o
s
t
.
I
n
t
h
e
f
i
e
ld
o
f
r
e
s
e
ar
c
h
,
t
h
e
m
o
s
t
c
o
m
m
o
n
ly
u
s
ed
r
a
n
g
e
-
f
r
e
e
t
e
c
h
n
iq
u
e
s
in
c
l
u
d
e
A
P
I
T
[
1
0
]
,
C
e
n
t
r
o
i
d
[
1
1
]
,
d
i
s
t
a
n
ce
v
e
c
t
o
r
-
h
o
p
(
DVHOP
)
[
1
2
]
,
[
1
3
]
a
n
d
A
m
o
r
p
h
o
u
s
a
l
g
o
r
i
t
h
m
[
1
4
]
.
O
n
t
h
e
o
th
e
r
h
a
n
d
,
r
an
g
e
-
b
a
s
ed
t
ec
h
n
i
q
u
es
[
1
5
]
m
a
k
e
th
e
lo
c
a
l
i
z
a
t
io
n
b
y
u
s
in
g
t
i
m
e
o
f
ar
r
i
v
a
l
(
T
O
A
)
[
1
6
]
,
a
n
g
l
e
o
f
a
r
r
iv
a
l
(
A
O
A
)
[
1
7
]
,
t
im
e
d
i
f
f
e
r
e
n
ce
o
f
a
r
r
i
v
a
l
(
T
D
O
A
)
[
1
8
]
a
n
d
r
e
c
e
iv
e
d
s
i
g
n
a
l
s
t
r
e
n
g
th
in
d
i
c
a
to
r
(
R
S
S
I
)
.
I
n
g
e
n
er
a
l
,
th
o
s
e
m
e
t
h
o
d
s
r
e
q
u
i
r
e
ad
d
i
t
io
n
a
l
m
a
t
er
i
a
l
,
b
u
t
th
e
y
o
f
f
e
r
a
h
i
g
h
l
ev
e
l
o
f
a
c
cu
r
a
c
y
,
m
ak
i
n
g
t
h
em
m
o
r
e
p
r
e
c
i
s
e
an
d
e
x
p
e
n
s
iv
e
th
a
n
r
an
g
e
-
f
r
e
e
t
e
ch
n
iq
u
e
s
.
Mo
r
eo
v
er
,
in
s
o
m
e
c
a
s
e
s
,
t
h
e
l
ea
k
a
g
e
o
f
d
e
p
lo
y
ed
a
n
c
h
o
r
s
i
n
W
S
N
m
ay
l
e
ad
t
o
w
e
a
k
c
o
v
er
a
g
e
o
f
th
e
n
e
t
w
o
r
k
.
T
o
m
i
t
i
g
a
t
e
t
h
i
s
i
s
s
u
e
,
m
u
lt
i
-
h
o
p
l
o
c
a
l
i
z
a
t
io
n
a
l
g
o
r
i
t
h
m
s
c
an
b
e
u
s
e
d
.
T
h
e
s
p
e
c
i
f
i
c
i
ty
o
f
th
o
s
e
a
lg
o
r
i
t
h
m
s
i
s
t
h
a
t
s
e
n
s
o
r
n
o
d
e
s
m
ay
b
e
l
o
c
a
te
d
ev
e
n
if
t
h
e
y
a
r
en
't
i
n
c
o
m
m
u
n
i
c
a
t
io
n
r
an
g
e
w
i
t
h
an
ch
o
r
s
.
T
h
e
m
o
s
t
k
n
o
wn
m
u
l
t
i
-
h
o
p
l
o
ca
li
z
a
t
i
o
n
a
l
g
o
r
i
th
m
i
s
D
V
H
O
P
.
T
h
e
a
d
v
an
t
a
g
e
s
o
f
D
V
H
O
P
r
e
s
i
d
e
i
n
i
t
s
s
i
m
p
l
i
c
it
y
o
f
im
p
l
em
e
n
t
a
t
io
n
.
A
l
s
o
,
th
i
s
a
l
g
o
r
i
t
h
m
g
iv
e
s
t
h
e
r
e
s
u
l
t
s
q
u
ic
k
ly
.
B
e
s
i
d
e
s
th
a
t
,
D
V
H
O
P
c
an
o
f
f
er
g
o
o
d
co
v
er
a
g
e
o
f
l
o
c
a
l
iz
a
t
i
o
n
i
n
c
o
m
p
a
r
i
s
o
n
w
i
th
o
th
e
r
l
o
c
a
l
i
z
a
t
io
n
a
lg
o
r
i
t
h
m
s
.
I
t
s
d
r
a
w
b
a
ck
i
s
t
h
e
lo
w
a
c
cu
r
a
cy
o
f
f
er
e
d
,
e
s
p
e
c
i
a
l
ly
wh
en
th
e
n
e
t
wo
r
k
b
e
co
m
e
s
s
m
a
l
l
.
T
h
er
e
f
o
r
e,
m
a
n
y
im
p
r
o
v
e
m
en
t
s
h
a
v
e
b
e
e
n
p
r
o
p
o
s
e
d
to
e
n
h
a
n
ce
th
e
p
r
ec
i
s
i
o
n
o
f
th
e
tr
a
d
i
t
io
n
a
l
D
V
H
O
P
.
I
n
o
u
r
ap
p
r
o
ac
h
,
we
c
r
e
a
t
e
th
r
e
e
im
p
r
o
v
e
d
v
er
s
io
n
s
o
f
D
V
H
O
P
in
o
r
d
e
r
t
o
av
o
i
d
t
h
e
l
e
a
s
t
s
q
u
ar
e
m
e
t
h
o
d
ad
o
p
t
e
d
b
y
t
h
e
tr
a
d
it
i
o
n
a
l
a
lg
o
r
i
t
h
m
b
ec
a
u
s
e
i
t
's
t
h
e
m
a
in
r
e
a
s
o
n
f
o
r
l
o
c
a
t
i
n
g
t
h
e
s
en
s
o
r
n
o
d
e
i
m
p
r
ec
i
s
e
l
y
.
I
n
f
ac
t,
in
u
n
if
o
r
m
d
e
p
lo
y
m
e
n
t,
it's
b
ee
n
f
o
u
n
d
th
at
DVH
OP
is
a
s
u
itab
le
alg
o
r
ith
m
in
ter
m
s
o
f
co
v
er
ag
e
o
f
lo
ca
lizatio
n
an
d
ca
n
also
o
f
f
er
an
ac
ce
p
tab
le
lev
el
o
f
ac
cu
r
ac
y
.
Ho
wev
er
,
wh
en
th
e
n
etwo
r
k
b
ec
o
m
es
an
is
o
tr
o
p
ic
d
u
e
to
t
h
e
p
r
esen
ce
o
f
a
n
ir
r
eg
u
lar
ity
in
th
e
d
is
tr
ib
u
tio
n
o
f
n
o
d
es,
th
e
ac
cu
r
ac
y
o
f
th
e
alg
o
r
ith
m
b
ec
o
m
es
wo
r
s
e
b
ec
au
s
e
th
e
h
o
p
-
s
ize
ca
lcu
latio
n
d
o
n
e
b
y
DVHO
P
in
a
n
o
n
-
u
n
i
f
o
r
m
n
etwo
r
k
lead
s
to
a
b
ig
in
ac
cu
r
ac
y
in
th
e
d
is
tan
ce
ca
lcu
latio
n
s
tep
.
C
o
n
s
eq
u
en
tly
,
th
e
av
e
r
ag
e
lo
ca
lizatio
n
er
r
o
r
(
AL
E
)
o
f
th
e
alg
o
r
ith
m
is
ch
a
r
ac
ter
ized
b
y
in
s
u
f
f
icien
cy
.
Aim
in
g
to
en
h
a
n
ce
th
e
lo
ca
lizatio
n
ac
cu
r
ac
y
o
f
DVHO
P
in
n
o
n
-
u
n
if
o
r
m
n
etwo
r
k
s
,
th
e
r
esear
ch
co
m
m
u
n
ity
h
as
in
v
en
te
d
Am
o
r
p
h
o
u
s
lo
ca
lizatio
n
alg
o
r
ith
m
th
at
m
ak
e
s
th
e
d
is
tan
ce
ca
lcu
latio
n
u
s
in
g
an
o
f
f
lin
e
m
eth
o
d
.
I
n
d
ee
d
,
Am
o
r
p
h
o
u
s
u
s
es
Klein
r
o
ck
an
d
Sil
v
ester
f
o
r
m
u
la
i
n
o
r
d
er
to
ca
lcu
late
h
o
p
-
s
ize
f
o
r
r
ed
u
cin
g
th
e
lo
ca
lizatio
n
er
r
o
r
.
I
n
o
u
r
co
n
t
r
ib
u
tio
n
,
we
b
r
in
g
DVHO
P
f
o
r
im
p
r
o
v
em
e
n
t
in
b
o
th
ca
s
es
o
f
th
e
d
is
tr
ib
u
tio
n
(
u
n
if
o
r
m
,
n
o
-
u
n
if
o
r
m
)
aim
in
g
to
co
r
r
ec
t
th
e
is
s
u
e
o
f
r
eso
lv
in
g
th
e
n
o
n
-
lin
ea
r
eq
u
atio
n
s
p
r
esen
ted
in
th
e
m
u
ltil
ater
atio
n
p
r
o
ce
s
s
.
As
we
k
n
o
w,
th
e
m
u
ltil
ater
atio
n
is
th
e
in
ter
s
ec
tio
n
o
f
th
e
cir
cles
with
th
e
p
u
r
p
o
s
e
o
f
lo
ca
tin
g
th
e
tar
g
et.
Ho
wev
er
,
m
o
r
e
cir
c
les
ar
e
r
eq
u
ir
ed
to
ca
lcu
late
th
e
c
o
o
r
d
i
n
ates
o
f
t
h
e
u
n
k
n
o
wn
n
o
d
e
m
o
r
e
p
r
ec
is
ely
.
T
h
at
m
ea
n
s
m
o
r
e
e
q
u
ati
o
n
s
ar
e
d
ev
o
ted
to
r
eso
lu
tio
n
p
u
r
p
o
s
es.
I
n
ad
d
itio
n
to
th
at,
th
o
s
e
eq
u
atio
n
s
ar
e
p
r
esen
ted
in
n
o
n
-
lin
ea
r
f
o
r
m
.
As
a
co
n
s
eq
u
en
ce
,
we
ar
e
f
ac
in
g
a
h
u
g
e
an
d
c
o
m
p
licated
p
r
o
b
lem
.
Ou
r
aim
wa
s
to
tr
an
s
f
o
r
m
th
e
cited
is
s
u
e
in
to
an
o
p
tim
izatio
n
p
r
o
b
lem
.
I
n
d
ee
d
,
it
was
s
ee
n
th
at
s
im
u
lated
an
n
ea
lin
g
[
19
]
,
[
2
0
]
,
p
a
r
ticle
s
war
m
o
p
tim
izatio
n
(
PSO
)
[2
1
]
,
[
2
2
]
,
Fm
in
c
o
n
[
2
3
]
,
[
2
4
]
th
e
c
o
n
v
en
ie
n
t m
eth
o
d
s
f
o
r
r
eso
lv
in
g
th
e
cited
p
r
o
b
lem
.
T
h
e
m
ain
co
n
tr
ib
u
tio
n
s
o
f
th
is
p
ap
er
a
r
e
as f
o
llo
ws:
i)
T
h
e
im
p
o
r
tan
ce
o
f
W
SN
h
as
led
th
e
r
esear
ch
c
o
m
m
u
n
ity
to
in
v
esti
g
ate
m
o
r
e
a
b
o
u
t
th
e
p
r
o
b
lem
o
f
lo
ca
lizatio
n
in
W
SN.
DV
HO
P
b
elo
n
g
s
to
r
an
g
e
-
f
r
ee
lo
ca
lizatio
n
tech
n
iq
u
es;
its
last
s
tep
is
ju
d
g
ed
to
b
e
th
e
m
ain
r
ea
s
o
n
f
o
r
th
e
im
p
r
ec
is
io
n
o
f
DVHO
P.
Fu
r
th
er
m
o
r
e,
th
e
tr
ad
itio
n
al
f
o
r
m
u
la
e
q
u
atio
n
u
s
ed
to
r
etr
iev
e
th
e
lo
ca
tio
n
s
ca
u
s
es a
n
er
r
o
r
.
Hen
ce
,
t
h
e
latter
ca
n
b
e
r
ef
o
r
m
u
lated
as a
n
o
p
tim
izatio
n
p
r
o
b
lem
.
ii)
T
h
e
r
eso
lu
tio
n
o
f
t
h
e
least
s
q
u
ar
e
m
et
h
o
d
a
d
o
p
te
d
b
y
D
VHOP
m
ay
b
e
in
ter
p
r
eted
a
s
a
m
in
im
izin
g
p
r
o
b
lem
th
at
h
as
th
e
ab
ilit
y
to
b
e
r
eso
lv
ed
eith
er
b
y
s
im
u
lated
an
n
ea
lin
g
,
PS
O
an
d
Fm
in
co
n
s
o
lv
er
d
ed
icate
d
to
m
ath
e
m
atica
l
o
p
tim
izatio
n
u
n
d
er
MA
T
L
AB
.
T
h
e
p
u
r
p
o
s
e
o
f
th
o
s
e
m
o
d
if
icatio
n
s
is
to
en
h
an
ce
th
e
ac
cu
r
ac
y
o
f
t
h
e
tr
ad
itio
n
al
DVHO
P.
iii)
T
h
e
p
er
f
o
r
m
an
ce
co
m
p
ar
is
o
n
o
f
s
im
u
lated
an
n
ea
lin
g
(
SA
)
-
DVHO
P,
F
m
in
co
n
-
DVHO
P
,
PS
O
-
DVHO
P
an
d
DVHO
P is
ca
r
r
ied
o
u
t u
n
d
er
two
d
if
f
er
en
t n
etwo
r
k
en
v
i
r
o
n
m
en
ts
.
T
h
e
ex
p
er
im
en
tal
r
esu
lts
p
r
o
v
e
th
at
th
e
p
r
o
p
o
s
ed
SA
-
DVHO
P
h
a
s
a
s
m
aller
lo
ca
lizatio
n
er
r
o
r
.
Als
o
,
it
'
s
s
h
o
wn
th
at
th
e
im
p
r
o
v
ed
m
eth
o
d
is
n
o
t d
ep
e
n
d
en
t
o
n
th
e
ad
d
itio
n
al
an
ch
o
r
s
to
g
iv
e
th
e
b
est r
esu
lt.
T
h
e
r
e
m
a
in
d
e
r
o
f
t
h
e
p
ap
e
r
i
s
a
s
f
o
l
lo
w
s
:
f
ir
s
t
l
y
,
w
e
ex
p
o
s
e
d
i
f
f
e
r
en
t
wo
r
k
s
t
h
a
t
h
av
e
a
l
r
e
a
d
y
b
ee
n
d
o
n
e
to
e
n
h
an
c
e
D
V
H
O
P
in
s
t
a
t
i
c
W
S
N
w
i
th
a
u
n
i
f
o
r
m
an
d
r
a
n
d
o
m
d
i
s
t
r
ib
u
t
io
n
o
f
n
o
d
e
s
.
I
n
s
e
c
t
i
o
n
3
,
we
d
e
f
in
e
t
h
e
r
e
s
e
a
r
ch
m
e
th
o
d
o
lo
g
y
f
o
l
lo
w
e
d
to
a
c
co
m
p
l
i
s
h
th
i
s
wo
r
k
.
I
n
s
e
c
t
io
n
4
,
w
e
i
n
tr
o
d
u
c
e
D
V
H
O
P
in
d
e
t
a
i
l
b
y
c
i
t
i
n
g
i
t
s
a
d
v
an
t
ag
e
s
an
d
d
r
a
w
b
a
ck
s
,
th
en
we
p
r
e
s
e
n
t
o
u
r
im
p
r
o
v
e
d
v
e
r
s
i
o
n
s
o
f
D
V
H
O
P
.
S
i
m
u
l
a
t
i
o
n
i
s
d
o
n
e
an
d
d
i
s
cu
s
s
e
d
i
n
s
e
c
t
i
o
n
5
.
F
i
n
a
l
l
y
,
w
e
c
o
n
c
l
u
d
e
t
h
e
p
a
p
er
a
n
d
p
r
e
s
e
n
t
f
u
tu
r
e
w
o
r
k
s
i
n
s
e
c
t
i
o
n
6
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
3
9
,
No
.
1
,
Ju
ly
20
25
:
720
-
7
3
6
722
2.
RE
L
AT
E
D
WO
RK
S
I
n
f
ac
t,
th
er
e
ar
e
two
f
ac
to
r
s
co
n
tr
ib
u
tin
g
to
th
e
im
p
r
ec
i
s
io
n
o
f
DVHO
P.
Firs
tly
,
b
y
th
e
least
s
q
u
ar
es
m
eth
o
d
u
s
ed
to
s
o
lv
e
th
e
n
o
n
-
lin
ea
r
eq
u
atio
n
s
.
Seco
n
d
ly
,
b
y
th
e
m
an
n
er
ad
o
p
ted
in
a
v
er
ag
in
g
h
o
p
-
s
ize.
Du
r
in
g
o
u
r
r
esear
ch
,
we
f
in
d
th
at
th
e
r
esear
c
h
co
m
m
u
n
ity
f
o
cu
s
es
o
n
r
eso
lv
in
g
DVHO
P
b
y
r
e
p
lacin
g
th
e
least
s
q
u
ar
es
m
eth
o
d
b
ec
au
s
e
th
e
er
r
o
r
i
n
tr
o
d
u
ce
d
in
t
h
e
d
is
tan
ce
ca
lcu
latio
n
s
tep
h
as
a
s
lig
h
t
im
p
ac
t
o
n
t
h
e
ac
cu
r
ac
y
o
f
DVHO
P.
I
n
g
en
er
al,
m
an
y
s
cien
tis
ts
ad
o
p
t
n
atu
r
e
-
in
s
p
ir
ed
m
eta
-
h
e
u
r
is
tic
alg
o
r
ith
m
s
[
2
5
]
to
en
h
an
ce
th
e
p
r
ec
is
io
n
o
f
DV
HOP.
Fo
r
ex
am
p
le,
we
f
in
d
th
at
PS
O
is
m
o
s
tly
u
s
ed
to
m
itig
ate
th
is
is
s
u
e.
Xu
e
[2
6
]
,
a
d
o
p
ts
PS
O
an
d
h
e
u
s
es
lin
ea
r
d
ec
r
ea
s
in
g
in
er
tia
weig
h
t
(
L
DI
W
)
[
2
7
]
to
h
av
e
a
b
alan
ce
b
etwe
en
th
e
ex
p
lo
r
atio
n
an
d
ex
p
lo
itatio
n
p
h
ases
o
f
PS
O
in
o
r
d
er
to
m
in
im
ize
th
e
co
s
t
f
u
n
ctio
n
a
n
d
r
ea
ch
th
e
g
l
o
b
al
s
o
lu
tio
n
.
T
h
en
,
th
e
s
o
lu
tio
n
ex
tr
ac
ted
b
y
PS
O
p
r
esen
ts
th
e
o
p
tim
al
lo
ca
tio
n
o
f
t
h
e
u
n
k
n
o
wn
n
o
d
e.
Sh
ar
m
a
an
d
Ku
m
ar
[2
8
]
,
th
e
s
tu
d
y
o
f
lo
ca
lizatio
n
is
ex
ten
d
ed
to
th
r
ee
d
im
e
n
s
io
n
s
.
I
n
a
d
d
itio
n
to
th
at,
th
e
g
en
etic
alg
o
r
ith
m
h
as
b
ee
n
u
s
ed
in
o
r
d
er
to
im
p
r
o
v
e
DVHO
P.
I
n
d
etail,
th
e
p
r
o
ce
s
s
o
f
p
o
s
itio
n
in
g
is
s
u
m
m
ar
ized
in
s
ix
s
tep
s
:
f
lo
o
d
in
g
p
h
ase,
h
o
p
-
s
ize
ca
lcu
latio
n
,
p
o
p
u
latio
n
in
itializatio
n
,
c
r
o
s
s
o
v
er
,
s
elec
tio
n
an
d
m
u
tatio
n
.
B
r
ief
ly
,
GA
-
D
VHOP
[
29
]
ch
an
g
es
th
e
last
p
h
ase
o
f
th
e
tr
ad
itio
n
al
DVHO
P
to
g
en
etic
s
tep
s
,
aim
in
g
to
r
ea
ch
a
b
etter
s
o
lu
ti
o
n
.
Alth
o
u
g
h
th
at
m
eth
o
d
g
iv
es
a
h
ig
h
d
eg
r
ee
o
f
ac
cu
r
ac
y
,
its
d
r
awb
ac
k
r
esid
es
in
i
ts
h
ig
h
co
m
p
lex
ity
in
c
o
m
p
ar
is
o
n
with
PS
O
-
DVHO
P.
Per
d
an
a
et
a
l.
[3
0
]
,
s
h
o
w
ed
th
at
Am
o
r
p
h
o
u
s
o
u
tp
er
f
o
r
m
s
DVHO
P
in
ter
m
s
o
f
ac
cu
r
ac
y
b
y
v
ar
y
in
g
th
e
n
u
m
b
er
o
f
n
o
d
es
an
d
th
e
p
er
ce
n
tag
e
o
f
an
ch
o
r
s
.
T
h
is
s
t
u
d
y
also
p
r
o
v
es
th
e
ef
f
icien
c
y
o
f
Am
o
r
p
h
o
u
s
in
ter
m
s
o
f
en
er
g
y
c
o
n
s
u
m
p
ti
o
n
.
Acc
o
r
d
in
g
to
th
e
e
x
p
er
im
e
n
tal
r
esu
lts
,
it
's
co
n
f
ir
m
ed
th
at
Am
o
r
p
h
o
u
s
r
ea
ch
a
s
atis
f
ac
to
r
y
p
r
ec
is
io
n
in
W
SN
with
a
f
ew
an
ch
o
r
s
.
Ho
we
v
er
,
DVHO
P
r
eq
u
ir
es
m
o
r
e
an
ch
o
r
s
to
p
er
f
o
r
m
b
etter
.
Ali
et
a
l.
[3
1
]
s
tated
a
p
er
f
o
r
m
an
ce
c
o
m
p
a
r
is
o
n
o
f
A
m
o
r
p
h
o
u
s
an
d
DVHO
P
h
as
b
e
en
d
o
n
e,
t
h
e
m
etr
i
c
o
f
ev
alu
atio
n
was
th
e
ac
cu
r
ac
y
o
f
lo
ca
lizatio
n
,
en
er
g
y
co
n
s
u
m
p
tio
n
an
d
n
etwo
r
k
o
v
er
h
ea
r
d
.
Als
o
,
it'
s
s
h
o
wn
f
o
r
b
o
th
alg
o
r
ith
m
s
cited
th
at
th
e
ac
cu
r
ac
y
o
f
lo
ca
lizatio
n
i
s
in
v
er
s
ely
p
r
o
p
o
r
tio
n
al
to
th
e
en
er
g
y
c
o
n
s
u
m
e
d
b
y
th
e
n
o
d
e.
As we
k
n
o
w,
in
a
n
o
n
-
u
n
if
o
r
m
n
etwo
r
k
,
we
n
ee
d
m
o
r
e
an
ch
o
r
s
.
Hen
ce
,
Am
o
r
p
h
o
u
s
o
u
tp
e
r
f
o
r
m
s
DVHO
P
in
ter
m
s
o
f
ac
cu
r
ac
y
an
d
en
e
r
g
y
co
n
s
u
m
p
tio
n
b
ec
au
s
e
Am
o
r
p
h
o
u
s
d
o
esn
'
t
r
eq
u
ir
e
m
an
y
an
ch
o
r
s
in
its
lo
ca
tin
g
p
r
o
ce
s
s
.
Han
et
a
l.
[3
2
]
,
u
s
e
a
g
en
e
tic
al
g
o
r
ith
m
t
o
im
p
r
o
v
e
DVHO
P a
n
d
th
ey
a
d
o
p
t PSO to
r
ef
in
e
th
e
cr
o
s
s
o
v
er
s
tep
.
T
h
e
s
im
u
latio
n
s
r
ea
lized
in
th
is
r
e
s
ea
r
ch
p
r
o
v
e
th
e
ef
f
icien
c
y
o
f
th
e
am
elio
r
ated
v
er
s
io
n
o
f
DVHO
P in
ter
m
s
o
f
p
r
ec
is
io
n
b
y
v
ar
y
in
g
t
h
e
p
er
ce
n
tag
e
o
f
a
n
ch
o
r
s
.
I
n
th
is
wo
r
k
,
we
attem
p
t
to
en
h
an
ce
DVHO
P
aim
in
g
to
r
ed
u
ce
its
im
p
r
ec
is
io
n
in
lo
c
atin
g
.
Ou
r
m
eth
o
d
co
n
s
is
ts
o
f
r
ep
lacin
g
th
e
least
s
q
u
ar
e
m
eth
o
d
with
s
im
u
lated
an
n
ea
lin
g
.
I
n
d
ee
d
,
t
h
e
latter
m
ak
es
th
e
ca
lcu
latio
n
with
lo
w
co
m
p
lex
i
ty
,
m
ak
in
g
SA
-
DVHO
P
m
o
r
e
p
r
ec
is
e
th
an
th
e
t
r
ad
itio
n
al
D
VHOP
lo
ca
lizatio
n
alg
o
r
ith
m
.
3.
RE
S
E
ARCH
M
E
T
H
O
D
Ou
r
r
esear
ch
m
eth
o
d
o
l
o
g
y
is
as
f
o
llo
ws:
f
ir
s
tly
,
we
s
tu
d
y
DVHO
P
d
ee
p
ly
b
y
a
n
aly
zin
g
th
e
r
ea
s
o
n
b
eh
in
d
its
h
u
g
e
er
r
o
r
.
Seco
n
d
l
y
,
we
f
o
r
m
u
late
th
e
last
s
tep
o
f
DVHO
P
in
to
an
o
p
tim
izatio
n
p
r
o
b
le
m
in
w
h
ich
we
m
in
im
ize
t
h
e
f
itn
ess
f
u
n
ct
io
n
.
T
h
at
m
ea
n
s
we
m
in
im
ize
th
e
s
u
m
o
f
e
r
r
o
r
s
ac
cu
m
u
lated
d
u
r
in
g
th
e
m
u
lti
-
later
atio
n
p
r
o
ce
s
s
,
o
b
v
io
u
s
ly
t
o
r
ea
ch
th
e
c
o
n
v
e
n
ien
t
lo
ca
tio
n
s
o
f
u
n
k
n
o
wn
n
o
d
es.
Fo
r
t
h
a
t
p
u
r
p
o
s
e,
we
h
a
v
e
ad
o
p
ted
SA
alg
o
r
it
h
m
,
PS
O,
a
n
d
Fm
in
c
o
n
s
o
lv
e
r
d
ed
icate
d
to
m
ath
em
atica
l
o
p
tim
izatio
n
u
n
d
er
MA
T
L
AB
t
o
r
ep
lace
th
e
s
tep
o
f
r
eso
lu
tio
n
d
o
n
e
b
y
DVHO
P lo
ca
lizatio
n
alg
o
r
ith
m
.
Fin
ally
,
o
u
r
e
x
p
er
ie
n
ce
is
s
p
lit in
to
two
p
h
ases
.
I
n
th
e
f
ir
s
t
s
tep
,
we
p
r
ep
ar
e
an
ex
p
e
r
im
en
tal
en
v
ir
o
n
m
en
t
b
y
f
ix
in
g
th
e
n
u
m
b
er
o
f
n
o
d
es.
T
h
e
n
,
we
co
m
p
ar
e
th
e
p
e
r
f
o
r
m
an
ce
o
f
o
u
r
im
p
r
o
v
ed
v
er
s
io
n
o
f
DV
HOP
an
d
th
e
tr
a
d
itio
n
al
DV
HOP
b
y
v
ar
y
in
g
th
e
p
er
ce
n
tag
e
o
f
a
n
ch
o
r
s
.
I
n
th
e
s
ec
o
n
d
s
tep
,
we
r
e
-
m
ak
e
t
h
e
co
m
p
ar
is
o
n
b
y
v
ar
y
in
g
th
e
n
u
m
b
er
o
f
n
o
d
es
an
d
k
ee
p
in
g
t
h
e
p
er
ce
n
tag
e
o
f
an
c
h
o
r
s
at
3
0
%.
4.
T
H
E
P
RO
P
O
SE
D
AP
P
RO
A
CH
F
O
R
DVH
O
P
I
M
P
RO
V
E
M
E
N
T
W
e
co
n
s
id
er
ed
a
W
S
N,
wh
er
e
n
is
th
e
n
u
m
b
er
o
f
n
o
d
es
d
i
s
tr
ib
u
ted
th
r
o
u
g
h
o
u
t
th
e
f
ield
o
f
s
en
s
in
g
,
wh
o
s
e
s
u
r
f
ac
e
eq
u
als
1
,
0
0
0
×
1
,
0
0
0
m
2
.
Ad
d
itio
n
ally
,
we
u
s
ed
th
r
ee
o
p
tim
izatio
n
m
eth
o
d
s
:
PS
O,
SA
,
an
d
F
m
in
co
n
in
o
r
d
er
to
m
in
im
ize
th
e
co
s
t
f
u
n
ctio
n
o
f
DVHO
P.
T
ab
le
1
s
u
m
m
ar
izes
all
th
e
p
ar
am
eter
s
u
s
ed
f
o
r
th
e
tr
ad
itio
n
al
alg
o
r
ith
m
DVH
OP a
n
d
th
e
im
p
r
o
v
ed
alg
o
r
ith
m
s
b
ased
o
n
PS
O,
SA
,
an
d
F
m
in
co
n
.
4
.
1
.
T
ra
ditio
na
l D
VH
O
P
a
lg
o
rit
hm
DVHOP
i
s
a
d
is
tr
ib
u
ted
lo
ca
lizati
o
n
alg
o
r
ith
m
.
I
t
was
in
v
en
ted
b
y
Nicu
lescu
an
d
Nath
in
2
0
0
3
;
it'
s
b
ased
o
n
v
ec
to
r
d
is
tan
ce
r
o
u
ti
n
g
an
d
co
n
s
is
ts
o
f
th
r
ee
d
if
f
er
en
t step
s
,
as f
o
llo
ws:
−
Step
1
:
Flo
o
d
in
g
E
ac
h
u
n
k
n
o
wn
n
o
d
e
k
n
o
ws
t
h
e
n
u
m
b
er
o
f
h
o
p
s
to
th
eir
a
n
ch
o
r
b
y
a
m
ec
h
an
is
m
o
f
b
r
o
ad
ca
s
t
d
o
n
e
b
y
an
ch
o
r
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
A
n
efficien
t D
V
HOP
lo
ca
liz
a
tio
n
a
lg
o
r
ith
m
b
a
s
ed
o
n
s
imu
la
ted
…
(
Oma
r
A
r
r
o
u
b
)
723
T
ab
le
1
.
Su
m
m
a
r
y
o
f
n
o
tatio
n
s
S
y
mb
o
l
D
e
scri
p
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h
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ze
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o
p
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z
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b
e
t
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a
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c
h
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r
s
h
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p
c
o
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n
t
u
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i
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f
h
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n
a
n
c
h
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r
i
a
n
d
a
n
c
h
o
r
j
d
u,
i
D
i
st
a
n
c
e
b
e
t
w
e
e
n
a
n
c
h
o
r
i
a
n
d
t
h
e
u
n
k
n
o
w
n
n
o
d
e
f
(
x,y
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C
o
s
t
f
u
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c
t
i
o
n
t
o
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p
t
i
m
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k
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mp
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r
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t
h
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so
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r
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r
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o
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s
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m
P(
E,
T
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Th
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p
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o
b
a
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c
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l
p
a
r
t
i
c
l
e
s
c
1
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c
2
A
c
c
e
l
e
r
a
t
i
o
n
c
o
e
f
f
i
c
i
e
n
t
s
r
1
, r
2
R
e
e
l
n
u
mb
e
r
s
t
h
a
t
a
d
j
u
st
t
h
e
d
i
s
p
l
a
c
e
men
t
o
f
p
a
r
t
i
c
l
e
s
A
,
b
,
Ae
q
,
b
e
q
,
x0
,
lb
,
ub
A
t
t
r
i
b
u
t
e
s
o
f
F
mi
n
c
o
n
f
u
n
c
t
i
o
n
−
Step
2
:
Ho
p
-
s
ize
an
d
d
is
tan
ce
ca
lcu
latio
n
Af
ter
th
e
f
lo
o
d
in
g
p
r
o
ce
s
s
,
we
ca
n
o
b
tain
th
e
h
o
p
-
s
ize
b
etwe
en
an
ch
o
r
s
ac
co
r
d
i
n
g
to
t
h
e
f
o
r
m
u
la
(
1
)
.
h
o
p
s
iz
e
i
=
∑
√
(
−
)
2
+
(
−
)
2
=
1
#
∑
ℎ
=
1
(
1
)
W
h
er
e
(x
i
,y
i
)
,
(
x
j
,y
j
)
r
ep
r
esen
t r
esp
ec
tiv
ely
th
e
co
o
r
d
in
ates o
f
an
ch
o
r
s
i,j.
Af
ter
o
b
tain
in
g
h
o
p
s
ize,
in
(
2
)
is
u
s
ed
to
ca
lcu
late
th
e
d
is
tan
ce
b
etwe
en
an
ch
o
r
i
an
d
th
e
u
n
k
n
o
wn
n
o
d
e.
,
=
ℎ
×
ℎ
,
(
2
)
−
Step
3
: Calcu
latio
n
o
f
u
n
k
n
o
wn
n
o
d
e
p
o
s
itio
n
I
n
th
is
s
tep
,
we
s
p
ec
if
y
th
e
co
o
r
d
in
ates
o
f
all
u
n
k
n
o
wn
n
o
d
e
s
.
Fo
r
ea
ch
u
n
k
n
o
wn
n
o
d
e,
we
ap
p
ly
th
e
least
s
q
u
ar
e
m
eth
o
d
to
esti
m
ate
its
lo
ca
tio
n
.
(
x,
y)
d
en
o
tes
th
e
co
o
r
d
in
ates
o
f
th
e
u
n
k
n
o
wn
n
o
d
es,
(a
i
,b
i
)
r
ep
r
esen
ts
th
e
lo
ca
tio
n
o
f
t
h
e
an
ch
o
r
n
o
d
e,
wh
er
e
i
=1
,
2
,
.
.
n
an
d
n
is
th
e
n
u
m
b
er
o
f
an
ch
o
r
s
,
th
u
s
th
e
d
is
tan
ce
b
etwe
en
u
n
k
n
o
wn
n
o
d
es
an
d
n
an
ch
o
r
s
is
ex
p
r
ess
ed
b
y
th
e
n
o
n
-
lin
ea
r
eq
u
atio
n
s
:
{
(
−
1
)
2
+
(
−
1
)
2
+
(
−
1
)
2
=
1
2
.
.
(
−
)
2
+
(
−
)
2
+
(
−
)
2
=
2
(
3
)
T
h
en
we
f
in
d
:
{
2
−
2
1
+
1
2
+
2
−
2
1
+
1
2
=
1
2
.
.
2
−
2
+
2
+
2
−
2
+
2
=
1
2
(
4
)
I
n
(
4
)
ca
n
b
e
ex
ten
d
ed
to
:
{
−
2
(
1
−
)
+
1
2
−
2
−
2
(
1
−
)
+
1
2
−
2
=
1
2
.
.
−
2
(
−
1
−
)
+
−
1
2
−
2
−
2
(
−
1
−
)
+
−
1
2
−
2
=
−
1
2
(
5
)
T
h
e
s
o
lu
tio
n
o
f
th
e
s
y
s
tem
m
a
y
b
e
in
ter
p
r
eted
to
th
e
r
eso
lu
ti
o
n
o
f
th
e
eq
u
atio
n
A
x=b
w
h
er
e
:
A
=
[
2
(
1
−
)
2
(
1
−
)
.
.
2
(
−
1
−
)
.
.
2
(
−
1
−
)
]
(
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
3
9
,
No
.
1
,
Ju
ly
20
25
:
720
-
7
3
6
724
b=
[
1
2
−
2
+
1
2
−
2
+
1
2
−
2
−
1
2
.
.
−
1
2
−
2
+
−
1
2
−
2
+
−
1
2
−
2
−
−
1
2
]
(
7
)
In
th
e
tr
ad
itio
n
al
DVHO
P
a
lg
o
r
ith
m
,
th
e
least
s
q
u
ar
e
e
s
tim
ato
r
d
o
n
e
in
th
e
last
s
tep
o
f
th
e
p
o
s
itio
n
in
g
p
r
o
ce
s
s
ca
u
s
es
a
h
u
g
e
er
r
o
r
in
lo
ca
tin
g
th
e
tar
g
et
n
o
d
e,
wh
ich
h
as
a
b
ig
in
f
lu
en
ce
o
n
th
e
ac
cu
r
ac
y
o
f
DVHO
P.
I
n
ad
d
itio
n
to
th
at
,
DVH
OP
r
eq
u
ir
es
ad
d
it
io
n
al
an
c
h
o
r
s
t
o
o
f
f
er
ac
ce
p
tab
le
co
v
er
ag
e
o
f
lo
ca
lizatio
n
.
Hen
ce
,
th
e
latter
h
as
th
e
d
is
ad
v
an
tag
e
o
f
h
ig
h
en
er
g
y
co
s
ts
.
As
a
co
n
s
eq
u
en
ce
,
it
is
s
ee
n
as
n
ec
ess
ar
y
to
b
r
in
g
DVHO
P f
o
r
im
p
r
o
v
em
en
t to
o
v
er
c
o
m
e
it
s
ex
is
tin
g
d
is
ad
v
an
tag
es.
I
n
o
u
r
ap
p
r
o
ac
h
,
we
attem
p
t
t
o
k
ee
p
th
e
two
f
ir
s
t
s
tep
s
o
f
DVHO
P
an
d
ch
an
g
e
th
e
last
s
tep
to
an
o
p
tim
izatio
n
p
r
o
b
lem
.
I
n
d
et
ail,
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
is
s
u
m
m
ar
ized
in
t
h
r
ee
s
tep
s
:
ea
ch
u
n
k
n
o
wn
n
o
d
e
k
n
o
ws
its
n
u
m
b
er
o
f
h
o
p
s
to
t
h
eir
an
ch
o
r
s
th
r
o
u
g
h
a
b
r
o
a
d
c
ast
d
o
n
e
b
y
t
h
e
an
ch
o
r
s
.
Seco
n
d
ly
,
we
ca
lcu
late
th
e
d
is
tan
ce
b
etwe
en
an
ch
o
r
s
an
d
u
n
k
n
o
wn
n
o
d
es
o
n
th
e
b
a
s
is
o
f
th
e
h
o
p
-
s
ize.
L
astl
y
,
we
s
elec
t
a
s
p
ec
if
ied
m
eta
-
h
eu
r
is
tic
to
m
in
im
ize
th
e
s
u
m
o
f
er
r
o
r
s
o
cc
u
r
r
i
n
g
i
n
t
h
e
m
u
ltil
ater
atio
n
p
r
o
ce
s
s
.
Hen
ce
,
th
e
p
o
s
itio
n
i
ng
p
r
o
b
lem
m
ay
b
e
in
ter
p
r
ete
d
to
s
o
lv
e
th
e
m
in
im
izatio
n
o
f
th
e
f
itn
ess
f
u
n
ctio
n
m
e
n
tio
n
ed
i
n
(
8
)
.
(
,
)
=
1
∑
ǀ
√
(
−
)
2
+
(
−
)
2
=
1
−
ǀ
(
8
)
W
h
er
e
n
is
th
e
n
u
m
b
er
o
f
an
c
h
o
r
s
,
(a
i
,b
i
)
ar
e
th
e
co
o
r
d
in
ate
s
o
f
an
ch
o
r
s
,
d
i
is
th
e
d
is
tan
ce
b
etwe
en
an
ch
o
r
i
an
d
u
n
k
n
o
w
n
n
o
d
e.
I
n
th
is
p
ar
t,
we
d
is
cu
s
s
th
r
ee
im
p
r
o
v
ed
v
e
r
s
io
n
s
o
f
th
e
tr
ad
itio
n
al
DVHO
P
lo
ca
lizat
io
n
alg
o
r
ith
m
am
elio
r
ated
b
y
ad
o
p
tin
g
two
m
eta
-
h
eu
r
is
tics
(
SA,
PS
O)
an
d
Fm
in
co
n
s
o
lv
er
d
ed
icate
d
to
o
p
tim
izatio
n
u
n
d
e
r
MA
T
L
AB
.
Ou
r
p
u
r
p
o
s
e
is
to
en
h
a
n
ce
th
e
p
r
ec
is
io
n
o
f
DVHO
P.
T
h
e
two
f
ir
s
t
s
tep
s
in
all
en
h
an
ce
d
alg
o
r
ith
m
s
ar
e
s
im
ilar
to
th
e
t
wo
f
ir
s
t
s
tep
s
o
f
DVHO
P
alg
o
r
ith
m
b
ec
au
s
e
th
ese
s
tep
s
ar
e
th
e
m
ain
r
ea
s
o
n
f
o
r
th
e
h
ig
h
co
v
er
ag
e
o
f
th
e
lo
ca
lizatio
n
o
f
DVHO
P.
Hen
ce
,
we
leav
e
th
ese
s
tep
s
as
t
h
ey
ar
e
an
d
tack
le
o
u
r
m
o
d
if
icatio
n
s
in
t
h
e
last
s
tep
o
f
DVHO
P.
Mo
r
eo
v
er
,
we
ch
an
g
e
th
e
least
s
q
u
ar
e
m
eth
o
d
ad
o
p
ted
b
y
th
e
tr
ad
itio
n
al
alg
o
r
ith
m
t
o
an
o
p
tim
izatio
n
p
r
o
b
lem
t
h
at
ca
n
b
e
r
eso
lv
ed
b
y
ea
c
h
o
f
th
e
m
e
th
o
d
s
cited
ab
o
v
e
.
I
n
th
e
f
o
llo
win
g
,
we
s
h
all
cite
in
d
etail
o
u
r
im
p
r
o
v
ed
v
er
s
io
n
s
o
f
DVHO
P.
4
.
2
.
DVH
O
P
a
lg
o
rit
h
m
ba
s
ed
s
im
ula
t
ed
a
nn
ea
lin
g
SA
is
a
s
to
ch
asti
c
g
lo
b
al
s
ea
r
ch
o
p
tim
izatio
n
th
at
was
in
tr
o
d
u
ce
d
b
y
Kir
k
p
atr
ick
et
a
l.
[3
3
]
in
1
9
8
3
.
As
a
n
o
r
m
al
lo
ca
l
s
ea
r
c
h
m
et
h
o
d
,
it
u
s
es
a
s
p
ec
ial
s
tr
ateg
y
to
av
o
i
d
th
e
lo
ca
l
m
i
n
im
a.
T
h
is
m
eta
-
h
eu
r
is
tic
is
b
ased
o
n
h
ea
tin
g
an
d
c
o
o
lin
g
i
n
o
r
d
e
r
to
o
b
tain
a
f
lawless
all
o
y
.
I
n
d
etail,
th
is
m
eth
o
d
alter
n
ates
th
e
cy
cles
o
f
h
ea
tin
g
a
n
d
co
o
lin
g
t
h
e
m
et
als
s
lo
wly
.
T
h
e
m
ain
ad
v
a
n
t
ag
e
o
f
th
is
tec
h
n
iq
u
e
is
th
e
u
s
e
o
f
p
r
o
b
ab
ilis
tic
m
eth
o
d
o
l
o
g
y
,
wh
ich
p
e
r
m
its
av
o
id
in
g
lo
ca
l so
lu
tio
n
s
an
d
in
c
r
ea
s
es th
e
ex
p
lo
r
atio
n
p
r
o
ce
s
s
.
I
n
g
e
n
er
al,
th
e
p
u
r
p
o
s
e
o
f
SA
is
to
tr
av
er
s
e
t
h
e
s
p
ac
e
o
f
s
o
lu
tio
n
s
in
an
iter
ativ
e
m
a
n
n
er
.
W
e
s
tar
t
with
an
in
itial
s
o
lu
tio
n
S
0
(
g
en
er
ated
r
an
d
o
m
ly
)
wh
ich
d
e
n
o
t
es th
e
in
itial e
n
er
g
y
E
0
.
Ad
d
itio
n
ally
,
we
d
ef
in
e
a
v
ar
iab
le
ca
lled
tem
p
er
atu
r
e
ch
an
g
es
f
r
o
m
th
e
in
itial
t
em
p
er
atu
r
e
(
T
0
)
(
g
en
er
ally
h
ig
h
)
t
o
th
e
f
in
al
tem
p
er
atu
r
e.
I
t’
s
ass
u
m
ed
th
at
an
elem
en
tar
y
ch
an
g
e
o
c
cu
r
r
ed
in
th
e
s
o
lu
tio
n
at
ea
ch
iter
atio
n
o
f
th
e
alg
o
r
ith
m
.
T
h
is
ch
a
n
g
e
ca
u
s
es
a
v
ar
iatio
n
in
th
e
e
n
er
g
y
o
f
th
e
s
y
s
tem
th
at
we
d
en
o
te
∆
E
.
I
f
∆
E
is
n
eg
ativ
e
,
th
e
n
ew
s
o
lu
tio
n
is
ac
ce
p
ted
b
ec
au
s
e
it
im
p
r
o
v
es
t
h
e
co
s
t
f
u
n
ctio
n
.
I
f
∆
E
is
p
o
s
itiv
e,
th
e
s
o
lu
tio
n
f
o
u
n
d
m
ax
im
izes
th
e
e
n
er
g
y
o
f
th
e
s
y
s
tem
.
Hen
ce
,
it
's
co
n
s
i
d
er
ed
wo
r
s
e
th
an
th
e
p
r
ev
i
o
u
s
s
o
lu
tio
n
.
As
a
co
n
s
eq
u
en
ce
,
th
e
n
ew
s
o
lu
tio
n
will
b
e
ac
ce
p
ted
with
a
p
r
o
b
ab
ilit
y
P
ca
lcu
lated
ac
c
o
r
d
in
g
to
th
e
f
o
llo
win
g
B
o
ltzm
an
d
is
tr
ib
u
tio
n
:
(
,
)
=
(
−
∆
/
)
(
9
)
W
h
er
e
T
d
en
o
tes th
e
tem
p
er
at
u
r
e
o
f
t
h
e
s
o
lid
.
T
h
e
ch
o
ice
o
f
tem
p
er
at
u
r
e
i
s
ess
en
tial
to
g
u
ar
an
teein
g
t
h
e
b
alan
ce
b
etwe
en
in
ten
s
if
icatio
n
an
d
d
iv
er
s
if
icatio
n
o
f
s
o
lu
tio
n
s
in
th
e
s
p
ac
e
o
f
r
esear
ch
.
First,
th
e
ch
o
ice
o
f
th
e
in
itial
tem
p
er
at
u
r
e
d
ep
en
d
s
o
n
th
e
q
u
ality
o
f
th
e
s
tar
tin
g
s
o
lu
tio
n
.
I
n
d
ee
d
,
th
e
in
itial
v
alu
e
o
f
th
e
tem
p
er
atu
r
e
m
u
s
t
b
e
r
e
lativ
ely
h
ig
h
.
T
is
ca
lcu
lated
iter
ativ
ely
as f
o
llo
ws:
+
1
←
×
(
1
0
)
α
ϵ
[
0
,
1
]
,
α
is
a
p
ar
am
eter
t
h
at
ex
p
r
ess
e
s
th
e
d
ec
r
ea
s
e
i
n
tem
p
er
at
u
r
e
o
f
th
e
iter
atio
n
.
T
h
e
d
ec
r
ea
s
e
in
tem
p
er
atu
r
e
ca
n
also
b
e
ca
r
r
ie
d
o
u
t
in
s
tag
es.
T
h
at
is
to
s
ay
,
th
e
d
ec
r
ea
s
e
o
n
ly
ch
an
g
es
af
te
r
a
ce
r
tain
n
u
m
b
e
r
o
f
iter
atio
n
s
.
On
t
h
e
o
t
h
er
h
an
d
,
we
ca
n
also
r
aise
th
e
tem
p
e
r
atu
r
e
wh
e
n
th
e
s
ea
r
ch
p
r
o
ce
s
s
s
ee
m
s
b
lo
ck
ed
in
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
A
n
efficien
t D
V
HOP
lo
ca
liz
a
tio
n
a
lg
o
r
ith
m
b
a
s
ed
o
n
s
imu
la
ted
…
(
Oma
r
A
r
r
o
u
b
)
725
a
r
eg
io
n
o
f
th
e
s
ea
r
ch
s
p
ac
e.
W
e
ca
n
t
h
en
co
n
s
id
er
a
h
ig
h
in
cr
ea
s
e
i
n
tem
p
er
atu
r
e
as
a
p
r
o
ce
s
s
o
f
d
iv
er
s
if
icatio
n
.
W
h
ile
th
e
d
ec
r
ea
s
e
in
tem
p
er
atu
r
e
c
o
r
r
esp
o
n
d
s
to
an
in
ten
s
if
icatio
n
p
r
o
ce
s
s
.
I
n
th
e
b
eg
i
n
n
in
g
,
we
g
en
er
at
e
th
e
i
n
itial
s
o
lu
tio
n
.
T
h
en
,
we
ca
lcu
late
=
(
)
−
(
)
s
o
if
<
0
,
we
ac
ce
p
t
th
e
n
ew
s
o
lu
tio
n
;
o
th
er
wis
e,
we
ac
ce
p
t
th
e
s
o
l
u
tio
n
ac
co
r
d
in
g
to
th
e
to
th
e
Me
tr
o
p
o
lis
r
u
le.
T
h
en
,
we
test
if
th
e
n
u
m
b
er
o
f
iter
atio
n
s
is
r
ea
ch
ed
,
s
o
if
th
e
f
in
al
c
o
n
d
itio
n
is
s
ati
s
f
ied
,
we
r
etu
r
n
t
h
e
f
in
al
s
o
lu
tio
n
; o
th
er
wis
e,
we
d
ec
r
ea
s
e
th
e
tem
p
e
r
atu
r
e
a
n
d
w
e
s
et
th
e
n
u
m
b
er
o
f
iter
atio
n
s
t
o
0
.
T
h
e
f
lo
wch
ar
t
in
d
icate
d
in
Fig
u
r
e
1
d
escr
ib
es
in
d
etail
th
e
f
u
n
ctio
n
in
g
o
f
SA
.
Fig
u
r
e
1
.
Flo
w
ch
a
r
t o
f
SA a
lg
o
r
ith
m
T
h
e
p
r
i
n
cip
le
o
f
SA
-
DVHO
P
is
as
f
o
llo
ws:
we
ex
ec
u
te
s
i
m
u
lated
an
n
ea
lin
g
alg
o
r
ith
m
in
s
id
e
th
e
b
r
o
wsi
n
g
o
f
u
n
k
n
o
wn
n
o
d
es,
m
o
r
e
p
r
ec
is
ely
af
ter
th
e
d
is
tan
ce
ca
lcu
latio
n
s
tep
.
I
n
d
ee
d
,
f
o
r
ea
ch
s
o
lu
tio
n
ex
tr
ac
ted
b
y
s
im
u
lated
an
n
e
alin
g
alg
o
r
ith
m
,
it
will
b
e
a
s
s
ig
n
ed
to
a
n
u
n
k
n
o
wn
n
o
d
e
.
T
h
e
p
s
eu
d
o
-
co
d
e
m
en
tio
n
ed
i
n
Alg
o
r
ith
m
1
d
es
cr
ib
es th
e
s
tep
s
o
f
SA
-
DVHO
P a
lg
o
r
ith
m
.
Alg
o
r
ith
m
1
.
SA
-
DVHO
P a
lg
o
r
ith
m
Initialization
:
number of nodes=NB,
number of anchors=NA,
area of experimentation =1000×1000
m
2
,
communication range=500
m
1.calculation of hopcount
i,j
by finding the shortest path between nodes
2.hopsize calculation according (1)
3.calculate the positions of unknown nodes
for
i=NA to NB
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
3
9
,
No
.
1
,
Ju
ly
20
25
:
720
-
7
3
6
726
4.distance calculation
unknown_to_anchrs_dist=hopsize(i) ×
shortest_path(i,1 to NA);
5.fitness function f is calculated according (8)
6.execution of Simulated annealing algorithm
initialize the temperature T according to the
cooling scheme (10)
while
(condition of cooling is not satisfied)
ge
nerate a random neighbor S' from S
calculate
∆
E = f(S')
-
f(S)
if
∆E ≤ 0
S←S'
else
accept S
0
as the new solution with
probability
P(E,T) = exp(
-
∆E/T)
end
update T based on cooling scheme
end
return pbest
6.assign the result of SA to an unknown node
node.estimated(i,1to 2)=pbest;
end
4
.
3
.
DVH
O
P
a
lg
o
rit
h
m
-
ba
s
ed
pa
rt
icle
s
wa
rm
o
ptim
iza
t
i
o
n
T
h
e
o
p
tim
izatio
n
b
y
p
ar
ticle
s
war
m
was
in
v
en
ted
b
y
Ken
n
e
d
y
an
d
E
b
er
h
ar
t
in
1
9
9
5
.
T
h
is
m
eth
o
d
is
b
ased
o
n
th
e
s
o
cial
b
e
h
av
io
r
o
f
an
im
als
liv
in
g
in
s
war
m
s
.
I
n
d
ee
d
,
th
e
p
ar
ticles
ar
e
i
n
d
iv
id
u
als
an
d
th
e
y
m
o
v
e
in
o
r
d
e
r
to
s
ea
r
ch
f
o
r
a
g
lo
b
al
s
o
lu
tio
n
,
ac
co
r
d
in
g
t
o
th
e
f
o
llo
win
g
in
f
o
r
m
atio
n
:
−
E
ac
h
p
a
r
ticle
h
as
th
e
ab
ilit
y
t
o
m
em
o
r
ize
th
e
b
est
p
o
in
t
al
r
ea
d
y
p
ass
ed
an
d
it
attem
p
ts
t
o
r
etu
r
n
t
o
th
is
p
o
in
t.
−
E
ac
h
p
ar
ticle
is
awa
r
e
o
f
t
h
e
b
est p
o
in
t in
its
ar
ea
an
d
it will
attem
p
t to
g
o
t
o
war
d
s
th
is
p
o
i
n
t.
PS
O
co
n
s
is
ts
o
f
a
s
war
m
o
f
p
ar
ticles
th
at
f
ly
th
r
o
u
g
h
o
u
t
th
e
s
p
ac
e
o
f
s
o
lu
tio
n
s
in
o
r
d
er
to
r
ea
ch
th
e
g
lo
b
al
s
o
lu
tio
n
.
An
aly
tically
,
in
R
n
,
th
e
p
ar
ticle
i
o
f
th
e
s
wa
r
m
(
p
o
te
n
tial
s
o
lu
tio
n
)
is
m
o
d
eled
b
y
its
p
o
s
itio
n
v
ec
to
r
x
i
=(
x
i1
,
x
i2
,
.
.
.
,
x
in
)
a
n
d
b
y
its
v
elo
city
v
ec
t
o
r
v
i
=(
v
i1
,
v
i2
,
.
.
.
,
v
in
)
.
T
h
is
p
ar
ticle
r
e
m
em
b
er
s
th
e
id
ea
l
p
o
s
itio
n
th
at
we
n
o
te
d
p
i
=(
p
i1
,
p
i2
,
.
.
.
,
p
in
)
,
th
e
b
est
p
o
s
itio
n
r
ea
ch
ed
b
y
all
th
e
p
a
r
ticles
o
f
th
e
s
war
m
is
n
o
ted
by
p
g
=(
p
g1
,
p
g2
,
.
.
.
,
p
gn
)
.
W
e
ca
n
ex
p
r
ess
th
e
v
el
o
city
v
ec
to
r
u
s
in
g
(
1
1
)
.
,
(
+
1
)
=
,
(
)
+
1
1
(
,
(
)
–
,
(
)
)
+
2
2
(
,
(
)
–
,
(
)
)
(
1
1
)
c
1
,
c
2
ar
e
two
co
n
s
tan
ts
ca
lled
ac
ce
ler
atio
n
c
o
ef
f
icien
ts
.
r
1
,
r
2
ar
e
two
r
an
d
o
m
n
u
m
b
er
s
th
at
ex
is
ted
in
t
h
e
in
ter
v
al
[
0
,
1
]
,
v
ij
(
t)
co
r
r
esp
o
n
d
s
to
th
e
p
h
y
s
ical
co
m
p
o
n
e
n
t o
f
th
e
d
is
p
lace
m
en
t.
T
h
e
p
o
s
itio
n
o
f
p
a
r
ticle
i is th
en
d
ef
in
e
d
b
y
:
(
+
1
)
=
(
)
+
(
+
1
)
(
1
2
)
t
h
e
p
ar
ticle
s
war
m
is
u
s
u
ally
r
ep
r
esen
ted
b
y
a
g
e
o
m
etr
ic
m
o
d
el,
ass
u
m
in
g
th
at
v
is
th
e
v
elo
city
o
f
th
e
p
ar
ticle,
x
is
th
e
in
itial
p
o
s
itio
n
o
f
th
e
p
ar
ticle
an
d
p
is
th
e
o
p
tim
al
p
o
s
itio
n
o
f
th
e
p
a
r
ticle.
W
e
al
s
o
s
u
p
p
o
s
e
th
at
th
e
p
ar
ticle
s
war
m
is
co
m
p
o
s
ed
o
f
N
p
ar
ticles.
B
r
ief
ly
,
i
n
th
e
p
r
o
ce
s
s
o
f
f
in
d
i
n
g
t
h
e
o
p
tim
al
s
o
lu
tio
n
,
ea
c
h
p
ar
ticle
m
o
d
if
ies
its
p
o
s
itio
n
a
n
d
v
elo
city
iter
ativ
ely
.
T
h
at
is
to
s
ay
,
th
e
u
p
d
atin
g
o
f
th
e
p
o
s
itio
n
an
d
v
elo
cit
y
o
f
th
e
p
ar
ticle
is
b
ased
o
n
its
p
r
ev
io
u
s
in
f
o
r
m
atio
n
a
n
d
th
e
p
r
ev
i
o
u
s
b
est
p
o
s
itio
n
f
o
u
n
d
b
y
th
e
s
war
m
.
T
h
e
g
eo
m
etr
ic
m
o
d
el
illu
s
tr
ated
in
Fig
u
r
e
2
d
ep
icts
th
e
m
o
v
e
m
en
t
s
tr
ateg
y
o
f
t
h
e
p
ar
ticle.
T
h
e
p
s
eu
d
o
-
co
d
e
m
en
tio
n
ed
i
n
Alg
o
r
ith
m
2
d
es
cr
ib
es th
e
s
tep
s
o
f
PS
O
alg
o
r
ith
m
.
Fig
u
r
e
2
.
Up
d
atin
g
s
tr
ateg
y
o
f
p
ar
ticle
p
o
s
itio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
A
n
efficien
t D
V
HOP
lo
ca
liz
a
tio
n
a
lg
o
r
ith
m
b
a
s
ed
o
n
s
imu
la
ted
…
(
Oma
r
A
r
r
o
u
b
)
727
Alg
o
r
ith
m
2
.
Par
ticle
s
war
m
o
p
tim
izatio
n
alg
o
r
ith
m
Randomly initialize Ps particles: Position and velocity
Assess particle position
while
the stopping criterion is not reached
for
i=1,...,P
s
move the particles according (11),
(12)
if
f(x
i
)<f(p
i
)
p
i
= x
i
if
f(x
i
)<f(p
g
)
p
g
= x
i
end
end
end
end
I
n
th
e
b
eg
in
n
in
g
,
we
ca
lcu
late
th
e
av
er
ag
e
h
o
p
s
ize.
T
h
en
,
w
e
ca
lcu
late
th
e
d
is
tan
ce
b
etwe
en
an
ch
o
r
s
an
d
n
o
d
es.
I
n
ad
d
itio
n
,
we
u
s
e
PS
O
alg
o
r
ith
m
in
o
r
d
er
to
r
ef
in
e
r
esu
lts
.
I
n
d
ee
d
,
we
u
p
d
a
te
th
e
p
o
s
itio
n
an
d
th
e
b
est
p
o
s
itio
n
o
f
PS
O
in
ea
ch
iter
atio
n
o
f
PS
O
alg
o
r
ith
m
u
n
til
we
r
ea
ch
th
e
n
u
m
b
er
o
f
i
ter
atio
n
s
.
T
h
e
f
in
al
s
o
lu
tio
n
ex
tr
ac
ted
b
y
PS
O
d
en
o
tes
th
e
o
p
tim
al
co
o
r
d
i
n
ates
o
f
th
e
g
lo
b
al
alg
o
r
ith
m
PS
O
-
DVHO
P.
T
h
e
f
lo
wch
ar
t in
d
icate
d
in
Fig
u
r
e
3
d
escr
ib
es in
d
etail
th
e
f
u
n
cti
o
n
in
g
o
f
PS
O
-
DVHOP
.
Figur
e 3.
Flo
w
ch
ar
t
o
f
PS
O
-
DVHO
P a
lg
o
r
ith
m
4.4. D
V
H
O
P al
gor
i
t
h
m
b
ase
d F
m
i
nc
on so
l
ver
Fm
in
co
n
s
o
lv
er
is
p
r
esen
ted
a
m
o
n
g
th
e
s
o
lv
e
r
s
th
at
b
el
o
n
g
to
th
e
lib
r
ar
y
o
f
o
p
tim
izatio
n
in
teg
r
ated
in
MA
T
L
AB
.
Mo
r
eo
v
er
,
th
is
p
r
ed
ef
in
e
d
f
u
n
ctio
n
allo
ws
u
s
to
f
in
d
th
e
m
i
n
im
u
m
o
f
a
co
n
s
tr
ain
ed
n
o
n
-
lin
ea
r
m
u
lti
-
v
ar
iab
le
f
u
n
ctio
n
u
s
in
g
t
h
e
in
ter
io
r
-
p
o
in
t
alg
o
r
ith
m
.
Ho
wev
er
,
Fm
in
co
n
d
ep
en
d
s
o
n
d
escr
ib
in
g
th
e
co
s
t
f
u
n
ctio
n
an
d
all
ac
c
o
m
p
a
n
y
i
n
g
in
f
o
r
m
atio
n
,
s
u
ch
as
th
e
in
itial
p
o
in
t
o
f
th
e
alg
o
r
ith
m
an
d
th
e
c
o
n
s
tr
ain
ts
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
3
9
,
No
.
1
,
Ju
ly
20
25
:
720
-
7
3
6
728
I
n
d
e
ed
,
th
e
c
o
s
t
f
u
n
ctio
n
is
in
th
e
f
o
r
m
o
f
@
o
b
jf
u
n
.
Als
o
,
th
e
co
n
s
tr
ain
ts
an
d
b
o
u
n
d
s
o
f
co
n
s
tr
ain
ts
ar
e
r
ep
r
esen
ted
b
y
th
e
a
d
eq
u
ate
m
atr
ix
.
T
h
er
e
ar
e
two
ap
p
r
o
ac
h
es
f
o
r
u
s
in
g
Fm
in
co
n
:
eith
er
in
a
g
r
ap
h
ical
m
o
d
e
p
r
esen
ted
b
y
a
win
d
o
w
o
f
MA
T
L
AB
with
d
if
f
er
en
t f
ield
s
th
at
allo
w
th
e
u
s
er
to
in
s
er
t t
h
e
r
eq
u
ir
e
d
in
f
o
r
m
atio
n
(
f
u
n
ct
io
n
,
s
tar
t p
o
in
t,
a
n
d
co
n
s
tr
ain
ts
)
o
r
b
y
ca
llin
g
Fm
i
n
co
n
v
ia
th
e
co
m
m
an
d
win
d
o
w
o
f
MA
T
L
AB
.
I
n
t
h
is
ca
s
e,
we
m
u
s
t
s
p
ec
if
y
th
e
co
s
t
f
u
n
ctio
n
in
s
cr
ip
t.
m
an
d
we
ca
ll
th
e
co
n
s
tr
ain
ts
an
d
th
e
in
itial
p
o
in
t
v
ia
co
m
m
a
n
d
wi
n
d
o
w.
I
n
b
o
t
h
ca
s
es
o
f
u
tili
za
tio
n
,
wh
e
n
we
r
u
n
th
e
s
o
lv
er
,
th
e
r
esu
lts
ar
e
s
h
o
w
n
,
in
clu
d
in
g
th
e
r
ea
s
o
n
th
e
al
g
o
r
ith
m
ter
m
in
ated
.
Ob
v
io
u
s
ly
,
th
e
r
esu
lts
d
en
o
te
th
e
f
in
al
p
o
in
t
r
ea
ch
e
d
.
I
n
o
u
r
ca
s
e,
we
h
av
e
u
s
ed
th
e
s
o
lv
er
v
ia
co
m
m
an
d
win
d
o
w.
Ho
wev
er
,
o
u
r
p
u
r
p
o
s
e
was to
r
eso
lv
e
th
e
o
p
tim
izatio
n
p
r
o
b
lem
f
o
r
m
u
lated
as
(
1
3
)
.
{
min
(
)
s
ubj
e
c
t
to
.
≤
.
=
≤
≤
(
1
3
)
W
h
er
e:
A
,
A
eq
d
e
n
o
te
th
e
m
atr
ices o
f
co
n
s
tr
ain
ts
b
,
b
eq
d
en
o
te
th
e
v
ec
to
r
s
o
f
co
n
s
tr
ain
ts
lb
,
ub
t
h
e
u
p
p
er
an
d
lo
west v
a
lu
es tak
en
b
y
x
S
ee
in
g
th
at,
in
th
e
f
ield
o
f
s
e
n
s
in
g
,
a
s
en
s
o
r
m
ay
b
e
p
lace
d
with
o
u
t
a
n
y
p
r
ed
ef
in
e
d
co
n
d
itio
n
,
we
h
av
en
'
t
s
et
an
y
c
o
n
s
tr
ain
ts
o
n
o
u
r
o
p
tim
izatio
n
p
r
o
b
lem
.
A
ls
o
,
we
s
et
th
e
d
i
m
en
s
io
n
o
f
t
h
e
p
r
o
b
lem
at
two
b
ec
au
s
e
we
d
o
th
e
lo
ca
lizatio
n
in
two
d
im
en
s
io
n
s
.
Hen
ce
,
x
is
d
esig
n
ed
b
y
[
x
(
1
)
x(
2
)
]
.
I
n
ad
d
itio
n
to
th
at,
we
r
ef
er
th
e
u
p
p
e
r
an
d
lo
wer
v
alu
es
tak
en
b
y
x
to
th
e
lo
wer
an
d
u
p
p
er
ab
s
ciss
a
an
d
o
r
d
in
ate
t
ak
en
b
y
a
s
en
s
o
r
i
n
th
e
s
en
s
in
g
f
ield
.
I
n
o
u
r
ca
s
e,
o
u
r
f
ield
h
as
1
0
0
0
×1
0
0
0
as
a
s
u
r
f
ac
e,
s
o
lb
,
ub
tak
e
r
esp
ec
tiv
ely
th
e
v
alu
es
[
0
,
0
]
a
n
d
[
1
0
0
0
,
1
0
0
0
]
.
Am
o
n
g
th
e
p
r
ed
ef
in
e
d
s
o
lv
er
s
in
MA
T
L
AB
(
lin
p
r
o
g
,
g
a
,
f
m
in
im
ax
)
,
we
h
av
e
im
p
licitly
o
p
ted
f
o
r
Fm
in
co
n
b
ec
au
s
e
th
e
latter
m
ay
b
e
s
e
t
with
o
u
t
g
r
a
d
ien
t
s
u
p
p
ly
ca
lc
u
latio
n
.
Hen
ce
,
we
a
v
o
id
t
h
e
ad
d
itio
n
al
co
m
p
lex
ity
ca
u
s
ed
b
y
th
e
d
er
i
v
ativ
e
ca
lcu
latio
n
.
C
o
n
s
eq
u
e
n
tially
,
Fm
in
co
n
m
ak
es
th
e
o
p
tim
izatio
n
in
a
s
h
o
r
t
p
er
io
d
o
f
tim
e
i
n
co
m
p
ar
is
o
n
with
th
eir
v
ar
ian
ts
.
Seco
n
d
ly
,
in
b
o
th
ca
s
es
o
f
u
tili
za
tio
n
cit
ed
ab
o
v
e
(
co
m
m
an
d
win
d
o
w,
g
r
ap
h
ical
m
o
d
e
)
th
is
s
p
ec
ial
f
u
n
ctio
n
is
s
im
p
le
to
i
m
p
lem
en
t.
I
n
d
ee
d
,
it
ju
s
t
n
ee
d
s
to
ass
ig
n
ea
ch
o
f
th
eir
attr
ib
u
tes
p
r
o
p
e
r
ly
.
T
h
ir
d
ly
,
Fm
in
co
n
s
o
lv
e
r
is
an
ef
f
icien
t
to
o
l
to
av
o
id
b
ei
n
g
tr
a
p
p
ed
in
p
r
em
atu
r
e
co
n
v
er
g
en
ce
d
esp
ite
th
e
m
u
lti
-
m
o
d
ality
p
r
esen
te
d
in
o
u
r
c
o
s
t
f
u
n
ctio
n
d
ed
icate
d
to
o
p
tim
izin
g
DVHO
P.
T
h
e
p
s
eu
d
o
-
co
d
e
m
e
n
tio
n
ed
i
n
Alg
o
r
ith
m
3
d
escr
ib
es th
e
s
tep
s
o
f
FMI
NC
ON
-
DVHO
P a
lg
o
r
i
th
m
.
Alg
o
r
ith
m
3
.
FMI
NC
ON
-
DV
HOP
alg
o
r
ith
m
Initialization
:
number of
nodes =NB,
number of anchors=NA,
area of experimentation =1000×1000
m
2
,
communication range=500
m
1.calculation of hopcount
i,j
by finding the shortest path between nodes
for
k=1 to NB
for
i =1 to NB
for
j=1 to NB
if
(
shortest_path(i,j)> shortest_path(i,k)+ shortest_path(k,j) )
shortest_path(i,j)= shortest_path(i,k)+shortest_path(k,j);
end
end
end
end
2.hopsize calculation according (1)
3.calculate the positions
of unknown nodes
for
i=NA to NB
4.distance calculation
unknown_to_anchors_dist=hopsize(i) × shortest_path(i,1 to NA);
5.fitness function f is calculated according (6)
A=[]; b=[]; Aeq=[]; beq=[]; x0=[0 0];
lb=[0 0]; ub=[10001000];
6.assign for each unknown node the result of fmincon
node.estimated(i,1to 2) = fmincon(f,x0,A,b,Aeq,beq,lb,ub);
end
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
A
n
efficien
t D
V
HOP
lo
ca
liz
a
tio
n
a
lg
o
r
ith
m
b
a
s
ed
o
n
s
imu
la
ted
…
(
Oma
r
A
r
r
o
u
b
)
729
5.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
NS
I
n
th
is
s
ec
tio
n
,
we
co
m
p
ar
e
t
h
e
p
er
f
o
r
m
an
ce
o
f
SA
-
DVH
OP,
PS
O
-
DVH
OP,
FMI
N
C
O
N
-
DVHOP
,
an
d
DVHO
P
in
ter
m
s
o
f
ac
cu
r
ac
y
.
I
t'
s
wo
r
th
m
en
tio
n
in
g
th
at
th
er
e
ar
e
s
ev
er
al
m
etr
ics
to
ju
d
g
e
th
e
q
u
ality
o
f
th
e
lo
ca
lizatio
n
alg
o
r
ith
m
,
s
u
ch
as
co
v
er
ag
e
o
f
lo
ca
lizatio
n
,
co
n
s
u
m
p
tio
n
o
f
en
e
r
g
y
.
Al
s
o
,
it
ex
is
ts
s
ev
er
al
wo
r
k
s
to
ass
ess
th
e
alg
o
r
ith
m
s
in
ter
m
s
o
f
c
o
m
p
lex
it
y
o
f
ca
lcu
latio
n
.
T
h
at'
s
to
s
ay
th
e
y
u
s
e
th
e
m
etr
ic
o
f
co
m
p
lex
ity
in
o
r
d
e
r
to
d
ed
u
ce
th
e
tim
e
o
f
ex
ec
u
tio
n
r
eq
u
ir
e
d
b
y
th
e
al
g
o
r
ith
m
.
Acc
o
r
d
in
g
to
o
u
r
e
x
p
er
im
e
n
tatio
n
,
DVHO
P
s
u
cc
ess
f
u
lly
l
o
ca
tes
th
e
wh
o
le
s
en
s
o
r
n
o
d
es
with
a
r
ea
s
o
n
ab
le
v
al
u
e
o
f
p
ar
am
eter
s
(
n
u
m
b
e
r
o
f
n
o
d
es,
a
n
ch
o
r
r
atio
)
in
s
ev
e
r
al
s
ce
n
ar
io
s
o
f
s
i
m
u
latio
n
.
T
h
at'
s
to
s
ay
DVHO
P
h
as
a
h
ig
h
co
v
er
ag
e
o
f
l
o
ca
lizatio
n
.
Als
o
,
we
ass
u
m
e
th
at
th
e
v
ar
ian
ts
SA
-
DVHO
P,
P
SO
-
DVHO
P,
an
d
FMI
NC
ON
-
DV
HOP
h
av
e
th
e
s
am
e
ad
v
an
tag
e
b
ec
au
s
e
th
o
s
e
im
p
r
o
v
e
d
v
e
r
s
io
n
s
o
f
DVHO
P
k
ee
p
th
e
two
s
tep
s
o
f
th
e
tr
a
d
itio
n
al
DVHO
P.
C
o
n
s
eq
u
en
t
ly
,
we
d
o
n
’
t
tak
e
in
to
ac
c
o
u
n
t
th
e
ev
alu
atio
n
o
f
co
v
er
ag
e
o
f
lo
ca
lizatio
n
,
an
d
we
ass
e
s
s
o
u
r
lo
ca
lizatio
n
tech
n
iq
u
es
ju
s
t
ac
co
r
d
in
g
to
th
eir
lo
ca
lizatio
n
ac
cu
r
ac
y
in
a
W
SN
with
a
u
n
if
o
r
m
a
n
d
r
an
d
o
m
d
is
tr
ib
u
tio
n
o
f
n
o
d
es.
I
n
d
etail,
in
o
u
r
s
im
u
latio
n
s
,
we
f
ir
s
t
co
n
s
id
er
ed
a
n
etwo
r
k
with
a
r
an
d
o
m
d
is
tr
ib
u
ti
o
n
o
f
n
o
d
es.
Als
o
,
we
h
av
e
as
s
es
s
ed
o
u
r
alg
o
r
ith
m
s
in
g
r
id
to
p
o
lo
g
y
.
T
h
at
is
to
s
ay
,
th
e
ar
ea
o
f
s
im
u
latio
n
is
p
ar
titi
o
n
ed
in
to
g
r
i
d
s
,
an
d
n
o
d
es
an
d
an
ch
o
r
s
ar
e
e
q
u
all
y
d
is
tr
ib
u
ted
th
r
o
u
g
h
o
u
t
th
ese
g
r
id
s
.
T
h
e
cr
iter
io
n
o
f
co
m
p
ar
i
s
o
n
is
AL
E
in
o
r
d
er
to
s
elec
t
wh
ich
lo
ca
lizatio
n
alg
o
r
ith
m
is
b
etter
in
a
s
p
ec
if
i
ed
co
n
f
i
g
u
r
atio
n
in
ter
m
s
o
f
a
cc
u
r
ac
y
.
I
n
o
r
d
er
to
am
elio
r
ate
DVHO
P,
we
h
av
e
cr
ea
ted
th
r
ee
im
p
r
o
v
ed
v
er
s
io
n
s
o
f
th
e
tr
ad
itio
n
a
l
DVHO
P.
I
n
d
ee
d
,
we
m
ak
e
s
im
u
latio
n
i
n
two
d
im
en
s
io
n
s
;
f
o
r
SA
-
DVHO
P
we
in
itialize
th
e
tem
p
er
atu
r
e
at
0
.
1
a
n
d
th
e
n
u
m
b
er
o
f
n
eig
h
b
o
r
s
p
er
in
d
iv
id
u
al
at
5
.
Fo
r
PS
O
-
DVHO
P,
we
u
s
e
5
0
in
d
iv
id
u
als,
a
n
d
we
in
itia
lize
th
e
co
g
n
itio
n
s
c
o
ef
f
icien
ts
at
d
ete
r
m
in
ate
v
al
u
es.
T
ab
le
s
2
an
d
3
d
escr
ib
e
th
e
p
ar
a
m
eter
s
ettin
g
s
o
f
SA
-
DVHO
P
an
d
PS
O
-
DVHO
P.
T
ab
le
2
.
Par
am
eter
s
ettin
g
s
o
f
SA
-
DVHOP
P
a
r
a
me
t
e
r
V
a
l
u
e
D
i
me
n
si
o
n
2
Lo
w
e
r
b
o
u
n
d
0
U
p
p
e
r
b
o
u
n
d
1
,
0
0
0
N
u
mb
e
r
o
f
i
t
e
r
a
t
i
o
n
s
10
I
n
i
t
i
a
l
t
e
m
p
e
r
a
t
u
r
e
0
.
1
α
0
.
9
9
P
o
p
u
l
a
t
i
o
n
s
i
z
e
10
N
u
mb
e
r
o
f
n
e
i
g
h
b
o
r
s
p
e
r
i
n
d
i
v
i
d
u
a
l
5
T
ab
le
3
.
Par
am
eter
s
ettin
g
s
o
f
PS
O
-
DVHO
P
P
a
r
a
me
t
e
r
V
a
l
u
e
P
o
p
u
l
a
t
i
o
n
s
i
z
e
50
N
u
mb
e
r
o
f
i
t
e
r
a
t
i
o
n
s
1
0
0
c1
1
.
7
7
5
c2
2
.
8
D
i
me
n
si
o
n
2
Lo
w
e
r
b
o
u
n
d
0
U
p
p
e
r
b
o
u
n
d
1
,
0
0
0
T
o
ev
alu
ate
th
e
p
er
f
o
r
m
an
c
e
o
f
ea
ch
lo
ca
lizatio
n
alg
o
r
ith
m
i
n
ter
m
s
o
f
ac
cu
r
ac
y
o
f
lo
ca
lizatio
n
.
T
h
e
f
o
llo
win
g
m
et
r
ic
h
as
b
ee
n
co
n
s
id
er
ed
:
AL
E
wh
ic
h
is
th
e
r
atio
o
f
t
o
tal
lo
ca
lizatio
n
er
r
o
r
to
th
e
n
u
m
b
er
o
f
s
im
p
le
n
o
d
es.
I
n
d
ee
d
,
AL
E
is
u
s
ed
to
as
s
ess
th
e
p
r
ec
is
i
o
n
o
f
ea
ch
lo
ca
lizatio
n
alg
o
r
ith
m
ac
co
r
d
in
g
to
d
if
f
er
en
t
p
a
r
am
eter
s
s
u
ch
as
n
o
d
e
d
e
n
s
ity
,
an
ch
o
r
n
o
d
e
r
at
io
an
d
s
h
ap
e
o
f
d
is
tr
ib
u
tio
n
.
I
n
d
ee
d
,
a
s
p
ec
if
ied
alg
o
r
ith
m
is
m
o
r
e
ac
cu
r
ate
if
it h
as
less
AL
E
.
AL
E
ca
n
b
e
ex
p
r
ess
ed
as
(
1
4
)
.
=
√
(
−
)
2
+
(
−
)
2
(
−
ℎ
)
(
1
4
)
W
h
er
e
(
,
)
an
d
(
,
)
ar
e
th
e
tr
u
e
an
d
esti
m
ated
co
o
r
d
in
ates o
f
s
en
s
o
r
n
o
d
es
r
esp
ec
tiv
el
y
.
n
t
d
en
o
tes th
e
t
o
tal
n
u
m
b
er
o
f
n
o
d
es.
n
h
p
r
esen
ts
th
e
n
o
n
-
l
o
ca
lized
n
o
d
es
.
r
p
r
esen
ts
th
e
co
m
m
u
n
icatio
n
r
an
g
e
o
f
a
n
o
d
e
.
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