TELKOM
NIKA
, Vol.14, No
.4, Dece
mbe
r
2016, pp. 14
38~144
5
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v14i4.3985
1438
Re
cei
v
ed Ma
y 12, 201
6; Revi
sed Septe
m
ber
13, 201
6; Acce
pted
Septem
ber 2
7
, 2016
Novel DV-hop Method Based on Krill Swarm Algorithm
Used for Wireless Sensor Network Localization
Yang Sun
1
, Shoulin Yin*
2
, Jie Liu
3
Soft
w
a
re Co
lle
ge, Shen
ya
n
g
Normal U
n
iv
ersit
y
, She
n
y
an
g
,
China
No.25
3
, Hua
n
g
H
e Bei Street, Hua
ngGu Distr
ict, Shen
yan
g
, P.C 1100
34 -
Chin
a
*
Corresp
on
din
g
author, em
ail
:
17247
61
3@q
q
.com
1
, 3527
2
021
4@q
q
.com
2
, nan127
@so
hu.com
3
A
b
st
r
a
ct
Wireless sens
or network (WSN) is self-organi
z
i
ng
n
e
tw
ork; it consists
of a large
nu
mb
er of
sensor nod
es w
i
th
percepti
o
n,
calc
ul
atio
n
abil
i
ty an
d co
mmu
n
icati
on
a
b
ility. Gen
e
ral
l
y
, the floor, w
a
lls or
peo
ple
movi
ng
has a
n
effect
on i
ndo
or l
o
cal
i
z
a
t
i
on, so
it w
ill result i
n
mu
lti
-
path p
h
e
n
o
m
e
na a
nd
decre
a
s
e
sign
al stren
g
th
; also the rec
e
ived si
gn
al strength i
n
d
i
cator
(RSSI) is una
ble to g
a
in
hig
her accur
a
cy
of
positi
oni
ng. In order to i
m
pr
o
v
e the
W
S
N positio
nin
g
accu
racy in in
do
or cond
ition, i
n
thi
s
paper, w
e
firstly
prop
ose kri
ll
sw
arm al
gor
ithm
use
d
for
W
S
N loca
l
i
zation. W
e
d
e
t
aile
d an
aly
z
e
the
multi
l
ate
r
al
me
asur
e
m
ent meth
od in
r
a
n
ge-free dista
n
c
e
vector-h
op
(DV-ho
p) loc
a
li
z
a
ti
on
al
gori
t
hm. T
he
pos
i
t
ion
prob
le
m can
b
e
transfor
m
ed
i
n
to a gl
oba
l op
timi
z
a
t
i
o
n
prob
l
e
m. T
h
e
n
, w
e
ade
qu
ately util
i
z
e
th
e adv
anta
ge
of calcul
atin
g opti
m
i
z
at
ion pr
obl
e
m
an
d ap
ply the
kril
l sw
arm al
gorith
m
into th
e stage of esti
ma
tin
g
unkn
o
w
n
nod
e
coordi
nates i
n
DV-hop
alg
o
ri
thm to re
al
i
z
e
local
i
z
a
ti
on. F
i
nally, the s
i
mu
latio
n
exp
e
rie
n
c
e
results show
that the loca
li
zation w
i
th krill
sw
arm alg
o
rith
m has a
n
obvi
ously hi
gh
er p
o
sitio
n
in
g preci
s
ion
and acc
u
racy s
t
ability w
i
th different anc
hor n
ode pr
op
ortion
and n
o
d
e
s.
Ke
y
w
ords
:
WSN, RSSI,
DV-ho
p
loca
li
z
a
ti
on a
l
g
o
rith
m,
krill sw
ar
m al
gor
ith
m
, rang
e-free dis
t
ance,
mu
ltilat
e
ral me
asure
m
ent
method
Copy
right
©
2016 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion.
Re
cently, pe
ople have
a gro
w
ing
dem
and for in
doo
r location info
rmation
se
rvice
s
. Th
e
traditional G
PS and cellu
lar network p
o
sitioni
ng technolo
g
y cann
ot meet the requireme
nts of
indoo
r p
o
sitio
n
ing. F
o
rtun
a
t
ely, wirel
e
ss
sen
s
o
r
netwo
rk (WSN) [1]
make
s up
for
the defi
c
ien
c
i
e
s
of the traditional po
sitioni
ng tech
nolo
g
y
, which is
widely u
s
ed i
n
exhibition
cente
r
, intelligent
building,
spo
r
ts venu
es
a
nd othe
r fiel
ds. In
ind
oor positio
ning t
e
ch
nolo
g
ies,
the localization
algorith
m
pe
rforman
c
e i
s
dire
ctly relat
ed to
the lo
cation a
c
cu
racy of se
nso
r
network no
de
.
Curre
n
tly, WSN lo
cali
zatio
n
technol
ogy
has two
majo
r meth
od
s: ra
nge
dista
n
ce
and
ran
g
e
-
fre
e
distan
ce. It
inclu
d
e
s
con
v
ex pro
g
ra
m
m
ing l
o
cali
zation al
gorit
hm [2], cent
roid
lo
calization
algorith
m
and
DV-h
op lo
cal
i
zation
algo
rithm [3]
based
on the rang
e
-
free
dista
n
ce
in WSN
nod
e
locali
zation. These
al
go
rithms wo
rk without
ad
ditio
nal h
a
rd
wa
re
su
ppo
rt an
d
high
co
st. T
h
e
positio
ning
preci
s
ion, h
o
wever, cann
ot
meet t
he
req
u
irem
ents of
indoo
r lo
cali
zation a
c
curacy.
The
rang
e
distan
ce l
o
calizatio
n alg
o
rithm
s
cont
ains tim
e
of
arrival (T
O
A
) algo
rithm
[4],
receive sig
nal
strengt
h
in
d
i
cation (RSSI)
al
gor
ith
m
and angl
e of
arrival (A
OA)
al
go
rith
m.
More
over, so
me ne
we
st machi
ne lea
r
ni
ng algo
rithm
s
have bee
n p
r
opo
se
d such
as [5-7]. In this
pape
r, we d
e
sig
n
a ne
w method ba
sed on Krill S
w
arm algo
rit
h
m used for wirel
e
ss se
nso
r
netwo
rk l
o
cal
i
zation.
What
’s mo
re, we
also
state its workin
g pri
n
ciple a
nd d
e
m
onst
r
ate th
e
indoo
r locali
zation p
e
rfo
r
mance thro
u
gh rig
o
ro
us
experim
ents.
The re
st o
f
this pape
r is
orga
nized as follows:
The
next
se
ction
of
the
p
ape
r i
n
trodu
ce
s t
h
e
gen
eral
p
r
in
ciples of the
K
r
ill
Swarm
algo
ri
thm and
DV-hop al
gorith
m
. Section3
propo
se
s the K
r
ill Swa
r
m al
gorithm
used
for
the WSN l
o
cali
zation. After that, experimenta
l results with the Krill Swarm
algorithm
are
pre
s
ente
d
in se
ction 4. Th
e final se
ction
of
the paper i
n
clu
d
e
s
the concl
uding
re
marks.
2. Nov
e
l DV-hop Method
Based on Krill S
w
arm Algorithm
In this secti
on, we detai
led illustrate
our new scheme. Anchor
nodes (i
ncludi
ng
unknown nodes and
known
nodes) are regard
ed as krill swarm.
T
he
gather
behavior of
krill is
a
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
No
vel DV
-ho
p
Method Ba
sed o
n
Krill Swarm
Algorith
m
Used for Wirele
ss Se
nso
r
… (Ya
ng Su
n)
1439
pro
c
e
s
s of m
u
lti-obje
c
tive, whi
c
h
is ve
ry
clo
s
ely to
se
nso
r
n
ode
s.
The ai
m of
o
u
r n
e
w meth
o
d
is
to add
sen
s
o
r
no
de
s de
nsi
t
y and app
ro
ach to
main
n
ode. Usin
g krill swarm
alg
o
rithm
will m
a
ke
each no
de
chang
e their
positio
n freq
uently towa
rd
the optim
a
l
value direction mode
rat
e
ly.
Position
chan
ging an
d fora
ging be
havior cau
s
ed by o
t
her an
ch
or n
ode
s co
ntain
a local
sea
r
ch
strategy and
a
glo
bal sea
r
ch strate
gy.
Two kin
d
s
of
strate
gie
s
work in
pa
rallel
.
After coll
ect
i
ng
the optimal position of nod
es ba
sed o
n
krill swa
r
m al
gorithm, then
we utilize DV-hop meth
o
d
to
cal
c
ulate
the
po
sition of unkno
wn no
des. Finally, we demo
n
st
rate
its high
perfo
rman
ce
and
efficien
cy through
many e
x
perien
c
e
s
. T
he an
ch
or
no
des
model
wi
th krill
swarm
algorith
m
is
as
follows
:
1.
Determine th
e anchor n
o
d
e
s La
gra
ngia
n
model ba
se
d on krill
swarm.
i
i
i
i
D
F
N
dt
dX
(1)
Whe
r
e
i
is
i-t
h
anchor
no
de.
X
i
is the state of anch
o
r nod
e.
N
i
d
enote
s
veloci
ty vector of
indu
ced
mov
e
ment.
F
i
is
veloc
i
ty vec
t
or
of finding key node.
D
i
i
s
ran
dom
diffusio
n
velo
city
vec
t
or
.
2.
Motion indu
ced by other a
n
ch
or no
de in
dividual
s.
old
t
n
et
t
i
local
i
new
i
N
N
N
)
(
arg
min
(2)
Whe
r
e
N
mi
n
=0.
1
m
/
s
is the minimum vel
o
city of induced
moveme
nt in WSN ba
sed on the rea
l
situation
.
)
1
,
0
(
n
is the
ine
r
tia
weig
ht of ind
u
ce
d move
m
ent.
old
i
N
is the last velocity
vector of indu
ced move
me
nt.
local
i
is lo
cal infl
uen
ce of adja
c
ent an
ch
or n
ode.
NN
j
j
i
j
i
local
i
X
K
1
,
,
ˆ
ˆ
(
3
)
best
worst
j
i
j
i
K
K
K
K
K
,
ˆ
(
4
)
||
||
ˆ
,
i
j
j
i
j
i
X
X
X
X
X
(
5
)
Whe
r
e
K
i
den
otes fitness o
f
i-th
ancho
r
node.
K
j
is fitness of
j-th
n
e
ighb
orh
ood
anchor n
ode.
K
best
and
K
wo
r
s
t
are th
e be
st fitness
and
the worst fitness respe
c
tively.
X
i
is the
state of
i-
th
anchor no
de.
X
j
is the
st
ate of
j-th
a
n
ch
or
nod
e.
ε
is a
small
positive n
u
m
ber to
avoid
sing
ularity.
NN
is the num
ber of adja
c
e
n
t anch
o
r no
de, whi
c
h ca
n determi
ned
by perce
ptio
n
distan
ce of e
a
ch a
n
chor n
ode
d
i
.
d
i
ca
n be expre
s
sed
as:
N
j
j
i
i
X
X
N
d
1
||
||
5
1
(6)
Whe
r
e N i
s
th
e total numbe
r of anchor n
ode.
et
t
i
arg
is influen
ce o
f
the optimal anchor n
ode
as (7
)
best
i
best
i
et
t
i
X
K
I
rand
,
,
max
arg
ˆ
ˆ
)
1
(
2
(7)
Whe
r
e
ran
d
i
s
rand
om n
u
m
ber
betwee
n
0 a
nd 1.
I
i
s
the current it
eration
s
num
ber.
I
ma
x
is the
maximum iteration.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 14, No. 4, Dece
mb
er 201
6 : 1438 – 144
5
1440
3. Finding
key
n
ode.
old
i
f
best
i
food
i
f
new
i
F
V
F
)
(
(8)
Whe
r
e
V
f
=0.
2
m
/
s
is spee
d
of finding
key
nod
e.
)
1
,
0
(
f
is the
inertia
wei
ght
of findin
g
ke
y
node.
best
i
is the
best p
r
eviou
s
ly visited po
si
tion of the
i-t
h
an
cho
r
no
d
e
individu
al.
old
i
F
is
the last velo
ci
ty vector of fi
nding
key n
o
de.
food
i
is i
n
fluen
ce of
i-
th
an
chor node, whi
c
h ca
n
be rep
r
e
s
e
n
ted by:
N
j
i
N
i
i
i
food
K
K
X
X
1
1
/
1
/
(9)
food
i
food
i
food
i
X
K
I
I
,
,
max
ˆ
ˆ
)
1
(
2
(10
)
So the influen
ce of cu
rrent i-th node i
s
:
ibest
i
ibest
i
best
i
X
K
,
,
ˆ
ˆ
(11)
This is th
e finding key nod
e stage.
4.
Stocha
stic dif
f
usion p
r
o
c
e
s
s.
)
1
(
max
max
I
I
D
D
new
i
(12)
Whe
r
e
D
ma
x
(0.002,0.01
)m
/s
is the spe
ed of rando
m diffusion.
δ
is the dire
ction vecto
r
,
whi
c
h is
subj
ected to (-1,1
)
uniform di
stribution.
5.
Upd
a
ting an
chor no
de po
si
tions.
)
(
1
new
i
new
i
new
i
I
i
I
i
D
F
N
t
X
X
(13)
Whe
r
e
t
is int
e
rval
sele
cte
d
a
c
cordi
ng t
o
the
real
situ
ation. In thi
s
pape
r,
t
=1s.
So every
anchor
node
will get the
optimal position in
the
WSN including the unknown nodes.
We
can
use the follo
wing figure to show the a
n
ch
or nod
es m
o
vement tra
ck.
(a)
(b)
Figure 1. This figure sh
ows the position
of anc
h
o
r no
d
e
s in WS
N be
fore and afte
r using
krill
swarm al
gorit
hm. (a) Po
sition of anchor
node
s wi
th
ou
t krill swarm a
l
gorithm; (b
)
Position of
anchor nodes with krill swarm algorithm
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
No
vel DV
-ho
p
Method Ba
sed o
n
Krill Swarm
Algorith
m
Used for Wirele
ss Se
nso
r
… (Ya
ng Su
n)
1441
2.1. Process
of nov
el DV-hop based o
n
krill s
w
arm
.
We de
sig
n
the novel DV-h
op algo
rithm
as follo
ws:
Ancho
r
no
de
s avera
ge ju
mp distan
ce
comp
utation formul
a is:
i
j
hop
i
j
jj
ii
jj
ii
hop
ij
i
S
y
y
x
x
S
/
)
(
)
(
2
2
(14)
Whe
r
e
i
hop
S
is co
rre
sp
ondi
ng
averag
e jum
p
distan
ce of
anch
o
r no
de
i
.
j
is other anch
o
r no
de
numbe
r in an
cho
r
nod
e
i
data table.
ij
hop
S
is the hop
cou
n
t betwee
n
i
an
d
j
.
(x
ii
, y
ii
)
an
d
(x
jj
,y
jj
)
is
the coordinat
e of
I
i
X
,
I
j
X
(the
obtained best
pos
ition by
krill swarm)
re
spectively. Therefore,
the
i
hop
S
is also the optimal
co
rre
sp
ondi
ng
averag
e
jum
p
distan
ce. A
c
cordi
ng to the re
co
rde
d
hop i
n
form
ation, un
kn
own
nod
es will
calcul
ate th
e
distan
ce
fro
m
itself to
a
n
ch
or
nod
e
after
receiving ave
r
age ju
mp di
stance by form
ula (15
)
.
i
hop
i
h
S
d
(15)
After cal
c
ulat
ing the di
sta
n
ce,
DV-h
op
algor
ithm
solves the
co
ordin
a
te of u
n
kn
own
node
s by mul
t
ilateral mea
s
urem
ent method.
Known
U
11
(x
11
,y
11
)
,
U
22
(x
22
,y
22
)
, …,
U
nn
(x
nn
,y
nn
)
and
the unkno
wn node
K(x
,
y)
w
hen
there
are
n(
n
≥
3)
no
de
s.
d
11
,
d
22
, …,
d
nn
are
the
dista
n
ce
from
U
11
,
U
22
,…,
U
nn
to
K
respec
tively.
So:
2
2
2
2
11
2
11
2
11
)
(
)
(
,
,
)
(
)
(
nn
nn
nn
d
y
y
x
x
d
y
y
x
x
(16)
It can be expressed by sy
st
em of linear e
quation
s
AL=B
,
L=(x,
y
)
T
,
T
nn
n
n
nn
n
n
nn
nn
y
y
x
x
y
y
x
x
A
))]
(
2
)
(
2
(
,
)),
(
2
)
(
2
[(
1
|
1
1
|
1
11
11
(17
)
T
nn
n
n
nn
n
n
nn
n
n
d
d
y
y
x
x
B
)
(
2
2
1
|
1
2
2
1
|
1
2
2
1
|
1
(18
)
Becau
s
e
of the ra
nge e
r
ror, enviro
n
m
ent factors a
nd co
mmuni
cation,
AL=
B
can
b
e
rewritten a
s
AL+
ε
=B
.
ε
d
e
notes the e
n
e
rgy
con
s
um
ption pa
ra
m
e
ter
in WSN. We ca
n
get
l
east-
squ
a
re
soluti
ons of eq
uati
ons by sta
n
d
a
rd lea
s
t sq
u
a
re
s metho
d
:
L=(A
T
A)
-1
A
T
B
.
d
n
is measuring
distan
ce
with error in
clud
ed
in the
B
. So the cal
c
ul
ation
result is limited by
d
n
. If th
e error of
d
n
is
small en
oug
h
,
L
can meet the requi
rem
ents.
Ho
weve
r, if the error
of
d
n
is big enoug
h, the erro
r
of result is bi
g too. Although this meth
o
d
simplif
ie
s th
e pro
c
e
s
s of solving n
onlin
ear e
quatio
ns, it
may redu
ce
a
c
cura
cy of so
lution. Aiming
at this
situati
on, this pa
per transfo
rm
s the problem i
n
to
global o
p
timization.
Assuming th
at
f
n
is the measuremen
t error
betw
een u
n
know
n nod
e a
n
d
ancho
r
node, so
n
nn
nn
n
d
y
y
x
x
f
2
2
)
(
)
(
.
Then the unk
nown n
ode
K(x,y)
can be solved.
n
i
i
ii
ii
d
y
y
x
x
y
x
f
1
2
2
)
)
(
)
(
(
)
,
(
(19
)
Whe
n
f
(
x,
y)
i
s
the minim
u
m value, the total error i
s
very small
and
(x,y
)
is th
e m
o
st app
ro
ach to
the real val
u
e
,
so the
(x,
y
)
i
s
opti
c
al valu
e. Solution of
f(x
,
y)
is
not li
mited to an e
quation, n
a
m
e
ly
althoug
h ran
g
e
error of so
me ancho
r no
des i
s
bi
g, it has little effect on the sol
u
tio
n
of
(x,y
)
.
As mention
e
d
above, nod
e locali
zation
probl
e
m
is converted into
global optimi
z
atio
n
probl
em. For formula (19), the traditional meth
ods are difficult
to solve it. But krill swarm
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TELKOM
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Vol. 14, No. 4, Dece
mb
er 201
6 : 1438 – 144
5
1442
algorith
m
is a better and
newe
s
t method to so
lve
global opti
m
ization p
r
o
b
lem. Experi
m
ent
results
show that krill swarm algorithm i
s
a better
scheme used fo
r WSN
locali
zation.
2.2. Detailed
DV-hop Algorithm Based
on Krill S
w
arm
Step 1: Initialization. Se
t the ge
neratio
n co
unter
Q=1
; initialize th
e pop
ulation
P
of
NP
anchor no
de
s rand
omly a
nd e
a
ch no
d
e
corre
s
po
nd
s to
a p
o
tenti
a
l solution to
the given
pro
b
lem;
set the
finding
key
node
spee
d
V
f
, the minim
u
m diffu
sion
spe
ed
D
mi
n
, a
nd the maxim
u
m indu
ced
speed
N
ma
x
.
Step 2: Fitness eval
uation.
Evaluate each anchor n
o
d
e
ac
cording t
o
its positio
n.
Step 3: While
the terminati
on crite
r
ia i
s
not satisfie
d or
Q
＜
M
a
xG
eneration
do.
Sort the popu
lation of node
s from be
st to worst.
for =
1
: NP do
Perform the followin
g
motion cal
c
ulation.
Motion indu
ce
d b
y
the prese
n
ce of other no
des.
Finding k
e
y node.
Phy
s
i
cal diffus
i
on.
Implement the geneti
c
ope
rato
rs.
Update the nod
e indiv
i
dual po
sition
in the sea
r
ch spa
c
e.
Evaluate each krill in
di
vidual acco
rdi
ng to its positi
on.
end for
i
Sort the popu
lation of node
from best to worst and fin
d
the cu
rre
nt best.
Q=Q
+
1
.
Step 4: End while.
Step 5: Get processe
d an
chor no
de po
si
tions.
Step 6: DV-h
op co
rrectio
n
.
If
RSSI v
a
lue >
T
, hop
s co
u
n
t=0.5. Othe
rwise, hop
s co
unt=1.
Step 7: Hops
betwe
en no
d
e
s a
c
qui
sition
.
Step 8: The average h
op di
stan
ce calcul
ation.
Step 9: Position to cal
c
ulat
e.
Step 10: Finish
3. Simulation Experiments and An
aly
s
is
.
In this sectio
n, we ma
ke
experim
ents
to
verify the perfo
rman
ce
our al
gorith
m
. Th
e
experim
ents
of DV-hop algorit
hm
based on
krill
swarm is m
a
de on MAT
L
AB platform. In
100m*
100m
region, we
ra
ndomly scatter 200
no
de
s. The fixed
n
ode
co
mmuni
cation
radiu
s
is
30m. Ch
angi
ng the num
b
e
r of an
cho
r
node from 20
to 55. We al
so ma
ke a
co
mpari
s
o
n
to DV-
hop
and
the
metho
d
(IDV-hop
) i
n
ref
e
ren
c
e
[8]
with ou
r n
e
w
scheme
(KS
D
V-h
op).
After
experim
ents,
we get the re
sults
a
nd ave
r
age valu
e as Figure 2.
Figure 2. The
effect of number of an
cho
r
node
on er
ror
rate
Figure 3. The
effect of com
m
unication ra
dius
on er
ror
rate
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
No
vel DV
-ho
p
Method Ba
sed o
n
Krill Swarm
Algorith
m
Used for Wirele
ss Se
nso
r
… (Ya
ng Su
n)
1443
From Fig
u
re
2, we can
know that this
new metho
d
is supe
rio
r
to DV-h
op al
gorithm.
Whe
n
the nu
mber of
an
chor node
is very
small,
t
he e
rro
r
rate
decre
ases
rapidly. Wh
en
the
anchor
nod
e
numbe
r i
s
st
eady, the error rate re
mai
n
s u
n
chan
ge
d, whi
c
h in
dicate
s that KSDV-
hop
algo
rithm
ha
s little
req
u
irem
ent for
anchor no
de numbe
r.
A
s
we all kno
w
, anchor
no
de co
st
with po
sitioni
ng fun
c
tion i
s
far l
a
rg
er t
han u
n
kno
w
n nod
e in
WSN, as
well
as the
ene
rg
y
con
s
um
ption.
Therefore, redu
cing a
n
ch
or no
de
s pla
y
s an imp
o
rt
ant role in
re
duci
ng net
wo
rk
co
st an
d imp
r
oving
network life
cycle.
T
able 1
is the
corre
s
p
ondin
g
data
of Fig
u
re
3. Keepi
n
g
the an
cho
r
n
ode 5
0
u
n
ch
ange
d, we
ch
ange th
e
co
mmuni
cation
radiu
s
from 1
5
m to 50
m. And it
con
d
u
c
ts 10
0
Monte-Carl
o simulatio
n
s a
s
Figu
re 3.
Table 1. Error rate value wi
th different an
cho
r
nod
es
Algorithm
Number of
ancho
r nodes
20 25 30
35 40 45 50 55
DV-hop
0.361
0.318
0.251
0.262
0.212
0.202
0.168
0.124
IDV-hop
0.301
0.245
0.221
0.197
0.131
0.109
0.105
0.079
KSDV-hop
0.301
0.199
0.146
0.118
0.057
0.061
0.035
0.038
Table 2 i
s
th
e co
rrespon
d
i
ng data
of F
i
gure
4. It sh
ows that Ma
x-Hop
of net
work i
s
decreasing from 15m to 50m. So the position ac
curacy
will im
prove. Th
e whole of
error
rate
experie
nces
a de
cre
a
si
ng
trend. On t
he wh
ole,
K
S
DV-ho
p
alg
o
rithm i
s
su
p
e
rio
r
to DV-h
op
algorith
m
und
er any
comm
unication radi
us. Compa
r
e
d
to [8], the error rate is
very s
m
all
with
our
new meth
od. And with prop
er co
mmuni
cation radi
us, result
s of KSDV-hop a
r
e mo
re stabl
e.
Table 2. Error rate value wi
th different co
mmuni
cation
radiu
s
Algorithm
Communication r
adius
15 20 25
30 35 40 45 50
DV-hop
0.291
0.235
0.232
0.183
0.184
0.179
0.152
0.151
IDV-hop
0.268
0.178
0.173
0.117
0.118
0.093
0.089
0.083
KSDV-hop
0.229
0.136
0.111
0.062
0.058
0.051
0.039
0.028
What’
s
m
o
re
, we
ma
ke
experim
ents
with 1
0
stan
dard
te
sting
functio
n
s (Multimoda
l
function
s: Ackley
f
1
, Fletch
er-Po
w
el
f
2
, Griewank
f
3
, Penalty
f
4
, Quartic
f
5
, Ra
st
rigin
f
6
; Unim
odal
function
s: Ro
sen
b
ro
ck
f
7
, Schwefel
12
f
8
, Sphere
f
9
, Step
f
10
) to
comp
are DV-hop, IDV-ho
p
,
KSCO (Krill
swarm crossover operato
r in [9]), CA (cuckoo algorith
m [10]), PSO (parti
cle
swarm
optimizatio
n i
n
[11]) to ou
r KSDV-h
op
method. Sup
posi
ng that
popul
ation si
ze
NP=5
0
, a
nd
maximum g
e
neratio
n
Ma
xgen
=50
for
e
a
ch
algo
rithm
.
We
ran
10
0
Monte
Ca
rlo
simul
a
tion
s
of
each algo
rith
m on each be
nch ma
rk fun
c
tion to
get re
pre
s
entative
perfo
rman
ce
s and the re
sul
t
s
are a
s
table4
inclu
d
ing ave
r
age mi
nima
value (
am
v
) a
nd be
st minima value (
bm
v
).
Table 3. Simulation re
sult
s
DV-hop
IDV-hop
KSCO
CA
PSO
KSDV-hop
am
v
bm
v
am
v
bm
v
am
v
bm
v
am
v
bm
v
am
v
bm
v
am
v
bm
v
f
1
4.42 7.64
3.75 5.38 3.52 4.13 2.58 5.84 3.64
5.87 1.42
1.29
f
2
6.87 6.59
4.62 3.35 2.38 2.84 3.64 1.62 4.73
7.66 1.23
1.08
f
3
32.64
36.12
18.97
18.05
9.65
16.87
11.32
20.85
20.56
22.37
4.26
1.59
f
4
2.3e
3
3.2e
3
25.63
18.67
18.95
15.66
1.4e
4
3.6e
4
3.1e
3
2.8e
3
5.57
3.17
f
5
86.34
67.59
52.87
48.67
35.64
35.65
44.83
45.84
96.57
87.34
18.23
9.63
f
6
86.34
78.65
75.12
65.34
46.95
45.77
50.28
46.29
87.64
60.85
20.31
1.67
f
7
8.87
18.36
6.53
11.78
5.55 6.53 6.13 5.78 7.86
10.46
1.25
1.45
f
8
6.95
12.47
5.21
12.31
3.37 5.87 4.29 6.75 5.28
8.87 1.46
1.11
f
9
12.64
9.76
10.28
8.76 8.98 6.54 6.51 6.66
13.74
7.85 1.12
1.13
f
10
7.87
13.81
3.94 8.57 3.87 5.36 4.62 4.21 9.55
4.45 1.57
1.05
From Figu
re 3,
we ca
n kn
ow
th
at
KSDV-hop
is th
e
most effe
ctivene
ss algo
rit
h
m to g
e
t
obje
c
tive function minimu
m
on ave
r
a
ge v
a
lue a
nd
be
st value o
n
the
ten fun
c
tion
s. Wh
at’s m
o
re
,
to further
pro
v
e the perfo
rmance of p
r
o
posed al
gor
it
hm, we u
s
e t
he ab
ove different al
go
rith
ms
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 14, No. 4, Dece
mb
er 201
6 : 1438 – 144
5
1444
to get be
st function val
ue
as Fig
u
re 4-1
3
for t
he ten f
unctio
n
s. And
the po
sition
value a
s
Figu
re
14. Figu
re 4
-
13 show th
at KSDV-ho
p can get optim
i
z
ation
re
sults in a sh
ort time with a l
o
w
gene
ration
n
u
mbe
r
. Amon
g the six o
p
timization
algo
rithms, o
u
r m
e
thod p
e
rfo
r
ms the
be
st an
d
most effectively
wh
en sol
v
ing
the glo
bal
n
u
me
rica
l optimization
pro
b
lem
s
a
nd
signifi
cant
ly
outperfo
rm
s the other five approa
che
s
.
Figure 4.
f
1
compa
r
ison
Figure 5.
f
2
compa
r
ison
Figure 6.
f
3
compa
r
is
on
Figure 7.
f
4
compa
r
ison
Figure 8.
f
5
compa
r
ison
Figure 9.
f
6
compa
r
is
on
Figure 10.
f
7
comp
ari
s
o
n
Figure
11.
f
8
comp
ari
s
o
n
Figure
12.
f
9
comp
ari
s
o
n
Figure 13.
f
1
0
comp
ari
s
o
n
Figure 14. True value with
different algo
rithms
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
No
vel DV
-ho
p
Method Ba
sed o
n
Krill Swarm
Algorith
m
Used for Wirele
ss Se
nso
r
… (Ya
ng Su
n)
1445
4. Conclu
sions
This p
ape
r make
s an
a
nalysi
s
for traditional
DV-hop. In that there a
r
e m
any extra
factors,
such as enviro
n
me
nt,
measurem
ent erro
r et
c.
So we
propo
se
a novel
DV-hop
ba
sed
on
krill swa
r
m al
gorithm. Thi
s
new meth
od can
spee
d up
the global co
nverge
nce rat
e
without losi
ng
the stron
g
ro
bustn
ess of the ba
si
c DV
-hop. From th
e analysi
s
of t
he experime
n
tal results, it can
be co
ncl
uded
that the proposed DV
-ho
p
method u
s
es the inform
ation in past
solutio
n
s mo
re
efficiently wh
en com
pared
to the other popul
ati
on ba
sed optimi
z
at
ion algo
rithm
s
su
ch a
s
IDV-
hop, CA, KSCO, PSO. Based o
n
the re
sults, KSD
V-hop si
gnifica
ntly improves the performa
n
ce
of DV-h
op o
n
most m
u
ltimodal a
nd u
n
imodal
pro
b
l
ems. In ad
di
tion, KSDV-h
op is
simpl
e
and
easy to imple
m
ent.
Referen
ces
[1]
Shahr
okhz
ade
h M, Hagh
igh
a
t AT
, Mahmoudi
F
,
et al.
A Heuristic Method fo
r W
i
reless Sen
s
or Netw
or
k
L
o
c
al
i
z
atio
n
. P
r
oced
ia Com
p
u
t
er Science. 2
0
11; 5: 812-
819.
[2]
K Ren, F
Z
hua
ng. Res
earch
and im
prov
em
ent of m
obi
le a
n
chor n
o
d
e
loc
a
lizati
on
alg
o
rit
h
m base
d
o
n
conve
x
pr
ogra
mming.
Chi
nes
e Journ
a
l of Se
nsors an
d Actu
ators.
2014; 2
7
(
10): 140
6-1
4
1
1
.
[3]
W Guo, J Wei. Optimiza
ti
o
n
Res
earc
h
of the
DV-Ho
p
L
o
cal
i
zatio
n
Algor
ithm.
TEL
K
OMNIKA
Indon
esi
an Jou
r
nal of Electric
al Eng
i
ne
eri
n
g
.
2014; 1
2
(4): 2
735-
274
2.
[4]
Sath
yan
T
,
Hedle
y
M,
Hump
h
r
e
y
D. A mu
ltip
le ca
nd
idate
ti
me of arr
i
val
al
gorithm for
trac
king
no
des
in
multip
ath envir
onme
n
ts.
Sign
al Process
i
ng.
201
2; 92(7): 16
11-1
623.
[5]
Salem O, Guerassimov A, Mehao
ua A, et al. Anom
a
l
y
D
e
tec
t
ion in Me
dica
l W
i
reless Sens
or Net
w
ork
s
usin
g SVM and Li
near R
egress
i
on Mo
dels.
Internati
ona
l Journ
a
l
of E-Health
and Med
i
ca
l
Co
mmun
icati
o
ns.
2016; 5(
1): 20-4
5
.
[6]
Lv T
,
Gao H, Li
X, et a
l
. Sp
ace-T
i
me Hier
a
rchi
c
a
l-Grap
h
Based
Co
ope
rative L
o
cal
i
zat
i
on
in W
i
re
less
Sensor N
e
t
w
or
ks.
IEEE
Transactions on Signal Proc
essing.
2016; 64(
2): 322-3
34.
[7]
Pan MS, L
ee
YH. F
a
st conv
ergec
ast for lo
w
-
d
u
t
y
-c
ycle
d
multi-cha
n
n
e
l
w
i
rel
e
ss se
nso
r
net
w
o
rks.
Ad
Hoc Netw
orks
. 201
6; 40: 1-14.
[8]
Qin Sha
n
Z
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