TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 14, No. 3, June 20
15, pp. 516 ~ 5
2
4
DOI: 10.115
9
1
/telkomni
ka.
v
14i3.786
1
516
Re
cei
v
ed Fe
brua
ry 10, 20
15; Re
vised
Ap
ril 23, 201
5; Acce
pted
May 13, 20
15
Wireless Sensor Networks Node Localization-A
Performance Comparison of Shuffled Frog Leaping and
Firefly Algorithm in LabVIEW
Chan
dirase
k
a
ran D*, T. J
a
y
a
barathi
VIT
Universit
y
,
Schoo
l of Elect
r
ical
Scie
nces,
Vell
ore, 63
201
4, India
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: chasan
2k@g
mail.com
A
b
st
r
a
ct
W
i
reless s
ens
or n
e
tw
orks (W
SN) hav
e b
e
co
me
po
pu
la
r in
many
a
p
p
licati
ons
ar
ea
incl
ud
i
n
g
envir
on
me
ntal
mo
nitori
ng, mil
i
tary and offsh
o
re oil
& gas i
ndustri
e
s. In W
S
N the sensors are rand
o
m
l
y
dep
loye
d
in th
e se
nsor fi
el
d
and
he
nce
esti
mati
on
of th
e l
o
cali
z
a
tio
n
of
each
de
pl
oyed
no
de
has
dra
w
n
mor
e
atte
ntion
by the
rec
ent
researc
hers, It
’s a u
n
i
que
pro
b
le
m to
id
entif
y an
d
maxi
mi
z
i
ng th
e cov
e
rag
e
w
here the
se
n
s
ors n
eed
to
b
e
p
l
ace
d
in
a
positi
on s
o
th
a
t
the se
nsi
ng
capa
bil
i
ty of th
e n
e
tw
ork is f
u
ll
y
utili
z
e
d
to e
n
s
u
re h
i
gh
qu
alit
y of service. In
order to
k
eep
the cost of se
n
s
or
netw
o
rks to a
mi
ni
mu
m, th
e
use of a
d
d
i
tion
al h
a
rdw
a
re l
i
k
e
gl
oba
l p
o
siti
oni
ng
syste
m
(
G
PS) can be
avoi
ded
by the
use of effecti
v
e
alg
o
rith
ms th
at
can
b
e
used
f
o
r the
same. In this
paper we
attempted to
use
b
o
th th
e s
h
uffled fro
g
le
ap
ing
(SF
L
A) and fir
e
fly alg
o
rith
ms
(F
F
A
)
to estimate th
e opti
m
a
l
loc
a
tion
of rando
mly de
pl
oyed se
nsors.
T
h
e
results w
e
re co
mp
are
d
an
d pu
blish
ed
for the
useful
ness of further rese
arch
.
Ke
y
w
ords
:
WSN, SFLA, F
F
A
, locali
z
a
t
i
on,
RSSI, ToA
Copy
right
©
2015 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Wirel
e
ss Sen
s
or
Networks are dist
ribute
d
se
lf-di
r
e
c
te
d contai
n nod
es which can
sen
s
e
s
and up
date t
he data’
s to the ba
se
station which
are
discu
s
sed in
article [1].
WSN te
chn
o
l
ogy
become
s
po
p
u
lar in
all a
r
e
a
s of a
ppli
c
at
ions i
n
cl
uding
military, med
i
ca
l, p
r
ocess
and el
ectroni
c
indu
strie
s
du
e to its easy implementat
ion and ma
i
n
tenan
ce. Th
e intere
st of rese
arch is to
analyse the
possibility of utilising it for pro
c
e
ss i
n
d
u
strie
s
a
nd h
a
za
rd lo
catio
n
is inte
re
st of
resea
r
ch; ho
weverth
e
i
s
sues with
WS
N a
r
e th
e
d
eployment
of the no
de
s,
locali
sation
a
nd
energy awa
r
e clu
s
terin
g
and an op
timized solut
i
on req
u
ire
d
to do the
same. Ge
ne
rally
locali
zation
in
WS
N i
s
d
o
n
e
by e
quip
p
in
g a
Glob
al p
o
sitioni
ng
system (GPS
)
wi
th ea
ch
se
nsor
node i
s
to
b
e
don
e; ho
wever e
quippi
ng a
GPS with each
sen
s
or no
de i
s
co
st wi
se m
o
re
expen
sive
sol
u
tion. The
r
ef
ore
an
altern
ate solution
n
eed to
be
fou
nd to
add
re
ss the lo
cali
zati
on
issues, whi
c
h come out in the form of utilising
the optimization algorithm
s
for locali
zation. The
conve
n
tional
optimizatio
n tech
niqu
es a
r
e useful
only for less nu
m
ber of node
s and req
u
ires
more
comput
ational effo
rts with
re
spe
c
t
to the p
r
o
b
le
m si
ze .
H
en
ce an
optimi
z
ation meth
od
is
requi
re
d to o
v
erco
me all t
hese issue
s
and curr
ently
our researchers ha
s dev
elope
d so m
any
algorith
m
s p
a
rticul
arly
ba
sed
on
the i
n
spi
r
ed
ch
a
r
acters from
the n
a
tural
living thin
gs.
T
hese
Bio-in
spired
algorith
m
s m
e
thod
s of
opt
imization
a
r
e
co
mputation
a
lly efficient
comp
ared to
the
conve
n
tional
analytical m
e
thods; mai
n
ly the Shu
ffled
Frog le
apin
g
algorithm
(S
FLA) an
dFire
f
ly
algorith
m
s
(F
FA) are pop
u
l
ar multi-dime
nsio
nal opt
im
ization te
chni
que
s. The fe
ature
s
of the
s
e
SFLA and FF
A are ea
sy impleme
n
tatio
n
, more a
c
cu
rate solution
s, computatio
n
a
l efficien
cy and
their fast con
v
ergen
ce.
Formul
ation
of work
:
A WS
N co
nsi
s
ts
of
N num
ber
of
n
o
des an
d
thecom
muni
cationra
nge
b
e
twee
n them
is
r, the
nod
es
are
di
strib
u
ted in
the
sensi
ng field.
The
WSN i
s
re
pre
s
ente
d
a
s
the Euclid
ean
grap
h
G
= (
X,
Y
), where
X
=
{a
1
, a
2
. . .an}
i
s
the set of
s
e
ns
or
no
d
e
s.
_i, j_
∈
Y
ij the dista
n
ce be
tween
ai
a
nd
Xj
is
dij
≤
r
. Un
kno
w
n
nod
es are th
e set
V
ofnon-bea
co
n
node
swhich locatio
n
to be
determin
ed.
Settled node
s are the set
S
of nodes th
at
manag
ed to e
s
timate their
positio
ns u
s
in
g the locali
zat
i
on algo
rithm.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Wirel
e
ss Sen
s
or
Networks Nod
e
Lo
caliz
ation-A Perfo
r
m
ance
…
(Chandi
ra
se
karan D)
517
Given a WS
N
G
= (
X,Y
), a
nd a set of be
aco
n
nod
es
B
and their p
o
sitions (
xb,
y
b
), for
all
b
∈
B
, it
is d
e
sired
to find
the
po
sition
(
xu,
y
u
) of a
s
many
u
∈
U
as
po
ssi
ble, t
r
an
sformi
ng
the
unkno
wn no
d
e
s into settled node
s
S
.
In the artic
l
e [2] exis
ting
loc
a
tion awarene
ss ap
pro
a
ch
es is di
scu
s
sed, the
r
e is two
techni
que
s commonly em
ployed, the first one
i
s
ba
sed on dista
n
c
e or a
ngle
measurement
and
se
con
d
isco
mbination of
distan
ce a
n
d
angle.
Re
cei
v
ed Signal Strength Indi
ca
tor (RSSI) i
s
the
most
popul
ar
method
of m
easurin
g the
node
po
sition
by calculatin
g the
dista
n
ce of n
ode
s. Ti
me
of arrival (T
oA) and An
gle-of
-Arrival
(AoA),
Tria
ngulatio
n an
d Maximum
Likelih
ood
(ML)
estimation a
r
e the othe
r method
s.
RSSIte
chni
que is b
a
sed on the
receivin
g power
andatten
uatio
n of
radi
o
sig
nal exp
one
ntially with th
e i
n
crea
se
of di
stan
ce. In
RS
SI the di
stan
ce
can
be
cal
c
ul
atedba
se
d o
n
thelo
ss i
n
powerby
com
parin
g the th
eoreti
c
al m
o
del. Time b
a
sed
method
s Tim
e
of Arrival (T
oA) and e
s
ti
mates the
di
stance by the
differen
c
e of prop
agatio
n time
betwe
en t
w
o
nod
es
with
kn
own vel
o
city of
sign
al
propa
gation.
Angle
-
of
-A
rr
iv
al (AoA)
al
so
kno
w
n a
s
Di
rection of Arri
val (DoA
) techniqu
es
cal
c
u
l
ates the po
si
tion by geom
etric
coo
r
din
a
t
es
with the
an
g
l
e from
where si
gnal
s
are re
ceive
d
.
As p
e
r
as a
c
cura
cy of
d
e
termin
ation
is
con
c
e
r
ne
d T
o
A, and AoA method
s are
ahead
RSSI, due to loss in radio
sig
n
a
l amplitud
e by
environ
menta
l
factors. Tri
a
ngulatio
n techniqu
e
is ba
sed on the d
i
rectio
n mea
s
urem
ent of the
node
in
stead
of the di
stan
ce me
asure
d
i
n
AoA
syste
m
s. Th
e
nod
e po
siti
on
s
are dete
r
min
e
d
by
trigono
metry
laws of si
nø
and
co
sinø.
Maximum L
i
kelih
ood
(M
L) e
s
timation
cal
c
ulate
s
t
he
positio
n
of a
no
de by minimizi
ng
t
he
diffe
re
n
c
es
between
the m
e
a
s
ured di
stan
ce
s and
estimated
di
stance
s
. T
he l
o
cali
zatio
n
in
WS
N i
s
d
o
n
e
in t
w
o
pha
ses, o
ne i
s
ra
nging
ph
ase
and
anothe
r o
ne i
s
e
s
timation
pha
se. T
he
n
ode
s e
s
timat
e
s th
eir di
sta
n
ce
s f
r
om
be
aco
n
s (o
r
set
t
led
node
s) u
s
in
g
the signal propag
ation time or the st
re
ngth of the receive
d
sign
al in the rang
ing
pha
se. Due t
o
noi
se a
c
cu
rate mea
s
u
r
e
m
ent of the
s
e pa
ramete
rs are
not po
ssible du
e to n
o
ise
and
hen
ce
the lo
cali
satio
n
alg
o
rithm
s
uses th
e
s
e para
m
eters may
not
b
e
accurate.
In the
se
con
d
pha
se, estimation
of the positio
n is carri
ed o
u
t using the
rangin
g
information. This
can
be do
ne eith
er by tra
d
itio
nal way of solving a
se
t
of simultan
eo
us e
quatio
ns,
or othe
r
way
b
y
usin
g an opti
m
ization al
go
rithm whi
c
h
minimizes the
locali
zation e
rro
r.
In the lo
cali
zation alg
o
rith
m whi
c
h
use
s
it
eration m
e
thod, the
no
des
whi
c
h
are settled
serve
as b
e
a
c
on
s an
d the
p
ro
ce
ssof localizatio
n is
co
ntinued u
n
til either all no
d
e
s a
r
e settled
, o
r
with no mo
re
node
s can be
locali
zed.
In this
pap
er
we
dealt t
w
o
bio-in
spi
r
ed
o
p
timization
al
gorithm
s fo
r
node
lo
cali
za
tion in
a
WSN. T
he first one
is
one
is
shuffled f
r
og lea
p
i
ng
al
gorithm
(SFL
A) whi
c
h
is
d
e
tailed in
arti
cle
[3], and the other on
e isfirefly algorithm
discusse
d
in
article [4]. Beca
use of ea
sine
ss in solv
ing
probl
em with
more efficie
n
cy in multidimen
sion
al sea
r
ch nature these two
algorithm
s are
popul
ar in the
rece
nt day’s
resea
r
ch.
The pa
per i
s
orga
nized a
s
follo
ws: se
cti
on 2
d
iscu
ssed
about th
e literatu
r
e survey of
previou
s
research in
WSN localization. Se
ction
3 pre
s
e
n
ts
SFLA and F
F
A optimizat
ion
algorith
m
s u
s
ed for lo
calization in this study. Sect
ion
4 explains h
o
w the lo
cali
zation pro
b
lem
is
approa
che
d
usin
g the a
b
o
ve mention
ed optimi
z
at
i
on metho
d
s.
Section 5
a
bout re
sult
s
and
discu
ssi
on b
a
se
d on th
e
simulatio
n
work
don
e an
d
se
ction6
pre
s
ent
s con
c
lu
sion
s a
nd fut
u
re
possibl
e re
se
arch path.
2
.
R
e
vi
ew
o
f
R
e
l
a
t
e
d
W
o
r
k
Article [5] i
s
a
su
rvey of localizatio
n sy
stem
s fo
r
WSNs u
s
ing
bio in
spired
algo
rithms. A
n
efficient local
i
zation sy
stem
that extends
GPS capabilities to
non-GPS
nodes i
n
an ad
hoc
netwo
rk i
s
p
r
opo
sed in [6
] using p
a
rticle swar
m
opt
imization. Art
i
cle [7] usi
n
g
shuffled fro
g
leapin
g
algo
rithm and fire
fly algorithm
in articl
e [8
], in which
anchors floo
d their lo
cati
on
informatio
n t
o
all
nod
es i
n
the
net
work a
n
d
ea
ch
d
u
mb
nod
e e
s
timates it
s lo
cation
by tril
a
t
eral
method, al
so
the lo
cali
zat
i
on a
c
curacy
is im
p
r
ove
d
by mea
s
u
r
i
ng the
dista
n
ce
between
the
neigh
bou
rs. I
n
arti
cle [9] th
e no
de lo
cali
zation i
s
di
scu
s
sed
usi
ng
co
nvex po
sition
estimation
an
d
then the
se
mi-definite
progra
mming
a
ppro
a
ch
i
s
f
u
rthe
r exten
ded to
non
-convex ineq
u
a
lity
con
s
trai
nts in
article [10]
W
S
N
lo
ca
lizatio
n
co
ns
id
ere
d
as
a mu
ltid
ime
n
sion
al optimizatio
n probl
em
a
nd evaluated
though
po
pul
ation-b
a
sed t
e
ch
niqu
es in
recent d
a
ys
. The cent
rali
sed
lo
cali
zatio
n
techniq
u
e
s
are
discu
s
sed in
article [11]
and this a
p
p
r
oa
ch r
equi
re
s a large nu
mber of be
a
c
on
s in o
r
de
r to
locali
ze
all
d
u
mb n
ode
s.
In arti
cle [1
2
]
a ge
netic
algorith
m
(G
A) ba
se
d n
o
de lo
cali
zation
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 14, No. 3, June 20
15 : 516 – 52
4
518
algorith
m
is p
r
esented
whi
c
h dete
r
min
e
s
location
s of all non-bea
co
n node
s by u
s
ing a
n
estim
a
te
of their di
sta
n
ce
s f
r
om
all
one
-ho
p
n
e
i
ghbo
urs. Si
m
ilarly in
arti
cl
e [13] a
two
-
pha
se
ce
ntral
i
zed
locali
zation
schem
e that use
s
simul
a
ted
anneali
ng an
d GA is pre
s
e
n
ted.
The adva
n
ta
ge of distri
but
e locali
zatio
n
techni
q
u
e
s
o
v
er the ce
ntralise
d
one i
s
becau
se
of the
com
p
l
e
xity in nature an
d
scalability issues present in
cent
ralised WS
Ntechniques.
T
h
e
distrib
u
ted lo
cali
zation al
g
o
rithm
s
will
be develo
p
e
d
andd
eploy
ed on ea
ch i
ndividual
sen
s
or
node in
stea
d
of central b
a
se
station
adopte
d
in
centrali
sed te
chni
que
s. Th
e target n
o
d
e
s
locali
ze b
a
se
d on dist
ance mea
s
urem
ent from
the
neigh
bou
ring
beacon
s or
alrea
d
y locali
sed
node
s. T
he
case
stu
d
y do
ne in
this p
a
per infers fe
w featu
r
e
s
fo
r in
pa
rticul
ar the l
o
cali
sati
on
accuracy a
n
d
the iterative
method
of lo
calizatio
n en
su
res
more nu
mber
of nod
e
s
are lo
cali
se
d in
s
h
ort s
p
an of time
3.
Bio-Inspir
ed Techniqu
es
– SFLA& FF
Afor
WSN L
o
caliza
t
ion
Natural living
organi
sm
provides
ri
ch
source
of id
ea
s fo
r
com
put
er
scienti
s
ts.
The
bio-
inspi
r
ed al
go
rithms offe
r better a
c
cura
cy and
mo
d
e
st co
mputat
ional time.SFLAand FFA
bio
inspi
r
ed al
gorithms are discu
s
sed in the
following
sub
s
e
c
tion
s.
3.1.
Shuffled Fr
og Leaping
Algorithm (S
FLA)
Shuffled fro
g
leapin
g
al
g
o
rithm i
s
swarm intellig
ence ba
se
d
biologi
cal
evolution
algorith
m
. Th
e algo
rithm
simulate
s a
grou
p of fro
g
s in
whi
c
h
eachfrog
rep
r
esents
a se
t of
feasibl
e
soluti
ons. The diffe
rent meme
ple
x
es are
a
s
su
med as diffe
rent culture of frogs
whi
c
h a
r
e
locate
d atdiff
erent
pla
c
e
s
in the
solutio
n
spa
c
e In
a
r
ticle [1
4] an
d [15] in
the
executio
n of
the
algorith
m
, In
orde
r to form a grou
p “F” frogs
a
r
e gen
e
r
ated an
d for a N-dim
e
n
s
io
nal optimization
probl
em, frog
“i” of the gro
up is re
prese
n
ted asXi
=
(x1i; x2i;
...;xNi). Then ba
se
d on the fitness
values the in
dividual frog
s in the grou
p
are ar
ra
nge
d in desce
ndi
ng ord
e
r, to determi
ne Px the
global b
e
st
solution. The
g
r
oup i
s
divid
e
d
into
m ethni
c group
s a
nd
each ethni
c g
r
oup i
n
cl
ude
s n
frogs
by satisfying the relation F = m _ n. The et
hnic
group divided such
thateach group will be
in to their sub
group li
ke first grou
p in to firs
t sub gro
up and secon
d
will be in se
con
d
sub g
r
o
up
and so on si
milarly frog m
into sub-gro
up m, frog
m + 1 into the first sub-gro
u
p
again and
so
on,
until all the frogs a
r
e divid
ed the obje
c
tive is
tofind the best frog in
each sub-group, denote
d
b
y
Pb and worst frog Pw co
rresp
ondi
ngly. The iterat
ive
formula
will b
e
written a
s
E
quation (1) a
nd
(2):
∗
(
1
)
;
(
2
)
Whe
r
e;
rand
() represents a rando
m
numbe
r be
tween 0 a
nd
1,
Pb denote
s
the po
sition of
the best frog,
Pw denote
s
the po
sition of
the worst fro
g
,
D rep
r
e
s
e
n
ts
the distan
ce
moved by the worst frog,
Pnew_
w
is th
e better po
sition of the frog
,
Dmax re
pre
s
ents the ste
p
length of frog
leapin
g
.
In the SFLA
algo
rithm e
x
ecution, if t
he up
dated
Pnew_
w
i
s
i
n
the fea
s
ibl
e
sol
u
tion
spa
c
e m th
e
n
the co
rrespondi
ng fitne
ss val
ue of
Pnew_
w
will be calcul
ated
. If the result
ant
fitness value
of Pne
w
_
w
i
s
wo
rse tha
n
the
co
rre
s
pondi
ng fitne
s
s value
of
Pw, then
Pwwill
repla
c
e P
b
i
n
Equation
(1) a
ndre-u
p
d
a
te Pn
e
w
_w.
If there is
still no im
provement, the
n
rand
omly g
e
nerate
a
ne
w frog
to
repl
a
c
ePw;
re
peat
the
upd
ate
pro
c
e
s
s u
n
til sati
sfying
st
op
conditions
SFLA Algorithms
step
s:
1)
Initialize grou
ps an
d para
m
et
ers su
ch
as group tota
l numbe
r of particle
s
N, total numbe
rof
frogs
N1, n
u
m
ber of
sub
-
grou
ps m, n
u
m
ber of
frog
s in
ea
ch
su
b-g
r
ou
p a
nd
the up
date
s
within the sub
group
2)
Analyze the i
n
itial fitness valu
e
s
of the p
a
rticle
s a
nd
save the initial
best p
o
sition
s an
d be
st
fitness valu
es, then sort all
N parti
cle
s
in
ascen
d
ing o
r
der a
s
pe
r the fitness valu
es;
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Wirel
e
ss Sen
s
or
Networks Nod
e
Lo
caliz
ation-A Perfo
r
m
ance
…
(Chandi
ra
se
karan D)
519
3)
Acco
rdi
ng to
the sub g
r
o
up divisio
n
rule
so
rt the N frog
s in a
s
cen
d
ing o
r
de
r and divide
them into sub
-
group
s.
4)
Find o
u
t the
best fitne
s
s i
ndividual P
b
and
th
e worst
fitness in
dividual P
w
of e
a
c
h
su
bgroup
in frog group
and al
so the
grou
p be
st individual Px
5)
Progress th
e
worst
solutio
n
within
a
sp
ecifi
ed
num
b
e
r of ite
r
ation
s
b
a
se
d o
n
e
quation
s
(1)
and (2
).
6)
Acco
rdi
ng to
the fitness va
l
ue, arran
ge
particl
es of th
e group
in a
s
cen
d
ing
order and
re
-mix
the particl
es t
o
form a ne
w grou
p.
7)
If stop conditi
ons a
r
e satisfied (the num
ber of
iteratio
ns exceed
s the maximum
allowabl
e
numbe
r
of ite
r
ation
s
o
r
th
e
optimal
sol
u
tion i
s
o
b
taine
d
), the
search sto
p
s,
and
output the
positio
n an
d f
i
tness value
of the first pa
rticle
of the g
r
oup;
otherwi
se, return to
step
(3
) to
contin
ue the
sea
r
ch.
3.2.
Firefly
Algor
ithms (FF
A
)
Firefly alg
o
rit
h
ms (FFA
) a
r
e devel
ope
d
based
on
th
e
ch
aracte
rs i
n
spi
r
ed
from
fireflies.
The firefly sp
ecie
s produ
ces sho
r
t and
rhythmic
fla
s
he
s of light and the patt
e
rn of flashe
s is
uniqu
e fo
r e
a
c
h
pa
rticul
ar
spe
c
ie
s. T
he
basi
c
motto o
f
su
ch
flashe
s i
s
to
attra
c
t
mating
partn
ers
and search fo
ods. The F
e
male flies respond to male’
s
uniq
ue patt
e
rn of flashi
n
g
within the same
spe
c
ie
s.
A
s
t
he dist
a
n
c
e
i
n
cr
ea
se
s t
h
e
int
ensit
y of light decre
ases for
any lig
ht emitting flies
whi
c
h
stri
ctly follows the i
n
verse
squa
re
law. W
hen
th
e air
ab
so
rb
s
light then it b
e
com
e
s wea
k
er
and
wea
k
e
r
as th
e di
stance in
crea
ses. Lu
cife
rin
is the te
rm
s u
s
ed
to d
enote the
bi
o-
lumine
scen
ce
from the body of the fir
e
flies
which
is a light em
ittingcomp
o
u
nd. The abo
ve
behavio
ur of
the fireflies
made t
he
re
searche
r
s to d
e
velop an al
gorithm
whi
c
h is called firefly
algorith
m
s
which
serve
s
a
s
heu
risti
c
alg
o
rithm in com
putational int
e
lligen
ce.
In optimi
z
atio
n p
r
obl
ems,
a
firefly at
parti
cula
r l
o
cation
“x” ha
s th
e
b
r
ightne
ss I
of
a firefly
can
have the
relation
shi
p
as I(x)
∝
f(x). The light int
ensity “I
r”
vari
es with
the d
i
stan
ce “r”
su
ch
that I
r
= I
0
e
–
γ
r
and also the light intensity is pr
o
portio
nal
to the attractiveness
β
su
ch t
hat
β
=
β
0
e
−γ
r2
. I
0
and
β
0
are the ori
g
inal light intensity and at
trac
tivene
ss con
s
tant at r=0 re
sp
ectiv
e
ly.
However, the attrac
tiveness
β
is rel
a
tive; it should be
see
n
in the e
y
es of the be
holde
r or ju
dg
ed
by the othe
r fireflies. T
h
u
s
, it will va
ry with
the
distance
rij b
e
twee
n firefly i
and firefly j. In
addition, light
intensity decrea
s
e
s
with the distan
ce
from its sou
r
ce
, and light is also ab
so
rb
e
d
in
the
me
dia, so
we sh
ould
allow
the attractivene
ss
to
vary
with th
e de
gree
of
absorptio
n. I
n
the
simple
st form
, the light intensity Ir varie
s
according to
the inverse square la
w Ir = I
s
r
2
whe
r
e I
s
is
the inten
s
ity at the so
urce
. For a give
n
medi
um
with
a fixed light absorptio
n co
efficient
γ
, the
light intensity I vary with the distan
ce r.
The im
pleme
n
tation of th
e
firefly be
havi
our a
s
d
e
scri
bed i
n
a
r
ticle
[16]. The
al
gorithm
wa
s org
ani
se
d based on th
e following a
s
sumptio
n
(i) a
ll fireflies are unisexual, wh
ich mea
n
s o
n
e
firefly will get
attracte
d to
all othe
r firefli
e
s. (ii
)
T
he at
traction
is
proportio
nal to
their b
r
ightn
e
s
s
and di
stan
ce,
hence for a
n
y two given
fireflies the
l
e
ss bri
ght on
e will tr
y to attract b
r
ight
er;
however. (iii)
If a firefly doesn’t find a b
r
ight fire
fly than its o
w
n th
en it will move ran
domly. The
followin
g
al
go
rithms con
s
id
er
as bri
ghtn
e
ss a
s
obje
c
t
i
ve functio
n
i
n
clu
d
ing
the
other a
s
socia
t
ed
con
s
trai
nts al
ong with the l
o
cal a
c
tivi
ties carried o
u
t by the fireflies.
Whe
r
e,
i= i
th
firefly, i 2
[1; n];
n= num
be
r of fireflies;
i- Max gene
ra
tion= count of
the generatio
ns
of fireflies
(indi
cate
s iteration limit);
Ii= Magnitud
e
of i
th
firefly Light Intensity; depe
nd
s on the obje
c
tive functio
n
f (x);
r
i,j
= di
stan
ce
betwe
en thei
th
and j
th
fireflies
res
p
ec
tively.
f (xi)
= obj
ect
i
ve function
o
f
i
th
firefly, which i
s
d
epe
nd
ent on
its l
o
cation
xi that is of
d-
d
i
me
ns
io
n
Whe
r
e d is the dimen
s
io
n
of x in space that
is also depen
dent
onthe conte
x
t of the firefly,
iteration va
ria
b
le (t
). Inten
s
ity or the
bri
g
htness
“I
” i
s
p
r
opo
rtion
a
l to
so
me
o
b
je
ctive functio
n
f(x)
and the lo
cati
on upd
ate eq
uation is give
n by (3).
γ
∈
(3)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 14, No. 3, June 20
15 : 516 – 52
4
520
Whe
r
e
α
is t
he ste
p
controlling pa
ram
e
ter, r is
th
e variabl
e that b
r
ing
s
ab
out random
ne
ss,
γ
is
the attraction
coefficient,
β
is the step size towa
rd
s the better soluti
on,
∈
is a vector of rando
m
numbe
r fro
m
Gau
ssi
an di
stributio
n an
d
Xi, Xj are
the firefly are t
he lo
cation in
formation
of the
observing e
n
tity.
Firefly Algorit
hm Pseu
do Code:
Begin
1: Generate initial population of firefly’s with location xi,
i = 1; 2; 3: n;
2: Define objective function f (x), where x = (x1; x2; xd) T;
3: Generate initial population of fireflies xi , i = 1;2;3:::n;
4: Light intensity Ii of a firefly ui at location xi is determined by f (xi);
5: Define light absorption coefficient
γ
;
6
:
while(t < max generation) do
/*for all n- fireflies*/
7: for i=1:n do
/*for all n- fireflies*/
8: for j=1:i do
9: if (Ij> Ii) then move firefly i towards j in d-dimension
10: else
11: end for
12: end for
13: Attractiveness varies with the distance r via exp (-
γ
r);
14: Evaluate new solutions and update light intensity;
15: end for
16: end while
17: Rank the fireflies and find the current best;
18: end
4.
Problem Sta
t
emen
t and
Metho
dolog
y
In WSN
nod
e localization
the obj
ectiv
e
is to
pe
rformestimatio
n of
coo
r
di
nate
s
of the
distrib
u
ted n
o
des to
kn
ow
their initial lo
cation
s. If there i
s
a maxi
mum of N ta
rget nod
es th
en
usin
g M
stati
onary
bea
co
n
s
who
s
e
kno
w
thei
r l
o
ca
tions then
the l
o
catio
n
of
un
kno
w
n
no
de
s will
be determine
d. The followi
ng study ap
proach is fo
rm
u
l
ated for the locali
zatio
n
of the same;
1)
Initialize the sensors ra
ndo
mly
2)
Initialize the b
eacon
s ran
d
o
m
ly
3)
Cal
c
ulate rea
l
distan
ce ie
the actual
d
i
stan
ce bet
ween the be
a
c
on a
nd ea
ch deploye
d
sen
s
o
r
nod
es
4)
Assig
n
mea
s
ured
distan
ce ie the dist
ance o
b
tain
ed by the bea
con
s
u
s
i
ng ra
nging
techni
que
s. This is d
one by
adding n
o
ise
to the real distan
ce.
5)
Find out ho
w many sen
s
o
r
s are
within the tran
smi
ssi
on ran
ge of 3
or more bea
con
s
6)
For e
a
ch se
n
s
or th
at ca
n
be lo
calized
SFLA and FF
A are ap
plied
to minimize t
he obje
c
tive
function
whi
c
h rep
r
e
s
ent
s the error
fun
c
t
i
on given by the Equation
(4)
∑
ei
R
i
xi
xm
y
i
y
m
2
(4)
Here Rii
s
the inexact ra
ngi
ng dista
n
ce.
(xi, yi) is the correspon
ding
bea
con p
o
siti
ons
(xm, ym) is the positio
n occupied by the
particl
e
“n” i
s
the num
ber of bea
co
n
s
having tra
n
s
missio
n cov
e
rag
e
over th
at sen
s
or.
7)
The
algo
rith
ms
retu
rn th
e cl
osest val
ues of
the
coordi
nate
s
(xm, ym)
su
ch
that e
rro
r i
s
minimized.
8)
The algo
rithm
is then appli
ed to the next sen
s
or in
ran
g
e
9)
The localized
sen
s
ors a
r
e removed from
the sen
s
o
r
list and now a
c
t
as bea
co
ns
10)
The lo
cali
zati
on e
r
ror i
s
co
mputed
after
all the
Nl n
o
d
e
s
estimate
their
co
ordi
nat
es, it i
s
the
mean
of squ
a
re
s of
dista
n
c
e
s
b
e
twe
en
actual
no
de l
o
catio
n
s (xi,
yi) and
the l
o
cation
s
(ˆxi,
ˆyi), i= 1, 2 ...Nl is dete
r
min
ed by SFLA
or FFA. This is compute
d
as Equation (5
).
El
1
/
xi
(5)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Wirel
e
ss Sen
s
or
Networks Nod
e
Lo
caliz
ation-A Perfo
r
m
ance
…
(Chandi
ra
se
karan D)
521
11)
All the ste
p
s from
3 to
9will
be
co
ntinued
unt
il eith
er
al
l un
kno
w
n
no
des get l
o
calized
or n
o
more n
ode
s coul
d be loca
lized furth
e
r. It is evi
dent that the perfo
rmance of the locali
zation
algorith
m
if o
b
se
rved from
the value
s
of
N
Nl
an
d El
whe
r
e
N
Nl
=
N
−
Nl i
s
the
numbe
r of
node
s that
could n
o
t be
locali
ze
d. Th
e lowerval
ue
s of
N
Nl
an
d
El rep
r
e
s
ent
the bette
r
perfo
rman
ce.
If the objective is to locali
ze more nu
mb
er
of node
s then the num
ber of
iteratio
ns ste
p
s,
then the n
u
m
ber of lo
cali
zed no
de
s in
creases. Thi
s
i
n
crea
se
s the
numbe
r of b
a
se referen
c
e
s
for
alrea
d
y locali
zed n
ode
s. Fi
rstly A node t
hat locali
ze
d usin
g just three refe
ren
c
e
s
in an iteratio
n k
may have more refere
nces in iteratio
n k+1.
Thu
s
the chan
ce
of ambiguity is decrea
s
ed.
Secon
d
ly, the time required for locali
zi
ng a node in
cre
a
ses, if a node ha
s mo
re refe
ren
c
e
s
in
iteration
k +
1 than in iteration
k. Th
e above issu
e i
s
overridd
en
in this pe
rformance stu
d
y by
limiting the maximum num
ber of refe
re
nce to six,
which i
s
arbit
r
a
r
ily cho
s
en. T
he simul
a
tion
is
done
u
s
ing
L
abVIEW g
r
ap
hical
u
s
er int
e
rface,
the a
d
vantage
s of
usi
ng LabVI
E
W can help
for
real time impl
ementation in
future scope
of rese
arch.
Simulation i
s
done
in L
a
b
V
IEW to und
ersta
nd th
e
perfo
rman
ce
of WSN Lo
calizatio
n.
We
cho
s
e
50
node
s a
s
ta
rget to be l
o
cali
zed
and
10 be
acon
s. The sen
s
o
r
field dime
nsi
o
nis
con
s
id
ere
d
a
s
10
0×100
square u
n
its a
nd the t
r
an
smissi
on
radi
u
s
of b
e
a
c
on
r = 2
5
unit
s
.
The
same
simul
a
tion setting
s i
n
LabVIEW for both the p
e
rform
a
n
c
e studies a
r
e ma
de sam
e
and
the
results a
r
e prese
n
ted.
For b
o
th SF
LA and FFA
perfo
rman
ce
study
, the
para
m
eters a
r
e: Popul
atio
n = 5
0
,
Iterations =
30. Parti
c
le
positio
nslimit
s: Xmin
=0 a
nd Xmax=10
0
.Total 30
tri
a
l expe
rimen
t
s of
SFLA base
d
locali
zatio
n
are cond
ucte
d for Pn = 2 and
Pn = 5. Average of total locali
zation e
r
ror
El defined in (5) in ea
ch iteration in 25 ru
ns is
comp
uted and the e
r
ror i
s
cal
c
ul
ated.
5.
Discus
s
ion
on the Resul
t
s
The two al
go
rithms a
nalysed here are stoc
ha
stica
n
d
hence they do not produ
ce the
same
solutio
n
s in
all itera
t
ionstho
ugh t
he initial
d
epl
oyment is
sa
me. That’s why the re
sult
s of
multiple trial
run
s
a
r
e ave
r
age
d. In ad
diti
on the init
ial deploym
e
nt is ra
ndom
and he
nce the
number of localizable nodes in ea
ch trial
w
ill not be same. This affects the total computing tim
e
.
The coo
r
dina
tes of the e
s
ti
mated an
d a
c
tual
lo
cation
s of no
des
as well a
s
the b
eacon
s
by SFLA and
FFA in a p
a
rti
c
ula
r
trial
run
are
sh
o
w
n i
n
Figure 1. Th
e
initial depl
oyment of no
de
s
and be
acon
s
for SFLA and
FFA based l
o
cali
zatio
n
is
the sam
e
in
a trial ru
n. Ta
ble 1 give
s the
summ
ary
of the va
riou
s
paramete
r
s
obtained
from the resu
lt of SFLA
and FFA ba
sed
locali
zation
a
l
gorithm
s. Th
e pe
rform
a
n
c
e of
both t
he alg
o
rithm
s
foun
d fairl
y
well in
WSN
locali
zation. I
t
has be
en o
b
se
rved that
the loca
li
zati
on accu
ra
cy is impa
cted b
y
adding the
Pn,
percenta
ge n
o
ise i
n
di
stan
ce m
easurem
ent. It is al
so
found that th
e avera
ge lo
calizatio
n erro
r in
both SFLA
a
nd F
F
A is re
duced
wh
en
Pn is cha
n
g
ed from
5 to
2. T
he
perf
o
rma
n
ce m
e
tric
doubl
et (N
Nl
,
E
l) for FFA is
less
than that for SFLA
,
indicting su
perio
r
pe
rf
ormance of Firefly.
Ho
wever,
co
mputing tim
e
requi
re
d for firefly is
si
g
n
ificantly mo
re
than th
at for
SFLA, whi
c
h
is
a
wea
k
n
e
ss
of
FFA. In ad
dition, the
amo
unt of
me
mo
ry re
quired f
o
r F
F
A is m
o
re th
an th
at for
SFLA. This
clearly calls for
a trade-off. A choi
ce between SF
LA
and FFA i
s
influenced by how
con
s
trai
ned
the n
ode
s a
r
e in te
rm
s of
memo
ry an
d computin
g
resou
r
ces,
h
o
w
accu
rate
the
locali
zation i
s
expected to
be and h
o
w q
u
ickly that sh
ould ha
ppen.
The effe
ct of
rangi
ng
dista
n
ce
erro
r o
b
servatio
n
s
m
a
de in
the first
five trial
run
s
o
u
t of
the 50, are
summari
ze
d in
Table 1. Thi
s
table
d
epicts increa
sin
g
Nl, the num
ber of lo
cali
zed
node
s in ea
chiteration. Ta
ble II shows the impa
ct
on the test results by
varying the tran
smissi
on
radiu
s
. It is
e
v
ident that th
e num
ber of
non-l
o
calized
node
s i
n
cre
a
se
s
whe
n
t
he tra
n
smi
s
si
o
n
radiu
s
is mad
e
a
s
20
units
from 2
5
units.
It is
also
fou
nd that
there
is a
corre
c
tio
n
of
error du
e
to
flip of ambigu
ity from the T
able 1. T
he a
v
er
age
erro
r i
s
dete
r
min
e
d
and
sho
w
n i
n
the Fig
u
re
2
with re
spe
c
t
to beacon
s a
nd the se
nso
r
node
s; fr
o
m
the results it is obvious that the SFL
A
perfo
rman
ce
looks b
e
tter
than the
FF
A. Also the
i
n
crea
se i
n
v
a
lue of
Ri i
n
dicate
s that t
h
e
accuracy ha
s been fairly improve
d
.
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TELKOM
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KA
Vol. 14, No. 3, June 20
15 : 516 – 52
4
522
(a) L
o
cation
s estimated by
SFLA with
r=2
5unit
s
&Pn
=2
(b) L
o
cation
s estimated by
FFA with
r=2
5unit
s
&Pn
=2
(c) Lo
cation
s
estimated by
SFLA with r=20
units &Pn=5
(d) L
o
cation
s estimated by
FFA with r=2
0units
&Pn=
5
Figure 1. Re
sult of trial run of SFLA and FFA
algorith
m
s for the sa
me deploym
e
nt with N=50;
M=10; an
d the sen
s
o
r
field
range i
s
100
x100 sq
uare units
Table 1. Effect of rangin
g
distan
ce e
r
ror of PSO and FFA (r=25 u
n
i
t
s)
Major Parame
te
rs
Percentage nois
e
in distance measurement(Pn
)
SFL
A
FF
A
2%
5%
2%
5%
Avg. no of non-lo
calized nodes(N
Nl
)
0.43
1.34
0.227
0.83
Avg. time taken*(s)
371.1
263.5
810.9
1121.5
Avg. localization
error
(El)
0.49
0.922
0.279
0.64
Table 2. Effect of varying the
tran
smi
ssi
on radi
us
(r) and Pn=2
Major Parame
te
rs
SFL
A
FF
A
Trans
m
i
ssion radius (r)
20
25
20
25
Avg no of non-lo
calized nodes
1.4
0.41
1.23
0.28
Avg. time taken*(s)
631.8
589.7
940.4
1365.2
Avg. localization
error
2.198
0.66
1.61
0.28
*All sim
u
lation are pe
rform
ed in the sam
e
com
puter
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Wirel
e
ss Sen
s
or
Networks Nod
e
Lo
caliz
ation-A Perfo
r
m
ance
…
(Chandi
ra
se
karan D)
523
(a) Average e
rro
r Vs Bea
c
o
n
ratio
(b) Average e
rro
r Vs Sen
s
o
r
node
s
Figure 2. Rel
a
tionship bet
wee
n
the ave
r
age e
r
ror
with respe
c
t to the bea
co
n rat
i
o and sen
s
or
node
s
6. Conclu
sion
This p
ape
r has di
scu
s
se
d SFLA and
FFA, bio-in
spired alg
o
rit
h
ms to find
out the
locali
se
d
no
d
e
s of
a WS
N
in a scattered
an
d
iterative method
. The lo
cali
zation p
r
obl
e
m
is
con
s
id
ere
d
a
s
a multidim
ensi
onal o
p
timization
pro
b
lem an
d sol
v
ed by the above mentio
ne
d
popul
ation-ba
sed
optimi
z
at
ion al
gor
ith
m
s. From th
e
results obt
ai
ned it
wa
s f
ound
that F
F
A
offers le
ss error valu
e in compa
r
ison to
SFLA
but take
s long
er
co
mputational ti
me to perfo
rm.
We al
so
ran
the pro
g
ra
m
with a small
e
r tra
n
sm
i
s
si
on ra
diu
s
an
d found that
it leads to le
ss
numbe
r
of n
o
des bei
ng l
o
calise
d
. Althou
gh the
r
e
is
not vas
t
difference in the errors offered
by
both the sele
ction of what
algorithm
s t
o
use
fo
r lo
calisatio
n dep
end
s entirely on the ha
rd
ware
available to
the u
s
e
r
an
d t
he time
con
s
t
r
aints
involve
d
. This pap
er has al
so b
r
ie
fly presented
a
statistical
su
mmary of th
e
re
sults for co
mpari
s
o
n
of b
o
th SFLA a
n
d
FFA. Both t
healg
o
rithm
s
are
effective in th
eir o
w
n
way
and
can b
e
furthe
r modifi
ed to suit the use
r
s
nee
d
by cha
nge
s i
n
the
prog
ram
cod
e
to give even better re
sult
s than what was obtai
ned.
This
wo
rk
ca
n be
extend
e
d
in m
any ot
her
directio
ns, in a
po
ssi
bl
e furthe
r
stud
y, both
SFLA and FF
Acan be u
s
e
d
in centrali
ze
d locali
zation
method so that to compa
r
e
the locali
sati
on
method
s
of centrali
zed
an
d di
strib
u
ted
techni
que
s,
whi
c
h
ca
n le
ad to
solve e
nergy
a
w
are
n
e
ss
issue in
WS
N. Also it
can lea
d
a
way to develo
p
a hyb
r
id
algorith
m
by
com
b
ining
the
advantag
es o
f
both the algorithm
s.
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