TELKOM
NIKA
, Vol.14, No
.2, June 20
16
, pp. 699~7
0
6
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v14i1.2752
699
Re
cei
v
ed
Jan
uary 28, 201
6
;
Revi
sed Ma
y 9, 2016; Accepte
d
May 2
0
, 2016
Application of Artificial Fish Swarm Algorithm in Radial
Basis Function Neural Network
Yuhong Zho
u
1
,
Jiguang Duan
2
, Limin Shao
1
*
1
Colle
ge of Me
chan
ical a
nd El
ectrical En
gin
e
e
rin
g
, Agricultu
r
al Univ
ersit
y
o
f
Hebei,
Baod
ing
071
00
1, Hebe
i, Chin
a
2
Institute for Nation
aliti
e
s Attached to He
be
i No
rmal U
n
iv
ersit
y
, Shij
iaz
hua
ng 05
00
91, He
bei, Ch
ina
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: shaolm@
12
6
.
com
A
b
st
r
a
ct
Neur
al n
e
tw
ork is one
of the br
anch
e
s
w
i
th
the most
active rese
ar
ch, deve
l
op
ment an
d
app
licati
on i
n
computati
ona
l intel
lig
enc
e
and
machi
ne
study. Rad
i
al
basis fu
nctio
n
ne
ural
netw
o
rk
(RBF
NN) has
achi
eved s
o
me
success in
mo
re than o
ne a
p
p
licati
on fie
l
d,
espec
ial
l
y in p
a
ttern reco
gniti
on
and functi
on
al
appr
oxi
m
ati
on.
Due to its simple struct
ure, fast trainin
g
sp
eed a
nd exc
e
ll
ent gen
era
l
i
z
a
t
io
n
abil
i
ty, it has
bee
n w
i
dely
u
s
ed. Artificial
fish sw
arm a
l
gorith
m
(AF
S
A) is a new
sw
arm inte
lli
g
ent
opti
m
i
z
at
ion a
l
gorith
m
d
e
rive
d from t
he stu
d
y on the pr
eyi
ng be
hav
ior of fi
sh sw
arm. T
h
is alg
o
rith
m is
not
sensitiv
e to the initial va
lu
e an
d t
he para
m
eter selecti
on, b
u
t strong in
ro
bustness a
nd
simple a
nd e
a
sy to
reali
z
e
an
d it also h
a
s par
al
lel pr
ocessi
ng
capab
ilit
y a
n
d
glo
bal s
earc
h
in
g abi
lity. This pa
per
mai
n
ly
researc
hes t
h
e
w
e
ight
an
d thr
e
sho
l
d
of AF
S
A
in
o
p
ti
mi
z
i
n
g
RBF
NN. T
h
e
si
mu
lati
on
exp
e
ri
me
nt pr
oves
th
at
AF
SA-RBF
NN is sig
n
ifica
n
tly
adva
n
tag
eous
in g
l
ob
al
opti
m
i
z
at
io
n cap
a
b
ili
ty and th
at it has o
u
tstand
in
g
glo
bal o
p
ti
mi
z
a
tion ab
ility a
nd
stability.
Ke
y
w
ords
: RBFNN, Artificial Fish Sw
arm, Appli
ed Opti
mi
zation
Copy
right
©
2016 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
Artificial neu
ral netwo
rk i
s
the artificial i
n
telligen
ce te
chn
o
logy dev
elope
d by referri
ng to
the biolo
g
ical neural net
work to sim
u
la
te the bi
olo
g
i
c
al p
r
o
c
e
s
s
of human
brain. RBF
NN i
s
a
special t
h
ree-layer feed-forward
lo
cal
ap
proximatio
n n
e
twork
with
single hi
dde
n l
a
yer. It take
s
the radi
al ba
sis fun
c
tion a
s
the ba
se of the hid
den n
e
u
ron to fo
rm t
he spa
c
e of t
he hid
den lay
e
r
[1]. Its learni
ng algo
rithm
and
stru
cture
prin
ciple
are
greatly different from tho
s
e of BP network
and it overcomes th
e sh
ortco
m
ing
s
o
f
BP (Back-
Propa
gation
)
netwo
rk to
certai
n exten
t. To
every trainin
g
sam
p
le, i
t
has st
ron
g
real
-time,
fast learni
ng speed
a
nd extrao
rdi
nary
conve
r
ge
nce. RBFNN has
been ap
plied
to every re
se
arch field and
it has made some p
r
og
re
ss
in rob
o
tic i
n
te
lligent control
,
pattern reco
gniti
on, comp
uter ima
ge p
r
oce
s
sing
and
expert
syste
m
[2].
The study of
neu
ral
net
work can
be
dat
ed
ba
ck to the
194
0s.
W.M
c
Cullo
ch, a
n
American p
sycholo
g
ist an
d W. Pitts, a mathemati
c
i
an have u
s
e
d
the mathe
m
atical m
ode
l of
formal ne
uro
n
to simulate
the activity functio
n
of bio
l
ogical neu
ro
ns for the first time and it has
su
ch charact
e
risti
cs a
s
th
e prelimi
nary
self-le
a
rning,
parall
e
l proce
ssi
ng an
d distributed mem
o
ry
[3]. The Hopf
ieid artificial
neural netwo
rk mo
del
raised by Professor
Ho
pfieid
from Califo
r
ni
a,
USA in 1
982
has create
d
q
u
ite an
up
surge in
arti
ficial
neu
ral n
e
two
r
k
co
mpute
r
.
D.E. Rum
e
lh
art
and J.L.McCl
elland have come
u
p
with BP
algorithm
in the yea
r
of
1986,
whi
c
h
has
be
come
the
most influenti
a
l netwo
rk l
e
arnin
g
algo
rit
h
m to
date [4]. After that, many schol
ars
have be
en
dedi
cated to
the research of vari
ous neu
ral n
e
tw
ork alg
o
rithm
s
so a
s
to
o
b
tain the
ne
ura
l
netwo
rk to
pol
ogy and p
a
ra
meters that can sati
sf
y the pra
c
tical
app
lication
s
, ho
wever, be
cau
s
e
peopl
e’s re
search
on
the
biolo
g
ical
n
e
rvou
s
syste
m
is still i
n
t
he expl
orato
r
y stage,
artifi
cial
neural netwo
rk mo
del can
not reali
z
e al
l the pra
c
tica
l function
s of human b
r
ain
,
therefore, t
h
e
theoreti
c
al exploratio
n
of a
r
tificial
n
e
u
r
al
netwo
rk m
o
del i
s
still to
be furth
e
r de
veloped. F
o
r
the
RBF neural network, there
are still a lot of problem
s that are
not solved, the performance of the
neural net
work is m
a
inly de
termine
d
by its struct
u
r
e, th
e trainin
g
pro
c
e
ss of
RBF
neural net
work
is the p
r
o
c
e
s
s of dete
r
mini
ng the hid
den
layer st
ru
cture and th
e co
n
nectio
n
weigh
t
values. In th
e
past, the
structure of RB
F netwo
rk h
a
s to b
e
sel
e
cted
by tria
l and
corre
c
t
i
ng metho
d
, the
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 14, No. 2, June 20
16 : 699 – 70
6
700
cal
c
ulatio
n q
uantity is larg
e, the spe
ed
is low
and
it i
s
difficult to e
v
aluate wh
ether the n
e
twork
stru
cture is b
e
tter. This
sel
e
ction m
e
tho
d
has
se
riou
sly hindere
d
th
e appli
c
ation
of RBF netwo
rk.
Ho
w to impro
v
e the operational efficie
n
c
y and redu
ce
the stru
ctu
r
e com
p
lexity is wo
rth furth
e
r
exploratio
n in the RBF network
re
se
arch area[5].Tog
ether with th
e continu
o
u
s
developme
n
t of
swarm intelli
gence optimi
z
ation al
gorithms in
recent
years, the research to utilize
swarm
intelligen
ce a
l
gorithm
s to
optimize th
e
neural
net
wo
rk
stru
cture i
s
still bei
ng
expand
ed an
d
explore
d
.
To
apply swarm intelligen
ce a
l
gorithm
s
i
n
t
he d
e
si
gn a
n
d
traini
ng
of
neural n
e
two
r
k
has be
en d
e
e
med
as the
com
p
licated
optimizatio
n
pro
b
lem
in
multi-dime
nsi
onal
sp
ace
a
n
d
every solutio
n
mea
n
s
a n
eural
net
work with diffe
rent
stru
ctu
r
es a
nd conn
ectio
n
wei
ghts. A
F
SA
has b
e
come
a frontier
research topi
c in
swa
r
m intelli
gen
ce alg
o
rit
h
m[6].
By using
AF
SA to optimi
z
e th
e pa
ra
meters of
RBF neu
ral
ne
twork, we
ca
n get th
e
global o
p
tima
l solution of t
he RBF pa
ra
meter set, AFSA can opti
m
ize the n
u
mber of hid
d
e
n
layer no
de
s i
n
the trai
ning
pro
c
e
s
s, an
d then
the
n
e
twork stru
ct
ure ca
n
be d
e
termin
ed.
T
h
is
pape
r mainly
investigate
s
the appli
c
atio
n of AF
SA in RBFNN, ma
ke
s ap
pro
p
ri
ate adju
s
tme
n
ts
and im
prove
m
ents and
u
s
e
s
it in
the t
r
ainin
g
of
RB
FNN for the
purp
o
se of
u
s
ing
the
ada
ptive
ability, parall
e
lism and gl
obality of AFSA to bette
r solve the parameter optimization problem of
RBFNN a
n
d
improve it
s overall p
e
rform
a
n
c
e.
The sim
u
l
a
tion expe
ri
ment proves the
effectivene
ss
and practi
cab
ility of
the idea
and sugg
estion prop
osed
in this pape
r.
2. Radial Ba
sis Functio
n
Neural Net
w
ork
RBFNN i
s
a t
y
pical lo
cal
a
pproxim
ation
arti
ficial
neu
ral network a
n
d
a forwa
r
d
n
e
twork
con
s
tituted b
y
the neuron
s of input layer, hidde
n la
yer and outp
u
t. Its basic i
dea is to u
s
e
the
radial b
a
si
s functio
n
as th
e base of the neuro
n
in the hidde
n layer and fo
rm the sp
ace of that
layer. The
hi
dden l
a
yer transfe
rs th
e i
nput vecto
r
s
to transf
e
r th
e low-dim
ensional mo
de i
nput
data into
the
high
-dim
en
si
onal
sp
ace
so a
s
to
ma
ke the li
nea
rly insepa
rabl
e
probl
em
s in
l
o
w
dimen
s
ion li
nearly
sep
a
rable in the
high-dime
n
s
i
onal spa
c
e.
RBFNN ta
ke
s the Eu
clid
ean
distan
ce
bet
wee
n
the
inp
u
t vecto
r
of
the training
sample
and
th
e weight ve
ct
or
of the
nod
es i
n
the hidde
n layer a
s
the
input and
as a stat
i
c
neural netwo
rk, it match
e
s the fun
c
tion
approximatio
n theory a
nd
has th
e only
optimal ap
pr
o
x
imation poin
t. Due to its
advantag
es li
ke
simple optimi
zation process, fast training sp
eed and optimal approxima
tion ability, RBFNN can
approximate
any co
ntinuo
us fun
c
tion
a
s
lon
g
a
s
there are
suffici
e
n
t neuron
s in
the hidde
n la
yer
and the units
in the hidden
layer is the p
e
rception u
n
its. There are t
h
ree p
a
ra
met
e
rs
whi
c
h affect
its netwo
rk p
e
rform
a
n
c
e, i
n
clu
d
ing the
weight ve
ctor in the o
u
tput layer, th
e cente
r
of the
neuron
s in the hidden laye
r and the wid
t
h (varian
c
e
)
of the neuron
s in the hidd
en layer. In th
e
neural netwo
rk trai
ning p
r
oce
s
s, inapp
ropriate p
a
ra
meter sele
ction will ca
use
insufficie
n
t fittin
g
and ove
r-fitting. The
ba
si
s fun
c
tion
ha
s
several fo
rms: multi-qu
adrati
c
fun
c
ti
on, inverse
multi-
quad
ratic fun
c
tion, spline f
unctio
n
an
d
Gau
ssi
an fun
c
tion. To
sel
e
ct the iteratio
ns a
nd n
e
two
r
k
stru
cture (na
m
ely the nu
m
ber
of the n
e
u
ron
s
i
n
the
hidde
n layer) rea
s
o
nably i
s
key to trai
n
the
applie
d neu
ral netwo
rk m
odel and it will directly
affect the pre
d
i
c
tion a
c
cura
cy. Generally, the
learni
ng
of radial b
a
si
s
n
e
twor
k
usuall
y
starts from
the net
wo
rk weig
ht an
d
then g
r
ad
uall
y
adju
s
ts the
o
t
her pa
ram
e
ters of the n
e
t
work. The
weight be
ars d
i
rect
releva
ncy to the cent
er
and wi
dth of the neu
ron [7]
.
Its stru
ctu
r
e
cha
r
t is seen
in Figure 1.
Figure 1. RBF Neu
r
al Network Stru
cture
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Applicatio
n of Artificial Fish
Swarm
Algorithm
in Radial Basis Fu
ncti
on Ne
ural
… (Yuhong Z
hou
)
701
RBFNN is m
ade up of an
input layer, a hidde
n layer incl
udin
g
the neu
ron
s
o
f
a radial
basi
s
fun
c
tio
n
(no
r
mally, it is Gau
ssi
an
func
tion
) an
d an output l
a
yer of linea
r neuron
s. The
cente
r
of the
unit
ba
sis fu
nction
in th
e
hidde
n laye
r
is
j
P
, the
width
is
j
and th
e
con
n
e
c
tio
n
weig
ht betwe
en the
units i
n
the hi
dden
l
a
yer a
nd tho
s
e in the
outpu
t layer is
j
W
. Becau
s
e it
ha
s
simple
st
ruct
ure
and
its n
e
u
ron
s
have
small sen
s
it
ive zo
ne
s, it ca
n
be exten
s
ive
l
y applied
in t
he
local a
pproximation of non
-linea
r fun
c
tio
n
s [8].
3. Behav
i
or
Des
c
ription
and Principle
of Ar
tificial
Fish S
w
a
r
m
Algorithm
As an o
p
timi
zation
algo
rithm ba
sed
on
the si
mul
a
tion of the b
e
haviors of fish swarm,
artificial fi
sh
swarm alg
o
rith
m (AFSA) i
s
evolved fr
om
the fish’
s
b
e
h
a
vior in
se
arching fo
r food
i
n
the water and it introduces the idea
of intellig
ence
algorithm based on
behaviors. T
h
ere
are
three fish beh
aviors i
n
the
water: p
r
eyin
g, swa
r
min
g
and follo
wing.
This alg
o
rith
m start
s
from
the
behavio
rs to
con
s
tru
c
t a
r
tificial fish and
reache
s
the gl
obal optim
um
throug
h the
search of all th
e
individual
s in the fish swarm[9]. The descrip
tio
n
s of th
ese b
ehavio
rs are a
s
follo
ws:
AFSA includ
es varia
b
le
s and be
havior function
s, includi
ng:
X
is the AF of the curre
n
t
positio
n,
s
tep
is t
he m
o
tion
ste
p
len
g
th,
vi
s
u
al
is t
he visual
dist
ance,
t
r
y
numb
e
r
is the
numbe
r
of tries,
detal
is the con
g
e
s
tion
factor a
nd
be
st
is the rang
e wi
th the highe
st
food within a
ll the
area
s.
bes
t
X
is the best statu
s
of
all AF region
s,
c
X
is the ce
nter po
sition of
the artificial fi
sh an
d
mi
n
X
is the positio
n of artificial fish minim
u
m distan
ce.
YF
X
is the food con
c
entration of t
h
e
artificial fish .
AF’s beh
aviors incl
ude Pre
y
ing, Swarmi
ng and Foll
o
w
ing.
(1) P
r
eying: t
he artificial fi
sh
swi
m
s f
r
eely in
the wat
e
r
and when it
finds the food, it will
swim to
wa
rd
s the food.
AFSA exte
nds thi
s
fish
behavior in
to the soluti
on of pra
c
tical
optimizatio
n probl
em
s, na
mely to get close to
the bet
ter optimal va
lue gra
dually
[10].
i
X
is th
e
cu
rre
n
t
status of th
e a
r
tificial fi
sh an
d
sele
ct
a statu
s
j
X
ran
domly fro
m
t
he
visual di
stan
ce.
()
ji
visual
Ra
nd
XX
(1)
1
()
t
t
ji
tt
be
st
i
ii
tt
ji
b
e
s
t
i
ste
p
Rand
XX
XX
XX
XX
X
X
(2)
(2) S
w
a
r
min
g
: the a
r
tifici
al fish
swa
r
m
clu
s
ter toget
her. Every fi
sh maintai
n
s
a certain
distan
ce
with
other fish to avoid con
gestio
n
with
and
keep
s
the sam
e
direction
with t
h
e
neigh
borhoo
d
fish. Th
e a
r
tificial fish
se
arche
s
t
he
n
u
mbe
r
of the
cu
rre
nt fish,
cal
c
ulate
s
t
he
cente
r
po
sitio
n
of current fish an
d move
s towa
rd
s to cente
r
[11].
i
X
is the
cu
rre
n
t
status of th
e artificial fi
sh,
the ce
nter of artificial fi
sh h
a
s l
o
w fit
ness
value and th
e
surro
undin
g
environ
ment i
s
not very
co
nge
sted a
nd
then the a
r
tificial fish mov
e
s
one ste
p
toward
s to vector sum of
c
X
and
bes
t
X
.
1
()
tt
tt
ci
b
e
s
t
i
ii
tt
ci
b
e
s
t
i
s
t
ep
Ran
d
XX
X
X
XX
XX
X
X
(3)
(3) Foll
owi
ng:
in the fish swarm, the artifici
al fish se
arche
s
the optimal positio
n of the
surro
undi
ng
neigh
borhoo
d
.
When on
e or more fish
finds food, th
e adja
c
ent fish will get to the
food
sou
r
ce f
o
llowin
g
it o
r
them qui
ckly. If the obj
ec
ti
ve functio
n
v
a
lue
of the o
p
timal po
sitio
n
is
bigge
r tha
n
t
hat of the
cu
rre
nt po
sition
and
it
is not
very
cong
ested,
then th
e
cu
rrent p
o
sit
i
on
moves on
e st
ep towa
rd
s the optimal nei
ghbo
rho
od fish [12].
i
X
is the curren
t status of the artificial fi
sh,
artificial fish
sea
r
che
s
its neigh
borhoo
d
and
finds a smalle
r
j
Y
.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 14, No. 2, June 20
16 : 699 – 70
6
702
1
mi
n
mi
n
()
t
t
ji
tt
i
ii
tt
ji
i
s
t
ep
Ran
d
XX
XX
XX
XX
X
X
(4)
The above
-
m
entione
d will
conve
r
t to ea
ch othe
r at di
fferent mome
nts. Such
co
nversi
on
is u
s
ually a
u
tonomo
u
sly
re
alize
d
by the
fish’s
pe
rcep
tion to the e
n
v
ironme
n
t. These be
havio
rs
are
clo
s
ely re
lated to the p
r
eying a
nd
su
rvival of
the fish. Th
e flowchart of AFSA
is indi
cate
d a
s
Figure 2.
Figure 2. The
flowch
art of AFSA
4. Applicatio
n of Ar
tificial
Fish S
w
a
r
m
Algorithm in RBF
NN
RBFNN i
s
a forward n
e
twor
k
with
excelle
nt perform
an
ce.
It has the
optimal
approximatio
n perfo
rman
ce. The hidde
n layer is con
s
tituted by a grou
p of radi
al basi
s
fun
c
tions.
What i
s
relev
ant to every node in th
e h
i
dden laye
r a
r
e the pa
ram
e
ter vecto
r
a
nd the wi
dth [13].
The co
mbin
ation mode of
AFSA and RBFNN i
s
sh
o
w
n a
s
Figu
re
3.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Applicatio
n of Artificial Fish
Swarm
Algorithm
in Radial Basis Fu
ncti
on Ne
ural
… (Yuhong Z
hou
)
703
Figure 3. The
combin
ation
diagram of AFSA and RB
FNN
The lea
r
ning
of the comm
on RBF
NN a
l
ways
st
arts f
r
om the net
work
weig
ht and then
grad
ually a
d
j
u
sts to oth
e
r
para
m
eters
o
f
the net
wo
rk sin
c
e th
e
weight i
s
cl
ose
l
y related
to t
h
e
cente
r
a
nd
width of the n
euro
n
s. T
he
transfe
r fun
c
t
i
on of the
hi
dden l
a
yer
select
s Ga
ussian
function, nam
ely
2
2
(
)
exp[
]
2
i
i
i
xc
Rx
.
Her
e
,
x
is a
n
-d
imensi
onal i
n
put vector;
c
is the ce
nter of
the ba
sis fu
nction
and it i
s
the vecto
r
with the
sam
e
d
i
mensi
o
n
s
a
s
x
and
determines the
wi
dth t
hat the
b
a
si
s fun
c
tion
surro
und
s the
center p
o
int. The output n
e
twork st
ru
cture of RBF
N
N is 10
-5-1, namely that there
are 1
0
nod
es, 5 node
s and
1 node in th
e input layer,
hidde
n layer
and outp
u
t la
yer re
spe
c
tively.
The output o
b
tained i
s
the
predi
ction va
lue of the pre
d
iction mo
me
nt.
This pa
pe
r a
pplie
s AFSA into the para
m
eter
adj
ust
m
ent of RBF
NN a
nd detai
led step
s
for the sp
ecifi
c
algo
rithm can be divide
d
into three ph
ase
s
.
Phase I: Initialization p
h
a
s
e
of AFSA-RBFNN.
Step 1: Gene
rate the traini
ng sam
p
le
11
2
2
{(
,
)
,
(
,
)
,
,
(
,
)}
mm
F
xy
x
y
x
y
.
Step 2: Clarif
y the number
of neuro
n
s in
ever
y layer a
nd the network obje
c
tive error.
Step 3: Set the pa
ram
e
ters of the fish
swar
m, in
clu
d
ing the
si
ze
of the fish
swarm
m
,
the maximu
m numb
e
r
of iteration
s
g
en
, the pe
rceptio
n ra
nge
of the artifici
al fish
vi
s
u
a
l
, the
maximum shi
ft step length
s
te
p
.
Phase II: Trai
n the neural network model
by us
ing AF
SA with coupl
ing prior information.
Step 1: The individuals
update thems
e
lves
th
rough preying,
s
w
ar
ming and following and
gene
rate ne
w fish swarm.
Step 2: Calcu
l
ate the fitness value of ev
ery i
ndividual
of the swarm
;
obtain the st
atus of
the optimal artificial fish an
d as
sign its v
a
lue to the bu
lletin board.
Step 3: Evaluate all the individual
s. If a ce
rtain in
dividual is b
e
tter than th
e bulletin
board, then repla
c
e the bu
lletin board wi
th this individ
ual.
Step 4: Whe
n
the
optimal
sol
u
tion in
the b
u
lletin b
oard
rea
c
he
s the
satisfa
c
t
o
ry e
rro
r
boun
d, the algorithm e
n
d
s
; otherwi
se, tu
rn to Step 1.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 14, No. 2, June 20
16 : 699 – 70
6
704
Phas
e III: The Retraining
of RBFNN.
Step 1: Co
rre
s
po
nd the
glo
bal optim
al value o
b
taine
d
from the ite
r
ation of AFS
A
to the
weig
ht and th
reshold of RB
FNN.
Step 2:
Conti
nue to
trai
n t
he n
eural
net
work
with
RB
F alg
o
rithm
u
n
til the o
b
je
ctive erro
r
is
r
e
ac
he
d
.
5. Simulation Experimen
t
and An
aly
s
is
This pap
er u
s
e
s
AFSA to
optimize th
e
ce
nter
,
widt
h, wei
ght a
n
d threshold
o
f
RBFNN
and e
s
tabli
s
h
e
s th
e mod
e
l
(AFSA-RBF) of RBF
N
N to
be o
p
timize
d
by artificial
fish
swarm.
Th
e
comp
uter h
a
rdwa
re
CPU i
n
the experi
m
ent us
es I
n
tel Co
re 2
Duo E8
400
3.0GHz with
an
internal m
e
mory of 4G
and the software
use
s
MatlabR2
0
1
2a simul
a
tio
n
platform. This
experim
ent use
s
two test functio
n
s to verify
the RBFNN alg
o
rithm
to be optimized by improv
e
d
AFSA. The numbe
r of dimensi
o
n
s
is D
and the two f
unctio
n
s a
r
e
sho
w
n a
s
Ta
ble 1.
Table 1. Te
st Functio
n
Set
1
1
2
D
i
i
f
x
[2
,
2
]
,
5
,
8
i
xD
2
21
2
s
i
n
(
6
)
9
c
o
s
(
5
)
ii
i
f
xx
x
[0
,
1
5
]
,
5
,
8
i
xD
This
pape
r t
a
ke
s 3
00 g
r
oup
s of 5
-
a
nd 8-dime
nsi
onal d
a
ta fro
m
the two f
unctio
n
s
respe
c
tively. Among the 3
00 gro
u
p
s
of
data, ran
d
o
m
ly select 2
7
0 grou
ps
of data to train
th
e
neural network and the rest 30 group
s o
f
data as
the predi
ction
sa
mples. Fig
u
re
4 and Figure
7
are the
com
pari
s
on di
ag
ram of the error
cha
nge
curves i
n
the training p
r
o
c
esse
s of AFSA-
RBFNN an
d RBFNN corre
s
po
ndin
g
to the 5- an
d
8-d
i
mensi
oanl in
put data of the two functio
n
s
r
e
spec
tively.
(a)
(b)
Figure 4. Co
mpari
s
o
n
of the test experi
m
ent
re
sults
of 5-dime
nsi
o
nal f1 functio
n
(a)
(b)
Figure 5. Co
mpari
s
o
n
of the test experi
m
ent
re
sults
of 8-dime
nsi
o
nal f1 functio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Applicatio
n of Artificial Fish
Swarm
Algorithm
in Radial Basis Fu
ncti
on Ne
ural
… (Yuhong Z
hou
)
705
(a)
(b)
Figure 6. Co
mpari
s
o
n
of the test experi
m
ent
re
sults
of 5-dime
nsi
o
nal f2 functio
n
(a)
(b)
Figure 7. Co
mpari
s
o
n
of the test experi
m
ent
re
sults
of 8-dime
nsi
o
nal f2 functio
n
In RBF neura
l
network, the
numbe
r of hidden laye
r n
ode
s and the
choi
ce of ce
nter and
width are the key to the whol
e net
work pe
rformance, dire
ctly
impact
on the network
approximatio
n ability. It doesn’t ne
ed to
make any
a
s
sumptio
n
s of
the cente
r
an
d width of RB
F
function, u
s
in
g AFSA to learn the
network co
nne
ctio
n wei
ghts, a
n
d
ca
n dete
r
m
i
ne the n
e
two
r
k
topology, the hidde
n neu
ral
unit location
and the corre
s
po
ndin
g
widt
h value.
From th
e trai
ning e
r
ror
cu
rve com
pari
s
o
n
di
ag
ram
s
of AFSA-RBF
N
N an
d
RBFNN, it ca
n
be see
n
that AFSA-RBF
N
N enha
nces t
he learning
e
fficiency of the netwo
rk we
ight, incre
a
se
s
the
conve
r
ge
nce, avoid
s
vibrat
ion
of
RBFNN i
n
th
e trai
ning
proce
s
s a
nd
m
a
ke
s th
e n
e
t
w
ork
inca
pable
of conve
r
ge
nce. It is quite effective to
extract pri
o
r i
n
formation from t
he data
by usin
g
AFSA-RBF
N
N to imp
r
ove
the se
arch
efficien
cy of
the algo
rithm.
Since AFSA
can
se
arch
the
global o
p
timal value a
c
curately, the locati
o
n
and
numbe
r of neuron
s in
RBFNN can
b
e
determi
ned
a
u
tomatically i
n
the p
r
o
c
e
s
s of p
a
ra
met
e
r o
p
timizatio
n
, it improve
s
the a
c
cura
cy
of
the traine
d n
e
twork
cla
ssi
fication mo
d
e
l and t
he converg
e
n
c
e spe
ed,
mea
n
w
hile
e
nha
nces
algorith
m
efficien
cy and
g
eneralization
perfo
rman
ce.
Usin
g AFSA to optimize t
he structu
r
e
of
RBFNN, it’s
effec
t
ive to improv
e the efficien
cy of network.
6. Conclusio
n
Artificial fish
swarm al
gori
thm has m
a
ny ch
aracteri
stics, includi
ng excell
ent
ability to
sea
r
ch the gl
obal extrem
u
m
, stron
g
ro
b
u
stne
ss, ea
si
ness to be
re
alize
d
and
pa
rallel p
r
o
c
e
s
sing
cap
ability. To solve the de
ficien
cy of RBFNN,
thi
s
p
aper i
n
trod
uces AFSA, wh
ich ha
s
stron
g
global optimi
z
ation ability, to train RBFNN and solv
e such p
r
obl
ems of traditional RBFNN as th
at
it is easy to
get trappe
d into local opti
m
um. It
can be see
n
fro
m
the experi
m
ent result that
AFSA-RBF
N
N
can
enh
an
ce th
e net
wo
rk l
earning
a
c
cura
cy a
nd
has better gl
obal
conve
r
g
ence
perfo
rman
ce.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 14, No. 2, June 20
16 : 699 – 70
6
706
Ackn
o
w
l
e
dg
ements
This work
wa
s su
ppo
rted by Baod
ing Scien
c
e
and Te
chn
o
logy Re
se
a
r
ch a
n
d
Develo
pment
Proje
c
t (1
4Z
G004
) an
d P
o
lytechni
c Fo
undatio
n of A
g
ricultural Un
iversity of He
bei
(LG2
014
020
3
)
.
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