TELKOM
NIKA
, Vol. 11, No. 9, September 20
13, pp.
5517
~55
2
2
ISSN: 2302-4
046
5517
Re
cei
v
ed Ap
ril 19, 2013; Revi
sed
Ju
n
e
12, 2013; Accepted June 2
7
, 2013
Bionic Intelligent Optimization Algorithm based on
MMAS and Fish-Swarm Algorithm
Jingjing Yang*
1
, Benzhen
Guo
1
, Jixiang Gou
2
, Xiao Zhang
1
1
School of inf
o
rmation Sci
enc
e & Engin
eer
in
g, Hebe
i North
Univers
i
t
y
, Z
h
a
ngji
a
ko
u 07
50
0
0
, Heib
ei,
P.R.Chin
a, +
86-313-
804
17
35
2
School of inf
o
rmation Sci
enc
e & Engin
eer
in
g, Lanzh
ou
U
n
i
v
ersit
y
, L
anzh
o
u
730
00
0, Gansu, P.R.China,
+
86-93
1-89
13
7
4
6
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: r78z-
y
an
g@1
26.com*
1
, 179
2
295
39
9@q
q
.co
m
, yjr78z
@gm
a
il.com
2
A
b
st
r
a
ct
W
i
th larg
e
nu
mb
er
of ants, t
he
ant c
o
lo
ny
alg
o
ri
th
m w
o
u
l
d a
l
w
a
ys take
a l
ong
ti
me
or
is rath
er
difficult to
fin
d
the
opti
m
al
p
a
th fro
m
c
o
mp
lex c
hapt
er
p
a
t
h, further
mor
e
, ther
e
ex
ists a c
ontra
dictio
n
betw
een sta
g
n
a
tion,
accel
e
ra
ted co
nverg
e
n
c
e a
nd
prec
oc
ity. In this p
a
per, w
e
pr
opo
se a
new
b
i
o
n
i
c
opti
m
i
z
at
ion
al
gorith
m
.
T
h
e ma
in id
ea of
the alg
o
rith
m
is
to intro
duc
e t
he
hori
z
o
n
s c
o
ncept
in th
e M
M
AS
fish sw
arm a
l
g
o
rith
m, so it w
oul
d take s
hort
e
r time
to fin
d
the opti
m
al p
a
t
h
w
i
th nu
mer
o
us ants, an
d t
he
introd
uction
of the conce
p
t of fish sw
arm al
g
o
rith
m
con
gest
i
on l
e
vel w
oul
d
enab
le the a
n
t colony find th
e
path of
glo
b
a
l
opti
m
i
z
at
ion w
i
t
h a stron
g
cro
w
ding l
i
m
it
w
h
i
c
h avo
i
ds th
e
emerg
ence
of l
o
cal
extre
m
e
a
n
d
improves th
e a
ccuracy an
d efficiency
of the a
l
gorit
hm.
Ke
y
w
ords
:
MMAS, artificial fish sw
arm al
go
rithm, visi
on, cong
estio
n
leve
l
Copy
right
©
2013 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
The ant colo
ny algorithm
(Ant Colony
Opti
mizatio
n
ACO)
was p
r
opo
sed in 19
91 by the
Italian schol
a
r
Dorig
o
M et
al. It is an ev
olutiona
ry alg
o
rithm b
a
sed
on swa
r
m int
e
lligen
ce
bio
n
ic
with the ch
aracteri
stics of
grou
pme
n
t, robu
stne
ss, collabo
ration a
nd rapi
dne
ss [1, 2]. However,
due to the fact that ant initial motion
is ran
dom, whe
n
the po
pulation
size
is too larg
e
,
it
become
s
very difficult or even impo
ssi
ble to
find an optimal pat
h in a sho
r
t perio
d of time,
furthermore,
with time
going on, it is
eas
y
to fall
i
n
to lo
cal mi
nim
a
later,
amo
u
n
ting to le
ss t
han
the global opt
imum. The M
M
AS (MAX-MIN Ant System
) is an imp
r
oved ant colo
ny algorithm
put
forwa
r
d by th
e Germ
an re
sea
r
che
r
s Stuetzle T.
The
difference b
e
twee
n the improve
d
algo
rithm
and th
e tra
d
itional
ant
colo
ny algo
rithm i
s
that
ea
ch it
eration
allo
ws only the
be
st
perfo
rmin
g a
n
t
to update pat
h pheromo
n
e
,
which
will h
e
lp to
prevent
prematu
r
e converg
e
n
c
e [3, 4].
Artificial fish
swarm algo
rith
m (Artificial Fi
sh Swarm Al
gorithm, AFS
A
) [5] is pro
p
o
se
d b
y
Li Xiaolei an
d Qian Jixin
in 2002. The
algorithm
ha
s the ability to overcome l
o
cal minim
a
to
obtain gl
obal
extreme, b
u
t AFSA ha
s a fa
ster converg
e
n
c
e j
u
st in th
e e
a
rly time, th
e
convergence speed
will be
come
slower l
a
ter, sometim
e
s ev
en stop the
process
of convergence
,
so it is difficu
lt to get an a
c
curate o
p
tim
a
l solution
wi
th the only hope to find the the soluti
o
n
domain [6, 7] of the optimal solution.
In this pa
pe
r, we a
nalyzes the ch
aracte
ri
stics
of MM
AS and fish
swarm
algo
rithm an
d
find the simila
rities of the o
p
timization m
e
ch
ani
sm
bet
wee
n
these two alg
o
rithm
s
, com
b
ine
d
wit
h
the advanta
g
e
s of
both me
thods,
we
pro
posed a
ne
w hybrid bioni
c optimizatio
n algorith
m
whi
c
h
can b
e
tter im
prove the opti
m
izati
on effici
ency of the al
gorithm.
2.
MMAS Algor
ithm and Fis
h
S
w
a
r
m
Alg
o
rithm
2.1. MMAS Algorithm
Assu
me that
the numb
e
r
o
f
ants in the
colony
m, the
distan
ce
bet
wee
n
any p
a
th i and j
is
,1
,
2
,
.
.
.
,
di
j
n
ij
,
bt
i
sta
n
d
s
fo
r the
num
be
r
of ants of
poi
nt i at time
t ,
1
n
mb
t
i
i
.
t
ij
is the
re
sidu
a
l
amou
nt of in
formation
of
path ij a
n
t time t. The valu
e of
0
ij
is 0, the
dire
ction
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ISSN: 23
02-4
046
TELKOM
NIKA
Vol. 11, No
. 9, September 201
3: 551
7 – 5522
5518
of movement
of ant
1,
2
,
.
.
.
kk
m
is d
e
termin
ed b
a
sed on th
e a
m
ount of info
rmation
on e
a
ch
path,
k
p
t
ij
indi
cates the probability of ant k choo
sing the
path ij
at time t,
parameter
01
is a factor
repre
s
e
n
ts inf
o
rmatio
n re
si
dual,
1
is a co
efficient whi
c
h can
signify
the conte
n
t of the pheromo
ne evapo
ratio
n
(i.e., t
he degree
of the passag
e
of informatio
n). Ea
ch
ant sho
u
ld be
have to meet the followin
g
con
d
ition
s
:
1)
Cho
o
se the n
e
xt path with the co
rre
sp
o
ndi
ng p
r
ob
abi
lity based on
the con
c
e
n
tra
t
ion of the
horm
one in th
e path.
2)
No l
ong
er sel
e
ct the
p
a
th t
r
averse
d a
n
d
st
o
r
e thi
s
po
int with
a
dat
a st
ru
cture,
called ta
bu
list to co
ntrol
it, the taboo list stored all
the
path
s
unt
il the momen
t
t and taboo
the ant to
find the optimal value agai
n before a
c
ce
ss the
m
after N intera
ction
s
.
3)
After the com
p
letion of th
e
first iteration,
ac
co
rdin
g to
the len
g
th of
the path to
relea
s
e the
corre
s
p
ondin
g
con
c
e
n
trati
ons of ph
ero
m
one.
2.1.1. Pheromone Upd
a
te Rules an
d Res
t
rictio
ns
[8]
(1)
Upd
a
te on
ly the best pe
rformin
g
ant pheromo
n
e
11
be
s
t
tt
ij
ij
i
j
(1)
in the above
equatio
n,
1
be
s
t
ij
be
st
L
.
(2) T
he p
heromone
re
stri
ction
s
: set a
uppe
r an
d lo
wer limit
s for the phe
romo
ne:
mi
n
、
max
and
ma
x
mi
n
t
ij
, in ord
e
r
to avoid p
r
e
m
ature
co
nve
r
gen
ce. If
ma
x
ij
, th
en
ma
x
ij
else if
mi
n
ij
, then
mi
n
ij
，
and eq
uati
on
0
mi
n
shoul
d b
e
assured. While re
sea
r
chi
n
g
,
set the
maxi
mum p
h
e
r
om
one to
b
e
a
n
estim
a
ted
m
a
ximum limit,
and
S
is a
gl
obal
optimal
s
o
lution:
11
li
m
1
t
ij
ij
t
f
S
(2)
If got global optimal solutio
n
, then refre
s
h
max
, try to get a
dynamic valu
e of
ma
x
t
.
1
1
max
ma
x
mi
n
1
1
n
P
P
be
s
t
dec
n
P
P
de
c
be
s
t
(3)
In the above equation,
max
1
max
mi
n
n
PP
dec
b
est
. The sele
ction of maximum and
minimum ph
erom
one val
ue is dete
r
m
i
ned by t
he averag
e pat
h length. By setting a p
a
th
pheromo
ne
concentratio
n
to en
sure it i
s
n
o
t t
oo hi
g
h
to avoid
premat
ure
stag
nation, an
d t
h
e
same
way to avoid red
u
ci
n
g
the possibili
ty of
finding a
new path.
2.1.2. Transition Rules
The probability of selecting path
ij for ant k at time t can be calculated with the following
equatio
n:
0
tt
ij
ij
k
pt
j
a
l
l
o
w
e
d
ij
k
k
a
llo
w
e
d
t
t
ki
k
i
k
ot
h
e
r
w
i
s
e
(4)
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TELKOM
NIKA
ISSN:
2302-4
046
Bionic Intelligent Optim
i
zation Algorith
m
based on
MMAS and Fi
sh-S
wa
rm
… (Jingji
ng Yang
)
5519
With
0,
1
,
1
a
llo
w
e
d
n
ta
b
u
kk
to provi
de all the po
ssible p
a
ths a
n
ant coul
d select.
2.2. FISH S
w
arm Algorith
m
The mai
n
be
haviors of fish swarm in
cl
ude
foragin
g
behavio
r, swarmin
g
be
ha
vior and
followin
g
beh
avior.
Fora
ging be
havior: assu
ming the cu
rre
nt st
ate of the artificial fish swa
r
m
is
X
i
,
rand
omly sel
e
ct a
state
X
j
within its sen
s
ing
ra
nge, f
o
r the
maxim
a
l value, if
YY
ij
, move a
step forwa
r
d
the dire
ction
,
else ra
ndo
mly sele
ct a state
X
j
, determine wh
ether i
t
meets the
forwa
r
d
co
nd
itions o
r
n
o
t. Try repeate
d
ly for seve
ral times, if it
doe
s not m
e
et the conditi
ons
forwa
r
d, ra
nd
omly move one step.
Swarmi
ng be
havior: assu
ming
the cu
rrent state to
be
X
i
, explore the numb
e
r of
partne
r
s
n
f
and
central lo
cati
on
X
c
in current
neigh
borhoo
d
d
V
is
a
b
le
ij
. I
f
Y
c
Y
i
n
f
, meaning
that the pa
rtn
e
rs have
more food
and th
e clu
s
te
r
is le
ss
cro
w
de
d, so m
o
ve on
e
step to
wa
rd t
he
dire
ction of the cente
r
of
pa
rtners, othe
rwise imple
m
en
t the foraging
behavio
r.
Bulletin boa
rd: Re
co
rd th
e statu
s
of t
he individ
ual
artificial fi
sh
. Each a
r
tificial fish
individual in t
he optimi
z
ati
on proc
ess
will examine
whether th
e in
dividual
state
is bette
r tha
n
the
state of the bulletin boa
rd whe
n
the optimization i
s
co
mpleted, if the state
of the
bulletin boa
rd
is
better tha
n
th
e individu
al
state, the bulle
tin boa
rd
stat
e will
be
ch
a
nged
to thei
r
own
state, th
us
makin
g
the b
u
lletin boa
rd to record the history optim
al state.
Its behavio
r
mech
ani
sm i
s
to sele
ct b
ehavior to
m
a
ke th
e big
g
e
st a
c
t in th
e optimal
dire
ction forward, if fail to
make the n
e
xt stat
e behavior better than
the current b
ehavior, take a
rand
om be
ha
vior.
3.
A Ne
w
Hy
brid Bionic Optimization Al
gorithm
3.1. Thought of the Alg
o
r
i
thm
MMAS fish swarm algo
rith
m belong
s to swar
m optimi
z
ation alg
o
rit
h
m, when the
number
of individual
s rea
c
h a cert
ain extent, the entire
po
pu
lation will exh
i
bit some inte
lligent beh
avior.
The ant colo
ny is to find the optimal p
a
ths,
whil
e fish swa
r
m is to find a food so
urce. T
h
e
simila
rities b
e
t
ween them a
r
e as follo
win
g
:
1)
For
ant colo
ny algo
rithm,
0
ij
is
equ
al e
v
erywhe
re
at the be
ginni
ng, all a
n
t
s
randomly sel
e
cted path; While the fish sw
arm algori
thm will try to
select a state
X
j
randomly.
2)
Ant colony al
gorithm
will perform the
conv
ergence of the algorit
hm
according to the
update
of p
h
e
rom
one,
na
mely
1
t
ij
. The
more
ph
ero
m
one
s, the m
o
re a
n
ts. Fi
sh
swarm
algorith
m
p
e
rform conve
r
g
e
s ba
sed
on
clu
s
ters
and
rea
r-e
nd
beh
avior. G
ene
rally, for a
r
tificial
fish, whe
r
e t
here
i
s
m
o
st
wate
r, the
r
e
is mo
st foo
d
,
that is,
the
optimal
soluti
on d
o
main.
T
he
large
r
the n
u
m
ber
of artificial fish is, the mo
re it
is lik
ely to attrac
t more artific
i
al fis
h
. So
the
clu
s
ters and
rear-en
d
beh
a
v
ior of ants is similar
to secrete phe
rom
o
nes b
ehavio
r of fish stocks.
Whe
n
the nu
mber of ant
colony is very
la
rge, the mo
vement of most ants
are
random,
so i
n
thi
s
a
r
ticle,
we i
n
trod
uce
d
visi
on
concept
b
e
fore
ea
ch ite
r
atio
n of the
fish
-swarm al
gorith
m
.
Whe
n
ant
k
u
pdate p
h
e
r
o
m
one to
choo
se
path ij
with
larg
est
k
p
t
ij
, if there
exists a b
e
tter path
in all paths
within visio
n
, that is
dt
d
t
ij
vi
s
ual
, then the ant will
try to select
be
st
iVisual
again, or, ij is the final choi
ce.
At the begi
n
n
ing
of the
algorith
m
, an
t colo
ny alg
o
rithm i
s
e
a
sy to fall int
o
lo
cal
conve
r
ge
nce, so in this p
a
per, we intro
duce a pa
ra
meter
, a degree of cong
e
s
tion of the fish
swarm
algo
ri
thm co
ncept
, which
can
avoid p
r
emat
ure self-agg
regation phe
romone
at
ea
rly
time, which n
o
t only preve
n
ts prematu
r
e ant col
ony redu
nda
nt co
nverge
nce, b
u
t also imp
r
o
v
es
the ability of
global o
p
timization.
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ISSN: 23
02-4
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TELKOM
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Vol. 11, No
. 9, September 201
3: 551
7 – 5522
5520
3.2.
Main Steps
of the
Algori
t
hm
Take th
e tra
v
eling salesman p
r
obl
em
(TSP) [9] a
s
exampl
e, the main
ste
p
s of the
algorith
m
are
as follo
wing:
Step 1
: Set i
n
itial time t =
0, put m a
n
t into n
cities
ra
ndomly, the i
n
itial co
ncent
ration
of
pheromo
ne for ea
ch path i
s
00
ij
;
Step 2
: Set
S = 1,(s is th
e su
bscri
p
t of the tabu
li
st), store th
e ini
t
ial city numb
e
r of Kth
ant into
ta
b
u
s
k
which stand
s for t
he Sth city the curre
n
t ant is traveling in.
Step 3
: The probability of ant k shifting
from position i to position
k is:
0
tt
ij
ij
k
p
t
j
a
llow
e
d
ij
k
ka
l
l
o
w
e
d
t
t
ki
k
i
k
ot
h
e
rw
i
s
e
(5)
Equation
0,
1
,
1
a
llo
w
e
d
n
ta
b
u
kk
indicate
s all the
cities the
ant coul
d ch
oo
se
,
and
are
two pa
ram
e
ters
re
pre
s
e
n
t the phe
rom
one the
ant
accumul
a
ted
while m
o
vin
g
, and g
ene
rally
t
ij
equal
s to
1
d
ij
.
Step 4
: Ant k fist inspe
c
t a
t
position i, the vision value
is
d
vi
s
u
a
l
, which
will
find a path ix
rand
omly and
then comp
are
k
p
t
ij
with the largest path ij, if
dd
ij
ix
, then choo
se path ij, else,
cho
o
se path i
x
.
Step 5
: Whe
n
the ant moving as the a
bov
e path, calcul
ate the conge
stion
ij
with the
followin
g
equ
ation:
2
t
ij
ij
t
ij
ij
(6)
If
t
ij
, we kno
w
that the path is
not that crowd
ed, then the ant will move from p
a
th i to
path j
according to this path, else, in
the fe
asible neighborhood
the ant will re-sel
ect a sub-
optimal p
a
th.
t
is th
e thre
shol
d ant ti
me t which
will up
date
a
c
cordi
ng to
the e
quation
1
ct
te
.
Step 6
: After n iteration
s
, update the ph
e
r
omo
ne,
11
best
tt
ij
ij
ij
(7)
In the a
bove
equ
ation,
1
be
st
ij
best
L
. Each
iteratio
n p
r
ocess just update
the
best
pe
rformi
ng
ant phe
romo
nes to avoi
d
sea
r
ching to
o co
nc
entrat
ed mainly a
d
opting ph
ero
m
one
smo
o
thing
mech
ani
sm to adju
s
t the
con
c
e
n
tration
of the phero
m
one, in a
ccorda
n
ce with
the pro
porti
on
update
d
.
Step 7
: On
e
cycle
to
upda
te the
bulletin
boa
rd, th
e
cycles of th
e o
p
timal p
a
th.
Until the
next cycle if there i
s
a better path than t
he
value, the
n
update the
bulletin boa
rd
again.
Step 8
:
Rep
e
a
t Step 2 to
Step 7 until
converg
e
n
c
e
a
s
a
path o
r
a
spe
c
ified
nu
mber
of
times
.
Step 9
: The a
l
gorithm termi
nated with th
e output of op
timal solution.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Bionic Intelligent Optim
i
zation Algorith
m
based on
MMAS and Fi
sh-S
wa
rm
… (Jingji
ng Yang
)
5521
4.
TSP Instanc
e
Simulation
In ord
e
r to te
st the effe
ctivene
ss
of the
al
gorith
m
, take the traveli
n
g sal
e
sman
p
r
oble
m
Oliver 30 a
s
an insta
n
ce o
f
the calcul
ation.
The p
a
ram
e
ter
setting
s are as foll
owi
n
gs: n
=
10
0, try_numbe
r=1
0
,
=1,
=5,
=
0
.1,
NC_max=20
0
, Q
=
100,
=0.
6
. The
alg
o
rit
h
m i
s
reali
z
e
d
with
Matla
b
7
.0, the
co
nfiguratio
n
of th
e
PC is: Pentiu
m Dual
-core
E5400
，
2G
RAM.
Optimizatio
n
curve a
nd the
shorte
st path
is sho
w
n in F
i
gure 1.
Figure 1. The
Optimizing
Curve of the I
m
prove
d
Algorithm
Figure 2. The
Average Le
n
g
th
and the Sho
r
test Path of the
Improved Alg
o
rithm
Figure 3. The
eil76 Path
of the Improved Algorithm
As the data show in the ab
ove figure, st
anda
rd optim
al solution i
s
423.74
06; the integer
distan
ce fo
r 420. The al
g
o
rithm of hi
s pape
r a
c
hiev
es a o
p
timal
distan
ce of 4
23.207
1, slig
htly
better than th
e optimal sol
u
tion whi
c
h i
m
pr
ove
d
the accuracy of the algo
rithm.
To furthe
r vali
date the me
rits of the imp
r
o
v
ed algo
rithm
comp
are
d
wi
th other al
gori
t
hms,
we take the T
SP problem e
il76 (76
cities) as exam
ple.
Table 1. Co
m
pari
s
on of the
Propo
sed Al
gorithm
with other Algo
rith
ms
Algorithm Maximum
length
Mi
nimum length
Average length
AFSA 588.14
554.32
570.27
ACO 565.16
545.97
553.04
SA 570.42
548.26
564.67
MMAS 561.38
544.08
551.83
Proposed
Algorithm
556.29
543.86
549.04
5. Conclu
sion
Bionic alg
o
rit
h
m based on
MMAS fish swarm algo
rith
m were intro
duced in the con
c
e
p
t
of vision and
conge
stion
of the fish swarm al
go
rithm enabli
ng the ant colon
y
optimizatio
n to
better avoid
l
o
cal
minim
a
and improve the effici
ency
of the algorithm. However, MMAS require
relatively hig
h
about pa
ra
meters com
p
ared
with
AFSA. The improved algo
rith
m of this pap
er is
mainly ba
se
d
on a
n
t colon
y
algorithm,
so pa
ramete
rs wo
uld h
a
ve
a direct im
pa
ct on t
he
re
sults
of algo
rithm.
Ho
w to
ma
ke
the m
o
st
ap
prop
riate
choi
ce
of p
a
ra
me
ters or
cho
o
se a
an
alg
o
rit
h
m
whi
c
h ha
s
le
ast req
u
ire
m
ents abo
ut
p
a
ram
e
ters
to
perfo
rm org
a
n
ically
i
n
tegration
of intelli
gent
algorith
m
s
an
d de
sign
efficient and m
o
re ada
ptive al
gorithm
used
to solve the
a
c
tual p
r
obl
em
is
what we must
continu
e
to do wi
th the following res
e
arc
h
work
.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NIKA
Vol. 11, No
. 9, September 201
3: 551
7 – 5522
5522
Ackn
o
w
l
e
dg
ement
This work was su
ppo
rted
by the National
Scien
c
e
and Te
chn
o
l
ogy Support
Program
(No. 20
12BA
J
18B0
8
) of M
i
nistry
of Scie
nce a
nd Te
ch
nology.
Referen
ces
[1]
Dorig
o
M, M
a
n
i
ezzo
V, Co
lor
n
i A. P
o
sitiv
e
f
eed
back
as
a
search
strateg
y
. T
e
chnic
a
l
R
eport
91-
016
,
Dipartim
ento d
i
Electronic
a
, Politec
nico d
i
Mil
ano, IT
. 1991.
[2]
Color
n
i A,
Dori
go M, Ma
niezz
o
V.
Distri
bute
d
opti
m
i
z
a
t
i
on
by ant c
o
l
oni
e
s
. Procee
din
g
s
of the F
i
rs
t
Europ
e
a
n
Conf
erenc
e on Artifi
cial Lif
e
. Elsevi
er. 1992; 1
34-1
42.
[3]
Stutzle T
,
Hoos H.
Improvements on the ant system
:
Introducing MAX-M
I
N ant system
.
Proce
edi
ng
s
of the Inter
nati
ona
l Co
nfere
n
c
e on
Artificia
l
Neur
al N
e
t
w
or
ks and
Gen
e
tic
Algor
ithms. W
i
en: Spr
i
n
ger
Verla
g
. 199
7; 245-2
49.
[4] Stutzle
T
.
MA
X-MIN ant system for Q
uadr
a
t
ic Assign
ment
Probl
e
m
s
. T
e
chnic
a
l R
e
p
o
rt AIDA-97-0
4
,
Intellect Grou
p
,
Department
of Comput
er Scienc
e,
Darm
stadt Univers
i
ty of T
e
chnol
o
g
y
,
Germa
n
y
.
199
7.
[5]
W
ang C
u
iru,
Z
hou C
h
u
n
le
i, Ma Jia
n
w
e
i.
An Improv
ed
Artificial F
i
s
h
-sw
a
rm Al
gorit
hm an
d Its
Appl
icatio
n in
F
eed-forw
ard
Neural N
e
tw
orks
. Proceed
i
ngs of 200
5 Internati
o
n
a
l C
onfere
n
ce o
n
Machine Learning and Cy
bernetics. Piscata
w
a
y
,
USA: IEEE Press.
2005: 289
0-28
94.
[6]
Jian
g Min
g
y
a
n
, Yuan D
o
n
g
feng.
Wavelet Threshold
Optim
i
z
a
t
i
on
with Artificial Fish Swarm
Algorit
h
m
.
Pro
c
eed
ings
of 2
005
Internati
o
nal
Co
nfer
enc
e o
n
N
eura
l
Net
w
orks. Pis
c
ata
w
a
y
, U
S
A
:
IEEE Press. 2005: 569-
57
2.
[7]
CR W
a
n
g
, C
L
Z
hou, JW
M
a
.
An
i
m
prove
d
artifici
al
fish
-sw
a
rm a
l
gor
ithm a
nd
its a
pplic
atio
n i
n
feedforw
a
rd
n
eura
l
n
e
tw
orks.
Proc. of th
e
F
ourth Int. C
o
nf. on M
a
ch
in
e L
earn
i
n
g
an
d C
y
b
e
rn
etics.
200
5; 289
0-28
94.
[8]
T
homas stutzl
e, Holg
er Hoo
s
.
MAX-MIN a
n
t system
and local searc
h
for combinatorial optim
i
z
at
io
n
prob
le
ms
. Proc
. Of 2nd Int. On Metahe
uristic
s
. W
i
en: Spring
er-Verla
g. 199
7.
[9]
Chio
ng R. Nat
u
re-Insp
i
red Al
gorithms
for Optimisati
on, Sp
ring
er. 200
9; 536.
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