TELKOM
NIKA
, Vol.11, No
.2, Februa
ry 2013, pp. 97
5
~
98
4
ISSN: 2302-4
046
975
Re
cei
v
ed Se
ptem
ber 21, 2012; Revi
se
d Jan
uary 3, 2012; Accept
ed Ja
nua
ry 1
5
, 2013
Chaotic Immune Genetic Hybrid Algorithms and Its
Application
Weijian Ren
*
,
Chaohai Ka
ng ,Ying
y
ing
Li, Li
y
i
ng G
ong
School of Ele
c
tri
c
al and Inf
o
rmatio
n Eng
i
neeri
ng,
North
e
a
s
t Petroleu
m Unive
r
sity, HeiLo
n
g
J
ian
g
Da
Qing
16331
8, Chi
n
a
*Co
rre
sp
ondi
ng autho
r, e-mail:ren
w
j
@
1
26.com
Ab
stra
ct
T
o
solve th
e shortag
e
in
g
enetic
alg
o
rith
ms,
such
as
slow
conver
ge
nce sp
eed, p
oor loc
a
l
search
ing
ca
pa
bility
an
d
easy
pre
m
atur
ity, firstly, t
he i
mmun
e
me
mory rec
o
gniti
on f
unctio
n
w
a
s intro
duc
e
d
,
to spe
ed
up t
he se
arch
ing
spee
d a
nd
i
m
prove t
he
over
all s
earch
in
g c
apa
bil
i
ties
of g
enetic
al
gorith
m
.
Secon
d
ly, th
e
Hén
on c
h
a
o
tic
map
w
a
s i
n
troduc
ed
into
th
e g
e
n
e
ratio
n
o
f
the i
n
iti
a
l
po
p
u
lati
on,
ma
de
the
gen
erate
d
in
iti
a
l p
opu
lati
on
unifor
m
ly
distri
buted
in th
e
soluti
on sp
ace
,
to
reduce d
a
ta
red
u
n
danc
y,
incre
a
se t
he
d
i
versity
of a
n
ti
body
p
opu
lati
o
n
a
n
d
the
sea
r
ch ra
nge
of
i
n
itial
p
o
p
u
lati
o
n
ma
nip
u
l
a
tion
,
preve
n
t the d
e
f
ect of fallin
g i
n
to loc
a
l o
p
ti
mum. Fin
a
l
l
y,
Lo
gistic
ma
p w
a
s introd
uced
int
o
man
i
pu
lati
on
of
crossover an
d mutati
on, mea
n
w
h
ile
the map
w
a
s
use
d
to
p
r
oduc
e the
ch
a
o
tic d
i
sturba
nc
e strategy
o
n
t
h
e
me
mory an
d p
opu
latio
n
s a
n
ti
bod
ies , to i
m
p
r
ove the q
u
a
lit
y of opti
m
al s
o
l
u
tion
and th
e s
earch
ing s
pee
d of
the a
l
gor
ith
m
, i
n
creas
e effici
e
n
t of se
archi
n
g
.
It w
a
s pr
oved
that the
a
bove
hybri
d
alg
o
rith
m
is co
nver
gen
c
e
by math
e
m
atic
s
metho
d
.
T
h
e
results of
functi
on opti
m
i
z
at
io
n
show
that
the
abov
e hy
bri
d
a
l
gorit
hm is
val
i
d
and h
a
s better
perfor
m
a
n
ce th
an other a
l
g
o
rit
h
ms.
Ke
y
w
ords
: ge
netic al
gorith
m
s, immun
e
al
go
rith
m
,
chaotic, function optim
i
z
ation
Copy
right
©
2013 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
In re
cent
de
cad
e
s, th
e e
x
amples to
optimize
the
functio
n
s in
theory
or p
r
acti
cal
appli
c
ation
can be
seen
everywh
e
re. There a
r
e
so
me fixed forms of m
a
the
m
atical m
ode
ling,
whi
c
h can be
obtained fro
m
many engi
neeri
ng pr
obl
ems throug
h the corre
s
p
o
nding
conve
r
sion.
That i
s
, the
pra
c
tical
p
r
o
b
lems in
en
ginee
ring
ca
n be
solved
by converti
ng them
into
the
optimizatio
n
probl
em
s of
mathemati
c
al
model. Th
er
e are a
wide
rang
e of p
r
ob
lems in
re
al li
fe,
but these
co
mplex functio
n
s formed by
a variety
of complex issu
e
s
, whi
c
h
can
not be solved
by
a gene
ral op
timization alg
o
rithm u
s
uall
y
. Now, t
here is not a be
tter optimizati
on algo
rithm to
optimize the
kind
s of com
p
lex function
s. In recent
ye
ars, the alg
o
ri
thms of genet
ic algo
rithm a
nd
immune al
gorithm are stu
d
i
ed much. Th
e geneti
c
al
g
o
rithm, a biol
ogical intellig
ent evolution
a
ry
algorith
m
, is
mainly dra
w
n
from the nat
ural
sele
ction
mech
ani
sm
of biologi
cal,
there a
r
e m
a
ny
advantag
es i
n
it, for exa
m
ple ,the
capabilit
y
of good glob
al
sea
r
chin
g and
b
e
ing e
a
sy
impleme
n
ted,
but the
r
e a
r
e some
pro
b
l
e
ms, fo
r
exa
m
ple , p
oor l
o
cal
se
archi
n
g capability,
slow
conve
r
ge
nce
spe
ed, a
n
d
easy
pre
m
aturely [1].
The imm
une
geneti
c
al
g
o
rithm [2] i
s
a
intelligen
ce e
v
olutionary al
gorithm
com
b
ining
with the biologi
cal,
and this al
go
rithm is de
riv
ed
from the
ma
n
i
pulation
me
chani
sm of
hu
man
and
oth
e
r
highe
r
ani
mals’. Ba
se
d
on the
theo
ry
of
geneti
c
al
go
rithm, the
immune
me
chani
sm i
s
i
n
trodu
ce
d in
to, and t
h
is is the
pri
m
ary
improvem
ent of
immune g
enetic algo
rithm.
Simult
an
eou
sly, it also ca
n be
con
s
ide
r
ed
as a
new
intelligen
ce e
v
olutionary al
gorithm mixin
g
with
the biologi
cal. The
population d
i
versity can
be
better mai
n
ta
ined a
nd p
h
e
nomen
a of p
r
ematu
r
e
co
n
v
ergen
ce
an
d oscillatio
n
can
be
red
u
ced
with the
imm
une
gen
etic
algorith
m
, to
o, but th
e im
mune
gen
etic algo
rithm
stil
l ha
s th
ree
m
a
in
sho
r
tco
m
ing
s
, re
spe
c
tively, falling into
local o
p
tim
a
l, a l
ong
computation
ti
me a
nd
a
sl
ow
sea
r
ching
sp
eed n
e
a
r
the
optimal
solu
tion. Since
Hénon
ch
aotic map [3] h
a
s som
e
excell
ent
cha
r
a
c
teri
stics, su
ch a
s
ra
ndomn
e
ss, e
r
godi
city and
the sen
s
itivity of initial value, these ma
ke
the gen
erate
d
initial po
pul
ation unifo
rml
y
distribut
e
d
i
n
the solutio
n
sp
ace, sim
u
ltaneo
usly, the
quality of e
v
olution i
s
i
m
prove
d
a
n
d
the
defe
c
t of data
redun
dan
cy
i
s
redu
ce
d
also.
Con
s
e
quently
, there
will
b
e
a
better
prosp
e
ct
by co
mpen
sating
the d
e
fect
s of
immun
e
ge
n
e
tic
algorith
m
wit
h
the se
ries f
eature
s
of ch
aotic theo
ry [4].
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NIKA
Vol. 11, No. 2, Februa
ry 2013 : 975 – 984
976
In ord
e
r to
solve the m
a
i
n
problem
s
o
f
geneti
c
alg
o
rithm
s
, sl
ow co
nverg
e
n
c
e speed,
poor l
o
cal searchin
g cap
ability and e
a
sy p
r
ematu
r
ity, in this paper,
Hybri
d
thinkin
g
[5] is
introdu
ce
d from el
se
whe
r
e. The
chaoti
c
imm
une
ge
netic
whi
c
h
is a n
e
w intelli
gent al
gorith
m
, is
formed
by ch
aotic
com
b
ini
ng with i
mmu
ne me
cha
n
ism. In this pa
per, the
pro
p
o
se
d alg
o
rith
m is
contraste
d
wi
th genetic
al
gorithm a
nd
immune g
e
n
e
tic algo
rith
m. At last, the glob
al se
arch
capability, converge
nce perform
a
nce and the sp
eed of searching the optimal solution are
all
tested by the simulatio
n
re
sults, me
anwhile a
com
p
a
r
ative analysi
s
is made ab
o
v
e the result
s.
2. The Des
c
r
i
ption Of Fu
nction Op
ti
mization Pro
b
lem
The functio
n
optimizatio
n probl
em [6] is main
ly use
d
to solve a more
compl
e
x function
optimizatio
n. The natu
r
e of
function opti
m
ization i
s
finding the o
p
timal solutio
n
of the objecti
ve
function
by iteration. In g
eneral, the target i
s
sea
r
che
d
by opti
m
izing th
e “f
unctio
n
” of t
he
obje
c
tive function. The d
e
scrib
ed cha
r
acte
ri
stic
s o
f
function usually in
clu
d
e
the continui
ty,
discrete, lin
e
a
r, non lin
ea
r and pu
nch. The soluti
on of
function
o
p
timization problem whi
c
h has
con
s
trai
nt
co
ndition
s
can
be al
way
s
m
ade to
remai
n
viable
by t
a
kin
g
a
d
vant
age
of spe
c
ia
lized
operator, o
r
it can be tra
n
s
form
ed into
an un
con
s
trai
ned p
r
oble
m
by using the
way of penalt
y
function. Th
erefo
r
e, the
main re
se
arche
s
are
focu
sed o
n
optimizin
g th
e function
with
uncon
strain
e
d
con
d
ition
s
. Gene
ral fun
c
tion opt
imi
z
ation proble
m
can
be d
e
scrib
ed a
s
the
following form [7]:
ma
x
n
i
i
i
f
xR
fx
xS
or
mi
n
n
i
i
i
f
xR
fx
xS
(
1
)
whe
r
e
i
x
f
is the
obje
c
tive function;
i
x
is the
domain
of the fun
c
tion;
n
R
is
the rang
e of
the
objec
tive func
tion;
S
is the v
a
riabl
e of o
b
j
e
ctive fun
c
tio
n
.
The
pro
b
le
m de
scribe
d i
n
equ
ation
(1
)
is the m
a
ximum or
minim
u
m value of t
he targ
et fun
c
tion. Usu
a
lly the maximu
m and mi
nim
u
m
probl
em
s ca
n be tra
n
sfo
r
med into e
a
c
h oth
e
r, th
a
t
is, the maximum proble
m
of the target
function
i
x
f
can
become the
minimum on
e
through n
e
g
a
tion, and the
converse i
s
also tru
e
.
3. Chao
tic Immune Gen
e
tic Algori
t
h
m
3.1.The gene
ration of
the
initial population
The initial
po
pulation
of an
tibodie
s
is
ge
nerate
d
by th
e use of
Hén
on chaoti
c
m
ap in thi
s
pape
r, and th
e spe
c
ific d
e
scriptio
n of the process is d
e
scrib
ed a
s
follows:
(1) T
he unit
matrix
m
m
is gen
erated at first;
(2) Set
1.
5
a
,
0.4
b
,
0
1
x
r
and
（
1
ra
n
d
is a
rand
om num
ber bet
wee
n
]
1
0
[
，
,
0
0
y
）
;
(3) T
he o
u
ter
loop is
ente
r
e
d
; the numb
e
r
of cy
cl
es i
s
t
he sum of the
individual
s’ n
u
mbe
r
of populatio
n and mem
o
ry;
(4) T
he inne
r
loop is re-ent
ered.
m
2
is the de
fined numb
e
r
of cycle
s
;
(5) T
he two chaotic
spa
c
e
2
,
1
y
y
as d
e
fined a
r
e gene
rate
d
by the Hén
o
n
cha
o
tic ma
p, at
the s
a
me time,
2
,
1
y
y
will be
converted to the internal
of space
]
1
,
0
[
, a
nd then they
will be
mappe
d to the spa
c
e
1,
m
, thus the corre
s
po
nding
j
i
,
value can be obtai
ne
d;
(6)The
size o
f
value
j
i
,
is jud
ged, if
ij
, the ch
aotic optim
al manipul
ation
need
n’t to be
con
d
u
c
ted,
a
nd chaoti
c
e
x
chan
ging a
nd chaoti
c
shifting
nee
d to
be con
d
u
c
ted on cha
o
tic
optimizatio
n manipul
ation
there, if
j
i
, the
cha
o
tic optim
al manipul
ation nee
d to be con
d
u
c
ted,
and th
e cha
o
tic ex
cha
ngi
ng ma
nipul
ation i
s
that th
e po
sition
s o
f
colum
n
val
u
e
i
and colum
n
value
j
in matrix should b
e
excha
nge
d d
u
ring, an
d t
he cha
o
tic shifting manipul
a
t
ion is that the
colum
n
i
is
moved out f
r
om the matrix firs
t, then the
c
o
lumn
i
extracted will be placed on
the
positio
n of col
u
mn
j
,and thus each
colum
n
after
1
i
is move
d forwa
r
d
with one column
in turn;
(7) Judgin
g
whether the
nu
mber of inn
e
r loop
i
s
re
ach
ed, if the n
u
m
ber of inn
e
r loop i
s
not rea
c
he
d, the requi
site
numbe
r of times
w
ill be
contin
ue com
p
leted, and if
the numbe
r of
inner lo
op is
reached, the n
e
xt step will b
e
starte
d;
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Cha
o
tic Im
mune ge
netic
Hybrid Alg
o
ri
t
h
m
s
and its Application (Weijian Ren)
977
(8) Judgi
ng
whether the
nu
mber of
outer loop
is rea
c
h
ed, if
the
nu
mber of
outer loop
i
s
not reached
the
requi
site
numb
e
r of ti
mes will
be
contin
ue
com
p
leted, a
nd if
the n
u
mbe
r
of
outer loo
p
is reached, the n
e
xt step will b
e
starte
d;
(9) At last,
the individu
a
l
s in
group
s and
memo
ry, which co
ntain the
on
e only
r
e
pr
es
e
n
t
ed
b
y
0,
1
, are conve
r
ted into a co
rrespon
ding a
r
ray of decim
a
l
and retu
rne
d
.
3.2.Carry
ing on th
e
Chao
tic op
timization for
the
indiv
i
dual
of outs
t
andin
g
population
a
nd
memor
y
The chaoti
c
d
i
sturb
a
n
c
e o
n
the outstan
di
ng indi
vidu
als is co
mplete
d
by Logisti
c
chaotic
map in this al
gorithm, an
d the main ste
p
s
are a
s
the f
o
llows:
(1) Fi
rstly, ind
i
viduals o
p
timized in a p
o
p
u
lation are co
nverted into
1
,
0
phalanx;
(2)The two sets of nume
r
ical sequ
en
ce, respe
c
tively
12
,
nn
, are gene
rated by Logi
stic
cha
o
tic map,
the initial value of Logistic
ch
a
o
tic map i
s
a ran
dom value in the sp
ace
]
1
,
0
[
, then it
will be transformed into the
space
[1,
]
m
and the
values
j
i
,
will be cal
c
ulated;
(3)
Jud
g
ing
whether the m
anipul
ation of
c
haoti
c
opti
m
ization
sho
u
ld be carried
out.
A thresh
old
factor
h
is defin
ed befo
r
e is the judgme
n
t made, an
d the com
p
arison
manipul
ation
will be
ma
de to jud
g
e
if the origi
n
al affinity of individual
s i
n
a tra
n
sfo
r
med
popul
ation i
s
greate
r
th
an t
he a
n
tibody a
ffinity of
origi
nal p
opulatio
ns, if the
cha
nging
conditi
ons
is m
e
t, the in
dividual
s in
o
r
iginal
po
pula
t
ion will
be
re
placed
by the
one
in
ne
w
p
opulatio
n, an
d if
not, the repla
c
e mani
pulati
on nee
d not to be don
e.
3.3.The inhibition and pro
m
otion of an
tibod
y
in the genera
tion proces
s
If the phen
om
enon
of affinity occurs
wh
e
n
the
a
n
tibod
y meeting th
e
antigen, it i
s
believe
that that antibody is relati
vely close to
the optim
al solutio
n
, othe
rwi
s
e, it is b
e
lieve that that
antibody is a
w
ay from the
optimal solut
i
on. If
some of the antibodies a
r
e foun
d being in hi
gher
concentrations relatively in the chrom
o
som
e
grou
p durin
g the
optimization
process, so
me
stagn
ation m
a
y be leade
d in the optimization
p
r
o
c
e
ss, an
d the pre
m
ature conve
r
ge
n
c
e
phen
omen
a of algorithm
may be cau
s
ed eventually
. In order to prevent the
above proble
m
s
from takin
g
pl
ace, the
way of con
c
ent
rati
on co
nt
rol
will
be used to controllin
g the
popul
ation si
ze
of same o
r
si
milar antib
od
y.
The vari
able
i
C
is u
s
ed
to re
p
r
esent the
an
tibody co
nc
e
n
tration,
whi
c
h refe
rs to th
e ratio
of similar anti
bodie
s
acco
u
n
ted for t
he e
n
tire antibo
d
y in the whole
grou
p,
i
C
is calculated as the
formula (2) b
e
low:
t
h
e
n
u
m
b
e
r
of anti
bod
ie
s
w
h
ich t
h
e
si
m
i
l
a
rity
wi
th t
h
e
anti
body
i
s
l
a
r
g
e
r
tha
n
N
i
C
(2)
whe
r
e
is the si
milarity con
s
t
ant, and its ra
nge is g
ene
ra
lly
1
95
.
0
.
The antib
ody con
c
e
n
tration
is cal
c
ulate
d
by
using the
equatio
n (2
).At the same time, the
antibody con
c
entration wh
ich
i
s
g
r
eate
r
than
a ce
rt
ain
value will
be
found o
u
t in a
ll antibody, a
n
d
they each
are re
corded
a
s
individu
al
t
,..,
3
,
2
,
1
resp
ectively, and the met
hod of calcul
ating the
concentration probability
d
P
of individuals
with a spe
c
ifi
c
numb
e
r is
defined a
s
the formula (3)
sho
w
n:
1
1
d
t
P
N
N
(
3
)
The method of calculating
the probabilit
y of other
t
N
antibody in the group
s is defin
ed
as the form
ul
a (4)
sho
w
n:
2
2
1
1
d
t
P
N
NN
t
(4)
The affinity probability
f
P
of single antib
od
y is calculate
d
by using t
he roul
ette wheel
sele
ction
met
hod. Th
e sel
e
ction
probab
ility
P
of ea
ch
a
n
tibody is co
mposed
with
two pa
rts, they
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02-4
046
TELKOM
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Vol. 11, No. 2, Februa
ry 2013 : 975 – 984
978
are the
affinity probability
f
P
and concentrat
ion
probabilit
y
d
P
resp
ectively, and
the
expression
can
be obtain
ed a
s
the formul
a (5)
sho
w
n:
1
f
d
PP
P
(5)
The affinity coefficient
s is
rep
r
e
s
ente
d
with
in the formula (5), wh
ere
0
,
1
f
P
and
1
d
P
. It can be
seen from the f
o
rmul
a
(5) that the
choi
ce probability of antibody i
s
determined
both by
the
affinity prob
abili
ty
f
P
and the concentration probability
d
P
, the
selection probability will
become
gre
a
ter
wh
en t
he valu
e of
antibo
d
y af
finity
f
P
be
come
greater,
an
d the
sele
ction
prob
ability m
u
st be
al
so
smaller
wh
en t
he value
of a
n
tibody affinity
d
P
becom
e g
r
e
a
ter. The
hig
h
antibody affin
i
ty can b
e
ret
a
ined
by such choice
way
,
whi
c
h
can
b
e
seen f
r
om t
he
calculatio
n,
and the pe
rfo
r
man
c
e of a
n
t
ibody diversity can be
im
proved
also,
the occu
rre
n
c
e of falling i
n
to
the prem
ature convergence
will be prevented eventually.
The
sele
ction
of affinity co
efficient valu
e
must
be
pai
d attention
to
wh
en
sele
cti
ng the
coeffici
ent of param
eter,
if the value is too sm
all, the role pl
ayed by the affinity choice
mechani
sm
will be
reduced in the genetic al
gorith
m
,
and this is
not cond
uciv
e to the evol
ution
manipul
ation,
and if the value is too l
a
rge,
the abi
lity of self-regulation me
chani
sms
will be
redu
ce
d in the immune g
e
netic alg
o
rith
m, and the di
versity of antibodie
s
is li
kel
y
to be destro
y
ed
in the popul
ation, the phen
omena of p
r
e
m
atur
e a
nd converg
e
n
c
e
may also be
cau
s
e
d
.
3.4.Chao
tic
crossov
e
r and chao
tic mutati
on ma
nipulation in genetic man
i
pulation
In this pa
per, the followi
ng mani
pulat
ions
will be
perfo
rmed
o
n
the ba
si
c
geneti
c
algorith
m
, crossover o
perator i
n
g
enet
ic al
go
ri
thm is repl
ace
d
with cha
o
tic cro
s
sove
r,
a
n
d
mutation op
e
r
ator i
n
the
geneti
c
algo
ri
thm is re
pla
c
ed with
cha
o
t
ic mutation,
the re
st of th
e
manipul
ation
is simil
a
r
with
the basi
c
g
e
netic alg
o
rith
m. The cro
s
sover an
d mut
a
tion ope
rato
r in
the geneti
c
manipul
ation
s
ca
n be ch
ange
d by us
ing the ch
ao
tic cont
rol st
rategy, and t
h
e
cro
s
sove
r an
d mutation
m
anipul
ations
of a strong
ra
ndom i
n
dete
r
minin
g
the p
r
oba
bility can
be
repla
c
e
d
. So
the "blindn
e
ss"
of the ra
ndom m
anip
u
lation in
ge
netic al
gorith
m
ca
n be
well
avoided. T
h
u
s
the
diversity of populatio
n individu
als
can
be e
n
sured, and th
e p
r
oble
m
of falli
ng
into local o
p
timum value can be prevent
ed.
The fou
r
ch
aotic
seq
uen
ce
s defin
ed
sep
a
rately a
s
12
3
4
,,
,
kk
k
k
x
xx
x
will be introduced
durin
g the genetic ma
nip
u
lation proce
ss, the
ch
aracteri
stics th
at hapha
za
rd and ran
d
o
m
distrib
u
tion of
cha
o
tic
seq
u
ence, whi
c
h i
s
a p
e
rfo
r
ma
nce i
n
a relati
vely short p
e
riod of time, b
u
t
all state p
r
o
p
e
rties can b
e
traver
sed
wi
thout re
plicati
on by comp
l
e
te ch
aotic
seque
nce du
ri
ng
the interval
]
1
,
0
[
are u
s
ed. Th
e individual d
i
versity of
population sho
w
ing in the short term can
be helpe
d gre
a
tly with the random
cha
r
a
c
teri
stic in su
ch a sh
ort pe
riod of time, so the falling into
local
optimu
m
can
be av
oided. Th
e o
t
her ha
nd,
th
e advanta
g
e
of cha
o
tic e
r
godi
city ca
n
be
made u
s
e of,
so the re
peti
t
ion and blin
d
manipulat
io
n
,
which
re
sult
of the rando
m manipul
ation
of ch
aotic ma
nipulation
in
a short
pe
rio
d
, ca
n b
e
p
r
e
v
ented by thi
s
a
d
vantag
e,
thus th
e dive
rsity
of popul
ation
s
can b
e
p
r
ot
ected, the
occurre
n
ce of p
r
ematu
r
e
phe
nomen
on
ca
n be p
r
eve
n
ted,
and the re
du
ction of the se
arching
spe
e
d
due to
the repeat searchi
ng ca
n be al
so prevente
d
.
The sp
ecifi
c
steps of ch
aoti
c
cro
s
sover a
nd ch
aotic m
u
tation are a
s
follows:
(1) T
he chaot
ic crossove
r
operator:
The cro
s
sov
e
r inte
rval is defined
as
1
,
0
m
c
, the que
stion
that wheth
e
r
the chaoti
c
seq
uen
ce
1
k
x
is i
n
the
crosso
ver-rang
e
m
c
is j
udge
d at first
,
at the sam
e
time, the q
uestio
n
that
wheth
e
r the t
w
o pai
r indivi
dual
s in a po
pulation a
r
e carri
ed on
cro
s
sover ma
nip
u
lation is ju
d
ged
too, if the chaotic sequ
en
ce
1
k
x
is in the interval
m
c
, the cro
s
sover
manipul
ation
need to be
carrie
d on, otherwise, the cro
s
sove
r ma
nipulation n
e
edn’t to be.
Before the ch
aotic cro
s
sover manip
u
lati
on, the rang
e
]
1
,
0
[
is divided into equal num
ber
of intervals b
a
se
d on the
gene fragme
n
t numbe
r in
the chromo
some, and e
a
ch subinte
r
va
l is
marked
with
numbe
r, th
e location of
gene f
r
agm
ent in chaoti
c
cro
s
sover
operator
ca
n
be
determi
ned
b
y
the numb
e
r of interval
2
k
x
, the cro
s
sover manipul
ation
is
carried
ou
t with ea
ch
other
co
rresp
ondin
g
ge
ne
fragm
ent of
ch
rom
o
som
e
pai
ring
wh
en the
po
sition of
crosso
ver
manipul
ation
has b
een d
e
termin
ed, so a
new sub-ch
romosome i
s
gene
rated.
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TELKOM
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ISSN:
2302-4
046
Cha
o
tic Im
mune ge
netic
Hybrid Alg
o
ri
t
h
m
s
and its Application (Weijian Ren)
979
(2) T
he chaot
ic mutation m
anipul
ation
The va
riation
interval i
s
defined
as
1
,
0
v
c
, the qu
estio
n
that wheth
e
r the chaoti
c
seq
uen
ce
3
k
x
is i
n
the va
riatio
n interval
v
c
is j
u
dged
at first, at the
sam
e
time, the q
u
e
stion
that
wheth
e
r th
e two p
a
ir i
ndividual
s in a
po
pulation
are
carri
ed o
u
t mu
tation manip
u
l
ation is j
udg
ed
too, if the chaotic seque
n
c
e
3
k
x
in the interval
v
c
, the mutation manipul
a
t
ion need to be ca
rrie
d
out, otherwi
se, the mutation manipul
atio
n need
n’t to be.
Before the ch
aotic mutatio
n
manipul
atio
n, the range
]
1
,
0
[
is divided into equal nu
m
ber
of intervals b
a
se
d on the
gene fragme
n
t numbe
r in
the chromo
some, and e
a
ch subinte
r
va
l is
marked
with
numbe
r, the l
o
catio
n
of ge
ne frag
ment
s in ch
aotic m
u
tation mani
p
u
lation
can
b
e
determi
ned b
y
the numbe
r of interval
4
k
x
,
the mutation
manipul
ation
is ca
rri
ed out
with each
other corre
s
pondi
ng gen
e fragme
n
t of chro
mo
so
me pairi
ng
whe
n
the po
sition of mut
a
tion
manipul
ation
has b
een d
e
termin
ed, so a
new sub-ch
romosome i
s
gene
rated.
3.5. The cha
o
tic distur
ba
nce mani
pul
ation for p
o
p
u
lation an
tibodies
The chaoti
c
disturban
ce f
o
r the antib
o
d
y
is com
p
le
ted by choo
sing the m
e
thod of
Logi
stic
cha
o
t
ic map, th
e
spe
c
ific meth
od i
s
t
he
sa
me ma
nipulat
ion a
s
cha
o
tic di
sturban
ce
for
individual
s in
excelle
nt pop
ulation a
nd m
e
mory, t
he p
u
rpo
s
e i
s
that
only the anti
body, whi
c
h
ha
s
the high sup
e
rio
r
ity of original antib
od
y, c
an be e
n
tered the n
e
xt cycle wit
h
the achi
eved
con
d
ition
s
, thus the state o
f
falling into the local opti
m
al solutio
n
can be avoid
e
d
.
4. Pro
v
ing of the Algorith
m
Conv
ergence
The glob
al searchin
g ca
p
ability and p
r
eci
s
io
n of the immun
e
geneti
c
opti
m
ization
algorith
m
an
d gen
etic
ch
aotic o
p
timization alg
o
rith
m are
all b
e
tter than a
singl
e ge
ne
tic
algorith
m
, at
the
same
time, the
cal
c
ulation effi
cie
n
cy of
a si
n
g
le ge
netic a
l
gorithm
can
be
improve
d
by
the two im
provem
ents
of the gen
et
ic alg
o
rithm
pre
s
ente
d
in
this pa
pe
r, the
pra
c
ticality of
the algorith
m
is incre
a
se
d, and
the co
nverge
nce
pe
rforma
nce of
the com
b
inati
o
n
algorith
m
ca
n
also be g
uaranteed.
The immun
e
geneti
c
algo
rithm combin
e
d
with immu
ne algo
rithm will be co
nve
r
ged to
global
optima
l
sol
u
tion
with proba
bility1. In the
p
ape
r, the im
prov
ement fo
r th
e ba
si
c g
ene
tic
algorith
m
, which
is the i
mmune
ge
ne
tic alg
o
rithm
ba
sed
on
chaotic,
ca
n
be
see
n
a
s
the
introdu
ction
of cha
o
tic th
eory on th
e
basi
s
of
the
immune
gen
etic alg
o
rith
m, the defects of
stand
ard g
e
n
e
tic algo
rith
m can be av
oided in the
o
ry, thus the
quality of o
p
timal solutio
n
is
improve
d
.
Theo
rem 1 t
he immun
e
g
enetic al
gorit
hm is
converged to the gl
obal optimal
solutio
n
with pro
babili
ty 1 based o
n
cha
o
tic. Prove that, set the equatio
n
ar
g
m
i
n
x
fx
, the sequ
en
ce
k
x
1
is a sequ
en
ce of
solution
s
that gen
era
t
ed
by the
im
mune
gen
etic algo
rithm
co
mbined
by
the ge
netic al
gorithm
an
d i
mmune
alg
o
ri
thm, The
se
q
uen
ce
k
x
2
is a se
quen
ce
of sol
u
tions
that
gene
rated by
the immune
genetic alg
o
r
ithm ba
sed
on the cha
o
tic theory. Wh
en the variab
le
j
i
, the inequalities
j
i
x
f
x
f
1
1
and
j
i
x
f
x
f
2
2
ca
n be
dedu
ce
d. T
he ine
quality
k
k
x
f
x
f
2
1
can be d
r
a
w
n a
c
cordi
n
g to the nature
of the recu
rsive al
g
o
rithm, and
th
e
seq
uen
ce
k
x
f
1
dra
w
n in f
r
ont i
s
a co
nvergen
t sequ
en
ce, the form
ula
1
li
m
{
}
1
k
k
Pf
x
f
x
can
be
drawn a
c
cordi
ng t
o
the
clip
pin
g
theo
re
m’
s f
eature
s
of co
nverge
nt seq
uen
ce, b
e
cau
s
e
the ineq
uality
12
kk
f
xf
xf
x
exists, the
kno
w
n
se
q
uen
ce
k
x
f
1
is a
s
a
conve
r
g
ent
seq
uen
ce,
so
the con
c
lu
sion that the
seque
nce
k
x
f
2
is also a conve
r
gent se
que
n
c
e can
be
dra
w
n, and
2
li
m
{
}
1
k
k
Pf
x
f
x
.
So the co
rre
ctness of this t
heor
em that the ch
aotic th
eory is int
r
od
uce
d
into the
immune
geneti
c
algo
ri
thm can be p
r
oved, the immune ge
netic
algorithm is
conve
r
ge
d wi
th proba
bility
1
based on
cha
o
tic theory in
this pap
er a
c
cording to of the above p
r
o
v
ing pro
c
e
ss.
5. Solv
ing The Problems
Of Func
tion
Optimizatio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
TEL
K
980
sele
c
of g
e
mani
simil
a
use
d
prob
a
base
d
gene
this
p
this
p
defin
e
by H
é
of p
o
fac
t
o
r
not
g
solut
i
dire
c
t
obtai
5.1.
T
valu
e
local
is ob
t
funct
Figu
r
local
opti
m
K
OM
NIKA
V
The ch
a
o
c
ted al
go
rith
m
(1) T
he
G
The ope
r
e
ne
tic
alg
o
r
pul
ation,
an
a
r, where th
e
(2) T
he I
m
The sa
m
in the imm
u
a
bility is 0.0
5
In orde
r
d
on
ch
aoti
ti
c al
gori
t
hm
p
ap
er a
r
e
us
e
The me
m
p
ap
er, the
p
e
d as 10
0,
t
h
é
non
ch
aoti
c
o
pulation
ind
i
r
i
n
the
cha
o
g
etting tran
s
i
on, if the s
e
t
ion of p
oor
ne
d by the
e
The test
c
T
est func
tio
n
Functio
n
1
The glob
a
e
clo
s
e t
o
t
h
e
optimal; the
Functio
n
2
Functio
n
2
t
ai
ned at
0
,
0
ion of ve
ry e
r
e 2:
Functio
n
The glob
optim
u
m
s
a
m
al; the extr
e
V
ol. 11, No.
2
o
tic i
mmune
m
s by the
si
m
G
en
etic
Alg
o
r
r
ator is sele
c
r
ithm, the
c
d th
e mu
ta
t
e
cr
os
sov
e
r
p
m
mu
ne Gen
e
m
e o
r
dinary
c
u
ne
ge
ne
tic
a
5
.
to p
r
ove th
e
c t
heo
ry
,
si
, immune
g
e
e
d in the t
e
s
t
m
or
y s
i
ze
is
d
p
op
ulatio
n si
h
e de
cima
l
e
c
map,
th
e
a
i
viduals. Th
e
o
tic optimi
z
a
t
s
form will n
o
e
lected
h
is t
o
s
o
lution, th
e
xperi
e
n
c
e [1
c
hart
s
and t
e
n
1
:
1
100
(
f
a
l m
a
ximum
e
optimal
v
a
extreme val
2
:
2
2
30
f
x
2
i
s
a functi
o
, and eig
h
t
asy falling i
n
3:
3
2
6(
f
x
al
m
a
ximu
m
a
roun
d the o
e
me value
di
s
2
, Februa
ry
ge
ne
tic alg
m
ulatio
n re
s
u
r
ithm [
8
]:
ted
by
usi
n
g
c
on
ve
n
t
io
na
l
t
ion mani
p
u
l
p
robability is
e
tic Algorith
m
c
rossover
m
a
lgorithm,
w
e
vali
dity of
x typic
a
l te
e
neti
c
al
gori
t
t
, the perfo
r
m
d
efine
d
as 4
0
ze is
define
e
ncodin
g
is
u
a
ffinity bet
w
e
e
sp
eci
a
l att
e
t
ion, if the
s
e
o
t be
conti
n
o
o small, a
p
us the glo
b
a
0].
e
st
re
s
u
lt
s o
b
22
(
)(
1
xy
valu
e 100
o
a
lue aro
u
n
d
1
ue di
stributi
o
2
10
cos(
2
x
o
n bel
ong
s t
o
local optim
u
n
to local opti
m
2
20
.
2
5
)
{
y
m
valu
e 6
of
rigin
0
,
0
, s
o
s
trib
ution of
f
Figure1.
T
2013 : 975
–
orithm
pre
s
e
u
lts.
th
e rot
a
ry
s
l
sin
g
le-poi
n
l
ation o
c
cu
r
s
0.6 and the
m
[9]:
m
anipul
ation
w
he
re
the
cr
o
the immune
st functio
n
s
hm an
d
cha
o
m
an
ce of ea
c
0
in the cha
o
d a
s
100,
a
u
se
d by the i
e
en
an
tib
o
d
i
e
e
ntion shoul
d
e
lected
h
is t
o
u
e
tr
an
s
f
or
m
p
art of
better
a
l optimal s
o
b
tained in
thi
2
)
x
whe
r
e
[
x
o
f function 1
1
,
1
, s
o
it be
l
o
n of functio
n
2
)1
0
c
o
s
x
y
o
multi
v
ariat
e
u
m value
ex
i
m
al; the extr
e
2
{
si
n
[
50
(
xy
fu
nc
tion
3 i
s
o
it belong
t
f
unction sho
w
T
he Image
o
f
–
984
e
nte
d
in
thi
s
ele
c
tion
op
e
n
t
cr
oss
o
ve
r
s
on
ly w
h
e
n
mutation pr
o
an
d co
mm
o
o
ss
over pr
o
b
g
eneti
c
alg
are sele
ct
e
o
tic immune
c
h on
e are
c
o
o
tic im
mune
a
nd the ma
x
n
dividual of
p
e
s ca
n
b
e
e
x
d
be paid to
o
o large, so
m
m
ed toward
s
solutions
w
o
lution ca
n
s pap
er
are
,]
[
2
,
2
]
x
y
is obtai
ned
a
l
on
g to a
fu
n
n
sho
w
n in
F
(2
)
y
wher
e
e
an
d m
u
lti-
p
i
st a
r
ound t
h
e
me value d
20
.
1
2
)]
1
}
w
s
obtai
n
e
d a
o a function
w
n in Figu
re
f
Func
tion1
s
p
ape
r i
s
c
o
e
rator in
sele
c
r
is
us
ed
n
the two
i
n
o
bability is 0
.
o
n mutation
b
ability is
0.
6
orithm p
r
op
o
e
d re
spe
c
ti
v
ge
n
e
tic a
l
g
o
o
mpared wit
g
e
neti
c
alg
o
x
i
m
um num
b
p
opulatio
n a
x
presse
d by
t
he sele
ct
i
o
m
e better so
l
s
the directi
o
ill be transf
o
no
t be obta
as
follows.
at
1
,
1
, and t
h
n
ctio
n of ve
r
F
ig
ure 1.
e
[,
]
[
1
.
5
,
xy
p
ea
ks, th
e gl
h
e origin
0
,
0
ist
r
ibution o
f
w
he
re
,
x
y
t
0
,
0
, and
t
of very ea
s
3:
ISSN: 230
2
o
mpared wi
t
c
tion manip
u
in the
cro
s
n
di
viduals a
r
.
05
;
ma
nipul
ati
o
6
and th
e m
u
o
se
d in th
e
v
el
y, the st
a
o
rit
h
m p
r
op
o
s
h t
he others
.
o
rithm propo
s
b
er of iterati
o
nti
b
ody ge
n
e
th
e
c
o
nc
en
t
o
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of the thr
e
l
u
t
io
ns
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c
a
u
o
n of the o
o
rme
d
tow
a
r
d
ined
, here
h
h
ere a
r
e
cou
r
y easy falli
n
1.5
]
l
ob
al maxi
m
u
, s
o
it belon
f
func
tion sh
o
0.
05
,
0
.
0
5
t
h
e
r
e ar
e
in
f
s
y falli
ng int
o
2
-4
046
t
h two
u
lation
s
sov
e
r
r
e t
o
o
o
n
ar
e
u
tation
pap
er
a
nd
ard
s
ed
in
.
s
ed in
o
ns is
e
rated
t
ra
tion
e
sh
old
u
se of
pti
m
al
d
s the
1.
5
is
ntless
n
g into
u
m 50
g to a
o
wn i
n
f
initel
y
o
local
Evaluation Warning : The document was created with Spire.PDF for Python.
TEL
K
opti
m
Figu
r
K
OM
NIKA
Functio
n
The m
a
x
m
um
s a
r
oun
d
r
e 4:
Cha
o
tic I
m
4: The Sch
a
x
imum valu
e
d
the origin
0
I
S
m
mune ge
n
e
Figure2.
T
Figure3.
T
Figure4.
T
a
ffer6 Func
ti
o
e
1 of
fun
c
0
,
0
; the
ext
r
S
SN: 2302-4
0
e
tic
Hybrid
A
T
he Image
o
f
T
he Image
o
f
T
he Image
o
f
o
n
6
(,
)
0
f
xy
c
tion
6 is
o
r
e
m
e valu
e
d
0
46
lgorit
hm
s a
n
f
Func
tion2
f
Func
tion3
f
Fun
c
tion 4
2
2
sin
0
.5
(
1
0.00
1
x
btaine
d
at
0
d
i
s
t
r
ibution
o
n
d its Applic
a
2
2
22
2
0.5
1
()
)
y
xy
w
0
,
0
, there
a
o
f S
c
haffer6
a
tion (Weijia
n
her
e
50
,
x
a
re infinitely
func
tion s
h
o
n
Ren)
981
50
y
lo
c
a
l
o
wn
in
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NIKA
Vol. 11, No. 2, Februa
ry 2013 : 975 – 984
982
5.2.Test re
su
lt
There are m
any uncertain
ties in the re
sults of
sin
g
l
e
run, in ord
e
r to avoid the impact
from the
exp
e
rime
ntal result. Each o
p
timized
fun
c
tio
n
,
the
two al
gorithm
s co
mpared with the
prop
osed alg
o
rithm
s
and
the prop
osed
algorithm
s
in this pap
er,
is run for 1
00 times. Th
e
absolute valu
e of the most advantag
e value
[x
,
y
]
, which is
solved by the
function:
22
2
1
10
0
(
)
(
1
)
f
xy
x
, and the function
22
2
30
10
c
o
s(
2
)
1
0
cos(
2
)
f
xx
y
y
,
and a give
n
optimal devia
tion value sh
ould be l
e
ss
than 10
-3;Th
e
ab
solute v
a
lue of the m
o
st
advantag
e value, whi
c
h is
solved by the
function:
2
2
0.
2
5
2
2
0.
1
2
3
6(
)
*
{
s
i
n
[
5
0
(
)
]
1
}
fx
y
x
y
,
and
a give
n
optimal d
e
via
t
ion value
sh
ould
be l
e
ss t
han
10-2. If the mo
st
adva
n
tage val
u
e
[x
,
y
]
can n
o
t be le
ss tha
n
the
minimum d
e
viation of accu
racy of it and
the optimal
value by usin
g a
certai
n algo
ri
thm when th
e requi
red te
rminatio
n ge
neratio
n
100
T
is achieved. The
con
c
lu
sio
n
can b
e
judg
e
d
that the optimizing m
ani
pulation for
th
e function fail
s by usin
g this algo
rithm. T
he
perfo
rman
ce
indicators sel
e
cted in this
pape
r ar
e the
convergen
ce
times,
the averag
e evoluti
on
gene
ration
of
the o
p
timal
solutio
n
b
e
in
g foun
d,
the averag
e conv
erge
nce
time
of searchi
n
g
the
optimal sol
u
tion, and the averag
e valu
e of satisf
a
c
tory solutio
n
. The more co
nverge
nce times
can
be
se
en
as th
e hig
h
e
r
pro
bability of
the o
p
timal
solution to
be f
ound,
and th
e glo
bal o
p
timal
solutio
n
can
be better sea
r
ch
ed by the algorith
m
; The more small averag
e evol
ution gene
rati
on
sho
w
th
at th
e mo
re fa
st
spe
ed fo
r the
optimal
sol
u
tion to b
e
fo
und, the
mo
re cl
ose b
e
tween
averag
e
conv
erge
nce valu
e, and
the
gi
ven optim
al
solution sh
ow that
the
high
er
accu
ra
cy o
f
a
satisfa
c
to
ry solution bein
g
solved by the
algorithm.
With the ab
o
v
e mentione
d
limitations, three
al
go
rith
ms, whi
c
h
are all ru
n for 1
00 times,
of gen
etic, i
mmune
ge
n
e
tic, an
d
ch
aotic im
mun
e
ge
netic are compa
r
e
d
. The
num
be
r of
satisfa
c
to
ry solution
can
b
e
foun
d by th
is ma
ni
pul
ation,
evolution
gene
ration, converg
e
n
c
e
ti
me
and the average of optim
al solution b
e
ing solv
ed durin
g the 10
0 times ru
nni
ng are
sho
w
n in
Table 1
-
4.
Table 1. The
Perform
a
n
c
e
Comp
ari
s
o
n
Of Optimizin
g
Function
1
Algorith-ms
The
numbe
r of
conve
r
ge
ce
The
gene
ration
-n of
averag
e evol
ution
The time
of average
conve
r
ge
n-ce
The
value of average
conve
r
ge
n-ce
Geneti
c
41
62.2
1.02s
100
ImmuneG
ene
tic 49
59.3
0.81s
100
Cha
o
tic Imm
une
Geneti
c
92
51.2
0.74s
100
Table 2. The
Perform
a
n
c
e
Comp
ari
s
o
n
Of Optimizin
g
Function
2
Algorith-ms
The
numbe
r of
conve
r
ge
ce
The
gene
ration
-n of
averag
e evol
ution
The time
of average
conve
r
ge
n-ce
The
value of average
conve
r
ge
n-ce
Geneti
c
25
100
1.63s
4.9999
ImmuneG
ene
tic 37
89.2
1.41s
50
Cha
o
tic Imm
une
Geneti
c
87
53.4
1.37s
50
Table 3. The
Perform
a
n
c
e
Comp
ari
s
o
n
Of Optimizin
g
Function
3
Algorith-ms
The
numbe
r of
conve
r
ge
ce
The
gene
ration
-n of
averag
e evol
ution
The time
of average
conve
r
ge
n-ce
The
value of average
conve
r
ge
n-ce
Geneti
c
21
100
2.20s
5.9851
ImmuneG
ene
tic 42
83.5
1.94s
5.9875
Cha
o
tic Imm
une
Geneti
c
91
63.3
1.78s
5.9907
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Cha
o
tic Im
mune ge
netic
Hybrid Alg
o
ri
t
h
m
s
and its Application (Weijian Ren)
983
Table 4. The
Perform
a
n
c
e
Comp
ari
s
o
n
Of Optimizin
g
Function
4
Algorith-ms
The
numbe
r of
conve
r
ge
ce
The
gene
ration
-n of
averag
e evol
ution
The time
of average
conve
r
ge
n-ce
The
value of average
conve
r
ge
n-ce
Geneti
c
78
25.6
0.374
s
0.9994
ImmuneG
ene
tic 93
21.3
0.138
s
0.9998
Cha
o
tic Imm
une
Geneti
c
98
8.2
0.099
s
1
It can
be
see
n
from
the
ru
nning
re
sult
s of Ta
ble
1-6
that the
con
v
ergen
ce
rate of th
e
cha
o
tic imm
u
ne ge
netic
al
gorithm
pro
p
o
se
d in thi
s
pape
r ha
s a
wide
ran
ge o
f
improveme
n
t
comp
ared to
immune
ge
n
e
tic al
gorith
m
and
sta
nda
rd ge
netic alg
o
rithm
und
er
the same
ba
sic
conditions. Thus the immune genetic
al
gorithm
has a stronger capab
ility of global
searching, so
the problem
of falling into
local
optimu
m
sol
u
tion
ca
n be
preve
n
ted, and
its
pe
rforma
nce i
s
more
sTabl
e. It also ca
n be
se
en from the
Table that
th
e avera
ge ev
olution ge
ne
ration of ch
ao
tic
immune
ge
ne
tic alg
o
rithm,
whi
c
h i
s
com
pare
d
with im
mune
gen
etic algo
rithm
an
d the
stan
da
rd
geneti
c
algo
ri
thm, is sig
n
ificantly le
ss u
n
der t
he co
nve
r
gen
ce ca
se, the
pre
m
ature
co
nverg
e
n
c
e
can be b
e
tter avoided by the immune g
enetic alg
o
rit
h
m based on
chaotic the
o
r
y propo
se
d in
this pap
er, at the same tim
e
, the global
optimal sol
u
tion ca
n be al
so found qui
ckly.
The co
ncept
of population perfo
rma
n
ce di
spe
r
si
on and po
p
u
lation geo
g
r
aphi
cal
disp
ersion
are introd
uced
respe
c
tively, in orde
r to
make th
e pe
rforma
nce of
the algorith
m
prop
osed in this pa
per o
b
served ea
sily.
Definition 1, the dispersio
n
of populatio
n
performan
ce
is defined a
s
follows:
12
,,
,
n
Df
x
f
x
f
x
That is the va
rian
ce of the indivi
dual pe
rf
orma
nce of in the populatio
n:
12
,,
n
px
x
x
Definition 2, the dispersio
n
of populat
ion
geographi
cal
is defined a
s
follows:
12
-,
-
,
,
-
n
n
Ex
c
x
c
x
wh
ere
12
=,
,
,
n
cE
x
x
x
is t
h
e cente
r
of
p
opulatio
n g
r
a
v
ity, th
e
Euclide
an di
stance i
s
defin
ed as
.
The d
egree
distrib
u
tion o
f
the popul
ation di
versity can be
exp
r
essed by
po
pulation
perfo
rman
ce
disp
ersion
and p
opulati
on ge
ograph
ic
al di
spe
r
si
on, the di
sp
ersi
on valu
e
s
of
popul
ation
wil
l
be different
by usin
g the
different
al
go
rithms to
calculate. If the d
i
spe
r
si
on val
u
e
cal
c
ulate
d
by an algo
rithm i
s
greater th
a
n
the
one tha
t
calcul
ated b
y
another al
g
o
rithm, it mea
n
s
that the perfo
rman
ce
of alg
o
rithm
with la
rge
r
va
lue
of the dispersio
n
cal
c
ul
ated i
s
bette
r, nam
ely
the diversity of the popula
t
ion is better
whe
n
usi
ng the algo
rithm
and the lo
ss
of genetic typ
e
s
can b
e
well a
v
oided.
Figure5.the contra
st of pop
ulat
ion pe
rformance dispe
r
sion by the o
p
timization fu
nction 2
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
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TELKOM
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Vol. 11, No. 2, Februa
ry 2013 : 975 – 984
984
Figure6. the contra
st of pop
ul
ation ge
ographi
cal di
spe
r
sio
n
by the optimization fu
nction 2
The
chan
ge curve of
pop
ulati
on pe
rformance di
spe
r
sio
n
an
d po
pulation g
e
o
g
rap
h
ical
disp
ersion
when optimi
z
i
ng the funct
i
on
)
2
cos(
10
)
2
cos(
10
30
2
2
2
y
y
x
x
f
by using the
geneti
c
alg
o
ri
thm, immune
geneti
c
al
go
rithm an
d
ch
aotic imm
une
geneti
c
al
go
rithm a
r
e
sho
w
n
on the Fig
u
re
5 and Fi
gu
re 6(T
he
cha
o
t
ic immun
e
g
enetic
algo
rithm propo
se
d
in this p
ape
r is
sho
w
n
with t
he g
r
ee
n line
,
the immun
e
geneti
c
al
go
rithm is sho
w
n with th
e bl
ue line,
and t
h
e
geneti
c
algo
ri
thm is sh
own
with the red li
ne),
The con
c
lu
si
ons ca
n
be dra
w
n
from the
te
st resu
lts of pop
ula
t
ion dispersi
on an
d
geog
rap
h
ical disp
ersion
sh
own o
n
the F
i
gure
5 and
F
i
gure
6, whi
c
h usin
g the three
algo
rith
ms
to optimi
z
e th
e fun
c
tion
2 ,
the
perfo
rma
n
ce
di
sp
e
r
sio
n
a
s
well
a
s
the ge
og
raph
ical
dispersio
n
can
be
mai
n
tained
a l
a
rge
r
valu
e b
e
tter by u
s
in
g the
immune
ge
ne
tic alg
o
rithm,
thus th
e l
o
ss
of
geneti
c
types can
be
bette
r avoid
ed, th
e pop
ulati
on
diversity i
s
m
a
intaine
d
, an
d the p
r
ob
abi
lity
of global opti
m
um se
archi
ng is greatly improve
d
.
6.Conclu
sion
T
he algo
rith
m of chaotic
immune ge
n
e
tic is
propo
sed mai
n
ly in this pape
r. More
over,
the alg
o
rithm
is u
s
e
d
in
the
optimization
of co
mp
lex
f
u
nct
i
on
s.
Th
e simulat
i
o
n
re
sult
s,
whi
c
h
a
r
e
comp
ared wit
h
the geneti
c
algorithm, i
mmune g
ene
tic algorith
m
, demon
strate
that the global
sea
r
ch ability and co
nverg
ence perf
o
rm
ance of t
he al
gorithm
can b
e
improve
d
. Simultaneo
usly,
the spe
ed for
sea
r
ching the
optimal soluti
on ha
s bee
n improve
d
sig
n
i
ficantly als
o.
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