TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 13, No. 1, Janua
ry 201
5, pp. 174 ~
179
DOI: 10.115
9
1
/telkomni
ka.
v
13i1.682
5
174
Re
cei
v
ed O
c
t
ober 1
1
, 201
4; Revi
se
d Novem
b
e
r
17, 2014; Accept
ed De
cem
b
e
r
11, 2014
Nonlinear Equations Solving Base on Immune Genetic
Algorithm
Peng Qiong
Schoo
l of Information Sci
enc
e and En
gi
neer
ing, Hu
na
n Internatio
nal Ec
on
omics Univ
ersit
y
Cha
ngsh
a
, Chi
na, postco
de: 410
20
5
email: matl
ab_
b
y
s
j
@1
26.com
A
b
st
r
a
ct
A stea
m c
onv
ersio
n
of
hydr
ocarb
o
n
mass
ba
l
anc
e
of th
e n
onl
in
ear
eq
uatio
ns
of the
i
m
mu
n
e
gen
etic al
gorit
h
m
meth
od is r
e
search
ed i
n
thi
s
pap
er.
T
he n
onli
n
e
a
r eq
uati
onsis tra
n
sfor
me
d int
o
no
nli
n
ear
opti
m
i
z
at
ion pr
obl
e
m
s; T
t
he transfor
m
ati
on
process a
n
d
im
pl
em
en
ta
ti
on a
r
e
d
i
scu
ssed
, th
i
s
m
e
tho
d
i
s
used
to quick
l
y
and easi
l
y obtai
n
the effective
sol
u
tion
of the pro
ducti
on tech
nol
ogy.
T
he pro
ducti
o
n
process us
ed to solve pr
actic
a
l pro
b
le
ms, o
p
timi
z
e
pr
oduct
i
on a
nd i
n
creas
e econ
o
m
ic effi
ciency.
Ke
y
w
ords
:
i
m
mu
ne g
e
n
e
tic alg
o
rith
m, non
li
near so
lver, hy
drocar
bon ste
a
m
refor
m
i
ng, materia
l
bal
anc
e
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
A colle
ction
of peopl
e called the hyd
r
o
c
arbon
hy
dro
c
arbon
s, a
c
cordin
g to its
pha
se in
turn
divided
i
n
to ga
se
ou
s
hydro
c
a
r
bo
ns, liquid
and
solid hyd
r
o
c
a
r
bon
s di
amete
r
. Hyd
r
o
c
a
r
bo
ns
with water va
por u
nde
r certain co
ndition
s, the c
hemi
c
al rea
c
tion to
prod
uce with
CO, CO2, CH4,
H2 a
nd oth
e
r
compo
nent
s of the
con
v
ersio
n
of
ga
s, peo
ple u
s
ed to ref
e
r t
o
the reactio
n
of
hydro
c
a
r
bo
n
steam
refo
rm
ing re
actio
n
. Into gas i
s
th
e ba
sic
ra
w
material
s, am
monia, synth
e
tic
hydroxyl, hydroge
n is
wid
e
ly available
and so on,
so steam
refo
rming of hyd
r
oca
r
bo
ns i
n
the
fertilizer industry, petrochemical indu
st
ry occupies a specifi
c
position.
For the
stea
m reforming
of gaseou
s h
y
drocarbon
s
are n
a
tural
g
a
s, oil ga
s, re
finery ga
s,
co
ke oven g
a
s
, etc.; liquid
hydro
c
a
r
bo
ns are na
pht
ha,
light distillate raffinate oil
,
to expand the
sou
r
ces of ra
w materi
als, rece
nt resea
r
ch has b
egu
n conve
r
si
on of
heavy oil steam.
Therm
odyna
mics of hyd
r
o
c
arbon
ste
a
m
reform
ing
an
d materi
als, e
nergy
cal
c
ula
t
ion for
two pu
rpo
s
e
s
: First, hyd
r
ocarbon
ste
a
m refo
rmin
g rea
c
tion in
vestigated th
e extent of the
cha
nge
s wit
h
the proce
ss
co
ndition
s for the
proce
s
s condit
i
ons
sele
cte
d
to provid
e
the
thermo
dynam
ic ba
sis. Se
cond, do the
material
s
of the syste
m
, heat cal
c
ulatio
ns, cal
c
ul
ate
d
con
s
um
ption indicators;
provide
the ba
sis for progra
m
rating
s.
With the h
y
drocarbon
steam
reforming
re
acti
on ch
aracte
ristics a
n
d
transfe
r
cha
r
a
c
teri
stics of the pro
c
e
ss d
eepe
n
s
the unde
rstanding, lea
r
n from relate
d disci
pline
s
to
develop
mat
hematical m
odelin
g tra
n
sformation
proce
s
s; an
d
be te
sted in
pra
c
tice, de
rived
stru
ctural pa
rameters an
d operating pa
rameters su
ch
as catalyst activity, water ca
rbo
n
rati
o ,
workin
g lo
ad,
exce
ss
air
ratio of th
e reacto
r
st
ate,
ope
rating
fl
exibilit
y, energy co
nsumpti
on,
temperature distrib
u
tion, con
c
e
n
tration
distri
b
u
tion
trend. By hydro
c
a
r
bo
n st
eam refo
rmi
ng
pro
c
e
ss,
wit
h
low en
erg
y
con
s
um
ption i
s
r
unnin
g
a lo
ng
cy
cle
of high
co
st si
gnifica
nt
advantag
es,
as chemi
c
al
s, fe
rtilizers, in
dustri
a
l ba
ckbone.
2. Material Balance Equa
tions of
Nonl
inear Binary
Hydro
c
a
r
b
on
steam
refo
rm
ing re
actio
n
o
f
t
he system,
peopl
e are int
e
re
sted in
the
three
rea
c
tion
s, na
mely ca
rbo
n
monoxide
shift re
a
c
tion,
methan
e conversion
re
action, m
e
th
ane
decompo
sitio
n
rea
c
tion.
Whe
n
condu
cting mate
ria
l
balan
ce, gi
ven two eq
u
ilibrium tem
p
eratu
r
e inte
rval, an
increa
se of t
w
o rest
rictio
n
equation
s
, t
he eq
uival
ent
of two key compon
ents
of a given that
th
e
following holds
:
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Nonli
nea
r Equation
s
Solvi
ng Base o
n
Imm
une Gene
tic Algorithm
(Peng Qiong
)
175
)
2
)(
1
(
n
10
)
2
m
-
4
-
4b
(3a
0.974P
K
2
T
-10
3
2
Pms
b
a
R
b
a
(
1
)
(
2
)
E
D
m
b
a
R
n
T
2
4
)
(
2
1
n
T
--to bal
an
ce the system'
s
total numbe
r of moles, m
o
l.
。
P--total pressure, Pa; bala
n
ce of the sy
stem con
s
tan
t
.
M--hyd
ro
ca
rb
on in th
e
hydro
c
a
r
bo
n feed
stock of hydro
g
en to
carb
on ratio,
dimen
s
ionl
ess.
R--ra
w hydro
c
arbon
mol
a
r ratio
of
ca
rb
on in
the
wa
ter, dime
nsi
o
nless; g
a
s
consta
nt,
8.3143K
J
／
(kmol.K)
D--hydrocarb
on ra
w materi
als in nitro
g
e
n
and carb
on
ratio of hydro
c
arbon
E--in the hyd
r
oca
r
bo
n feed
stock hy
d
r
ocarbo
n ca
rb
on
ratio of argo
n
K
Pms
--ca
r
bo
n monoxide
shi
ft reaction eq
uilibriu
m
con
s
tant
K
Pmgs
-- the co
nversi
on of m
e
thane e
quili
brium
con
s
ta
nts
General form
ula for the equilib
rium constant expressi
on:
J
3
*
2
*
*
ln
*
*
lnKp
3
4
2
3
2
1
0
R
T
a
R
T
a
R
T
a
R
T
a
T
R
a
(
3
)
T - temperatu
r
e, K;
J - re
act
i
o
n
is
split
busi
n
e
s
s;
ln - natural lo
garithm.
Polynomial coefficient
s in
enthalpy an
d
stand
ar
d free
enthalpy of the kn
own co
ndition
s,
obtaine
d:
29.878849
-
T
10
4.289387
T
10
5.138576
T
10
5.3148
-
T
8.771694ln
47T
-22632.811
lnK
3
12
-
2
7
-
3
-
-1
Pms
4.991881
-
T
10
5.99947
T
10
4.886386
-
T
10
1.807258
T
0.158666ln
-
6T
5041.39944
lnK
3
11
-
2
7
-
3
-
-1
Pwgs
The va
riou
s t
y
pe (1
), (2),
only a, b
are
two
un
kno
w
ns, in
the p
a
s
t an
d mo
re
with the
style differen
c
e, gen
eratio
n method, to sen
d
on be
ha
lf of the method is very cu
mbersom
e
. With
the proliferation of comput
ers, some wit
h
quas
i
-
Ne
wton method, b
u
t also troubl
e; Here we u
s
e
geneti
c
algo
ri
thm, to solve quickly and a
c
cura
tely an
d
to avoid local
minimum poi
nts.
We a
r
e in the
hydrog
en m
a
terial b
a
lan
c
e, pro
c
e
ss
op
timization, en
ergy saving d
e
vice
s,
the no
nlinea
r bina
ry en
co
unter
equ
atio
ns
(1
), (2
) of
the solutio
n
.
In
the obtai
ned a,
b value,
rec
e
iv
e:
T
n
b
a
)
1
(
100
mol%)
(
CH
4
T
n
b
a
R
O
)
2
(
100
mol%)
(
H
2
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02-4
046
TELKOM
NI
KA
Vol. 13, No. 1, Janua
ry 2015 : 174 –
179
176
T
n
m
b
a
)
2
2
4
3
(
100
mol%)
(
H
2
T
n
a
100
mol%)
CO(
T
n
D
100
mol%)
(
N
2
3. Immune Genetic
Algori
t
hm
Immune ge
n
e
tic algo
rithm
(IGA) is b
a
sed
on bi
ologi
cal immu
ne
mech
ani
sm i
n
re
cent
years, a
n
i
m
prove
d
ge
netic alg
o
rith
m is pr
opo
sed, is a n
e
w
computati
onal intellig
e
n
ce
approa
ch, which i
s
the p
r
inci
ple of life scien
c
e a
n
d
tradition
al geneti
c
immu
ne grate met
hod
combi
nation.
Biological di
versity of the immun
e
system ha
s a
n
tibodie
s
, self-reg
u
lation,
and
other characteristics of t
he imm
une
memory
fun
c
tion [3], im
mune
ge
neti
c
al
go
rithm
is
in
tr
o
d
u
c
e
d
ba
s
e
d
on
ge
ne
tic
a
l
g
o
r
i
th
ms
th
e ba
s
i
c
chara
c
te
risti
c
s of bi
ologi
cal
immune
sy
stem.
No
w re
sea
r
ch and appli
c
ation sho
w
that the
immune gen
etic
algorith
m
both the sea
r
ch
ing
spe
ed, glob
al
sea
r
ch ability and local
search
capa
bil
i
ties, optimal
desi
gn is b
e
coming on
e of the
hot area
s of rese
arch [4].
Immune
gen
etic al
gorithm
to solve the
probl
em to
b
e
corre
s
pon
di
ng to the
anti
gen, the
solutio
n
of the pro
b
lem co
rre
sp
ondi
ng to antibodi
es
,
antigen
s an
d antibodi
es by
affinity feasible
solutio
n
an
d
optimal
soluti
on de
scrib
ed
in the ap
proximation [5-6]. Firstly, to re
ceive an a
n
tig
en
(co
r
respon
din
g
to a spe
c
i
f
ic pro
b
lem
)
, then
ran
d
o
m
ly generate
d
a set of i
n
itial antibodi
es
(co
r
respon
din
g
to the initial can
d
idate
solutio
n
); the
n
cal
c
ulate t
he fitness of each a
n
tibo
d
y
(affinity), crossover an
d m
u
tation of
anti
body; ag
ain Con
c
e
n
tratio
ns of
po
pulati
on-b
a
sed up
date
strategy g
e
n
e
rate
s the n
e
xt
generatio
n of antibod
y group, u
n
t
il a terminati
ng condition,
the
algorith
m
end
s.
Figure 1. Immune ge
netic al
gorithm flo
w
ch
art shown
The ba
sic
ste
p
s are as foll
ows:
1) Algo
rithm i
n
itialization.
Antigen inp
u
t and p
a
ramet
e
r
setting: en
ter the target
function
and
con
s
trai
nts, as th
e a
n
tigen in
put; set po
pulatio
n si
ze Po
psi
z
e, sele
ct the pro
bability
Ps,
cro
s
sove
r pro
bability Pc, mutation metho
d
and othe
r p
a
ram
e
ters.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Nonli
nea
r Equation
s
Solvi
ng Base o
n
Imm
une Gene
tic Algorithm
(Peng Qiong
)
177
2) The initial
antibody. In the first iteration,
the antib
ody use
d
in the sol
u
tion space is
usu
a
lly the method of ran
d
o
m gene
ratio
n
.
3) T
h
e
affinity and
co
nce
n
tration
calculatio
n
s
. Cal
c
ulate
the fit
ness
of antib
ody an
d
antigen a
nd a
n
tibody co
ncentration
s we
re cal
c
ul
ated.
4) Te
rmin
ation of conditi
onal. Determ
ine w
hethe
r
the termin
ating condition
is the
highe
st fitne
ss
will be
wi
th the antige
n
ant
ibody i
mmune m
e
m
o
ry datab
ase
join, and th
en
terminate; oth
e
rwi
s
e
contin
ue.
5) T
h
e
sele
ction,
crosso
ver a
nd m
u
tation.
Acco
rding to
the
choi
ce
of
se
tting the
prob
ability of Ps, the crossover
pro
bability
Pc and
mutatio
n
method
s sele
cted anti
body
sele
ction, cro
s
sover an
d m
u
tation.
6) Acco
rding
to the above update the g
r
oup after the
operation go t
o
step 3
)
.
4. Design Pr
oblem Solv
ing
4.1. Design
of Affinit
y
F
unction
At a tempera
t
ure T
= 7
0
5
Ԩ
, the cl
aim
to: ca
rbon
monoxide
shift reactio
n
eq
uilibriu
m
con
s
tant K
Pms
=14.50
39.
At a tempe
r
ature
T
= 7
40
Ԩ
, th
e
cl
aim to: the
conve
r
si
on
o
f
methane
e
quilibri
um
con
s
t
ant
sK
Pwgs
=1.3211.
In the example, ente
r
: P=9.84e5
，
m
=
3
.
6683
，
D=0.0
1133
，
R
＝
3.8
618
；
Into th
e
above
(1), (2) have
a, b of the binary nonlin
ear
equatio
ns:
(4)
0
14.5039
-
)
2
8618
.
3
)(
1
(
)
7073
.
4
2
2
(
0.1659)
-
4b
+
94.3081(3a
)
,
(
2
3
1
b
a
b
a
b
a
b
a
g
(5)
0
1.3211
-
)
2
8618
.
3
(
0.1659)
-
4b
+
b(3a
)
,
(
2
b
a
a
b
a
g
Set affinity
func
tion:
2
2
2
1
))
,
(
(
))
,
(
(
1
1
)
,
(
b
a
g
b
a
g
b
a
f
(
6
)
1
)
,
(
0
b
a
f
Affinity function imag
es
shown in Fig
u
r
e 2,
the o
r
ig
inal eq
uation
s
an
d into Qi
uqin a
nd
the maximum
value of the solutio
n
functi
on.
Figure 2. The
fitness fun
c
tion
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 13, No. 1, Janua
ry 2015 : 174 –
179
178
4.2. Upda
te
on the Conc
entra
t
ion of
Population
To en
sure the diversity of
antibodie
s
to im
prove th
e global
sea
r
ch capa
bility, using a
Euclide
a
n
distance
ba
se
d
on a
n
tibody
and
antibo
d
y to
cal
c
ulate
the similarity
of fitness a
nd
con
c
e
n
tration
method
s. An
tibody x
i
and
x
j
in mind the
Euclid
ean
di
stan
ce
D(x
i
，
x
j
) re
spe
c
tiv
e
l
y
,
the fitness f(x
i
) and
f(x
j
), given
the ap
prop
riate
co
n
s
tant
δ
> 0,
ε
> 0,
su
ch
as
t
o
s
a
t
i
sf
y
t
h
e
following formula:
D(x
i
，
x
j
)
≤δ
| f(x
i
)- f(x
j
)|
≤ε
x
j
, x
j
antibody and antib
ody called
si
milar to
antib
odie
s
and an
tibody similar to th
e
numbe
r of
x
i
as
x
i
the co
n
c
entration
of antibody,
d
e
noted by C
i
;
antibodi
es were
sele
cted
as
likely x
i
,p(x
i
), namely:
)
(
)
(
]
)
(
)
(
1
[
)
(
x
M
x
f
x
M
x
f
C
x
p
i
i
i
i
Whe
r
e,
α
,
β
for the
(0,1
) b
e
twee
n the a
d
justa
b
le p
a
rameters, M
(x) for all
antibodie
s
of
the large
s
t fitness value, C
i
is the con
c
e
n
tration of ant
ibody x
i
.
It can
be
se
e
n
from
the
a
bove e
quatio
n: Wh
en
th
e antibody co
n
c
entration
i
s
high,
the
antibody i
s
selecte
d
to
ad
apt to hi
gh
probability to
small; wh
en th
e antib
ody
co
nce
n
tration
is not
high, the anti
body is selected to adapt to high pr
o
b
ability for large. This not
only retain
s the
excelle
nt indi
viduals, but a
l
so redu
ce th
e choi
ce
of si
milar antib
odi
es, to ensure
the diversity of
the individual.
4.3. Genetic
Opera
t
ion
Immune ge
n
e
tic algo
rith
m can mai
n
tain the diversity of antibodie
s
and e
v
entually
conve
r
ge to the optimal solutio
n
to a major ope
ration, that is, a choice i
n
the algorit
hm,
cro
s
sove
r a
n
d
mutatio
n
o
perato
r
exist
s
,
so th
at th
e fitness of t
he
whol
e a
n
tibody p
opul
ation
along the di
re
ction of better search.
1)
Sele
ct the operator. Sel
e
ction o
perator with the fol
l
owin
g:
i
C
n
i
i
i
i
s
e
N
x
x
x
P
1
)
1
(
)
(
)
(
)
(
1
Whe
r
e:
)
(
i
x
is the type of fitness fun
c
ti
on for the
vector di
stan
ce; C
i
is the
con
c
e
n
tration
of antibody x
i
.
α
and
β
is the co
nsta
nt adjustme
n
t factor, N is the total numbe
r of
antibodi
es
within the pop
ul
ation.
2)
Two cros
s-c
u
tting method.
Let
]
,...,
,
[
1
2
1
1
1
1
n
l
x
x
x
X
，
]
,...,
,
[
2
2
2
1
2
2
n
l
x
x
x
X
is l o
n
beh
alf o
f
the two
antibodi
es, in
the first point and d, i-p
o
int arit
hmeti
c
impleme
n
tation of two cro
s
s-cutting
to
prod
uce the n
e
xt generatio
n of antibodie
s
are:
]
,...,
,
,...,
,...,
[
1
1
1
'
'
1
1
1
1
n
j
j
i
l
x
x
x
x
x
X
]
,...,
,
,...,
,...,
[
2
1
2
"
"
1
2
2
1
n
j
j
i
l
x
x
x
x
x
X
Whe
r
e
，
x’
k
an
d x”
k
(i
≤
k
≤
j
)
G
enerated by a
linear combi
nation of the followin
g
:
x’
k
=
ζ
x
1
k
+(1
-
ζ
)x
2
k
x”
k
=
ζ
x
2
k
+(
1-
ζ
)x
1
k
Whe
r
e
，
ζ
∈
[0
，
1]
，
the scal
e factor.
3) Ga
ussian
mutation met
hod. Gau
s
sia
n
mutati
on, the first de
cod
i
ng of the antibody to
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TELKOM
NIKA
ISSN:
2302-4
046
Nonli
nea
r Equation
s
Solvi
ng Base o
n
Imm
une Gene
tic Algorithm
(Peng Qiong
)
179
the co
rrespo
nding n
e
two
r
k struct
u
r
e, i
n
acco
rda
n
ce with the f
o
llowin
g
formula to cha
nge
own
e
rship of
the netwo
rk v
a
lue:
)
1
,
0
(
)
(
i
x
f
i
i
m
e
x
x
Whe
r
e, x
m
i
i
s
the va
riatio
n of th
e a
n
tibody, x
i
is a
variatio
n of
the antib
ody
befo
r
e;
)
1
,
0
(
is mean 0,
varian
ce 1 n
o
rmal rand
o
m
variable;
γ
∈
(-1
，
1), the mutation rate of th
e
individual; f(x
i
) Is
the fitnes
s of antibody x
i
, that is t
he fitne
s
s val
ue of th
e o
b
jective fun
c
tio
n
.
Instru
ction
s
o
n
the type of variation an
d adaptat
io
n
antibody is inversely pro
portion
al to the
degree th
at t
he lo
we
r fitne
s
s (th
e
small
e
r th
e fitne
s
s value
of the
obje
c
tive fun
c
tion),
the
hig
her
the mutation rate of the individual, and vice versa. Vari
ation, the re-f
ormatio
n
of a new a
n
tibody
.
Take
the i
n
itial po
pulation
size
N
= 20
a
nd
oth
e
r para
m
eters,
the
cl
aim
to:
a = 0.2052, b
= 0.359
1, the fitness f (a, b)
= 0.9
9
98, the total School to t
hen come to
the numbe
r of
coeffici
ents n
T
= 5.835
9, and thus
Con
s
i
dere
d
as
cont
ent of each
compon
ent in Table 1.
Table 1. The
conte
n
t of each compo
nen
t
Components
CH4
H2O H2
CO CO2
N2
mol%
7.4661
50.3506
32.3195
3.5157
6.1536
0.1941
5. Conclusio
n
This p
ape
r prese
n
ts a
stea
m conve
r
si
on
of
hydrocarb
on ma
ss b
a
la
nce of the n
o
n
linea
r
equatio
ns of t
he imm
une
g
enetic alg
o
rit
h
m meth
od, and achieved
goo
d results.
Immune
ge
n
e
tic
algorith
m
i
s
a refe
re
nce
adaptive im
mune
syst
e
m
re
co
gni
ze
and
elimin
a
t
e foreig
n b
ody
penetrated th
e body of the
function of a
n
tigen,
the immune
syste
m
, learnin
g
, memory, an
d
the
diversity of the introdu
ction
of genetic algorithm
s. Gai
algorithm ha
s the geneti
c
algorith
m
based
on the introd
uction
Gau
ssian mutation
and u
pdat
e
strategy ba
se
d on antib
od
y con
c
entration
adju
s
tment m
e
ch
ani
sm, ca
n effectively maintain the
diversity of a
n
tibodie
s
, wh
ich exi
s
t in the
geneti
c
algo
rithm to avoid the prem
ature conv
e
r
gen
ce probl
em [3]. In
solving p
r
a
c
tical
probl
em
s, the obje
c
tive fu
nction
and
constraint
s a
s
the antig
en i
nput, then
ge
nerate
the ini
t
ial
antibody gro
up, and thro
ugh a se
rie
s
of genetic
manipul
ation and the cal
c
ulation of antibody
affinity, antibody diversity in maintai
n
in
g the
ci
rcum
stance
s
, to id
e
n
tify the antig
en for A
n
tibo
dy,
that is, the
solution
of th
e proble
m
. Immune
ge
ne
tic alg
o
rithm
The
ba
sic feature
s
i
n
cl
u
de:
improve
d
a
b
il
ity of global
sea
r
ch
algo
rithm, to avoi
d
falling into
th
e lo
cal
optim
al solution;
with
best individ
u
a
l
memory; wit
h
fast global
conve
r
ge
nce.
Referen
ces
[1]
Z
un-Ho
ng Yu. ed h
y
dr
ocarb
o
n
steam reforming e
ngi
ne
eri
ng. H
y
droc
arb
on Pr
ocess
i
ng
Press. 1989
;
78-1
10.
[2]
W
ang
Xiao
pi
n
g
, so
on. Ge
n
e
tic a
l
gor
ithms
- the
o
r
y
,
a
ppl
i
c
ation
an
d s
o
ftw
a
r
e
imp
l
eme
n
tation
of [M].
Xi'
a
n: Xi'
an Jia
o
tong U
n
iv
ersity Press. 20
02.
[3]
Xi
e Kem
i
ng,
Guo Ho
ng
bo
Xi
e Gan
g
. Artificial
immu
ne
alg
o
rithm a
n
d
its ap
plic
ati
on.
Co
mpute
r
Engi
neer
in
g an
d Appl
icatio
ns
. 200
5; 29(1
8
): 77-80.
[4] W
o
ldem
ariam
KM
.
Vacci
ne-E
nha
nce
d
Artific
i
al Immu
ne
S
ystem for Multi
m
oda
l F
uncti
o
n
Optimiz
a
tion.
IEEE transactions on systems, m
an, an
d cybernetics. Part B, Cybernetics
.
2010; 4
0
(1).
[5] Jieqi
on
g
Z
hen
g
,
Yu
nfan
g C
hen
,
W
e
i Z
h
a
ng. A Surve
y
of artifici
al immune a
ppl
ic
ations.Artifici
a
l
Intelli
genc
e Re
vie
w
. 20
10; 34(
1).
[6] Castro
LND
，
T
i
mmis J
．
Arti
ficial immune
s
y
stems
：
A ne
w
comp
utatio
n
a
l
i
n
tell
ig
ence
appr
oach. UK;
Sprin
ger-Ver
la
g. 2002.
Evaluation Warning : The document was created with Spire.PDF for Python.