TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.5, May 2014, pp
. 3555 ~ 35
5
9
DOI: http://dx.doi.org/10.11591/telkomni
ka.v12i5.3892
3555
Re
cei
v
ed
Jul
y
14, 201
3; Revi
sed
De
ce
m
ber
14, 201
3; Acce
pted Janua
ry 3, 20
1
4
The Optimization of Finishing Train Based on Improved
Genetic Algorithm
Hong
xia Liu*, Xin Chen, Rongy
u
Li
Electron
ics an
d Information E
ngi
neer
in
g, Na
njin
g Un
iversit
y
of
T
e
chnolo
g
y
, Nanji
ng, Chi
n
a
*Corres
p
o
ndi
n
g
author, em
ail
:
lhx_cec@
126
.com
A
b
st
r
a
ct
T
he ce
ntral
is
sue
of fin
i
shi
n
g trai
n is
that
w
e
s
hou
ld
dist
ribute
the
thic
kness
of e
a
ch
exit w
i
th
reaso
n
a
n
d
det
ermine
the
rol
l
i
ng forc
e a
n
d
re
lative c
onv
exity
.
T
he o
p
ti
mi
z
a
ti
on
methods
cu
rrently us
ed
ar
e
empiric
a
l d
i
stri
butio
n
metho
d
and th
e lo
ad c
u
rve
meth
od, but
they
b
o
th have dr
aw
bac
ks. T
o
solve th
ose
prob
le
ms w
e
e
s
tablis
hed
a
mathe
m
atic
al
mode
l of t
he fin
i
shin
g train
and
introduc
ed
an
improve
d
Gen
e
tic
Algorit
h
m
. In this al
gorit
hm
w
e
used rea
l
nu
mb
er
enc
odi
ng, selecti
on
oper
ator
of a
roul
ette and
el
itist
selecti
on a
nd
then i
m
prove
d
crossover a
n
d
mutatio
n
op
erators. T
he r
e
sults sh
ow
that the mod
e
l
and
alg
o
rith
m
is fe
asibl
e
an
d co
ul
d e
n
sure
the
o
p
timal
e
ffect a
nd c
onv
erge
nc
e sp
ee
d. T
h
e
prod
ucts
me
et
the
prod
uction r
e
q
u
ire
m
e
n
ts.
Ke
y
w
ords
:
s
te
el roll
in
g, loa
d
distrib
u
tion, i
m
prove
d
ge
netic
algor
ith
m
Copy
right
©
2014 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
In rolling production pr
ocess, the
optimization probl
em
of
train finishing load di
stri
bution
is very important. The optimization m
e
thod
s cu
rrentl
y
used are e
m
piri
cal di
stri
bution metho
d
and th
e lo
ad
curve
meth
od
[1], but they
both h
a
ve d
r
awb
a
cks. Th
e em
piri
cal
di
stributio
n m
e
thod
is simpl
e
and
reliable, but it would ca
use t
he inequali
t
y of each assembli
ng unit
and can
not self-
adapt o
n
line.
The mo
del of
the load
cu
rv
e method
is
simple but
req
u
ire
s
a lot
of measured d
a
t
a
and complex
cal
c
ulatio
ns t
o
compl
e
te.
In this pa
per we ta
ke th
e sh
ape, thi
c
kne
ss
and
load b
a
lan
c
i
ng into a
c
co
unt and
establi
s
h
ed t
he m
a
themat
ical
model
of
the fini
shin
g
train
an
d int
r
odu
ce
d a
n
i
m
prove
d
G
e
netic
Algorithm for Load Di
strib
u
tion Model.
This alg
o
rith
m is based o
n
the mathe
m
atical mod
e
l
we
establi
s
h
ed. Then
we u
s
e
it to do the
simulati
o
n
experim
ent. Th
e re
sults
sho
w
that the mode
l
and alg
o
rithm
is feasibl
e
.
2. The Math
e
m
atical Mod
e
l of the Fini
shing Train
The main
aim is dist
ributi
ng the thickn
ess of
eac
h
exit. At
the s
a
me time, we s
h
ould
take the shap
e into accou
n
t
to ensure that t
he striped
steel meet
s p
r
odu
ction
req
u
irem
ents.
An impo
rtant
issue
of the
model i
s
to
d
e
term
in
e the
obje
c
tive fun
c
tion [2]. We
consi
der a
model with
n
(
10
3
n
) frames.
We will
divide t
he
whol
e
process into th
ree phases.
The
former two
p
hases
sh
ould
maximize th
e amou
nt
of
redu
ction
an
d ke
ep lo
adi
ng bal
an
ced.
The
third pha
se
should redu
ce
the amount of
redu
ction an
d kee
p
the sh
ape optimal.
The obje
c
tive
function:
3
2
1
J
J
J
J
(1)
}
)
min{(
2
2
1
1
1
P
K
P
J
(2)
1
J
ensures that we fully
use t
he facilities.
}
)
min{(
2
3
2
2
2
P
K
P
J
(3)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3555 – 35
59
3556
2
J
ensu
r
e
s
that the load bal
a
n
cin
g
ha
s be
en ke
pt.
}
)
(
min{
2
4
3
i
n
i
n
n
i
i
h
CR
h
CR
J
(4)
3
J
ensu
r
e
s
that the sha
pe ha
s bee
n well o
p
timized.
In the formul
a
i
P
is rolling f
o
rce of i-th f
r
ame.
1
K
,
2
K
is scale factor, in this paper
9
.
0
1
K
,
1
2
K
;
i
i
h
CR
is th
e rel
a
tive convexity of the stri
p af
ter getting th
rough th
e i-th
frame.
n
n
h
CR
is the relative convexity of the end pro
d
u
ct,
i
is the op
timal adjustm
ent variable.
So the last ob
jective functio
n
is:
}
)
(
)
(
)
min{(
2
4
2
3
2
2
2
2
1
1
i
n
n
n
i
i
i
h
CR
h
CR
P
K
P
P
K
P
J
(5)
is
the weight c
oeffic
i
ent.
Con
s
trai
nts:
max
0
P
P
i
(6)
max
0
M
M
i
(7)
i
i
h
h
1
(8)
max
P
,
max
M
is the maximum rollin
g force and
rolli
ng mome
nt for a singl
e dev
ice.
i
h
is
the thickne
ss
of the strip after getting through the i-th f
r
ame.
3. The Improv
ed Genetic Algorithm
The Ge
netic
Algorithm i
s
a stocha
stic
global o
p
timization al
go
rithm [3]. It not only ha
s
stron
g
glo
bal
sea
r
ch capa
b
ilities and th
e
ability to solv
e pro
b
lem
s
, b
u
t also
ha
s a
simple
gen
eri
c
and ro
bust, suitabl
e
fo
r parall
e
l
p
r
o
c
essing, etc.
But it ha
s t
w
o si
gnificant
dra
w
ba
cks:
First,
pron
e to pre
m
ature, seco
nd, due to selectio
n and
hybridi
z
ation
and mutation
operato
r
rol
e
in
makin
g
some
excelle
nt ge
ne fra
g
ment
prem
aturel
y
l
o
st.
To solve these proble
m
s,
the stand
ard
Geneti
c
Algorithm has be
e
n
improve
d
a
nd su
cce
ssf
ul
ly applied to the model in t
h
is pa
per [4].
Encodi
ng:
The cu
rre
ntly
used en
codi
ng
a
r
e bina
ry
en
c
odi
ng, G
r
ay en
co
ding,
letter
en
codi
ng a
n
d
real nu
mbe
r
encodin
g
[5]. In this paper we use
a re
al numbe
r en
codi
ng. Com
pare
d
with ot
her
encodin
g
, rea
l
numbe
r en
coding i
s
with
a high preci
s
i
on and
sea
r
ch rang
e.
Fitness fun
c
tion:
In traditional
Geneti
c
Algo
rithm fitness
func
tion a
nd
the obje
c
tive function i
s
a linea
r
relation
shi
p
,
and
even in
some
si
mple
model
s the
o
b
jective fun
c
t
i
on
can
be
u
s
ed
directly a
s
a
fitness fun
c
tion. However,
this
app
roa
c
h ha
s
seve
ra
l disadvantag
es:
(1
) In th
e
early
stag
e t
he
maximum fitness value an
d the minimu
m fitness va
l
ue is likely to vary greatl
y
, it is easy to
eliminate ma
ny of the indi
vidual gen
e fragm
ent
s
co
ntaining ex
ce
llent inform
ation, and m
a
ke
s
the de
stru
ctio
n of p
r
e-pop
u
l
ation dive
rsit
y. (2)
In the
l
a
te sta
ge in
the alg
o
rithm
the differen
c
e
of
fitness valu
e
betwe
en indi
viduals i
s
very small,
maki
ng the ability
to sea
r
ch the global
opti
m
al
solutio
n
[6] reduced.
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TELKOM
NIKA
ISSN:
2302-4
046
The Optim
i
za
tion of Finishi
ng Trai
n Based
on Im
proved Gen
e
tic Algorithm
(Ho
n
g
xia Li
u)
3557
To solve the
s
e probl
em
s, we intro
d
u
c
e
a seq
uen
ce
-b
ase
d
fitness functio
n
:
1
'
)
1
(
)
(
i
i
x
eval
,
;
...
2
,
1
m
i
(9)
{
'
i
x
} is o
b
tained
by sorting th
e the obje
c
tive function val
ue of {
i
x
}. {
i
x
} are individual
s
of the populat
ion. m is the popul
ation si
ze.
The adva
n
ta
ge of su
ch i
m
prove
d
is to
ensure po
pulation dive
rsity and d
e
c
re
ase
sele
ction
pre
s
sure
ea
rly i
n
the
algo
rithm; in th
e
la
tter pa
rt of t
he al
gorithm
relative i
n
crease
sele
ction p
r
e
s
sure a
nd a
c
cele
rate the converg
e
n
c
e.
Selection o
p
e
r
ator, cro
s
sov
e
r ope
rato
r a
nd mutation o
perato
r
:
Selection
op
erato
r
: In thi
s
p
ape
r
we
use
a
ro
ulette an
d elite
sele
ction
[7] model.
Roul
ette sel
e
ction i
s
an
a
ppro
a
ch Pro
posed by
Professor J.
H. Holla
nd to
sele
ct individ
ual
according to f
i
tness ra
ndo
mly. Individual is co
pi
ed d
epen
ds o
n
the individual fi
tness. The b
a
si
c
idea of elite
selectio
n is th
a
t
if
the fitness of the be
st in
dividual
in th
e
next gene
rati
on is l
e
ss tha
n
the current
p
opulatio
n fitn
ess of th
e b
e
s
t individ
ual
,
copy th
e
cu
rrent be
st in
dividual to
the
n
e
xt
gene
ration di
rectly and re
pl
ace the
worst
individual in the next gene
ration.
This
strategy
not only ensure
s
the po
p
u
lati
on diversity of the next generatio
n, but also
ensure
s
that the cu
rrent ge
nerat
io
n of the best individ
ual retain
ed to the next generatio
n.
c
r
oss
o
ver operator: In this paper, the arithmet
ic
crossover op
erator i
s
u
s
e
d
, in
the fo
rm
belo
w
:
t
A
X
,
t
B
X
are two parent individual
s in
t-gen
eration, of which:
]
...
...
,
[
)
(
)
(
)
2
(
)
1
(
t
n
A
t
i
A
t
A
t
A
t
A
X
X
X
X
X
,
]
...
...
,
[
)
(
)
(
)
2
(
)
1
(
t
n
B
t
i
B
t
B
t
B
t
B
X
X
X
X
X
；
)
,
(
,
)
(
)
(
)
(
)
(
i
i
t
i
B
t
i
A
b
a
X
X
,
)
,
(
,
)
1
(
)
1
(
)
1
(
)
1
(
i
i
t
i
B
t
i
A
b
a
X
X
The two ne
w
individual
s re
sulting fr
o
m
the crossove
r
operator a
r
e:
t
B
t
A
t
A
X
X
X
)
1
(
1
,
t
A
t
B
t
B
X
X
X
)
1
(
1
(10)
is
a rand
om
numbe
r,
1
0
; The solution
pro
duced from t
h
is m
e
thod
is between
the rang
e of the two pa
rent
individuals, e
n
su
ring n
o
feasibl
e
sol
u
tion.
mutation o
p
e
r
ator: In
this
pape
r
we
use no
n-u
n
iform mutation
o
perato
r
, the
operating
pro
c
ed
ures a
r
e:
Duri
ng th
e
n
k
x
x
x
x
X
...
...
2
1
to
n
k
x
x
x
x
X
...
...
'
2
1
'
non-uniform mutation
o
peratio
n, if
a ge
ne
mutat
i
on p
o
int val
ue
ran
ge i
s
[
k
U
min
,
k
U
max
], the ne
w g
ene val
ue i
s
determi
ned
b
y
the
following:
)
,
(
'
z
t
x
x
k
k
,
1
)
1
,
0
(
random
；
(11)
)
,
(
'
z
t
x
x
k
k
,
0
)
1
,
0
(
random
；
(12)
)]
/
1
(
[
)
,
(
T
t
random
z
z
t
(13)
In the Formul
a
k
k
U
U
z
min
max
,
random
is a rand
om numb
e
r from (0, 1), t is cu
rrent
gene
ration, T
is the total generation,
is the para
m
ete
r
for the syste
m
.
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02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3555 – 35
59
3558
4. Simulation
In this pa
pe
r
the data u
s
e
d
is
colle
cted
fr
om the
sce
ne. Experime
n
tal steel
s a
r
e high
-
quality ca
rbo
n
stru
ctu
r
al st
eel 20. The
material
widt
h:
0
B
=105
0 mm
; the material
thickne
ss:
0
H
=30 mm; en
d prod
uctio
n
thickn
es
s: 3.5 mm; aiming convexity:
n
CR
=0.012 mm;
the frame
numbe
r: n=7. The rem
a
inin
g para
m
eters are in Tabl
e 1.
Table 1. Re
m
a
ining Pa
ram
e
ters
frame
paramete
r
F1
F2
F3
F4
F5
F6
F7
Work
roll
diameter[mm]
800 800
800 760 760
760 760
Support
r
o
ll
diameter[mm]
1570
1570
1570
1570
1570
1570
1570
Motor
rat
ed
po
wer[k
w
]
7600
7600
7600
7600
7350
7350
5000
Motor
rat
ed
spee
d[m/s]
1.74 2.82
4.33 5.97 7.36
8.56 9.55
In the experi
m
ent, the pa
rameters of th
e algo
rithm a
r
e: popul
ation
size M=50, M
a
ximum
gene
ration:
T
=
20
0, Cro
s
so
ver p
r
ob
ability
c
P
=0.8, Mutati
on probability
m
P
=0.01. T
he
result
s of
the experi
m
e
n
t are give
n
in Table
2 a
nd Tabl
e 3.
The thickn
ess c
ontra
st c
u
rv
es fo
r
i
h
ar
e
sho
w
n in Fig
u
re 1. The re
lative convexi
t
y contra
st cu
rves a
r
e sho
w
n in Figu
re
2.
Table 2. Re
sults of Empiri
cal Di
strib
u
tio
n
frame
paramete
r
Thickness in the
entrance
[h/mm]
Thickness in the
exit
[h/mm]
Rolling force
[P/KN]
Relative convexity
[CR/h(
3
10
)]
F1
30.00
24.11
18100
2.35
F2
24.11
16.55
13500
2.47
F3
16.55
12.68
14820
3.78
F4
12.68
9.55
15180
4.29
F5
9.55
6.84
9240
4.04
F6
6.84
5.52
8460
4.75
F7
5.52
3.50
6530
3.70
Figure 1. Thickne
s
s
Co
ntra
st Cu
rv
e for
i
h
Figure 2. Rel
a
tive Convexi
t
y Contra
st Curve
From the
si
mulation results we
ca
n see the
re
sul
t
of improve
d
Geneti
c
Algorithm i
s
sup
e
rio
r
to th
e re
sults o
b
ta
ined from
em
pirical di
st
rib
u
tion: The thi
c
kne
ss of exi
t
and the rolli
ng
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
The Optim
i
za
tion of Finishi
ng Trai
n Based
on Im
proved Gen
e
tic Algorithm
(Ho
n
g
xia Li
u)
3559
force
of e
a
ch
frame
are
more
re
ason
able. Th
e
first few frames c
a
n have a
s
u
ffic
i
ently large
amount of re
ductio
n
, and
the later fram
es can
k
eep
the sha
pe op
timal to meet the prod
ucti
on
requi
rem
ents.
Table 3. Re
sults of Improv
ed Gen
e
tic Algorithm
frame
paramete
r
Thickness in the
entrance
[h/mm]
Thickness in the
exit
[h/mm]
Rolling force
[P/KN]
Relative convexity
[CR/h(
3
10
)]
F1
30.00
16.62
18239
2.26
F2
16.62
8.56
21380
3.93
F3
8.56
6.92
10320
2.62
F4
6.92
5.38
8260
2.75
F5
5.38
4.50
6590
2.77
F6
4.50
3.96
5780
2.81
F7
3.96
3.51
5260
3.06
5. Conclusio
n
In this pap
er,
the tradition
al
Geneti
c
Algo
rith
m premat
ure
conve
r
ge
nce, a
nd the
result is
not a
global
search fo
r
optimal solution
s as well
a
s
th
e
late evolutionary disadv
antage
s su
ch
a
s
low efficie
n
cy has be
en
improved,
and we succe
ssfully ap
plied it to the finishi
ng
train
optimizatio
n
allocation m
odel. Th
e im
proved
Gen
e
t
ic Algorith
m
in glob
al converg
e
n
c
e
and
conve
r
ge
nce spe
ed ha
s b
een greatly improve
d
.
And by comp
ari
ng the experi
ence distri
but
ion
method
com
m
only used
with the grap
h, we sho
w
that improve
d
Genetic Alg
o
rithm ha
s a
great
advantag
e when de
aling
with com
p
lex issue
s
.
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