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201
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e
s
o
f
o
p
tim
izatio
n
.
A
f
ea
s
ib
le
ti
m
et
ab
le
is
a
s
ch
ed
u
le
w
h
ic
h
ess
e
n
tiall
y
m
u
s
t
s
a
tis
f
y
s
ev
er
al
co
n
s
tr
ain
t
s
.
C
o
n
s
tr
ain
t
s
ar
e
alm
o
s
t
u
n
iv
er
s
all
y
e
m
p
l
o
y
ed
b
y
p
eo
p
le
d
ea
lin
g
w
ith
ti
m
etab
le
s
ch
ed
u
li
n
g
p
r
o
b
lem
[
4
]
.
A
lt
h
o
u
g
h
m
an
y
r
esear
ch
er
s
in
v
o
l
v
ed
in
s
o
l
v
in
g
t
h
e
ti
m
etab
li
n
g
p
r
o
b
le
m
,
it
i
s
i
m
p
o
s
s
ib
le
to
p
er
f
ec
tl
y
s
o
l
v
e
it
b
ec
au
s
e
o
f
th
e
v
ar
iet
y
o
f
co
n
s
tr
ai
n
ts
i
n
ea
ch
p
r
o
b
lem
[
5
]
.
T
h
er
e
a
r
e
t
w
o
ca
teg
o
r
ies
o
f
co
n
s
tr
ain
ts
w
h
ich
ar
e
s
o
f
t
an
d
h
ar
d
co
n
s
tr
ain
t
s
.
H
ar
d
co
n
s
tr
ain
ts
ar
e
co
n
s
tr
ai
n
t
s
th
at
ca
n
n
o
t
b
e
v
io
lated
an
d
an
y
v
io
latio
n
i
s
u
n
ac
ce
p
tab
le.
Fo
r
ex
a
m
p
le,
a
lectu
r
er
ca
n
n
o
t
b
e
in
t
w
o
p
lace
s
at
t
h
e
s
a
m
e
ti
m
e,
t
w
o
s
u
b
j
ec
ts
ca
n
n
o
t
h
a
v
e
co
m
m
o
n
s
tu
d
e
n
t
s
s
c
h
ed
u
led
in
th
e
s
a
m
e
t
i
m
e
s
lo
t
an
d
co
u
r
s
es
ca
n
n
o
t
b
e
a
s
s
i
g
n
ed
to
t
h
e
s
a
m
e
r
o
o
m
at
t
h
e
s
a
m
e
ti
m
e.
I
f
th
e
h
ar
d
co
n
s
tr
ai
n
t
i
s
v
io
lated
,
t
h
e
n
s
u
c
h
a
s
ch
ed
u
le
w
i
ll
b
e
co
n
s
id
er
ed
as
a
f
ail
u
r
e.
W
h
ile
s
o
f
t
co
n
s
tr
ain
t
s
ar
e
co
n
s
tr
ain
t
s
t
h
at
ca
n
b
e
b
r
o
k
en
,
b
u
t
m
u
s
t
b
e
m
i
n
i
m
ized
.
A
lt
h
o
u
g
h
it
f
ail
s
to
s
ati
s
f
y
th
ese
co
n
s
tr
ai
n
ts
,
it
i
s
s
aid
to
b
e
leg
al
if
i
t
s
ati
s
f
ies
all
h
ar
d
co
n
s
tr
ain
ts
[
6
]
.
Fo
r
ex
a
m
p
le,
t
h
e
tr
av
el
d
is
tan
ce
o
f
lectu
r
er
s
an
d
s
t
u
d
en
t
s
b
et
w
ee
n
class
r
o
o
m
s
s
h
o
u
ld
b
e
m
in
i
m
ized
.
I
t
is
v
er
y
d
if
f
ic
u
lt
to
g
et
a
s
o
lu
tio
n
to
s
o
lv
e
ti
m
etab
li
n
g
p
r
o
b
lem
w
it
h
all
t
h
e
co
n
s
tr
a
i
n
t
s
.
T
h
er
ef
o
r
e,
m
an
y
r
esear
c
h
er
s
h
av
e
co
m
e
u
p
w
i
th
s
e
v
er
al
te
ch
n
iq
u
es
to
s
o
l
v
e
h
ar
d
co
n
s
tr
ain
ts
w
h
il
e
m
i
n
i
m
ize
t
h
e
s
o
f
t
co
n
s
tr
ai
n
ts
ev
en
i
t
is
d
i
f
f
ic
u
lt
to
f
i
n
d
th
e
b
est
f
ea
s
ib
le
t
i
m
e
tab
le.
I
t
h
as
b
ee
n
r
esear
ch
f
e
w
d
ec
ad
es
ag
o
in
v
ar
io
u
s
d
o
m
a
in
s
r
elate
d
to
ti
m
etab
le
in
cl
u
d
in
g
as
s
ig
n
m
e
n
t
an
d
s
ch
ed
u
li
n
g
[
7
]
-
[
1
6
]
.
Var
ies
o
p
tim
izatio
n
alg
o
r
it
h
m
s
h
ad
b
ee
n
ap
p
lied
an
d
e
n
h
an
ce
d
t
o
s
u
p
p
o
r
t
th
e
ti
m
etab
li
n
g
p
r
o
b
lem
s
a
s
s
u
c
h
t
h
e
co
m
b
i
n
atio
n
o
f
s
tan
d
ar
d
g
e
n
et
ic
alg
o
r
it
h
m
a
n
d
h
ill c
li
m
b
i
n
g
alg
o
r
ith
m
th
at
u
tili
ze
a
m
e
m
e
en
co
d
ed
s
co
r
e
as
a
p
er
f
o
r
m
a
n
ce
i
n
d
icato
r
to
cr
ea
t
e
n
e
w
ca
n
d
id
ate
s
o
l
u
tio
n
s
d
u
r
i
n
g
t
h
e
p
r
o
ce
s
s
o
f
c
h
o
o
s
in
g
o
p
er
ato
r
s
[
1
7
]
,
I
n
ad
d
itio
n
,
lo
ca
l
o
p
tim
iza
tio
n
w
it
h
h
il
l
cli
m
b
i
n
g
alg
o
r
ith
m
[
2
]
,
an
t
co
lo
n
y
o
p
t
i
m
izatio
n
s
tr
ateg
y
[
1
8
]
,
Har
m
o
n
y
s
ea
r
ch
a
n
d
a
m
o
d
i
f
ied
h
ar
m
o
n
y
s
ea
r
ch
al
g
o
r
ith
m
[
1
9
]
,
T
ab
u
Sear
ch
[
2
0
]
,
H
y
p
er
-
h
eu
r
i
s
tics
s
ea
r
ch
th
e
s
p
ac
e
o
f
h
eu
r
i
s
tics
an
d
u
s
e
th
e
li
m
ited
p
r
o
b
lem
s
p
ec
i
f
ic
i
n
f
o
r
m
atio
n
t
o
co
n
tr
o
l th
e
s
ea
r
ch
p
r
o
ce
s
s
ca
n
b
e
s
ee
n
a
s
a
n
ad
ap
tiv
e
v
er
s
io
n
o
f
iter
ated
lo
ca
l
s
ea
r
ch
s
tr
ateg
y
co
m
b
i
n
i
n
g
s
o
m
e
m
o
v
e
o
p
er
ato
r
s
.
I
n
s
h
o
r
t,
t
h
is
ap
p
r
o
ac
h
co
n
s
i
s
ts
o
f
n
u
m
b
er
o
f
m
o
v
e
o
p
er
ato
r
s
o
f
d
if
f
er
en
t
s
tr
en
g
th
s
a
n
d
ch
ar
ac
ter
is
tic
s
co
m
b
i
n
ed
i
n
to
an
ad
ap
ti
v
e
h
y
p
er
-
h
eu
r
i
s
tic
ap
p
r
o
ac
h
to
p
r
o
d
u
ce
b
etter
r
es
u
lts
[
1
5
]
.
Ho
w
e
v
er
,
clash
es
-
f
r
ee
s
lo
t
is
s
till
n
o
t
ad
d
r
e
s
s
w
ell
w
h
en
co
n
s
id
er
in
g
th
e
n
u
m
b
er
s
o
f
le
ctu
r
er
s
an
d
th
e
n
u
m
b
er
o
f
class
es,
alt
h
o
u
g
h
,
o
n
e
o
f
t
h
e
s
o
lu
tio
n
f
o
r
clas
h
es
-
f
r
ee
s
lo
ts
h
a
v
e
b
ee
n
ad
d
r
ess
ed
f
o
c
u
s
i
n
g
o
n
an
ex
a
m
i
n
atio
n
ti
m
etab
le
b
ased
o
n
s
m
al
l d
ata
s
et
an
d
s
ti
ll n
ee
d
i
m
p
r
o
v
e
m
e
n
t i
n
its
s
o
lu
t
io
n
[
2
]
,
[
2
1
]
.
T
h
is
p
ap
er
a
d
d
r
ess
es
th
e
L
ec
t
u
r
er
s
’
ti
m
etab
li
n
g
s
o
lu
tio
n
i
n
Facu
lt
y
o
f
C
o
m
p
u
ter
a
n
d
Ma
th
e
m
a
tica
l
Scien
ce
s
,
Un
i
v
er
s
iti
T
ek
n
o
lo
g
i
M
A
R
A
,
Ma
la
y
s
ia
as
a
ca
s
e
s
tu
d
y
.
T
h
e
in
ter
est
is
o
n
th
e
L
T
P
s
tu
d
en
ts
a
n
d
lectu
r
er
s
to
f
i
x
ed
ti
m
eslo
t
s
w
it
h
i
n
n
u
m
b
er
s
o
f
co
n
s
tr
ai
n
ts
.
Ass
i
g
n
i
n
g
t
i
m
e
s
an
d
p
lac
es
to
lectu
r
er
s
ar
e
co
n
s
id
er
ed
h
ar
d
p
r
o
b
le
m
s
f
ac
ed
in
e
v
er
y
u
n
i
v
er
s
it
y
.
T
h
er
e
ar
e
t
w
o
t
y
p
es
o
f
co
n
s
tr
ain
t
s
,
w
h
ic
h
ar
e
t
h
e
h
ar
d
co
n
s
tr
ain
t
a
n
d
s
o
f
t
co
n
s
tr
ain
t.
Har
d
co
n
s
tr
ain
t
ca
n
n
o
t
b
e
v
io
l
ated
s
u
c
h
as
all
lect
u
r
er
s
m
u
s
t
b
e
s
ch
ed
u
led
an
d
ass
i
g
n
ed
to
a
d
is
ti
n
ct
r
o
o
m
at
s
p
ec
if
ied
p
er
io
d
s
.
A
p
r
ac
tical
ti
m
etab
le
m
u
s
t
s
at
is
f
y
h
ar
d
co
n
s
tr
ain
ts
as
i
t
is
s
tr
ictl
y
i
m
p
o
s
ed
.
W
h
ile
s
o
f
t
co
n
s
tr
ain
ts
ar
e
d
esira
b
le,
b
u
t
th
e
y
ar
e
n
o
t
ess
en
tial.
T
h
ey
ca
n
b
e
v
io
lated
,
b
u
t
th
e
y
m
u
s
t
b
e
m
i
n
i
m
ized
.
T
h
e
r
em
ain
d
er
o
f
th
i
s
ar
ticle
is
o
r
g
an
ized
as
f
o
llo
w
s
.
Sect
io
n
2
ex
p
lain
s
t
h
e
L
T
P
an
d
its
f
it
n
es
s
.
T
h
e
G
A
is
d
is
c
u
s
s
ed
i
n
Sectio
n
3
.
S
ec
tio
n
4
p
r
esen
t
s
co
m
p
u
tatio
n
al
r
es
u
lt
s
f
o
r
th
e
to
u
r
n
a
m
en
t
(
T
)
an
d
to
u
r
n
a
m
e
n
t
eliti
s
m
(
T
E
)
s
elec
tio
n
.
Sectio
n
5
d
is
cu
s
s
io
n
o
f
t
h
e
f
in
d
in
g
s
a
n
d
Sectio
n
6
co
n
clu
d
es t
h
is
p
ap
er
.
2.
L
E
C
T
UR
E
R
T
I
M
E
T
AB
L
I
NG
P
RO
B
L
E
M
L
ec
t
u
r
er
T
im
etab
li
n
g
P
r
o
b
lem
(
L
T
P
)
em
p
h
a
s
izes
o
n
th
e
a
s
s
i
g
n
m
e
n
t
o
f
ea
c
h
o
f
lect
u
r
er
s
to
ea
ch
o
f
th
e
clas
s
es.
L
ec
t
u
r
es
o
f
d
i
f
f
e
r
en
t
ca
p
ac
it
y
lo
ad
f
o
r
lect
u
r
i
n
g
m
u
s
t
ac
co
m
m
o
d
ate
t
h
e
cl
ass
r
eq
u
ir
e
m
en
t
f
o
r
ev
er
y
w
ee
k
.
T
h
e
s
lo
t
f
o
r
ea
ch
lect
u
r
er
m
u
s
t
b
e
d
eter
m
in
ed
an
d
s
ati
s
f
ied
th
e
allo
ca
tio
n
o
f
ti
m
e
-
s
lo
t.
T
h
e
f
o
llo
w
in
g
m
at
h
e
m
atica
l
f
o
r
m
u
latio
n
co
n
s
id
er
s
t
h
is
r
eq
u
ir
e
m
en
t
as
an
o
b
j
ec
tiv
e
f
u
n
ctio
n
.
T
h
e
L
T
P
ca
n
b
e
lin
ea
r
l
y
d
ef
i
n
ed
as
f
o
llo
w
s
.
T
h
e
L
T
P
co
n
s
is
ts
o
f
a
s
et
o
f
lec
tu
r
es,
l,
a
s
e
t
o
f
s
u
b
j
ec
ts
,
a
s
et
o
f
t
ti
m
e
s
lo
t,
a
s
et
o
f
r
clas
s
r
o
o
m
s
,
a
n
d
a
s
et
o
f
g
s
t
u
d
en
t
g
r
o
u
p
s
.
T
h
e
m
at
h
e
m
a
tical
m
o
d
el
f
o
r
m
u
lat
io
n
i
s
p
r
e
s
en
ted
i
n
f
o
llo
w
i
n
g
s
ec
tio
n
.
I
t
w
as a
d
ap
ted
f
r
o
m
[
2
2
]
.
T
h
e
n
o
tatio
n
s
an
d
p
ar
a
m
e
ter
s
u
s
ed
i
n
th
e
m
o
d
el
ar
e
as f
o
llo
w
s
:
L
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
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J
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lec
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g
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p
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N:
2502
-
4752
Gen
etic
A
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w
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q
u
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.
(
1
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T
h
e
m
o
d
el
is
as
f
o
llo
w
s
:
Min
i
m
ize
Z
=
∑
(
1
)
Su
b
j
ec
t to
:
(
2
)
(
3
)
<
(
4
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(
5
)
A
co
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tr
ain
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in
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u
at
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2
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en
s
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n
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t
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m
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th
a
n
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e
co
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r
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at
th
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s
a
m
e
ti
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e.
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atio
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3
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en
s
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co
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u
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m
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n
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i
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u
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(
5
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d
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6
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en
s
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r
e
t
h
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ca
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s
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s
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ld
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en
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ize
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lect
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th
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ed
it h
o
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r
,
r
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ec
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y
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ab
l
e
1
s
h
o
w
s
th
e
v
io
latio
n
a
n
d
its
p
en
alt
ie
s
.
T
ab
le
1
.
Vio
latio
n
an
d
its
P
en
alt
y
Val
u
e
No
V
io
latio
n
P
e
n
a
l
ty
V
a
lu
e
1.
L
e
c
tu
re
r
c
a
n
n
o
t
tea
c
h
m
o
re
th
a
n
o
n
e
c
o
u
rse
a
t
th
e
sa
m
e
ti
m
e
50
2.
No
ro
o
m
c
a
n
o
c
c
u
p
y
m
o
re
th
a
n
o
n
e
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tu
re
a
t
th
e
sa
m
e
ti
m
e
50
3.
No
stu
d
e
n
t
c
a
n
a
tt
e
n
d
m
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re
th
a
n
o
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tu
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a
t
t
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sa
m
e
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m
e
50
4.
T
h
e
c
a
p
a
c
it
y
o
f
c
l
a
ss
ro
o
m
s sh
o
u
l
d
m
a
tch
w
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h
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d
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siz
e
.
20
5.
L
e
c
tu
re
r
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a
n
n
o
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tea
c
h
les
s th
a
n
g
i
v
e
n
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re
d
it
h
o
u
r
2
0
3.
CO
NST
R
UCT
I
O
N
O
F
G
E
N
E
T
I
C
AL
G
O
R
I
T
H
M
3
.
1
.
So
lutio
n
M
a
pp
ing
T
h
e
d
ev
elo
p
m
en
t
G
A
r
eq
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ir
e
s
a
r
ep
r
ese
n
tatio
n
o
f
th
e
p
r
o
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le
m
.
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e
r
ep
r
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t
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s
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a
d
i
s
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r
ete
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al
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e
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d
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ess
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h
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ti
m
e
s
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r
o
o
m
an
d
s
u
b
j
ec
t.
Fig
u
r
e
1
is
th
e
c
h
r
o
m
o
s
o
m
e
r
ep
r
esen
t
atio
n
f
o
r
G
A
.
T
h
e
r
an
g
e
is
b
ased
o
n
t
h
e
d
ataset
s
o
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tain
ed
f
o
r
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SKM.
T
h
e
r
a
n
g
e
o
f
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o
f
1
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1
8
f
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s
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1
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4
3
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1
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t
1
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......
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n
c
n
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ss
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la
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n
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u
r
e
1
.
So
lu
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n
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p
p
in
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f
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L
T
P
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t
n
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r
ep
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m
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ep
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s
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t
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u
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ts
[1
-
1
8
]
[
1
-
4
3
]
[
1
-
3
4
]
[1
-
1
8
]
[
1
-
4
3
]
[
1
-
3
4
]
[1
-
1
8
]
[
1
-
4
3
]
[
1
-
3
4
]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4752
I
n
d
o
n
esia
n
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
12
,
No
.
1
,
Octo
b
er
2
0
1
8
:
30
3
–
309
306
E
ac
h
o
f
t
h
e
s
u
b
j
ec
ts
ca
n
h
av
e
m
o
r
e
th
a
n
o
n
e
cla
s
s
.
Hen
ce
,
t
h
e
c
h
r
o
m
o
s
o
m
e
le
n
g
th
w
o
u
ld
d
ep
en
d
o
n
th
e
n
u
m
b
er
o
f
th
e
clas
s
es.
So
m
eti
m
es
clas
s
ca
n
ac
co
m
m
o
d
ate
f
o
r
o
n
e
g
r
o
u
p
o
n
l
y
a
n
d
ca
n
b
e
m
o
r
e
d
ep
en
d
i
n
g
o
n
th
e
n
u
m
b
er
s
tu
d
e
n
ts
.
T
h
e
l
en
g
t
h
o
f
c
h
r
o
m
o
s
o
m
es i
n
th
e
p
o
p
u
latio
n
w
ill b
e
as f
o
llo
w
s
:
C
h
r
o
m
o
s
o
m
e
le
n
g
th
=
n
u
m
b
er
o
f
class
e
s
*
3
(
g
en
e
s
)
3
.
2
.
G
A
Ste
ps
f
o
r
t
he
L
T
P
S
o
lutio
n
B
asicall
y
,
t
h
e
g
e
n
etic
al
g
o
r
ith
m
p
r
o
ce
s
s
f
o
r
s
o
lv
in
g
t
h
e
L
T
P
is
as f
o
llo
w
s
:
Ste
p
1
:
R
ep
r
ese
n
t
t
h
e
p
r
o
b
lem
a
s
s
tr
in
g
s
o
f
c
h
r
o
m
o
s
o
m
es
o
f
a
f
i
x
ed
len
g
t
h
,
w
i
th
a
p
o
p
u
latio
n
s
ize
o
f
N,
a
s
d
ep
icted
in
Fig
u
r
e
1
.
P
o
p
u
latio
n
s
ize
is
t
h
e
n
u
m
b
er
o
f
in
d
i
v
id
u
al
s
th
a
t
r
ep
r
esen
t
t
h
e
s
o
l
u
tio
n
.
I
f
t
h
er
e
ar
e
to
o
m
an
y
c
h
r
o
m
o
s
o
m
es,
GA
te
n
d
s
to
s
lo
w
d
o
w
n
.
Ho
wev
er
,
G
A
h
as
v
er
y
f
e
w
p
o
s
s
ib
i
liti
es
to
p
er
f
o
r
m
cr
o
s
s
o
v
er
a
n
d
ca
n
e
x
p
lo
r
e
o
n
l
y
a
s
m
al
l p
ar
t o
f
th
e
s
ea
r
c
h
s
p
ac
e
if
t
h
er
e
ar
e
to
o
f
e
w
ch
r
o
m
o
s
o
m
es.
Ste
p
2
:
Def
i
n
e
a
f
i
tn
e
s
s
f
u
n
c
t
io
n
to
m
ea
s
u
r
e
t
h
e
f
itn
e
s
s
o
f
ea
ch
c
h
r
o
m
o
s
o
m
e
f
o
r
s
e
lecti
n
g
c
h
r
o
m
o
s
o
m
e
s
as
p
ar
en
ts
to
m
ate
d
u
r
i
n
g
t
h
e
r
ep
r
o
d
u
ctio
n
p
r
o
ce
s
s
to
p
r
o
d
u
ce
n
e
w
o
f
f
s
p
r
in
g
s
.
T
h
e
f
i
tn
e
s
s
f
u
n
ctio
n
s
tated
in
E
q
.
(
1
)
an
d
all
co
n
s
tr
ain
ts
ar
e
co
n
s
id
er
ed
.
Ste
p
3
:
Dete
r
m
i
n
e
G
A
p
ar
am
eter
s
(
cr
o
s
s
o
v
er
p
r
o
b
ab
i
lit
y
,
m
u
ta
tio
n
p
r
o
b
ab
ilit
y
an
d
m
ax
i
m
u
m
n
u
m
b
er
o
f
g
en
er
atio
n
s
)
an
d
s
et
t
h
e
i
n
itial
b
est f
it
n
es
s
eq
u
al
to
1
.
Ste
p 4
:
R
an
d
o
m
l
y
g
e
n
er
ate
an
in
itial p
o
p
u
latio
n
o
f
s
ize
N:
X
1
, X
2
,
…,
X
N
T
h
e
im
p
le
m
e
n
tatio
n
o
f
th
e
c
u
s
to
m
ized
r
an
d
o
m
f
u
n
ctio
n
i
s
as
f
o
llo
w
s
:
1.
T
h
e
p
r
o
g
r
am
w
i
ll
g
en
er
ate
c
l
ass
es
f
o
r
ev
er
y
g
r
o
u
p
an
d
t
h
e
s
u
b
j
ec
ts
ta
k
en
to
g
et
n
u
m
b
er
o
f
clas
s
es
th
at
n
ee
d
to
b
e
s
ch
ed
u
led
.
2.
T
h
e
p
r
o
g
r
a
m
w
ill r
an
d
o
m
l
y
g
e
n
er
ate
ti
m
eslo
t,
r
o
o
m
,
an
d
lect
u
r
er
f
o
r
ea
ch
o
f
t
h
e
class
e
s
3.
T
h
e
ch
r
o
m
o
s
o
m
e
le
n
g
th
d
ep
en
d
s
o
n
t
h
e
n
u
m
b
er
o
f
t
h
e
class
es.
T
h
e
le
n
g
th
o
f
ch
r
o
m
o
s
o
m
e
s
i
n
t
h
e
p
o
p
u
latio
n
w
ill b
e
as f
o
llo
w
s
:
C
h
r
o
m
o
s
o
m
e
le
n
g
th
=
n
u
m
b
er
o
f
class
e
s
*
3
(
g
en
e
s
)
Ste
p 5
: Calcu
la
te
th
e
f
it
n
es
s
f
o
r
ea
ch
ch
r
o
m
o
s
o
m
e
i
n
t
h
e
p
o
p
u
latio
n
u
s
i
n
g
th
e
f
o
r
m
u
la
i
n
(
2
)
.
Ste
p 6
:
Star
t th
e
f
ir
s
t g
e
n
er
ati
o
n
.
Ste
p 7
:
C
o
m
p
u
te
f
it
n
es
s
an
d
d
o
s
elec
tio
n
.
Select
p
ar
en
t f
r
o
m
th
e
c
u
r
r
en
t
p
o
p
u
latio
n
f
o
r
cr
o
s
s
o
v
er
u
s
in
g
T
o
u
r
n
a
m
e
n
t se
lectio
n
m
et
h
o
d
T
h
e
T
o
u
r
n
a
m
e
n
t selec
tio
n
alg
o
r
ith
m
i
s
as f
o
llo
w
s
:
1
.
R
an
d
o
m
l
y
c
h
o
o
s
e
in
d
i
v
id
u
als f
r
o
m
t
h
e
w
h
o
le
p
o
p
u
latio
n
.
2
.
C
o
m
p
ar
e
f
i
tn
e
s
s
a
n
d
ch
o
o
s
e
th
e
f
i
ttes
t i
n
d
iv
id
u
al
to
b
e
th
e
p
ar
en
t
Ste
p 8
:
Do
cr
o
s
s
o
v
er
an
d
m
u
t
atio
n
C
r
ea
te
o
f
f
s
p
r
in
g
ch
r
o
m
o
s
o
m
es
b
y
ap
p
l
y
in
g
cr
o
s
s
o
v
er
a
n
d
m
u
tatio
n
o
p
er
ato
r
s
ac
co
r
d
in
g
to
th
e
ir
p
r
o
b
a
b
ilit
ies
an
d
p
u
t
t
h
e
n
e
w
l
y
cr
ea
ted
o
f
f
s
p
r
in
g
i
n
t
h
e
n
e
w
p
o
p
u
latio
n
.
A
s
f
o
r
t
h
e
cr
o
s
s
o
v
er
,
u
n
i
f
o
r
m
cr
o
s
s
o
v
er
s
ch
e
m
e
i
s
u
s
ed
w
h
e
r
e
in
d
iv
id
u
a
l
b
its
i
n
th
e
c
h
r
o
m
o
s
o
m
e
s
ar
e
co
m
p
ar
ed
b
et
w
e
en
t
w
o
p
ar
en
ts
.
On
e
o
f
t
h
e
p
ar
en
t
s
is
t
h
e
p
ar
en
t
ch
o
s
en
d
u
r
i
n
g
th
e
s
elec
ti
o
n
s
ta
g
e.
T
h
e
b
its
ar
e
s
w
ap
p
ed
w
it
h
a
f
ix
ed
p
r
o
b
a
b
il
it
y
,
0
.
5
.
Mu
tatio
n
is
u
s
ed
to
m
ain
ta
in
g
e
n
etic
d
iv
er
s
i
t
y
an
d
a
v
o
id
lo
ca
l
m
in
i
m
a.
T
h
e
p
r
o
g
r
am
w
i
ll
cr
ea
te
r
an
d
o
m
i
n
d
iv
id
u
al
to
s
w
ap
g
e
n
es
w
i
th
t
h
e
i
n
d
iv
id
u
al
s
in
t
h
e
cu
r
r
en
t p
o
p
u
latio
n
.
Ste
p 9
: E
v
alu
ate
c
u
r
r
en
t p
o
p
u
l
atio
n
(
b
ased
o
n
s
elec
ted
p
o
p
u
latio
n
f
r
o
m
s
tep
7
)
.
Ste
p 1
0
: U
p
d
ate
g
en
er
atio
n
.
Ste
p 1
1
:
I
f
th
e
n
u
m
b
er
o
f
g
en
er
atio
n
h
as r
ea
c
h
ed
its
ter
m
i
n
a
tio
n
cr
iter
io
n
s
,
g
o
to
Step
1
2
.
Ste
p 1
2
: T
h
e
alg
o
r
ith
m
is
f
i
n
i
s
h
ed
.
T
h
e
b
est s
o
lu
tio
n
f
o
u
n
d
w
h
e
n
th
e
f
it
n
es
s
is
r
ec
o
r
d
ed
as th
e
b
est f
i
tn
e
s
s
.
4.
CO
M
P
UT
AT
I
O
NAL
R
E
SU
L
T
S AN
D
DI
SUS
SI
O
N
An
i
n
-
d
ep
th
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n
al
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s
o
f
t
h
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o
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tp
u
ts
p
r
o
d
u
ce
d
b
y
t
h
e
G
A
is
r
ep
o
r
ted
r
eg
ar
d
in
g
it
s
p
er
f
o
r
m
a
n
ce
,
o
n
h
o
w
d
i
f
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er
e
n
t
p
ar
a
m
eter
tu
n
in
g
a
f
f
ec
t
t
h
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ef
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GA
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f
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g
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lu
t
io
n
s
f
o
r
th
e
L
T
P
,
an
d
to
test
th
e
r
o
b
u
s
tn
e
s
s
o
f
ea
c
h
G
A
w
h
ile
s
ati
s
f
y
i
n
g
all
t
h
e
co
n
s
tr
ain
t
s
.
A
co
m
p
ar
i
s
o
n
o
f
p
er
f
o
r
m
a
n
ce
b
et
w
ee
n
s
i
m
p
le
GA
w
ith
T
o
u
r
n
a
m
e
n
t
s
elec
t
io
n
s
c
h
e
m
e
co
m
b
in
ed
w
i
th
E
li
ti
s
m
(
T
E
)
an
d
a
GA
w
i
th
T
o
u
r
n
a
m
en
t
(
T
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s
elec
tio
n
s
ch
e
m
e
is
al
s
o
p
er
f
o
r
m
ed
4
.
1
.
P
a
ra
m
et
er
Set
t
ing
T
h
e
s
elec
tio
n
o
f
p
ar
a
m
et
er
was
h
a
n
d
lin
g
u
s
i
n
g
tr
ial
a
n
d
er
r
o
r
d
u
e
to
GA
i
s
a
p
r
o
b
lem
d
ep
en
d
en
t
b
ased
[
2
4
]
.
T
h
e
an
al
y
s
is
o
f
o
v
er
all
GA
p
er
f
o
r
m
a
n
ce
w
a
s
d
o
n
e
u
s
in
g
t
h
e
p
ar
a
m
eter
r
an
g
es
s
et
as in
T
ab
le
2
.
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.
P
ar
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eter
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g
P
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t
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e
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t
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o
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2
.
Co
m
p
uta
t
io
na
l Ex
peri
m
e
nts A
cc
o
rding
t
o
P
o
pu
la
t
io
n Size
T
h
e
d
if
f
er
en
t
n
u
m
b
er
o
f
p
o
p
u
l
atio
n
s
ize
o
f
2
0
,
5
0
,
1
2
0
an
d
1
8
0
ar
e
ev
alu
ated
u
s
i
n
g
th
e
L
T
P
d
atasets
co
n
s
is
t
o
f
a
r
a
n
g
e
o
f
1
-
1
8
f
o
r
ti
m
e
s
lo
t
s
,
1
-
4
3
f
o
r
t
h
e
n
u
m
b
er
r
o
o
m
s
a
n
d
1
-
3
4
f
o
r
th
e
n
u
m
b
er
s
u
b
j
ec
ts
.
T
h
e
co
n
s
tan
t
v
alu
e
o
f
cr
o
s
s
o
v
er
r
ate
=
0
.
9
,
m
u
tatio
n
r
ate=
0
.
0
0
1
,
m
ax
i
m
u
m
n
u
m
b
er
o
f
g
e
n
er
atio
n
o
f
2
0
,
to
u
r
n
a
m
en
t
s
ize
o
f
5
ar
e
u
s
e
d
.
B
o
th
T
E
an
d
T
ar
e
ev
alu
ated
.
T
h
e
r
esu
lt
w
as
d
e
m
o
n
s
tr
ated
in
T
ab
le
3
.
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
G
A
b
a
s
ed
o
n
p
o
p
u
latio
n
s
ize
w
i
th
r
esp
ec
t
to
th
e
T
o
u
r
n
a
m
e
n
t
(
T
)
an
d
T
o
u
r
n
a
m
en
t
s
elec
tio
n
s
c
h
e
m
e
co
m
b
i
n
ed
w
it
h
E
liti
s
m
(
T
E
)
.
T
h
e
o
p
tim
al
g
e
n
er
atio
n
an
d
o
p
ti
m
al
s
o
lu
tio
n
f
o
r
ea
c
h
p
o
p
u
latio
n
s
ize
w
as
f
i
n
all
y
o
b
tain
ed
af
ter
e
x
ec
u
ti
n
g
m
an
y
e
x
p
er
i
m
e
n
t
s
u
s
i
n
g
d
i
f
f
er
en
t
p
ar
a
m
eter
s
.
T
h
e
p
o
p
u
latio
n
s
ize
o
f
1
8
0
ac
h
iev
ed
f
it
n
es
s
v
alu
e
o
f
1
.
0
at
g
en
er
at
io
n
1
7
w
h
ile
p
o
p
u
latio
n
s
ize
o
f
5
0
ac
h
iev
ed
t
h
e
h
ig
h
es
t
f
i
tn
e
s
s
at
g
en
er
atio
n
1
8
w
h
e
n
e
m
p
l
o
y
ed
T
E
s
elec
tio
n
.
T
h
e
p
o
p
u
latio
n
s
ize
o
f
5
0
ac
h
iev
ed
f
it
n
es
s
v
al
u
e
o
f
1
.
0
at
g
en
er
atio
n
1
7
w
h
en
ap
p
l
y
i
n
g
T
s
elec
tio
n
.
T
ab
le
3
.
P
er
f
o
r
m
a
n
ce
o
f
T
E
a
n
d
T
u
s
in
g
Dif
f
e
r
e
n
t P
o
p
u
latio
n
Size
P
o
p
u
l
a
t
i
o
n
s
i
z
e
TE
T
G
e
n
e
r
a
t
i
o
n
N
o
F
i
t
n
e
ss V
a
l
u
e
G
e
n
e
r
a
t
i
o
n
N
o
F
i
t
n
e
ss V
a
l
u
e
20
20
0
.
0
4
7
7
20
0
.
0
1
2
3
50
18
1
.
0
17
1
.
0
1
0
0
20
0
.
0
4
7
20
0
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0
4
7
6
1
2
0
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0
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2
4
4
20
0
.
0
0
7
1
1
8
0
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1
.
0
20
0
.
0
0
1
0
4
.
3
.
Co
m
p
uta
t
io
na
l
E
x
peri
m
e
nts a
cc
o
rding
t
o
P
ro
ba
bil
it
y
o
f
Cro
s
s
o
v
er
T
h
is
s
ec
tio
n
r
ep
o
r
ts
th
e
r
es
u
l
ts
f
o
r
d
if
f
er
en
t
v
al
u
e
o
f
cr
o
s
s
o
v
er
r
ates
o
f
0
.
7
,
0
.
8
,
0
.
9
an
d
0
.
9
5
ar
e
test
ed
.
Oth
er
p
ar
am
eter
s
ar
e
f
ix
ed
;
p
o
p
u
latio
n
s
ize:
1
0
,
m
u
ta
tio
n
r
ate:
0
.
0
0
,
m
ax
i
m
u
m
n
u
m
b
er
o
f
g
en
er
at
io
n
s
:
3
0
,
to
u
r
n
a
m
e
n
t
s
ize:
5
.
T
h
e
o
p
ti
m
al
g
en
er
atio
n
a
n
d
o
p
ti
m
a
l
s
o
lu
t
io
n
f
o
r
ea
ch
cr
o
s
s
o
v
er
r
ates
w
er
e
d
o
n
e
b
y
r
u
n
n
i
n
g
a
f
e
w
test
s
to
g
et
t
h
e
b
est
r
esu
lts
.
T
o
s
u
m
m
ar
ize
t
h
e
ab
o
v
e
f
i
g
u
r
e
s
,
a
s
u
m
m
ar
iz
atio
n
o
f
th
e
o
p
ti
m
al
g
en
er
atio
n
a
n
d
o
p
ti
m
al
s
o
l
u
ti
o
n
b
y
e
ac
h
s
elec
tio
n
s
c
h
e
m
e
is
e
x
h
ib
ited
i
n
T
ab
le
4
.
C
r
o
s
s
o
v
er
r
ate
o
f
0
.
9
ac
h
iev
ed
t
h
e
h
i
g
h
e
s
t
f
it
n
es
s
v
alu
e,
1
.
0
at
g
en
er
atio
n
6
w
h
e
n
u
s
i
n
g
T
E
.
Me
an
w
h
ile
t
h
e
cr
o
s
s
o
v
er
r
ate
o
f
0
.
9
ac
h
iev
ed
f
it
n
es
s
v
al
u
e
o
f
1
.
0
at
g
en
er
atio
n
9
f
o
r
T
.
T
ab
le
4
.
B
est R
es
u
lts
f
o
r
T
E
a
n
d
T
u
s
in
g
Dif
f
er
e
n
t Cro
s
s
o
v
e
r
R
ates
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s
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ize,
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ased
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T
s
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et
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t
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ll
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h
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v
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s
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icate
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im
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o
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tr
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o
lv
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L
T
P
in
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s
m
all
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n
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lar
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ca
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5.
C
O
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C
L
U
SIO
N
S
T
h
e
an
al
y
s
is
o
f
b
o
th
s
e
lectio
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s
ch
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es,
T
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d
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d
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ar
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t
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ter
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Evaluation Warning : The document was created with Spire.PDF for Python.
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309
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Un
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Dep
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Ma
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T
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MA
R
A
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Ala
m
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Ma
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f
o
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s
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n
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k
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g
e
f
o
r
th
e
w
o
r
k
.
RE
F
E
R
E
NC
E
S
[1
]
A
b
d
u
l
-
Ra
h
m
a
n
,
S
.
,
S
o
b
ri,
N.
S
.
,
O
m
a
r,
M
.
F
.
,
Be
n
jam
in
,
A
.
M
.
,
Ra
m
li
,
R.
Gr
a
p
h
c
o
l
o
rin
g
h
e
u
ri
stics
fo
r
so
lvin
g
e
x
a
min
a
ti
o
n
t
ime
ta
b
l
in
g
p
ro
b
lem
a
t
Un
ive
rs
it
i
Uta
ra
M
a
la
y
sia
.
In
AIP
Co
n
fer
e
n
c
e
Pro
c
e
e
d
in
g
s
.
2
0
1
4
;
1
6
3
5
(
1
):4
9
1
-
4
9
6
.
A
IP
.
[2
]
Ba
b
a
e
i,
H.,
Ka
ri
m
p
o
u
r,
J.,
Ha
d
id
i
,
A
.
A
su
rv
e
y
o
f
a
p
p
ro
a
c
h
e
s
f
o
r
u
n
iv
e
rsity
c
o
u
rse
ti
m
e
t
a
b
li
n
g
p
ro
b
l
e
m
.
Co
mp
u
ter
s
&
In
d
u
stria
l
E
n
g
in
e
e
rin
g
,
2
0
1
5
;
8
6
:
4
3
-
5
9
.
[3
]
M
a
h
ib
a
,
A
.
A
.
,
Du
ra
i,
C.
A
.
D.
Ge
n
e
ti
c
a
lg
o
rith
m
wit
h
se
a
rc
h
b
a
n
k
stra
teg
ies
fo
r
u
n
ive
rs
it
y
c
o
u
rs
e
ti
me
ta
b
li
n
g
p
ro
b
lem
.
P
ro
c
e
d
ia
En
g
in
e
e
rin
g
;
2
0
1
2
.
3
8
:
2
5
3
-
2
6
3
.
[4
]
Ku
m
a
r,
K.,
S
ik
a
n
d
e
r,
R.
S
.
,
&
M
e
h
ta,
K
.
G
e
n
e
ti
c
A
l
g
o
rit
h
m
A
p
p
ro
a
c
h
to
A
u
to
m
a
te
Un
iv
e
rsit
y
T
i
m
e
tab
le.
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
T
e
c
h
n
ica
l
Res
e
a
rc
h
(
IJ
T
R
),
2
0
1
2
;
1
(1
)
:
4
7
-
5
1
.
[5
]
T
i
m
il
sin
a
,
S
.
,
Ne
g
i,
R.
,
K
h
u
ra
n
a
,
Y.,
&
S
e
th
,
J.
(2
0
1
5
).
G
e
n
e
ti
c
a
ll
y
e
v
o
lv
e
d
so
lu
ti
o
n
to
ti
m
e
tab
le sc
h
e
d
u
li
n
g
p
ro
b
lem
.
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Co
mp
u
ter
Ap
p
li
c
a
t
io
n
s
,
2
0
1
5
;
1
1
4
(1
8
):
1
2
–
1
7
.
[6
]
G
a
n
g
u
li
,
R.
,
&
Ro
y
,
S
.
A
S
tu
d
y
o
n
Co
u
rse
T
i
m
e
tab
le
S
c
h
e
d
u
li
n
g
u
sin
g
G
ra
p
h
Co
lo
rin
g
A
p
p
ro
a
c
h
.
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Co
m
p
u
t
a
ti
o
n
a
l
a
n
d
Ap
p
li
e
d
M
a
t
h
e
ma
ti
c
s
,
2
0
1
7
;
12
(
2
):
4
6
9
-
4
8
5
.
[7
]
S
ig
l,
B.
,
G
o
lu
b
,
M
.
,
&
M
o
rn
a
r,
V.
S
o
lvi
n
g
ti
me
ta
b
le
sc
h
e
d
u
l
in
g
p
ro
b
lem
u
si
n
g
g
e
n
e
ti
c
a
l
g
o
rith
ms
.
In
2
5
t
h
In
tern
a
ti
o
n
a
l
C
o
n
f
e
re
n
c
e
In
f
o
r
m
a
ti
o
n
T
e
c
h
n
o
lo
g
y
In
terf
a
c
e
s,
2
0
0
3
:
5
1
9
-
5
2
4
.
[8
]
Bu
rk
e
,
E.
K.,
El
li
m
a
n
,
D.
G
.
,
&
W
e
a
r
e
,
R.
A
g
e
n
e
ti
c
a
lg
o
rith
m
b
a
se
d
u
n
ive
rs
it
y
ti
me
ta
b
li
n
g
sy
ste
m
.
In
P
r
o
c
e
e
d
in
g
s
o
f
th
e
2
n
d
e
a
st
-
w
e
st i
n
tern
a
ti
o
n
a
l
c
o
n
f
e
re
n
c
e
o
n
c
o
m
p
u
ter t
e
c
h
n
o
lo
g
ies
in
e
d
u
c
a
ti
o
n
,
1
9
9
4
;
1
:
3
5
-
40.
[9
]
Ch
u
,
S
.
C.
,
Ch
e
n
,
Y.
T
.
,
&
Ho
,
J.
H.
T
ime
ta
b
le
sc
h
e
d
u
li
n
g
u
si
n
g
p
a
rticle
swa
rm
o
p
ti
miz
a
ti
o
n
.
F
ir
st
In
tern
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
o
n
In
n
o
v
a
ti
v
e
Co
m
p
u
ti
n
g
,
In
f
o
rm
a
ti
o
n
a
n
d
Co
n
tro
l,
2
0
0
6
.
ICICIC'
0
6
,
2
0
0
6
;3
:
3
2
4
-
3
2
7
[1
0
]
S
u
n
,
H.,
Ch
e
n
,
S
.
P
.
,
Jin
,
C.
,
&
G
u
o
,
K.
(2
0
1
3
).
R
e
se
a
rc
h
a
n
d
sim
u
latio
n
o
f
tas
k
s
c
h
e
d
u
li
n
g
a
l
g
o
rit
h
m
in
c
lo
u
d
c
o
m
p
u
ti
n
g
.
In
d
o
n
e
sia
n
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
En
g
i
n
e
e
rin
g
a
n
d
Co
m
p
u
ter
S
c
ien
c
e
,
11
(
1
1
)
,
6
6
6
4
-
6
6
7
2
.
[1
1
]
Ra
z
a
k
,
H.
A
.
,
Ib
ra
h
im
,
Z.
,
&
Hu
ss
in
,
N.
M
.
(2
0
1
0
,
M
a
rc
h
).
Bip
a
rti
te
g
ra
p
h
e
d
g
e
c
o
lo
ri
n
g
a
p
p
r
o
a
c
h
t
o
c
o
u
rse
ti
m
e
tab
li
n
g
.
In
In
fo
rm
a
t
io
n
Retrie
v
a
l
&
Kn
o
wled
g
e
M
a
n
a
g
e
me
n
t,
(
CA
M
P),
2
0
1
0
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
(p
p
.
229
-
2
3
4
).
IEE
E.
[1
2
]
Yu
so
f
f
,
M
.
,
A
ri
ff
in
,
J.,
&
M
o
h
a
m
e
d
,
A
.
(2
0
1
5
).
D
P
S
O
b
a
se
d
o
n
a
m
in
-
m
a
x
a
p
p
ro
a
c
h
a
n
d
c
lam
p
in
g
stra
teg
y
f
o
r
th
e
e
v
a
c
u
a
ti
o
n
v
e
h
icle
a
ss
ig
n
m
e
n
t
p
ro
b
lem
.
Ne
u
ro
c
o
mp
u
ti
n
g
,
1
4
8
,
3
0
-
38.
[1
3
]
Ke
n
d
a
ll
,
G
.
,
&
Hu
ss
in
,
N.
M
.
(2
0
0
4
,
A
u
g
u
st).
A
tab
u
se
a
rc
h
h
y
p
e
r
-
h
e
u
risti
c
a
p
p
r
o
a
c
h
to
th
e
e
x
a
m
in
a
ti
o
n
ti
m
e
tab
li
n
g
p
ro
b
lem
a
t
th
e
M
ARA
u
n
iv
e
rsit
y
o
f
te
c
h
n
o
lo
g
y
.
I
n
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
t
h
e
Pr
a
c
ti
c
e
a
n
d
T
h
e
o
ry
o
f
Au
to
ma
te
d
T
ime
t
a
b
li
n
g
(p
p
.
2
7
0
-
2
9
3
).
S
p
ri
n
g
e
r,
Be
rli
n
,
He
id
e
lb
e
rg
.
[1
4
]
Co
w
li
n
g
,
P
.
,
Ke
n
d
a
ll
,
G
.
,
&
H
u
ss
in
,
N.
M
.
(2
0
0
2
,
A
u
g
u
st).
A
su
rv
e
y
a
n
d
c
a
se
stu
d
y
o
f
p
ra
c
ti
c
a
l
e
x
a
m
in
a
ti
o
n
ti
m
e
tab
li
n
g
p
ro
b
lem
s.
In
PA
T
AT
(
p
p
.
2
5
8
-
2
6
1
).
[1
5
]
A
l
w
a
d
o
o
d
,
Z.
,
S
h
u
ib
,
A
.
,
&
Ha
m
id
,
N.
A
.
(2
0
1
3
,
A
u
g
u
st).
M
a
th
e
m
a
ti
c
a
l
re
s
c
h
e
d
u
li
n
g
m
o
d
e
ls
f
o
r
ra
il
w
a
y
se
r
v
ice
s.
In
Pro
c
e
e
d
i
n
g
s
o
f
W
o
rl
d
Aca
d
e
my
o
f
S
c
ien
c
e
,
En
g
i
n
e
e
rin
g
a
n
d
T
e
c
h
n
o
l
o
g
y
(N
o
.
8
0
,
p
.
6
2
0
).
W
o
rld
A
c
a
d
e
m
y
o
f
S
c
ien
c
e
,
En
g
in
e
e
rin
g
a
n
d
T
e
c
h
n
o
lo
g
y
(
WA
S
ET
).
[1
6
]
A
z
iz,
R.
W
.
A
.
,
S
h
u
i
b
,
A
.
,
A
z
iz,
W
.
N.
H.
W
.
A
.
,
T
a
w
il
,
N.
M
.
,
&
Na
w
a
w
i,
A
.
H.
M
.
(
2
0
1
3
).
P
a
re
to
a
n
a
ly
sis
o
n
b
u
d
g
e
t
a
ll
o
c
a
ti
o
n
f
o
r
d
if
f
e
r
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J.,
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&
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.
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