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CC B
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p
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tr
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s
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1.
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UCT
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lo
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p
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g
tec
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n
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lo
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a
lo
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s
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to
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ter
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g
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s
ca
lab
le
an
d
v
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tu
al
ized
r
eso
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s
.
T
h
e
m
ain
o
b
j
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tiv
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o
f
th
e
clo
u
d
is
to
p
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v
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all
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v
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w
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w
it
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m
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n
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m
u
m
co
s
t
an
d
h
i
g
h
p
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f
o
r
m
a
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ce
[
1
,
2
]
.
To
h
av
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t
h
e
ab
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to
a
llo
w
all
h
u
g
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.
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tr
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k
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lt
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r
esp
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s
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ti
m
e
o
f
th
e
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g
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tas
k
s
[3
-
5
]
.
L
o
ad
b
alan
cin
g
is
an
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f
icie
n
t
tech
n
iq
u
e
u
s
ed
to
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is
tr
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u
te
w
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r
k
lo
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r
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in
a
w
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th
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d
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-
lo
ad
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[
6
]
.
T
r
a
d
itio
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alg
o
r
it
h
m
s
[
7
-
11]
ar
e
u
s
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to
s
o
l
v
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t
h
is
p
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b
le
m
.
Ho
w
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,
th
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s
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g
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m
s
h
a
v
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s
in
th
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ca
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o
f
co
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p
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an
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lar
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e
s
ca
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p
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m
s
.
Me
tah
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h
m
s
s
u
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as
p
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
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0
8
8
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8708
I
n
t J
E
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&
C
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p
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g
,
Vo
l.
11
,
No
.
3
,
J
u
n
e
2
0
2
1
:
2
4
7
7
-
2489
2478
o
p
tim
izatio
n
(
P
SO)
[
1
2
]
,
an
t
co
lo
n
y
o
p
ti
m
izatio
n
(
AC
O)
[
1
3
]
,
a
r
tif
icial
b
ee
co
lo
n
y
(
A
B
C
)
[
1
4
]
,
an
d
g
en
etic
alg
o
r
ith
m
(
G
A
)
[
1
5
,
1
6
]
a
r
e
p
o
p
u
lar
to
s
o
lv
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n
o
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-
d
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i
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(
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Usi
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f
f
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t
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o
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ith
m
t
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at
p
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d
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ce
s
g
o
o
d
in
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tio
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o
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m
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r
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s
tic
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m
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ir
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s
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co
m
p
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r
an
d
o
m
in
i
tialize
d
p
r
o
b
lem
s
[
1
7
,
1
8
]
.
Gen
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al
g
o
r
ith
m
(
G
A
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as
a
n
ev
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u
tio
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m
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ith
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p
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s
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A
h
as
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ee
n
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s
s
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c
h
a
s
q
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ti
m
izatio
n
[
1
9
]
,
m
e
d
ical
s
c
i
e
n
c
e
[
2
0
]
,
a
g
r
i
c
u
l
t
u
r
e
[
2
1
]
,
m
a
n
a
g
e
m
e
n
t
[
2
2
]
,
f
e
a
t
u
r
e
s
e
l
e
c
t
i
o
n
[
2
3
]
,
p
o
w
e
r
f
l
o
w
m
a
n
a
g
e
m
e
n
t
[
2
4
]
,
a
n
d
s
e
n
s
o
r
n
e
t
w
o
r
k
s
[
2
5
]
.
GA
i
s
b
asicall
y
d
e
s
ig
n
ed
f
o
r
t
h
e
d
is
cr
ete
o
p
ti
m
izatio
n
p
r
o
b
l
e
m
w
h
er
e
b
its
o
f
0
’
s
a
n
d
1
’
s
ar
e
u
s
ed
to
en
co
d
e
d
is
cr
ete
d
esig
n
v
ar
iab
les.
Un
l
ik
e
b
io
-
in
s
p
ir
ed
alg
o
r
ith
m
s
t
h
at
ar
e
d
esig
n
ed
f
o
r
co
n
tin
u
o
u
s
p
r
o
b
lem
s
an
d
ca
n
ch
o
o
s
e
an
y
v
al
u
e
to
e
n
co
d
e
d
esig
n
v
ar
iab
les,
w
h
ich
m
ak
e
s
G
A
m
o
r
e
s
u
itab
le
th
a
n
o
t
h
e
r
alg
o
r
ith
m
s
i
n
t
h
e
lo
ad
b
alan
cin
g
p
r
o
b
lem
.
C
h
o
o
s
in
g
g
o
o
d
in
itial
p
o
p
u
latio
n
o
f
G
A
i
s
a
n
i
m
p
o
r
tan
t
s
tep
to
g
en
er
ate
n
e
w
b
etter
g
en
er
atio
n
s
w
it
h
h
ig
h
-
q
u
al
it
y
s
o
lu
tio
n
s
w
it
h
i
n
les
s
ti
m
e
[
2
6
]
.
I
n
t
h
is
p
ap
er
,
a
h
y
b
r
id
lo
ad
b
alan
ce
b
ased
o
n
g
e
n
etic
a
lg
o
r
ith
m
(
H
L
B
G
A
)
i
s
p
r
o
p
o
s
ed
t
o
d
is
tr
ib
u
te
th
e
lo
ad
s
o
v
er
all
v
ir
tu
a
l
m
ac
h
in
es
(
VM
s
)
i
n
an
ef
f
icie
n
t
w
a
y
.
HL
B
G
A
is
i
m
p
le
m
en
ted
i
n
t
w
o
p
h
ases
.
I
n
t
h
e
f
ir
s
t
p
h
ase,
t
h
e
h
eter
o
g
o
n
o
u
s
in
it
ialized
lo
ad
b
alan
ci
n
g
(
HI
L
B
)
alg
o
r
it
h
m
is
p
r
o
p
o
s
ed
.
I
t
d
is
tr
ib
u
tes
tas
k
s
o
v
er
all
VM
s
i
n
an
e
f
f
icie
n
t
wa
y
to
av
o
id
o
v
er
lo
ad
ed
o
r
u
n
d
er
lo
ad
ed
VM
s
.
I
n
th
e
s
ec
o
n
d
p
h
ase,
G
A
is
u
s
ed
to
en
h
a
n
ce
t
h
e
o
v
er
all
s
y
s
te
m
p
er
f
o
r
m
an
ce
.
I
t
i
s
i
n
itialize
d
w
it
h
t
h
e
o
u
tp
u
t
o
f
t
h
e
HI
L
B
alg
o
r
ith
m
a
s
a
g
o
o
d
in
itial
p
o
p
u
latio
n
f
o
r
G
A
.
T
h
i
s
p
h
a
s
e
u
s
e
s
a
n
e
w
l
y
f
o
r
m
u
lat
ed
f
it
n
es
s
f
u
n
ct
io
n
f
o
r
G
A
t
h
a
t
h
elp
s
t
h
e
HL
B
G
A
to
r
ea
ch
th
e
o
p
ti
m
al
lo
ad
d
ev
i
atio
n
.
T
h
e
r
es
t
o
f
th
is
p
ap
er
is
o
r
g
an
ized
as:
Sectio
n
2
p
r
esen
ts
t
h
e
r
elate
d
lo
ad
b
alan
cin
g
alg
o
r
ith
m
s
.
I
n
Sectio
n
3
,
t
h
e
p
r
o
p
o
s
ed
lo
ad
-
b
alan
cin
g
al
g
o
r
it
h
m
is
in
tr
o
d
u
ce
d
.
I
n
Sectio
n
4
,
t
h
e
p
er
f
o
r
m
an
ce
e
v
alu
a
tio
n
o
f
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
is
p
r
esen
ted
an
d
co
m
p
ar
ed
w
it
h
t
h
e
ex
i
s
tin
g
lo
ad
b
alan
cin
g
al
g
o
r
ith
m
s
.
Sectio
n
5
p
r
ese
n
ts
t
h
e
m
a
in
co
n
c
lu
s
io
n
s
an
d
f
u
tu
r
e
w
o
r
k
.
2.
RE
L
AT
E
D
WO
RK
A
lar
g
e
ar
ea
o
f
r
esear
ch
es
was
in
tr
o
d
u
ce
d
to
s
o
lv
e
th
e
lo
ad
b
alan
cin
g
p
r
o
b
le
m
to
g
et
an
o
p
ti
m
a
l
ass
i
g
n
m
e
n
t
s
o
lu
tio
n
.
T
h
ese
r
esear
ch
es
ca
n
b
e
ca
te
g
o
r
ized
in
to
th
r
ee
m
a
in
t
y
p
e
s
o
f
al
g
o
r
ith
m
s
:
tr
ad
itio
n
al,
m
eta
h
eu
r
i
s
tic,
an
d
h
y
b
r
id
alg
o
r
ith
m
s
.
2
.
1
.
T
ra
ditio
na
l a
lg
o
rit
h
m
s
T
r
a
d
itio
n
al
al
g
o
r
ith
m
s
ar
e
wo
r
k
ed
b
ased
o
n
k
n
o
w
in
g
in
f
o
r
m
at
io
n
ab
o
u
t
r
eso
u
r
ce
s
a
n
d
task
s
to
ca
lcu
late
th
eir
ev
al
u
atio
n
p
ar
a
m
eter
s
.
Mo
s
t
o
f
t
h
e
m
r
el
y
o
n
ex
ec
u
tio
n
ti
m
e
to
ass
ig
n
ta
s
k
s
to
r
eso
u
r
ce
s
i
n
a
w
a
y
th
at
m
i
n
i
m
izes
m
ak
e
s
p
an
,
lo
ad
d
ev
iatio
n
,
o
r
b
o
th
.
Min
-
Min
alg
o
r
it
h
m
i
s
a
w
el
l
-
k
n
o
w
n
alg
o
r
it
h
m
i
n
th
i
s
ca
teg
o
r
y
.
Mi
n
-
Min
alg
o
r
it
h
m
is
t
h
e
b
ase
o
f
m
a
n
y
s
c
h
ed
u
l
in
g
al
g
o
r
ith
m
s
[
8
]
.
I
n
t
h
i
s
al
g
o
r
ith
m
,
th
e
co
m
p
letio
n
ti
m
e
o
f
a
ll
s
u
b
m
i
tted
tas
k
s
a
m
o
n
g
all
VM
s
is
ca
lc
u
lated
.
T
h
e
task
w
i
th
m
i
n
i
m
u
m
co
m
p
leti
o
n
ti
m
e
i
s
as
s
i
g
n
ed
to
th
e
co
r
r
esp
o
n
d
in
g
VM
.
T
h
en
t
h
e
co
m
p
letio
n
ti
m
e
o
f
all
o
th
er
tas
k
s
o
n
t
h
at
m
ac
h
i
n
e
i
s
u
p
d
ated
b
y
ad
d
in
g
th
e
co
m
p
let
io
n
ti
m
e
o
f
t
h
e
a
s
s
i
g
n
ed
ta
s
k
to
th
e
ir
co
m
p
let
io
n
ti
m
es.
T
h
is
tas
k
i
s
r
e
m
o
v
ed
f
r
o
m
a
li
s
t
o
f
u
n
a
s
s
i
g
n
ed
task
s
,
an
d
t
h
en
t
h
i
s
p
r
o
ce
d
u
r
e
is
r
ep
ea
ted
u
n
til al
l ta
s
k
s
ar
e
ass
i
g
n
ed
.
L
o
ad
b
a
l
a
n
c
e
i
m
p
r
o
v
e
d
M
i
n
-
M
i
n
(
L
B
I
M
M
)
a
l
g
o
r
i
t
h
m
i
m
p
r
o
v
e
s
t
h
e
s
t
a
n
d
a
r
d
M
i
n
-
M
i
n
a
lg
o
r
it
h
m
[
9
]
.
I
n
th
e
f
ir
s
t
s
tep
,
th
e
Min
-
Mi
n
alg
o
r
ith
m
is
e
x
ec
u
ted
to
g
iv
e
t
h
e
in
itial
s
o
lu
tio
n
to
s
tar
t
th
e
n
e
x
t
s
tep
.
I
n
th
e
n
e
x
t
s
tep
,
th
e
co
m
p
letio
n
ti
m
e
o
f
t
h
e
s
m
al
lest
s
ize
ta
s
k
f
r
o
m
t
h
e
h
ea
v
ie
s
t
lo
ad
ed
r
eso
u
r
ce
is
ca
l
cu
lated
o
n
all
o
t
h
er
VM
s
.
Ma
k
esp
an
is
ca
lc
u
lated
in
ca
s
e
t
h
at
tas
k
i
s
r
e
m
o
v
ed
t
o
th
e
VM
w
it
h
th
e
m
in
i
m
u
m
co
m
p
let
io
n
t
i
m
e
o
f
th
at
tas
k
a
n
d
co
m
p
ar
ed
w
i
th
t
h
e
m
a
k
esp
an
p
r
o
d
u
ce
d
b
y
Mi
n
-
Min
.
I
f
it
is
less
t
h
an
t
h
e
ta
s
k
,
it
is
r
ea
s
s
ig
n
ed
to
th
e
r
eso
u
r
ce
t
h
at
p
r
o
d
u
ce
s
i
t,
an
d
th
e
r
ea
d
y
ti
m
e
o
f
b
o
th
r
e
s
o
u
r
ce
s
i
s
u
p
d
ated
.
T
h
e
p
r
o
ce
s
s
r
ep
ea
ts
u
n
til
n
o
o
th
er
r
ea
s
s
ig
n
m
e
n
ts
ca
n
p
r
o
d
u
ce
less
m
a
k
esp
a
n
.
T
h
u
s
th
e
h
e
av
y
lo
ad
r
eso
u
r
ce
s
ar
e
f
r
ee
d
an
d
th
e
li
g
h
t
lo
ad
o
r
id
le
r
eso
u
r
ce
s
ar
e
m
o
r
e
u
tili
ze
d
.
A
lth
o
u
g
h
th
e
tr
ad
itio
n
al
alg
o
r
ith
m
s
ar
e
s
i
m
p
le
to
im
p
le
m
e
n
t
an
d
ca
n
i
m
p
r
o
v
e
m
a
k
esp
a
n
,
s
o
m
e
o
f
t
h
e
m
d
o
n
’
t
ta
k
e
th
e
lo
ad
d
ev
ia
tio
n
in
it
s
co
n
s
id
er
atio
n
esp
ec
iall
y
i
n
ca
s
e
o
f
b
i
g
d
if
f
er
e
n
ce
i
n
r
eso
u
r
ce
s
p
ee
d
.
A
l
s
o
,
th
e
y
ca
n
'
t
f
i
n
d
th
e
o
p
ti
m
al
s
o
lu
t
io
n
esp
ec
ial
l
y
w
h
e
n
t
h
e
p
r
o
b
lem
b
ec
o
m
e
s
co
m
p
le
x
o
r
to
o
lar
g
e
[
2
5
]
.
2
.
2
.
M
et
a
heuris
t
ic
a
lg
o
rit
h
m
s
Me
tah
e
u
r
is
tic
al
g
o
r
ith
m
s
ar
e
th
e
m
o
s
t
p
o
w
er
f
u
l
tech
n
iq
u
e
s
f
o
r
th
e
o
p
ti
m
izat
io
n
o
f
co
m
p
lex
n
o
n
-
lin
ea
r
p
r
o
b
le
m
s
w
h
ic
h
is
th
e
ca
s
e
o
f
m
o
s
t
ta
s
k
s
c
h
ed
u
li
n
g
an
d
lo
ad
b
alan
ci
n
g
is
s
u
e
s
[
2
6
]
.
Me
tah
eu
r
is
tic
alg
o
r
ith
m
s
ca
n
b
e
class
if
ied
in
to
s
w
ar
m
i
n
telli
g
e
n
ce
b
ased
alg
o
r
ith
m
s
an
d
ev
o
l
u
tio
n
ar
y
alg
o
r
ith
m
s
.
S
w
ar
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
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n
g
I
SS
N:
2
0
8
8
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8708
H
yb
r
id
lo
a
d
b
a
la
n
ce
b
a
s
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o
n
g
en
etic
a
lg
o
r
ith
m
in
clo
u
d
e
n
viro
n
men
t (
W
a
la
a
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a
b
er)
2479
in
telli
g
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n
ce
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ased
alg
o
r
ith
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s
s
u
ch
as
P
SO,
AC
O,
an
d
A
B
C
o
p
ti
m
ize
a
ce
r
tain
p
r
o
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lem
b
y
s
i
m
u
lati
n
g
t
h
e
co
llectiv
e
b
e
h
av
io
r
o
f
n
a
tu
r
al
s
w
ar
m
s
.
E
v
o
lu
tio
n
ar
y
a
lg
o
r
it
h
m
s
s
u
c
h
a
s
G
A
ar
e
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ased
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h
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t
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o
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te
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o
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ith
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h
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alg
o
r
it
h
m
s
u
s
ed
in
lo
ad
b
alan
c
in
g
a
n
d
als
o
in
o
th
er
ap
p
licatio
n
s
[
2
7
,
2
8
]
.
I
t
is
a
s
w
ar
m
in
te
lli
g
en
t
alg
o
r
it
h
m
,
in
s
p
ir
ed
b
y
n
at
u
r
e
f
o
r
s
o
lv
i
n
g
n
o
n
li
n
ea
r
o
p
tim
izatio
n
p
r
o
b
le
m
s
[
1
0
]
.
P
SO
is
a
s
i
m
u
latio
n
o
f
t
h
e
ad
v
an
ta
g
es
o
f
b
ir
d
f
lo
ck
s
.
I
t
s
tar
ts
w
ith
i
n
itia
l
in
d
iv
id
u
als
ca
lled
p
ar
ticles r
ep
r
esen
ti
n
g
i
n
itial
s
o
lu
t
io
n
s
f
o
r
t
h
e
p
r
o
b
le
m
.
Du
r
i
n
g
t
h
e
s
ea
r
c
h
p
r
o
ce
s
s
,
k
illi
n
g
o
f
an
y
i
n
d
iv
id
u
al
i
s
n
o
t
p
er
m
itt
ed
.
I
n
P
SO,
all
in
d
iv
id
u
al
s
r
em
ai
n
aliv
e
a
n
d
tr
y
to
m
a
k
e
t
h
e
m
s
el
v
es
s
tr
o
n
g
e
r
th
r
o
u
g
h
o
u
t
t
h
e
s
ea
r
ch
p
r
o
ce
s
s
.
I
n
e
v
er
y
g
e
n
er
atio
n
/iter
atio
n
,
in
d
iv
id
u
als
m
a
k
e
th
e
m
s
e
lv
e
s
b
etter
.
T
h
e
id
en
tit
y
o
f
th
e
i
n
d
iv
id
u
al
d
o
es n
o
t c
h
a
n
g
e
o
v
er
th
e
iter
atio
n
s
.
GA
i
s
an
ev
o
l
u
tio
n
ar
y
o
p
ti
m
izatio
n
alg
o
r
ith
m
b
ased
o
n
th
e
b
io
lo
g
ical
co
n
ce
p
t
o
f
p
o
p
u
latio
n
g
en
er
atio
n
[
1
3
]
.
A
n
e
w
p
o
p
u
l
atio
n
is
ev
o
l
v
ed
in
ev
er
y
g
en
er
atio
n
b
ased
o
n
p
r
ed
ef
i
n
ed
f
i
tn
es
s
f
u
n
ctio
n
.
G
A
w
o
r
k
s
b
etter
f
o
r
v
ast
a
n
d
co
m
p
lex
s
ea
r
ch
s
p
ac
e
p
r
o
b
lem
s
.
I
t
w
o
r
k
s
b
ased
o
n
th
r
ee
m
ai
n
o
p
er
atio
n
s
w
h
ic
h
ar
e
s
elec
tio
n
,
cr
o
s
s
o
v
er
,
an
d
m
u
t
atio
n
.
T
h
e
s
tr
en
g
th
o
f
G
A
is
in
t
h
e
p
ar
allel
n
at
u
r
e
o
f
its
s
ea
r
ch
.
T
h
e
g
en
etic
o
p
er
ato
r
s
u
s
ed
ar
e
th
e
m
ain
p
o
w
er
f
u
l
r
ea
s
o
n
f
o
r
th
e
s
u
cc
ess
o
f
th
e
s
ea
r
c
h
.
C
r
o
s
s
o
v
er
is
th
e
m
a
in
g
e
n
etic
o
p
er
ato
r
,
w
h
er
ea
s
m
u
tatio
n
i
s
u
s
ed
less
f
r
eq
u
e
n
tl
y
.
C
r
o
s
s
o
v
er
atte
m
p
t
s
to
b
en
ef
it
o
f
f
s
p
r
in
g
s
o
lu
tio
n
s
a
n
d
to
eli
m
i
n
ate
u
n
d
esira
b
le
co
m
p
o
n
en
t
s
.
B
y
r
estricti
n
g
t
h
e
r
ep
r
o
d
u
ctio
n
o
f
w
ea
k
o
f
f
s
p
r
i
n
g
s
,
GAs
eli
m
i
n
ate
s
n
o
t
o
n
l
y
t
h
at
s
o
l
u
t
io
n
b
u
t
al
s
o
all
o
f
its
d
escen
d
an
ts
.
T
h
is
m
a
k
es
th
e
al
g
o
r
ith
m
co
n
v
er
g
e
to
w
ar
d
s
h
ig
h
-
q
u
alit
y
s
o
lu
tio
n
s
w
i
th
i
n
a
f
e
w
g
e
n
er
a
tio
n
s
.
I
n
o
r
d
er
to
r
ea
lize
p
o
w
er
f
u
l
cr
o
s
s
o
v
er
a
n
d
m
u
tatio
n
o
p
er
ato
r
s
,
w
e
m
u
s
t
ch
o
o
s
e
g
o
o
d
in
itial p
o
p
u
latio
n
f
o
r
GA
[
1
4
]
.
Ho
w
e
v
er
m
etah
e
u
r
is
tic
al
g
o
r
ith
m
s
ar
e
p
o
w
er
f
u
l
tech
n
iq
u
es
f
o
r
o
p
ti
m
iza
tio
n
,
t
h
e
y
ar
e
i
n
e
f
f
icien
t
to
h
an
d
le
th
e
lo
ad
in
c
lo
u
d
co
m
p
u
ti
n
g
in
ca
s
e
o
f
r
an
d
o
m
i
n
itial
p
o
p
u
latio
n
.
A
l
s
o
,
th
e
y
s
u
f
f
er
f
r
o
m
i
n
cr
ea
s
i
n
g
t
h
e
co
m
p
u
tatio
n
al
co
s
t
i
n
t
h
e
lar
g
e
s
ca
le
p
r
o
b
le
m
s
[
2
9
]
.
T
h
e
r
e
f
o
r
e
,
h
y
b
r
i
d
a
l
g
o
r
i
t
h
m
s
a
r
e
i
n
t
r
o
d
u
c
e
d
t
o
e
n
h
a
n
c
e
t
h
e
p
e
r
f
o
r
m
a
n
c
e
o
f
b
o
t
h
t
h
e
t
r
a
d
i
t
i
o
n
a
l
a
n
d
m
e
t
a
h
e
u
r
i
s
t
i
c
a
l
g
o
r
i
t
h
m
s
i
n
o
r
d
e
r
t
o
h
a
n
d
l
e
t
h
e
i
r
p
r
o
b
le
m
s
.
2
.
3
.
H
y
brid
a
lg
o
rit
h
m
s
H
y
b
r
id
tas
k
s
ch
ed
u
li
n
g
al
g
o
r
ith
m
s
ar
e
b
ased
o
n
co
m
b
i
n
in
g
t
w
o
s
c
h
ed
u
l
in
g
a
lg
o
r
i
t
h
m
s
to
m
a
k
e
u
s
e
o
f
th
e
ad
v
an
tag
e
o
f
b
o
th
t
h
ese
t
w
o
alg
o
r
it
h
m
s
.
T
h
is
p
a
p
er
p
r
esen
ts
s
o
m
e
o
f
th
e
m
o
s
t
p
o
p
u
lar
h
y
b
r
id
alg
o
r
ith
m
s
to
s
tate
t
h
e
r
ea
s
o
n
f
o
r
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
.
H
GA
-
AC
O
a
lg
o
r
it
h
m
[
3
0
]
co
m
b
in
es
G
A
a
n
d
AC
O
alg
o
r
ith
m
s
to
g
e
th
er
.
R
a
n
d
o
m
l
y
i
n
itia
li
ze
d
G
A
is
u
s
ed
to
p
r
o
d
u
ce
t
h
e
i
n
itia
l
p
h
er
o
m
o
n
e
f
o
r
A
C
O.
AC
O
s
tar
ts
to
iter
ate
i
n
o
r
d
er
to
g
i
v
e
th
e
b
est
s
o
lu
tio
n
.
T
h
e
b
est
t
wo
s
o
lu
tio
n
s
f
r
o
m
G
A
an
d
A
C
O
ar
e
m
er
g
ed
b
y
cr
o
s
s
o
v
er
to
g
i
v
e
t
h
e
g
lo
b
al
b
est
s
o
lu
tio
n
.
Ho
w
e
v
er
,
t
h
e
al
g
o
r
ith
m
f
o
c
u
s
e
s
o
n
r
esp
o
n
s
e
t
i
m
e,
e
x
ec
u
tio
n
ti
m
e
an
d
th
r
o
u
g
h
p
u
t,
it
d
o
es
n
’
t
s
u
b
j
ec
t
to
th
e
lo
ad
b
alan
cin
g
p
r
o
b
le
m
.
G
A
is
n
o
t
an
e
f
f
ec
ti
v
e
a
lg
o
r
ith
m
to
g
iv
e
a
n
in
itial
s
o
lu
t
io
n
w
h
en
it i
s
r
an
d
o
m
l
y
i
n
itia
lized
.
Os
m
o
tic
h
y
b
r
id
ar
ti
f
icial
b
ee
a
n
d
an
t c
o
lo
n
y
(
OH_
B
AC
)
alg
o
r
ith
m
i
s
p
r
esen
ted
i
n
[
31
]
.
I
t
ap
p
lies
th
e
o
s
m
o
s
i
s
tech
n
iq
u
e
f
o
r
p
r
o
v
id
in
g
en
er
g
y
e
f
f
icien
t
clo
u
d
en
v
ir
o
n
m
e
n
t.
I
n
th
is
alg
o
r
it
h
m
,
A
B
C
an
d
AC
O
co
o
p
er
ate
to
s
elec
t
t
h
e
ap
p
r
o
p
r
iate
VM
to
b
e
m
ig
r
ated
to
th
e
m
o
s
t
s
u
itab
le
p
h
y
s
ical
m
ac
h
in
e.
I
n
ad
d
itio
n
,
i
t
m
ak
e
s
ac
ti
v
atio
n
f
o
r
th
e
m
o
s
t
s
u
itab
le
o
s
m
o
tic
h
o
s
t
a
m
o
n
g
all
p
h
y
s
ical
m
ac
h
i
n
es
i
n
th
e
s
y
s
te
m
to
d
ec
r
ea
s
e
p
o
w
er
co
n
s
u
m
p
tio
n
.
Mo
r
eo
v
er
,
in
teg
r
atin
g
m
ac
h
i
n
e
lear
n
in
g
tech
n
iq
u
es
w
it
h
lo
ad
b
alan
cin
g
a
l
g
o
r
i
t
h
m
s
r
e
i
n
f
o
r
c
e
m
e
n
t
t
h
e
l
e
a
r
n
i
n
g
p
r
o
c
e
s
s
a
n
d
h
e
l
p
t
o
i
m
p
r
o
v
e
t
h
e
p
e
r
f
o
r
m
a
n
c
e
a
n
d
t
h
e
c
o
n
v
e
r
g
e
n
c
e
r
a
t
e
o
f
t
h
e
l
o
a
d
b
a
l
a
n
c
i
n
g
p
r
o
c
e
s
s
[
3
2
]
.
Ho
w
e
v
er
,
th
e
g
o
al
o
f
m
o
s
t
o
f
th
ese
al
g
o
r
ith
m
s
i
s
to
m
i
n
i
m
ize
th
e
o
v
er
all
co
m
p
letio
n
ti
m
e
w
it
h
o
u
t
lo
o
k
i
n
g
in
to
th
e
m
i
n
i
m
izatio
n
o
f
t
h
e
o
v
er
all
lo
ad
d
ev
iatio
n
.
Mo
s
t
o
f
p
r
ev
io
u
s
al
g
o
r
ith
m
s
ch
o
o
s
e
m
i
n
i
m
izi
n
g
m
ak
e
s
p
an
as
th
e
m
ain
g
o
al
i
n
s
ch
ed
u
li
n
g
;
h
o
w
e
v
er
t
h
i
s
ta
r
g
et
al
w
a
y
s
c
h
o
o
s
es
f
as
ter
V
Ms
to
p
er
f
o
r
m
t
h
e
ass
i
g
n
ed
tas
k
s
.
T
h
i
s
r
es
u
lt
s
i
n
o
v
er
lo
ad
ed
VM
s
w
it
h
h
i
g
h
p
r
o
ce
s
s
in
g
s
p
ee
d
th
at
y
ield
s
to
s
tar
v
atio
n
p
r
o
b
le
m
o
f
o
th
er
VM
s
w
i
th
lo
w
er
p
r
o
ce
s
s
i
n
g
t
i
m
e.
I
n
ad
d
itio
n
,
th
e
e
x
p
er
i
m
e
n
ts
o
f
m
o
s
t
o
f
r
elate
d
w
o
r
k
ar
e
li
m
ited
as
th
e
y
test
ed
t
h
eir
al
g
o
r
ith
m
s
o
n
s
m
all
s
ca
le
p
r
o
b
le
m
s
[
3
3
]
.
I
n
th
is
p
ap
er
,
a
n
e
w
h
y
b
r
id
HL
B
G
A
b
ala
n
cin
g
alg
o
r
ith
m
is
p
r
o
p
o
s
ed
w
h
ic
h
co
m
b
i
n
es
G
A
a
n
d
a
n
e
w
p
r
o
p
o
s
ed
HI
L
B
s
ch
ed
u
lin
g
al
g
o
r
i
th
m
w
h
ic
h
h
elp
s
g
en
et
ics to
co
n
v
er
g
e
m
o
r
e
q
u
i
ck
l
y
to
b
etter
s
o
lu
tio
n
b
y
f
ee
d
i
n
g
it
w
ith
g
o
o
d
in
itial p
o
p
u
lati
o
n
.
3.
T
H
E
P
RO
P
O
SE
D
H
L
B
G
A
3
.
1
.
Arc
hite
ct
ure
o
v
er
v
ie
w
In
t
h
is
s
ec
t
io
n
,
t
h
e
p
r
o
p
o
s
ed
H
L
B
G
A
is
p
r
ese
n
ted
.
T
h
e
m
ai
n
p
u
r
p
o
s
e
o
f
t
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
i
s
to
i
m
p
r
o
v
e
th
e
a
s
s
i
g
n
m
en
t
p
er
f
o
r
m
an
ce
f
o
r
all
th
e
s
u
b
m
itted
t
ask
s
o
n
all
VM
s
.
I
t
tr
ies
to
as
s
ig
n
tas
k
s
to
ea
ch
VM
b
ased
o
n
its
co
m
p
u
ti
n
g
ca
p
ab
ilit
ies
to
m
a
k
e
u
s
e
o
f
all
o
f
th
e
m
w
h
ic
h
lead
s
at
th
e
en
d
to
b
alan
ce
th
e
lo
ad
a
m
o
n
g
all
VM
s
.
L
o
ad
b
alan
ce
is
an
o
p
ti
m
izatio
n
p
r
o
b
le
m
in
w
h
ich
lo
ad
d
ev
iatio
n
is
t
h
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
n
ee
d
ed
to
b
e
m
in
i
m
ized
.
G
A
is
o
n
e
o
f
th
e
p
o
p
u
lar
alg
o
r
it
h
m
s
t
h
at
ar
e
u
s
ed
t
o
s
o
lv
e
o
p
tim
izatio
n
p
r
o
b
lem
s
.
T
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
u
s
es
GA
w
i
th
a
g
o
o
d
in
itial p
o
p
u
lat
io
n
to
g
et
th
e
o
p
ti
m
a
l so
l
u
tio
n
w
it
h
le
s
s
ti
m
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
3
,
J
u
n
e
2
0
2
1
:
2
4
7
7
-
2489
2480
T
h
e
p
r
o
p
o
s
ed
HL
B
G
A
i
s
b
ase
d
o
n
t
w
o
m
ai
n
p
h
a
s
es.
T
h
e
f
ir
s
t
p
h
a
s
e
i
s
ap
p
l
y
i
n
g
t
h
e
p
r
o
p
o
s
ed
HI
L
B
alg
o
r
ith
m
th
at
d
is
tr
ib
u
tes
tas
k
s
o
v
er
all
VM
s
b
ased
o
n
ea
ch
r
eso
u
r
ce
co
m
p
u
tin
g
ca
p
ab
ilit
i
es
to
e
n
s
u
r
e
t
h
at
n
o
s
in
g
le
V
M
is
e
ith
er
o
v
er
lo
ad
ed
o
r
u
n
d
er
u
tili
ze
d
e
s
p
ec
iall
y
in
ca
s
e
o
f
m
aj
o
r
d
if
f
er
e
n
ce
s
b
et
w
ee
n
r
eso
u
r
ce
s
co
m
p
u
ti
n
g
ca
p
a
b
ilit
ie
s
.
T
h
e
s
ec
o
n
d
p
h
ase
u
s
e
s
th
e
o
u
tp
u
t
o
f
th
e
HI
L
B
alg
o
r
ith
m
as
an
i
n
itial
p
o
p
u
latio
n
f
o
r
th
e
G
A
w
h
ic
h
o
p
ti
m
izes lo
ad
d
ev
iatio
n
o
b
j
ec
tiv
e
f
u
n
ct
io
n
to
ac
h
iev
e
o
p
ti
m
u
m
lo
ad
d
is
tr
ib
u
tio
n
.
T
h
e
p
r
o
p
o
s
ed
HL
B
GA
alg
o
r
it
h
m
in
tr
o
d
u
ce
s
a
n
e
w
o
b
j
ec
tiv
e
f
u
n
ct
io
n
to
i
m
p
r
o
v
e
t
h
e
p
er
f
o
r
m
an
ce
o
f
th
e
a
s
s
i
g
n
m
e
n
t
p
r
o
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lem
ev
e
n
w
h
e
n
t
h
e
p
r
o
b
le
m
b
ec
o
m
e
s
c
o
m
p
le
x
o
r
to
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lar
g
e.
I
t
i
m
p
le
m
en
ted
in
d
if
f
er
e
n
t
en
v
ir
o
n
m
e
n
t
s
,
h
o
m
o
g
en
eo
u
s
,
h
eter
o
g
en
eo
u
s
-
lo
w
a
n
d
h
et
er
o
g
o
n
o
u
s
-
h
ig
h
en
v
ir
o
n
m
e
n
ts
.
HL
B
G
A
also
is
i
m
p
le
m
en
ted
o
n
a
d
if
f
er
e
n
t
n
u
m
b
er
o
f
tas
k
s
.
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t
i
m
p
r
o
v
es
r
eso
u
r
ce
u
tili
za
t
io
n
an
d
it
also
d
ec
r
ea
s
es
b
o
th
th
e
lo
ad
d
ev
iatio
n
an
d
th
e
m
a
k
esp
an
.
3
.
2
.
L
o
a
d
ba
la
ncing
pro
ble
m
a
n
a
ly
s
is
A
lt
h
o
u
g
h
clo
u
d
co
m
p
u
ti
n
g
is
d
y
n
a
m
ic,
at
an
y
p
ar
tic
u
lar
i
n
s
t
an
ce
t
h
e
lo
ad
b
ala
n
ci
n
g
p
r
o
b
le
m
ca
n
b
e
f
o
r
m
u
lated
as
ass
i
g
n
in
g
a
s
et
o
f
n
task
s
o
n
a
s
et
o
f
m
VM
s
.
Ass
u
m
e
t
h
a
t
t
h
e
c
l
o
u
d
t
a
s
k
s
c
h
e
d
u
l
e
r
r
e
c
e
i
v
e
s
n
in
d
ep
en
d
en
t
t
a
s
k
s
1
2
3
…
…
.
wi
t
h
d
i
f
f
e
r
e
n
t
l
e
n
g
t
h
s
,
wh
i
c
h
a
r
e
e
x
p
r
e
s
s
e
d
i
n
m
i
l
l
i
o
n
i
n
s
t
r
u
c
t
i
o
n
s
(
M
I
)
a
s
(
1
)
:
=
[
1
2
3
…
…
.
]
w
h
er
e
is
th
e
len
g
t
h
o
f
tas
k
i
a
n
d
=
{
1
.
2
.
…
.
}
(
1
)
A
l
s
o
,
a
s
s
u
m
e
t
h
a
t
t
h
e
c
l
o
u
d
t
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s
k
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c
h
e
d
u
l
e
r
c
o
n
t
a
i
n
s
i
n
f
o
r
m
a
t
i
o
n
a
b
o
u
t
t
h
e
m
V
M
s
;
1
2
3
…
…
.
wi
t
h
d
i
f
f
e
r
e
n
t
p
r
o
c
e
s
s
i
n
g
s
p
e
e
d
s
,
wh
i
c
h
a
r
e
e
x
p
r
e
s
s
e
d
i
n
m
illi
o
n
in
s
tr
u
c
tio
n
s
p
er
s
ec
o
n
d
(
M
I
P
S
(
a
s
:
=
[
1
2
3
…
…
.
]
T
(
2
)
whe
r
e
is
the
pr
oc
e
s
s
or
s
pe
e
d
of
VM
a
n
d
=
{
1
.
2
.
…
.
}
T
h
e
ass
ig
n
m
en
t
m
atr
i
x
o
f
task
s
o
v
er
VM
s
ca
n
b
e
r
ep
r
esen
t
ed
as:
=
[
11
1
1
⋮
…
⋮
1
⋮
⋮
⋮
1
]
(
3
)
whe
r
e
=
1
if
ta
s
k
is
a
s
s
ign
e
d
to
VM
,
othe
r
wi
s
e
=
0
Ass
u
m
e
a
l
s
o
t
h
a
t
a
t
a
n
y
t
i
m
e
t
h
e
r
e
wi
l
l
b
e
l
o
a
d
m
a
t
r
i
x
X
c
o
n
t
a
i
n
s
i
n
f
o
r
m
a
t
i
o
n
a
b
o
u
t
t
h
e
c
u
r
r
e
n
t
l
o
a
d
o
f
t
h
e
m
V
M
s
1
2
3
…
…
.
.
T
h
e
V
M
s
l
o
a
d
s
a
r
e
d
e
f
i
n
e
d
i
n
t
h
e
l
o
a
d
m
a
t
r
i
x
a
s
:
=
[
1
2
3
…
…
.
]
(
4
)
=
∑
=
1
whe
r
e
is
the
c
urr
e
n
t
l
oa
d
of
VM
a
n
d
=
{
1
.
2
.
…
.
}
(
5
)
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
t
h
e
as
s
ig
n
m
e
n
t
s
o
lu
tio
n
ca
n
b
e
m
ea
s
u
r
ed
u
s
in
g
m
ak
e
s
p
an
,
lo
ad
d
ev
iatio
n
(
)
,
an
d
r
eso
u
r
ce
u
til
izatio
n
(
U
)
.
T
h
e
y
ca
n
b
e
ca
lcu
lated
as [
2
3
]
:
=
ma
x
(
)
∀
w
h
er
e
is
th
e
co
m
p
letio
n
ti
m
e
o
f
VM
j
.
(
6
)
=
√
∑
(
−
)
2
=
1
w
h
e
r
e
=
∑
=
1
(
7
)
=
×
100
(
8
)
3
.
3
.
T
he
pro
ble
m
f
o
r
m
u
la
t
io
n o
f
H
L
B
G
A
T
h
e
g
o
al
o
f
t
h
e
p
r
o
p
o
s
e
d
H
L
B
GA
alg
o
r
it
h
m
i
s
t
o
o
p
t
i
m
a
l
l
y
a
s
s
i
g
n
a
s
e
t
o
f
t
a
s
k
s
o
n
a
s
e
t
o
f
V
M
s
i
n
a
wa
y
t
h
a
t
m
i
n
i
m
i
z
e
t
h
e
l
o
a
d
d
e
v
i
a
t
i
o
n
o
f
a
l
l
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M
s
.
M
i
n
i
m
i
z
i
n
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l
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a
d
d
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v
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a
t
i
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m
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p
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m
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m
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t
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l
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t
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d
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e
r
e
n
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
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&
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p
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g
I
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N:
2
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8
8
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o
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j
ec
tiv
e
in
ter
m
s
o
f
t
h
e
ass
i
g
n
m
e
n
t
m
atr
ix
.
I
t
tr
ies
to
g
et
th
e
ass
i
g
n
m
e
n
t
m
atr
i
x
t
h
at
p
r
o
v
i
d
es
th
e
s
o
lu
t
io
n
w
i
th
m
i
n
i
m
u
m
lo
ad
d
ev
iatio
n
.
T
h
e
lo
ad
v
ar
ian
ce
ca
n
b
e
o
b
tain
ed
as:
2
=
∑
(
−
)
2
=
1
(
9
)
a
s
s
u
m
e
̇
=
[
1
2
.
.
]
−
[
1
1
.
.
1
]
=
−
1
(
1
0
)
t
h
en
∑
(
−
)
2
=
1
=
̇
̇
(
1
1
)
b
ec
au
s
e
∑
=
1
=
1
(
1
2
)
th
en
=
1
(
1
3
)
Su
b
s
ti
tu
te
(
1
3
)
in
(
1
0
)
̇
=
(
–
1
1
)
(
1
4
)
w
h
er
e
I
is
an
id
en
tit
y
m
atr
i
x
,
let
=
(
–
1
1
)
th
e
n
̇
=
(
1
5
)
A
ll
th
e
d
ia
g
o
n
al
e
le
m
e
n
t
s
o
f
t
h
e
Q
m
atr
i
x
ar
e
−
1
an
d
it
s
o
f
f
-
d
iag
o
n
al
e
le
m
e
n
t
s
ar
e
−
1
,
s
o
Q
is
a
n
id
e
m
p
o
ten
t
m
atr
ix
[
3
4
]
.
T
h
e
m
atr
i
x
Q
is
u
s
e
f
u
l i
n
co
m
p
u
ti
n
g
s
u
m
s
o
f
s
q
u
ar
ed
d
ev
iatio
n
s
.
=
1
[
−
1
−
1
−
1
−
1
…
−
1
−
1
⋮
⋮
−
1
−
1
…
⋱
−
1
−
1
−
1
]
(
1
6
)
B
y
s
u
b
s
t
itu
tin
g
(
1
1
)
in
(
9
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
3
,
J
u
n
e
2
0
2
1
:
2
4
7
7
-
2489
2482
2
=
̇
̇
=
w
h
er
e
=
,
th
en
(
1
7
)
2
=
(
1
8
)
=
∑
2
=
1
+
∑
∑
=
1
≠
=
1
(
1
9
)
w
h
er
e
=
−
1
,
=
1
,
2
,
…
.
,
an
d
≠
=
−
1
,
,
=
1
,
2
,
…
.
,
2
=
1
2
[
(
−
1
)
∑
2
−
∑
∑
=
1
≠
=
1
=
1
]
(
2
0
)
w
h
er
e
=
∑
=
1
(
2
1
)
=
∑
=
1
an
d
(
2
2
)
2
=
∑
∑
2
=
1
=
1
(
2
3
)
T
h
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
i
s
co
n
clu
d
ed
b
y
s
u
b
s
ti
tu
ti
n
g
(
2
1
)
,
(
2
2
)
,
an
d
(
2
3
)
in
(
2
0
)
th
at
y
iel
d
s
(
2
4
)
.
As
s
h
o
w
n
i
n
(
2
5
)
is
th
e
n
o
n
li
n
e
ar
o
b
j
ec
tiv
e
f
u
n
c
tio
n
o
f
H
L
B
GA
w
h
er
e
t
,
v,
m,
an
d
n
a
r
e
co
n
s
tan
t
s
f
o
r
ea
ch
p
r
o
b
lem
w
h
ic
h
r
ep
r
esen
t ta
s
k
s
len
g
th
,
VM
s
p
r
o
ce
s
s
o
r
s
p
ee
d
,
n
u
m
b
er
o
f
VM
s
,
a
n
d
n
u
m
b
er
o
f
tas
k
s
n
ee
d
to
b
e
ass
i
g
n
ed
,
r
esp
ec
tiv
e
l
y
.
W
h
i
le
θ
co
n
tain
s
th
e
as
s
i
g
n
m
e
n
t v
ar
i
ab
les n
ee
d
to
b
e
s
o
lv
ed
f
o
r
th
e
o
p
t
i
m
u
m
s
o
l
u
t
i
o
n
.
T
h
i
s
o
b
j
e
c
t
i
v
e
f
u
n
c
t
i
o
n
i
s
s
u
b
j
e
c
t
t
o
t
h
r
e
e
c
o
n
s
t
r
a
i
n
s
w
h
i
c
h
a
r
e
f
o
r
m
u
l
a
t
e
d
i
n
(
2
6
-
2
8
)
.
A
s
s
h
o
w
n
i
n
(
2
6
)
m
ea
n
s
t
h
at
ea
ch
ta
s
k
s
h
o
u
ld
b
e
ass
ig
n
ed
to
o
n
l
y
o
n
e
VM
.
θ
in
(
2
7
)
is
a
b
in
ar
y
v
ar
iab
le
w
h
ich
ca
n
b
e
1
o
r
0
,
i
.
e.
,
ass
i
g
n
ed
o
r
n
o
t
ass
ig
n
ed
.
A
s
s
h
o
w
n
i
n
(
2
8
)
s
tate
s
t
h
at
,
th
e
co
m
p
letio
n
ti
m
e
f
o
r
a
n
y
VM
f
o
r
o
p
ti
m
u
m
s
o
lu
tio
n
s
h
o
u
ld
b
e
less
t
h
an
o
r
eq
u
al
to
th
e
m
a
k
esp
a
n
o
f
t
h
e
i
n
itial a
s
s
i
g
n
m
e
n
t
m
atr
ix
(
Ma
k
esp
an
initial
).
2
=
1
2
[
(
−
1
)
∑
∑
∑
2
=
1
=
1
=
1
−
∑
∑
∑
∑
=
1
=
1
=
1
=
1
≠
]
(
2
4
)
=
√
1
2
[
(
−
1
)
∑
∑
∑
2
=
1
=
1
=
1
−
∑
∑
∑
∑
=
1
=
1
=
1
=
1
≠
]
(
2
5
)
s
u
b
j
ec
t
t
o
:
∑
=
1
=
1
∀
(
2
6
)
{
0
,
1
}
∀
∀
,
=
1
,
2
,
…
.
.
=
1
,
2
,
…
…
.
(
2
7
)
∑
=
1
≤
∀
=
1
,
2
,
…
.
,
(
2
8
)
3
.
4
.
T
he
H
L
B
G
A
ph
a
s
e
s
T
h
e
p
r
o
p
o
s
ed
HL
B
G
A
a
lg
o
r
ith
m
h
as
t
w
o
p
h
ases
.
Firs
t,
HI
L
B
al
g
o
r
ith
m
i
s
p
r
o
p
o
s
ed
as
a
n
e
w
tr
ad
itio
n
al
alg
o
r
it
h
m
i
n
o
r
d
er
to
d
is
tr
ib
u
te
task
s
o
v
er
all
VM
s
in
an
e
f
f
icien
t
w
a
y
to
av
o
id
o
v
er
lo
ad
ed
o
r
u
n
d
er
lo
ad
ed
VM
s
.
T
h
e
s
ec
o
n
d
p
h
as
e
u
s
e
s
t
h
e
o
u
tp
u
t a
s
an
i
n
itial
p
o
p
u
latio
n
f
o
r
G
A
.
Fi
g
u
r
e
1
s
h
o
w
s
t
h
e
m
ai
n
s
tep
s
o
f
th
e
t
w
o
p
h
a
s
es o
f
t
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
.
T
h
ese
t
w
o
p
h
a
s
es a
r
e
i
m
p
le
m
e
n
ted
as:
3
.
4
.
1
.
P
h
a
s
e
I
:
I
ni
t
i
a
l
p
o
p
ul
a
t
i
o
n
ph
a
s
e
In
th
is
p
h
a
s
e,
t
h
e
HI
L
B
alg
o
r
i
th
m
is
p
r
o
p
o
s
ed
in
o
r
d
er
to
b
alan
ce
t
h
e
lo
ad
an
d
m
in
i
m
ize
m
ak
e
s
p
an
.
A
l
g
o
r
ith
m
s
tr
ateg
y
is
b
ased
o
n
m
o
v
i
n
g
ta
s
k
s
f
r
o
m
h
ea
v
y
lo
ad
ed
m
ac
h
in
e
s
to
least lo
ad
ed
o
n
es a
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
H
yb
r
id
lo
a
d
b
a
la
n
ce
b
a
s
ed
o
n
g
en
etic
a
lg
o
r
ith
m
in
clo
u
d
e
n
viro
n
men
t (
W
a
la
a
S
a
b
er)
2483
Fig
u
r
e
1
.
Flo
w
s
tr
u
ct
u
r
e
o
f
th
e
HL
B
G
A
al
g
o
r
ith
m
a.
HI
L
B
g
ets
an
i
n
itial
as
s
i
g
n
m
en
t
s
o
lu
t
io
n
f
o
r
all
th
e
s
u
b
m
i
tted
task
s
o
v
er
all
th
e
av
ailab
le
r
eso
u
r
ce
s
b
y
ass
i
g
n
in
g
t
h
e
ta
s
k
w
it
h
m
in
.
c
o
m
p
let
io
n
ti
m
e
to
th
e
co
r
r
esp
o
n
d
in
g
m
ac
h
i
n
e.
T
h
en
,
i
t
ca
lc
u
lates
m
a
k
esp
a
n
an
d
lo
ad
d
ev
iatio
n
f
o
r
th
i
s
i
n
it
ial
s
o
lu
tio
n
as t
h
e
cu
r
r
en
t
m
a
k
esp
an
,
an
d
lo
ad
d
ev
iatio
n
,
r
es
p
ec
tiv
el
y
.
b.
HI
L
B
ca
lc
u
lates
t
h
e
co
m
p
leti
o
n
ti
m
e
o
f
all
th
e
av
a
ilab
le
VM
s
.
I
t
tr
ie
s
to
m
o
v
e
t
h
e
s
h
o
r
test
tas
k
i
n
t
h
e
h
ea
v
ie
s
t
lo
ad
ed
r
eso
u
r
ce
to
th
e
least
lo
ad
ed
r
eso
u
r
ce
.
HI
L
B
co
n
s
id
er
s
t
w
o
co
n
d
itio
n
s
f
o
r
ac
ce
p
tin
g
an
y
n
e
w
ta
s
k
m
o
v
e
m
e
n
t
f
r
o
m
o
n
e
VM
to
a
n
o
t
h
er
.
I
t
g
u
ar
a
n
te
es
t
h
at
ea
c
h
n
e
w
tas
k
m
o
v
e
m
en
t
i
s
a
f
o
r
w
ar
d
s
tep
in
en
h
a
n
cin
g
m
ak
e
s
p
an
a
n
d
lo
ad
d
ev
iatio
n
.
T
h
e
t
w
o
co
n
d
itio
n
s
ar
e
:
(
1
)
New
Ma
k
es
p
an
<=
C
u
r
r
en
t
Ma
k
esp
a
n
,
an
d
(
2
)
Ne
w
lo
ad
d
ev
iatio
n
<=
C
u
r
r
en
t
lo
ad
d
ev
iatio
n.
HI
L
B
m
a
k
es
a
ll
t
h
e
av
a
ilab
le
task
m
o
v
e
m
e
n
t
s
f
o
r
t
h
e
cu
r
r
e
n
t
h
ea
v
ie
s
t
lo
ad
ed
VM
to
an
y
o
n
e
o
f
t
h
e
r
e
m
ain
in
g
VM
s
.
HI
L
B
r
ep
ea
ts
th
ese
p
r
ev
io
u
s
o
p
er
atio
n
s
o
n
all
th
e
av
ailab
le
r
eso
u
r
ce
s
.
I
t
b
alan
ce
s
th
e
lo
ad
o
v
er
all
r
eso
u
r
ce
s
ev
e
n
v
er
y
s
l
o
w
o
n
e
s
i
n
a
w
a
y
th
at
ac
h
iev
es
h
i
g
h
lo
ad
b
alan
ci
n
g
a
n
d
o
p
ti
m
u
m
co
m
p
letio
n
ti
m
e.
T
h
is
al
g
o
r
ith
m
av
o
id
s
s
t
ar
v
atio
n
p
r
o
b
le
m
b
et
w
ee
n
V
Ms.
3
.
4
.
2
.
P
h
a
s
e
I
I
:
G
A
p
h
a
s
e
HL
B
G
A
al
g
o
r
ith
m
r
elie
s
o
n
GA
as
a
p
o
w
er
f
u
l
s
o
lu
t
io
n
f
o
r
n
o
n
lin
ea
r
p
r
o
g
r
a
m
m
in
g
o
p
ti
m
izat
io
n
NP
-
co
m
p
lete
p
r
o
b
le
m
s
.
Gen
e
tics
i
n
t
h
i
s
al
g
o
r
ith
m
r
elie
s
o
n
th
r
ee
m
a
in
o
p
er
atio
n
s
;
eli
te,
cr
o
s
s
o
v
er
,
an
d
m
u
tatio
n
.
I
n
E
lite
o
p
er
atio
n
,
th
e
alg
o
r
ith
m
c
h
o
o
s
es
th
e
ass
i
g
n
m
e
n
t
m
a
tr
ices
th
a
t
g
i
v
e
th
e
b
est
f
it
n
es
s
f
u
n
ctio
n
s
to
p
ass
to
th
e
n
ex
t
g
en
er
atio
n
.
I
n
cr
o
s
s
o
v
er
a
n
d
m
u
tatio
n
o
p
er
atio
n
s
,
t
h
e
al
g
o
r
ith
m
r
ea
s
s
ig
n
s
ta
s
k
s
to
d
if
f
er
en
t
VM
s
to
f
o
r
m
n
e
w
s
o
l
u
tio
n
s
i
n
d
if
f
er
en
t
w
a
y
s
.
C
r
o
s
s
o
v
er
r
ec
o
m
b
i
n
es
ea
c
h
t
w
o
ass
i
g
n
m
en
t
m
atr
ices
t
o
f
o
r
m
t
w
o
n
e
w
o
n
e
s
w
h
ic
h
p
r
ac
ticall
y
m
ea
n
r
ea
s
s
ig
n
m
en
t
o
f
ta
s
k
s
to
f
o
r
m
t
w
o
n
e
w
s
o
l
u
tio
n
s
.
T
h
e
r
ec
o
m
b
i
n
atio
n
m
u
s
t
b
e
d
o
n
e
o
n
a
co
m
p
lete
r
o
w
b
a
s
is
i.e
.
,
co
m
p
lete
r
o
w
s
ar
e
s
w
ap
p
ed
b
et
w
ee
n
m
atr
ices.
W
h
ile
in
m
u
tatio
n
,
r
an
d
o
m
ch
an
g
es
d
o
n
e
to
a
s
i
n
g
le
a
s
s
ig
n
m
e
n
t
m
atr
i
x
.
A
lg
o
r
it
h
m
1
s
h
o
w
s
th
e
m
ai
n
p
r
o
ce
s
s
es o
f
th
e
p
r
o
p
o
s
ed
HL
B
GA
.
Alg
o
rit
h
m
1
:
T
he
pro
po
s
ed
H
L
B
G
A
Begin
//
start Phase I: HILB Algorithm
1.
Fo
r
an
y
su
bm
it
te
d
ta
sk
Ti
calculate
co
mpletion
time
Ctij
fo
r
Re
so
ur
ce
j
Rj
Ctij=Etij+rtj;
2. while the non
-
submitted task list is not empty
3. Find task I with minimum completion time and assign to corresponding Resource
4. Remove the task from non
-
submitted task list and update resource ready time rtj
5. End
6. Calculate current Makespan Mc and load deviation Lc
7. Add all VMs to Resources list R
8. while list R not empty
9. Find Heaviest loaded VM RH in Resource List
10. Add other Resources to load list L and find least load Resource RL
11. move the
shortest task in the heaviest loaded resource to RL
12. a. IF New Makespan Mn <= Mc And New Load Deviation Ln<= Lc
b.
Then Mc= Mn and Lc=Ln And Goto step 9
c.
Else if L is not empty
d.
Then undo step 11 And remove RL from List
L And go to step 11
e.
Else remove RH from list R And go to step 8
13. End
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
3
,
J
u
n
e
2
0
2
1
:
2
4
7
7
-
2489
2484
// start Phase II: Applying GA
14. Initialize population by adding the result of phase 1 to random initial population
15. Set initial parameters
E
El
it
e
co
un
t
fr
action,
P
populati
on
s
iz
e,
C
Cr
os
so
ve
r
fr
ac
t
io
n
G
nu
mb
er
of
generations
16. Calculate number of variables V= n×m
17. Set mutation fraction U= 1
-
( E + C )
18. while termination condition not satisfied
19. Evaluate each chromosome using fitness function
20
.
Ch
oo
se
(E
×
P)
c
hr
om
os
om
es
wi
th
th
e
be
st
fi
tn
es
s
fu
nc
ti
on
as
el
i
te
fo
r
th
e
ne
xt
generation
21. Select (C × P) chromosomes for crossover operation
22. For k=1 to ( C × P)
23. Select two random chromosomes as input for crossover
operation
24. Perform crossover operation on selected chromosomes
25. Select the two output chromosomes to the next generation
26. End For
27. Select ( U × P ) chromosomes for mutation operation
28. For k=1 to ( U × P)
29.
Select one random chromosome as input for mutation operation
30. Perform Mutation process on the selected chromosome
31. Select the output chromosome to the next generation
32. End For
33. Replace the current population by new generati
on
34. End
3
.
5
.
Co
m
plex
it
y
o
f
H
L
B
G
A
T
h
e
HL
B
GA
is
b
ased
o
n
t
w
o
m
ai
n
p
h
ases
.
I
n
t
h
e
f
ir
s
t
p
h
a
s
e
,
it
r
u
n
s
th
e
HI
L
B
.
T
h
e
tim
e
co
m
p
le
x
it
y
o
f
t
h
is
p
h
a
s
e
i
s
b
ased
o
n
t
h
e
n
u
m
b
er
o
f
t
h
e
m
o
v
e
m
e
n
t
s
t
h
a
t
p
er
f
o
r
m
ed
to
r
ea
ch
th
e
i
n
itia
l
p
o
p
u
latio
n
.
I
t
ca
n
b
e
co
m
p
u
ted
as:
O(
n
1
)
.
I
n
th
e
s
ec
o
n
d
p
h
ase,
th
e
H
L
B
G
A
r
u
n
s
th
e
G
A
.
T
h
e
co
m
p
le
x
it
y
in
th
is
p
h
ase
ca
n
b
e
co
m
p
u
ted
as
O(
G×
N)
[
3
5
]
.
C
o
m
p
ar
in
g
t
h
e
ti
m
e
co
m
p
lex
it
y
o
f
t
h
e
f
ir
s
t
p
h
a
s
e
to
th
e
s
ec
o
n
d
p
h
ase,
it
w
a
s
f
o
u
n
d
th
at
n
1
<<
G×
N,
s
o
it
c
an
b
e
n
e
g
lecte
d
.
T
h
er
ef
o
r
e,
t
h
e
to
tal
co
m
p
le
x
it
y
o
f
t
h
e
H
L
B
G
A
a
lg
o
r
it
h
m
is
:
O(
G×
N)
.
T
h
e
in
itial
p
o
p
u
lati
o
n
th
at
i
s
u
s
ed
in
t
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
h
elp
s
t
h
e
g
en
e
ti
cs
to
r
ea
ch
a
b
etter
s
o
lu
tio
n
w
it
h
less
p
o
p
u
latio
n
s
ize
a
n
d
n
u
m
b
er
o
f
g
e
n
e
r
atio
n
s
w
h
ic
h
d
ec
r
ea
s
es
t
h
e
co
m
p
lex
i
t
y
o
f
th
e
alg
o
r
ith
m
.
T
ab
le
2
s
h
o
w
s
t
h
e
t
i
m
e
co
m
p
le
x
it
y
o
f
t
h
e
H
L
B
GA
a
n
d
a
d
escr
ip
tio
n
o
f
th
e
co
m
p
lex
i
t
y
p
ar
a
m
eter
s
.
T
ab
le
2.
T
im
e
co
m
p
le
x
it
y
o
f
t
h
e
H
L
B
G
A
A
l
g
o
r
i
t
h
m
T
i
m
e
c
o
m
p
l
e
x
i
t
y
D
e
s
c
r
i
p
t
i
o
n
P
h
a
s
e
I
:
H
I
L
B
O(n
1
)
n
1
:
N
u
m
b
e
r
o
f
mo
v
e
s
t
o
r
e
a
c
h
t
h
e
i
n
i
t
i
a
l
p
o
p
u
l
a
t
i
o
n
P
h
a
s
e
I
I
:
G
A
O
(
G
×
N)
G:
N
u
m
b
e
r
o
f
g
e
n
e
r
a
t
i
o
n
s
N:
n
×
m
×
P
(
t
i
m
e
o
v
e
r
h
e
a
d
o
f
a
l
l
c
h
r
o
m
o
so
m
e
s
)
w
h
e
r
e
n
×
m
:
N
u
m
b
e
r
o
f
v
a
r
i
a
b
l
e
s
t
h
a
t
r
e
p
r
e
se
n
t
t
h
e
n
u
m
b
e
r
o
f
g
e
n
e
s
i
n
e
a
c
h
c
h
r
o
m
o
s
o
me
(
t
i
m
e
o
v
e
r
h
e
a
d
o
f
o
n
e
c
h
r
o
mo
s
o
me
)
P:
P
o
p
u
l
a
t
i
o
n
s
i
z
e
(
n
u
m
b
e
r
o
f
c
h
r
o
m
o
s
o
m
e
s
i
n
e
a
c
h
g
e
n
e
r
a
t
i
o
n
)
H
L
B
G
A
O
(
G
×
N)
4.
P
E
RF
O
RM
ANCE E
VA
L
U
AT
I
O
N
S
In
t
h
is
s
ec
tio
n
,
t
h
e
p
er
f
o
r
m
an
ce
o
f
t
h
e
p
r
o
p
o
s
ed
HL
B
GA
al
g
o
r
ith
m
i
s
e
v
al
u
ated
i
n
d
i
f
f
er
e
n
t
en
v
ir
o
n
m
e
n
t
s
a
n
d
co
n
d
itio
n
s
.
T
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
i
s
c
o
m
p
ar
ed
ag
a
in
s
t
v
ar
ian
t
tec
h
n
iq
u
es;
M
in
-
Mi
n
[
8
]
an
d
L
B
I
MM
[
9
]
as
tr
ad
itio
n
al
alg
o
r
ith
m
s
,
P
SO
[
1
0
]
w
it
h
t
w
o
d
if
f
er
en
t
o
b
j
ec
tiv
e
f
u
n
ct
io
n
s
as
m
etah
e
u
r
is
tic
tech
n
iq
u
es
; P
SO1
is
t
h
e
b
asic
P
SO a
lg
o
r
ith
m
w
h
er
e
t
h
e
o
b
j
e
ctiv
e
f
u
n
ctio
n
i
s
to
m
in
i
m
ize
t
h
e
m
ak
e
s
p
an
w
h
il
e
P
SO2
is
an
u
p
d
ated
v
er
s
io
n
o
f
t
h
e
b
asic
P
SO
a
lg
o
r
it
h
m
w
h
er
e
th
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
is
t
o
m
i
n
i
m
ize
t
h
e
lo
ad
d
ev
iatio
n
,
a
n
d
G
A
[
1
3
]
as
a
n
e
v
o
lu
tio
n
ar
y
al
g
o
r
ith
m
w
h
i
ch
is
th
e
o
r
ig
i
n
al
o
f
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
.
I
n
ad
d
itio
n
,
th
e
co
m
p
ar
is
o
n
i
n
cl
u
d
es
th
e
p
r
o
p
o
s
ed
HI
L
B
th
at
r
ep
r
esen
ts
th
e
i
n
it
ial
p
o
p
u
lati
o
n
o
f
HL
B
G
A
.
T
h
e
ev
alu
a
tio
n
i
s
b
ased
o
n
th
e
r
es
u
lts
o
f
s
i
m
u
latio
n
d
o
n
e
u
s
in
g
C
lo
u
d
Si
m
[
3
5
].
4
.
1
.
Si
m
ula
t
io
n
o
v
er
v
iew
C
lo
u
d
Si
m
i
s
a
s
i
m
u
latio
n
to
o
l
th
at
s
i
m
u
lates
th
e
b
e
h
av
io
r
o
f
lo
ad
b
alan
cin
g
al
g
o
r
ith
m
s
w
h
en
r
u
n
o
n
r
ea
l
d
ata
ce
n
ter
s
.
I
t
w
as
u
s
ed
t
o
test
th
e
p
er
f
o
r
m
a
n
ce
o
f
t
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
a
n
d
co
m
p
ar
e
th
e
r
esu
lt
s
w
it
h
th
e
o
t
h
er
al
g
o
r
ith
m
s
in
ter
m
s
o
f
m
a
k
esp
an
,
r
eso
u
r
ce
u
til
iz
atio
n
,
a
n
d
lo
ad
s
ta
n
d
ar
d
d
ev
i
atio
n
[
2
5
]
.
T
ab
le
2
s
h
o
w
s
t
h
e
C
lo
u
d
Si
m
co
n
f
i
g
u
r
atio
n
f
o
r
th
e
f
o
u
r
s
i
m
u
lati
o
n
s
u
s
ed
to
test
th
e
b
eh
a
v
i
o
r
o
f
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
in
d
if
f
er
e
n
t
r
u
n
n
i
n
g
co
n
d
itio
n
s
.
E
ac
h
s
i
m
u
lat
io
n
w
a
s
r
u
n
1
0
5
ti
m
es
an
d
t
h
e
av
e
r
ag
e
w
as
co
n
s
id
er
ed
in
th
e
r
es
u
lt
s
.
T
h
e
p
ar
am
eter
s
o
f
G
A
an
d
P
SO a
r
e
s
h
o
w
n
in
T
ab
le
3
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
H
yb
r
id
lo
a
d
b
a
la
n
ce
b
a
s
ed
o
n
g
en
etic
a
lg
o
r
ith
m
in
clo
u
d
e
n
viro
n
men
t (
W
a
la
a
S
a
b
er)
2485
T
ab
le
3
.
C
lo
u
d
Si
m
co
n
f
i
g
u
r
ati
o
n
s
S
i
mu
l
a
t
i
o
n
_
1
S
i
mu
l
a
t
i
o
n
_
2
N
u
mb
e
r
o
f
D
a
t
a
c
e
n
t
e
r
s
1
1
N
u
mb
e
r
o
f
H
o
st
s
1
1
N
u
mb
e
r
o
f
V
M
s
4
5
N
u
mb
e
r
o
f
T
a
sk
s
10
:
1
5
0
15
T
a
sk
l
e
n
g
t
h
(
M
I
)
2
0
0
:
3
0
0
0
1
5
0
:
3
0
0
V
M
S
c
h
e
d
u
l
e
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p
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i
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sh
a
r
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C
l
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d
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A
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p
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t
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se
t
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P
a
r
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t
e
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V
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e
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r
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.
8
El
i
t
e
0
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0
5
M
a
x
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n
u
m
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e
r
o
f
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e
n
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i
o
n
s
2
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P
o
p
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l
a
t
i
o
n
s
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z
e
mi
n
.
(
1
0
×
n
u
mb
e
r
o
f
g
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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g
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m
p
ar
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o
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o
f
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m
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n
3
.
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t
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e
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at
t
h
e
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o
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o
s
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ith
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i
s
m
in
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m
ized
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n
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m
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h
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e
o
th
e
r
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o
r
ith
m
s
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g
u
r
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o
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e
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ar
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f
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m
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ith
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ith
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Fig
u
r
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5
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k
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n
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ir
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ts
Fig
u
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if
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ir
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Fig
u
r
e
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.
Utilizatio
n
i
n
d
if
f
er
e
n
t e
n
v
ir
o
n
m
e
n
ts
Evaluation Warning : The document was created with Spire.PDF for Python.