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g
th
e
o
p
ti
m
al
s
o
lu
tio
n
.
T
h
u
s
,
B
B
-
B
C
co
u
ld
b
e
s
elec
ted
a
s
a
p
r
o
p
er
ch
o
ice
f
o
r
a
v
ar
iet
y
o
f
d
if
f
er
en
t
o
p
ti
m
izatio
n
an
d
i
n
tr
ac
tab
l
e
p
r
o
b
lem
s
.
W
h
ile
th
e
B
B
-
B
C
is
u
s
ed
in
s
e
v
er
al
wo
r
k
s
,
it
s
u
f
f
er
s
f
r
o
m
d
is
ad
v
a
n
ta
g
es
s
u
c
h
as
s
lo
w
co
n
v
er
g
e
n
ce
s
p
ee
d
an
d
tr
ap
p
in
g
in
lo
ca
l o
p
tim
u
m
s
o
l
u
tio
n
s
av
ailab
le
in
m
o
s
t o
f
th
e
o
p
ti
m
iza
tio
n
p
r
o
b
lem
s
[
2
5
]
.
T
h
e
p
r
o
b
l
e
m
o
f
co
n
v
er
g
in
g
to
lo
ca
l o
p
tim
u
m
s
o
l
u
tio
n
s
o
cc
u
r
r
ed
f
o
r
th
e
B
B
-
B
C
ap
p
r
o
ac
h
d
u
e
to
g
r
ee
d
il
y
lo
o
k
i
n
g
ar
o
u
n
d
th
e
b
est ev
er
f
o
u
n
d
s
o
lu
tio
n
s
.
Du
e
to
its
ex
p
lo
r
ativ
e
n
at
u
r
e,
B
B
-
B
C
lack
s
a
s
p
len
d
id
ex
p
lo
itatio
n
f
ac
to
r
.
Su
c
h
o
p
ti
m
izatio
n
s
tr
ateg
ie
s
s
h
o
u
ld
h
a
v
e
a
m
ec
h
an
is
m
to
m
a
k
e
a
tr
ad
e
-
o
f
f
b
etw
ee
n
ex
p
lo
r
atio
n
an
d
ex
p
lo
ita
tio
n
.
T
h
e
p
r
o
p
o
s
ed
E
B
C
alg
o
r
ith
m
ta
k
es
ad
v
a
n
ta
g
es
o
f
t
y
p
ical
B
B
-
B
C
alg
o
r
ith
m
an
d
en
h
an
ce
s
it w
i
th
th
e
p
r
o
p
er
b
alan
ce
b
etw
ee
n
ex
p
lo
r
atio
n
an
d
e
x
p
lo
itatio
n
f
ac
to
r
s
.
P
r
o
p
o
s
ed
E
B
C
alg
o
r
ith
m
h
as
b
ee
n
ev
a
lu
ated
i
n
s
tan
d
ar
d
I
E
E
E
1
1
8
&
p
r
ac
tical
1
9
1
b
u
s
test
s
y
s
te
m
s
.
Si
m
u
latio
n
r
es
u
lts
s
h
o
w
th
at
o
u
r
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
o
u
tp
er
f
o
r
m
s
all
t
h
e
e
n
titl
ed
r
ep
o
r
ted
alg
o
r
ith
m
s
i
n
m
i
n
i
m
i
za
tio
n
o
f
r
ea
l p
o
w
er
lo
s
s
.
2.
P
RO
B
L
E
M
F
O
R
M
UL
AT
I
O
N
T
h
e
o
p
tim
al
p
o
w
er
f
lo
w
p
r
o
b
l
e
m
is
tr
ea
ted
as
a
g
en
er
al
m
i
n
i
m
izatio
n
p
r
o
b
le
m
w
it
h
co
n
s
tr
ain
ts
,
a
n
d
ca
n
b
e
m
at
h
e
m
a
ticall
y
w
r
itte
n
in
th
e
f
o
llo
w
i
n
g
f
o
r
m
:
Min
i
m
ize
f
(
x
,
u
)
(
1
)
s
u
b
j
ec
t to
g
(
x
,
u
)
=0
(
2
)
an
d
h
(
x
,
u
)
≤
0
(
3
)
w
h
er
e
f
(
x
,
u
)
i
s
th
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
.
g
(
x
.
u
)
a
n
d
h
(
x
,
u
)
ar
e
r
esp
ec
tiv
el
y
th
e
s
et
o
f
eq
u
a
lit
y
a
n
d
in
eq
u
alit
y
co
n
s
tr
ain
ts
.
x
i
s
th
e
v
ec
to
r
o
f
s
tate
v
ar
iab
les,
an
d
u
i
s
t
h
e
v
ec
to
r
o
f
co
n
tr
o
l v
ar
iab
les.
T
h
e
s
tate
v
ar
iab
les ar
e
th
e
lo
ad
b
u
s
es (
P
Q
b
u
s
es)
v
o
ltag
e
s
,
an
g
le
s
,
th
e
g
en
er
ato
r
r
ea
ctiv
e
p
o
w
er
s
an
d
t
h
e
s
lac
k
ac
tiv
e
g
e
n
er
ato
r
p
o
w
er
:
x
=
(
P
g1
,
θ
2
,
.
.
,
θ
N
,
V
L1
,
.
,
V
L
N
L
,
Q
g1
,
.
.
,
Q
gng
)
T
(
4
)
T
h
e
co
n
tr
o
l
v
ar
iab
les
ar
e
th
e
g
e
n
er
ato
r
b
u
s
v
o
lta
g
es,
t
h
e
s
h
u
n
t
ca
p
ac
ito
r
s
/
r
ea
cto
r
s
an
d
th
e
tr
an
s
f
o
r
m
er
s
tap
-
s
etti
n
g
s
:
u
=
(
V
g
,
T
,
Q
c
)
T
(
5
)
or
u
=
(
V
g1
,
…
,
V
gng
,
T
1
,
.
.
,
T
Nt
,
Q
c1
,
.
.
,
Q
cNc
)
T
(
6
)
W
h
er
e
n
g
,
n
t
an
d
n
c
ar
e
th
e
n
u
m
b
er
o
f
g
e
n
er
ato
r
s
,
n
u
m
b
er
o
f
tap
tr
an
s
f
o
r
m
er
s
an
d
th
e
n
u
m
b
er
o
f
s
h
u
n
t
co
m
p
e
n
s
ato
r
s
r
esp
ec
ti
v
el
y
.
3.
O
B
J
E
CT
I
V
E
F
UNC
T
I
O
N
3
.
1
.
Act
i
v
e
po
w
er
lo
s
s
T
h
e
o
b
j
ec
tiv
e
o
f
th
e
r
ea
ctiv
e
p
o
w
er
d
is
p
atch
i
s
to
m
i
n
i
m
ize
t
h
e
ac
tiv
e
p
o
w
er
lo
s
s
i
n
th
e
tr
a
n
s
m
i
s
s
io
n
n
et
w
o
r
k
,
w
h
ich
ca
n
b
e
d
escr
ib
ed
as
f
o
llo
w
s
:
=
=
∑
∈
(
2
+
2
−
2
)
(
7
)
Or
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8938
IJ
-
AI
Vo
l.
7
,
No
.
4
,
Dec
em
b
er
201
8
:
1
9
0
–
1
9
6
192
=
=
∑
−
=
+
∑
−
≠
∈
(
8
)
w
h
er
e
g
k
: is t
h
e
co
n
d
u
cta
n
ce
o
f
b
r
an
ch
b
et
w
ee
n
n
o
d
es i
an
d
j
,
Nb
r
: is th
e
to
tal
n
u
m
b
er
o
f
tr
an
s
m
i
s
s
i
o
n
li
n
es i
n
p
o
w
er
s
y
s
te
m
s
.
P
d
:
is
th
e
to
tal
ac
tiv
e
p
o
w
er
d
e
m
a
n
d
,
P
gi
:
is
t
h
e
g
e
n
er
ato
r
ac
tiv
e
p
o
w
er
o
f
u
n
i
t
i,
an
d
P
g
salc
k
:
i
s
th
e
g
e
n
er
ato
r
ac
tiv
e
p
o
w
er
o
f
s
lack
b
u
s
.
3
.
2
.
Vo
l
t
a
g
e
pro
f
ile
i
m
pro
v
e
m
e
nt
Fo
r
m
in
i
m
iz
in
g
t
h
e
v
o
lta
g
e
d
ev
iatio
n
i
n
P
Q
b
u
s
e
s
,
th
e
o
b
j
ec
t
iv
e
f
u
n
ctio
n
b
ec
o
m
e
s
:
=
+
×
(
9
)
w
h
er
e
ω
v
: is a
w
ei
g
h
t
in
g
f
ac
to
r
o
f
v
o
ltag
e
d
ev
ia
tio
n
.
VD
is
th
e
v
o
lta
g
e
d
ev
iatio
n
g
i
v
en
b
y
:
=
∑
|
−
1
|
=
1
(
1
0
)
3
.
3
.
E
qu
a
lity
Co
ns
t
ra
int
T
h
e
eq
u
alit
y
co
n
s
tr
ai
n
t
g
(
x
,
u
)
o
f
th
e
OR
P
D
p
r
o
b
lem
is
r
ep
r
esen
ted
b
y
th
e
p
o
w
er
b
alan
ce
eq
u
atio
n
,
w
h
er
e
th
e
to
tal
p
o
w
er
g
en
er
at
i
o
n
m
u
s
t c
o
v
er
t
h
e
to
tal
p
o
w
er
d
em
a
n
d
an
d
t
h
e
p
o
w
er
lo
s
s
e
s
:
=
+
(
1
1
)
T
h
is
eq
u
atio
n
i
s
s
o
l
v
ed
b
y
r
u
n
n
in
g
Ne
w
to
n
R
ap
h
s
o
n
lo
ad
f
lo
w
m
et
h
o
d
,
b
y
ca
lcu
la
tin
g
t
h
e
a
ctiv
e
p
o
w
er
o
f
s
lac
k
b
u
s
to
d
eter
m
in
e
ac
t
iv
e
p
o
w
er
lo
s
s
.
3
.
4
.
I
nequ
a
lity
Co
ns
t
ra
ints
T
h
e
in
eq
u
alit
y
co
n
s
tr
ain
t
s
h
(
x
,
u
)
r
ef
lect
th
e
li
m
its
o
n
co
m
p
o
n
en
t
s
in
t
h
e
p
o
w
er
s
y
s
te
m
as
w
ell
as
t
h
e
li
m
it
s
cr
ea
ted
to
en
s
u
r
e
s
y
s
te
m
s
ec
u
r
it
y
.
Up
p
er
an
d
lo
w
er
b
o
u
n
d
s
o
n
t
h
e
ac
tiv
e
p
o
w
er
o
f
s
lac
k
b
u
s
,
a
n
d
r
ea
ctiv
e
p
o
w
er
o
f
g
e
n
er
ato
r
s
:
≤
≤
(
1
2
)
≤
≤
,
∈
(
1
3
)
Up
p
er
an
d
lo
w
er
b
o
u
n
d
s
o
n
th
e
b
u
s
v
o
lta
g
e
m
a
g
n
it
u
d
es:
≤
≤
,
∈
(
1
4
)
Up
p
er
an
d
lo
w
er
b
o
u
n
d
s
o
n
th
e
tr
an
s
f
o
r
m
er
s
tap
r
atio
s
:
≤
≤
,
∈
(
1
5
)
Up
p
er
an
d
lo
w
er
b
o
u
n
d
s
o
n
th
e
co
m
p
e
n
s
ato
r
s
r
ea
ct
i
v
e
p
o
w
e
r
s
:
≤
≤
,
∈
(
1
6
)
W
h
er
e
N
is
t
h
e
to
tal
n
u
m
b
er
o
f
b
u
s
es,
N
T
i
s
t
h
e
to
tal
n
u
m
b
er
o
f
T
r
an
s
f
o
r
m
er
s
;
N
c
is
t
h
e
to
t
al
n
u
m
b
er
o
f
s
h
u
n
t
r
ea
ctiv
e
co
m
p
en
s
ato
r
s
.
4.
B
I
G
B
ANG
-
B
I
G
CRU
NCH
O
P
T
I
M
I
Z
AT
I
O
N
AL
G
O
R
I
T
H
M
T
w
o
p
r
o
m
in
e
n
t
t
h
eo
r
ies
s
u
b
s
is
t
n
u
m
er
o
u
s
t
h
eo
r
ies
r
eg
ar
d
in
g
h
o
w
t
h
e
u
n
i
v
er
s
e
d
ev
elo
p
ed
,
in
th
i
s
r
eg
ar
d
ar
e
s
p
ec
if
icall
y
B
ig
b
a
n
g
a
n
d
B
ig
cr
u
n
c
h
,
h
y
p
o
th
e
s
is
.
E
r
o
l
et
al.
,
[
2
1
]
em
p
lo
y
o
f
th
ese
h
y
p
o
t
h
esi
s
an
d
lau
n
c
h
ed
t
h
e
B
B
-
B
C
o
p
ti
m
iz
atio
n
al
g
o
r
ith
m
.
A
cc
o
r
d
in
g
to
th
i
s
h
y
p
o
th
e
s
is
,
o
w
in
g
to
d
e
b
au
ch
er
y
,
B
i
g
B
an
g
p
h
ase
p
r
o
d
u
ce
s
ar
b
itra
r
in
ess
alo
n
g
w
it
h
m
u
d
d
le,
ev
e
n
as
i
n
th
e
B
ig
C
r
u
n
c
h
p
h
ase
t
h
e
ar
b
itra
r
ily
p
r
o
d
u
ce
d
p
ar
ticles
w
il
l
b
e
h
ag
g
ar
d
in
to
an
o
r
d
er
.
B
ig
B
an
g
-
B
i
g
C
r
u
n
c
h
alg
o
r
ith
m
(
B
B
-
B
C
)
co
m
m
e
n
c
e
w
it
h
th
e
b
i
g
b
an
g
s
eg
m
e
n
t
t
h
r
o
u
g
h
th
e
p
r
o
d
u
cti
o
n
o
f
ar
b
itra
r
y
p
o
in
ts
i
n
t
h
e
r
eg
io
n
o
f
a
p
r
i
m
ar
il
y
elec
ted
p
o
in
t
a
n
d
it
ai
m
s
to
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Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
-
AI
I
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N:
2252
-
8938
Dw
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W
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m
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al
l c
an
d
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ates.
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l
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t
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ce
s
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eq
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−
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1
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e
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v
al
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l
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m
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ss f
u
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u
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b
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s
O
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p
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a.
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n
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t
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mi
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a
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p
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p
r
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t
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y
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n
st
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n
t
s
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c.
n
u
m
_
o
f
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st
a
r
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n
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mb
e
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o
f
st
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r
s
d.
d
i
m
=
d
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me
n
s
i
o
n
o
f
so
l
u
t
i
o
n
e.
r
e
p
l
i
c
a
t
e
f.
Bi
g
B
a
n
g
Ph
a
se
:
⊲
f
a
b
r
i
c
a
t
e
mass
i
n
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h
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r
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g
i
o
n
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p
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l
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mi
n
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n
t
g.
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m
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st
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r
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h.
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i.
mass
[
i
,
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]
=
f
a
b
r
i
c
a
t
e
a
st
a
r
b
a
se
d
o
n
(
1
8
)
j.
e
n
d
f
o
r
k.
e
n
d
f
o
r
l.
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g
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r
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h
P
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se
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c
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c
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mp
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t
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f
mass
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se
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n
(
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)
n.
p
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l
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mi
n
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=
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⊲
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n
v
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e
n
c
e
5.
E
NRI
CH
E
D
B
I
G
B
ANG
-
B
I
G
CRUN
CH
(
E
B
C)
AL
G
O
RIT
H
M
T
w
o
s
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g
n
i
f
ica
n
t
m
ec
h
a
n
is
m
s
o
f
ev
o
lu
tio
n
ar
y
al
g
o
r
ith
m
s
ar
e
E
x
p
lo
r
atio
n
an
d
ex
p
lo
itatio
n
.
I
n
o
r
d
er
to
p
r
o
ce
ed
p
r
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d
u
ctiv
el
y
,
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v
er
y
s
e
ar
ch
alg
o
r
ith
m
n
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d
s
to
p
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e
a
ex
ce
llen
t
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ad
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f
f
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et
w
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n
th
ese
t
w
o
f
ac
to
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s
.
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x
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t
h
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p
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ce
d
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r
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f
p
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f
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s
p
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p
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n
t
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e
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th
er
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a
n
d
is
to
s
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r
ch
in
t
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f
f
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r
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er
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n
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t
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s
.
As an
e
x
a
m
p
le
o
f
ex
p
lo
r
atio
n
i
n
t
h
e
BB
-
B
C
alg
o
r
ith
m
eq
u
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n
(
1
8
)
s
ee
k
s
to
ex
p
lo
r
e
in
th
e
n
e
w
-
f
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g
le
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s
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ily
d
is
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ts
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tio
n
s
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t c
a
n
b
e
o
b
s
er
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f
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m
th
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r
ch
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n
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ch
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u
r
t
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m
o
r
e,
it
is
m
o
r
e
li
k
el
y
to
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s
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m
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lo
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th
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m
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l
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ted
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ter
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s
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e
p
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d
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r
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o
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t
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g
o
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ith
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ter
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n
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f
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e
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lg
o
r
ith
m
,
a
m
e
m
o
r
y
w
it
h
r
estricte
d
s
ize
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s
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ed
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e
p
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ce
d
u
r
e
o
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h
m
in
a
n
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t
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n
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s
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g
g
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t
a
n
o
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el
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h
.
A
t t
h
e
en
d
o
f
ea
c
h
b
ig
b
an
g
an
d
b
ig
cr
u
n
ch
c
y
cles,
t
h
e
co
m
p
u
ted
ce
n
ter
o
f
m
ass
w
i
ll b
e
s
to
r
ed
in
th
e
m
e
m
o
r
y
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8938
IJ
-
AI
Vo
l.
7
,
No
.
4
,
Dec
em
b
er
201
8
:
1
9
0
–
1
9
6
194
A
t
f
ir
s
t i
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elie
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f
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in
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alg
o
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it
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m
[
2
8
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.
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lts
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v
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p
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[
2
6
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.
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n
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m
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d
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Evaluation Warning : The document was created with Spire.PDF for Python.
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RE
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[1
]
O.A
lsa
c
,
a
n
d
B.
S
c
o
tt
,
“
Op
ti
m
a
l
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ste
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d
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7
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[2
]
L
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e
K
Y
,
P
a
ru
Y
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,
Oritz J L
,
A
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A
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ra
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[4
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[6
]
K.Y
L
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Y
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M
P
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rk
,
a
n
d
J.L
Oritz,
“
F
u
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l
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st
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]
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K.Y
.
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,
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2
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[8
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C.
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d
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tan
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4
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6
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[9
]
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n
b
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f
lo
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ti
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h
m
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tr
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Po
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0
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v
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ra
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a
n
d
B
.
Y
e
g
a
n
a
ra
y
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n
a
,
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e
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e
ti
c
a
lg
o
rit
h
m
b
a
se
d
o
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t
i
m
a
l
p
o
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f
lo
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f
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rit
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e
n
h
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n
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m
e
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t
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,
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ro
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e
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e
ra
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issio
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6
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m
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e
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2
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0
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1
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A
.
Be
rizz
i,
C.
Bo
v
o
,
M
.
M
e
rlo
,
a
n
d
M
.
De
l
f
a
n
ti
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“
A
g
a
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p
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se
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ry
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tric P
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[1
2
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-
F
.
Y
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n
g
,
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.
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.
L
a
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C.
-
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L
e
e
,
C.
-
T
.
S
u
,
a
n
d
G
.
W
.
Ch
a
n
g
,
“
Op
ti
m
a
l
se
tt
in
g
o
f
re
a
c
ti
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o
m
p
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ti
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d
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s
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im
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ro
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e
d
v
o
lt
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g
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b
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it
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in
d
e
x
f
o
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g
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il
it
y
e
n
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a
n
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m
e
n
t,
”
In
ter
n
a
ti
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a
l
J
o
u
rn
a
l
o
f
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l
e
c
trica
l
Po
we
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d
En
e
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ms
,
v
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l.
3
7
,
n
o
.
1
,
p
p
.
5
0
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7
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2
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1
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.
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3
]
P
.
Ro
y
,
S
.
G
h
o
sh
a
l,
a
n
d
S
.
T
h
a
k
u
r
,
“
Op
ti
m
a
l
v
a
r
c
o
n
tro
l
f
o
r
im
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ro
v
e
m
e
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ts
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v
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lt
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g
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p
ro
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e
s
a
n
d
f
o
r
re
a
l
p
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w
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r
lo
ss
m
in
i
m
iza
ti
o
n
u
sin
g
b
i
o
g
e
o
g
ra
p
h
y
b
a
se
d
o
p
ti
m
iza
ti
o
n
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
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lec
trica
l
P
o
w
e
r
a
n
d
E
n
e
r
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y
S
y
ste
ms
,
v
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l.
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3
,
n
o
.
1
,
p
p
.
8
3
0
-
8
3
8
,
2
0
1
2
.
[1
4
]
B.
V
e
n
k
a
tes
h
,
G
.
S
a
d
a
siv
a
m
,
a
n
d
M
.
Kh
a
n
,
“
A
n
e
w
o
p
t
im
a
l
re
a
c
ti
v
e
p
o
w
e
r
sc
h
e
d
u
li
n
g
m
e
th
o
d
f
o
r
lo
ss
m
in
i
m
iza
ti
o
n
a
n
d
v
o
l
tag
e
sta
b
il
it
y
m
a
r
g
in
m
a
x
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m
iz
a
ti
o
n
u
sin
g
su
c
c
e
ss
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e
m
u
lt
i
-
o
b
jec
ti
v
e
f
u
z
z
y
lp
tec
h
n
iq
u
e
,
”
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E
T
ra
n
sa
c
ti
o
n
s
o
n
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we
r S
y
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ms
,
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l.
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5
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n
o
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2
,
p
p
.
8
4
4
-
8
5
1
,
m
a
y
2
0
0
0
.
[1
5
]
W
.
Y
a
n
,
S
.
L
u
,
a
n
d
D.
Y
u
,
“
A
n
o
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o
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rid
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ry
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ra
m
m
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iq
u
e
,
”
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n
sa
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ti
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n
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n
P
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m
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l.
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9
1
3
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8
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2
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0
4
.
[1
6
]
W
.
Y
a
n
,
F
.
L
iu
,
C
.
Ch
u
n
g
,
a
n
d
K.
W
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n
g
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h
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e
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e
p
o
w
e
r
f
lo
w
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
P
o
w
e
r S
y
ste
ms
,
v
o
l.
2
1
,
n
o
.
3
,
p
p
.
1
1
6
3
-
1
1
6
9
,
A
u
g
.
2
0
0
6
.
[1
7
]
J.
Y
u
,
W
.
Y
a
n
,
W
.
L
i,
C.
C
h
u
n
g
,
a
n
d
K.
W
o
n
g
,
“
A
n
u
n
f
ix
e
d
p
iec
e
w
ise
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
w
e
r
-
f
lo
w
m
o
d
e
l
a
n
d
it
s
a
lg
o
rit
h
m
f
o
r
a
c
-
d
c
s
y
ste
m
s,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
P
o
we
r S
y
ste
ms
,
v
o
l.
2
3
,
n
o
.
1
,
p
p
.
1
7
0
-
1
7
6
,
F
e
b
.
2
0
0
8
.
[1
8
]
F
.
Ca
p
it
a
n
e
sc
u
,
“
A
ss
e
ss
in
g
re
a
c
ti
v
e
p
o
w
e
r
re
se
r
v
e
s w
it
h
re
sp
e
c
t
to
o
p
e
ra
ti
n
g
c
o
n
stra
in
ts
a
n
d
v
o
l
tag
e
sta
b
il
it
y
,
”
IEE
E
T
ra
n
s
a
c
ti
o
n
s o
n
P
o
we
r S
y
ste
ms
,
v
o
l.
2
6
,
n
o
.
4
,
p
p
.
2
2
2
4
-
2
2
3
4
,
n
o
v
.
2
0
1
1
.
[1
9
]
Z.
Hu
,
X.
W
a
n
g
,
a
n
d
G
.
T
a
y
lo
r
,
“
S
to
c
h
a
stic
o
p
t
im
a
l
re
a
c
ti
v
e
p
o
we
r
d
isp
a
tch
:
F
o
rm
u
latio
n
a
n
d
so
l
u
ti
o
n
m
e
th
o
d
,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
E
lec
trica
l
Po
we
r a
n
d
En
e
r
g
y
S
y
ste
ms
,
v
o
l.
3
2
,
n
o
.
6
,
p
p
.
6
1
5
-
6
2
1
,
2
0
1
0
.
[2
0
]
A
.
Ka
r
g
a
rian
,
M
.
Ra
o
o
f
a
t,
a
n
d
M
.
M
o
h
a
m
m
a
d
i,
“
P
r
o
b
a
b
i
li
stic
r
e
a
c
ti
v
e
p
o
we
r
p
ro
c
u
re
m
e
n
t
in
h
y
b
rid
e
lec
tri
c
it
y
m
a
rk
e
ts
w
it
h
u
n
c
e
rtain
l
o
a
d
s,
”
El
e
c
tric P
o
we
r S
y
ste
ms
Res
e
a
r
c
h
,
v
o
l.
8
2
,
n
o
.
1
,
p
p
.
6
8
-
8
0
,
2
0
1
2
.
[2
1
]
O.
K.
Ero
l
a
n
d
I.
Ek
sin
,
“
A
n
e
w
o
p
ti
m
iza
ti
o
n
m
e
th
o
d
:
b
ig
b
a
n
g
-
b
ig
c
r
u
n
c
h
,
”
A
d
v
a
n
c
e
s
i
n
En
g
i
n
e
e
rin
g
S
o
ft
w
a
r
e
,
v
o
l.
3
7
,
n
o
.
2
,
p
p
.
1
0
6
-
1
1
1
,
2
0
0
6
.
[2
2
]
H.
V
e
rm
a
a
n
d
P
.
M
a
f
id
a
r
,
“
T
lb
o
b
a
se
d
v
o
lt
a
g
e
sta
b
le
e
n
v
iro
n
m
e
n
t
f
rien
d
ly
e
c
o
n
o
m
ic
d
isp
a
tch
c
o
n
s
id
e
rin
g
re
a
l
a
n
d
re
a
c
ti
v
e
p
o
we
r
c
o
n
stra
in
ts,
”
J
o
u
r
n
a
l
o
f
T
h
e
In
sti
tu
ti
o
n
o
f
E
n
g
in
e
e
rs
(
In
d
ia
)
:
S
e
ries
B,
v
o
l.
9
4
,
n
o
.
3
,
p
p
.
1
9
3
-
2
0
6
,
2
0
1
3
.
[2
3
]
C.
F
.
Ku
c
u
k
tez
c
a
n
a
n
d
V
.
I.
G
e
n
c
,
“
P
re
v
e
n
ti
v
e
a
n
d
c
o
rre
c
ti
v
e
c
o
n
tr
o
l
a
p
p
li
c
a
ti
o
n
s
in
p
o
w
e
r
s
y
ste
m
s v
ia
b
ig
b
a
n
g
-
b
ig
c
ru
n
c
h
o
p
ti
m
iza
ti
o
n
,
”
I
n
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
P
o
we
r
&
En
e
r
g
y
S
y
ste
ms
,
v
o
l
.
6
7
,
p
p
.
1
1
4
-
1
2
4
,
2
0
1
5
.
[2
4
]
H.
T
a
n
g
,
J.
Z
h
o
u
,
S
.
Xu
e
,
a
n
d
L
.
X
ie,
“
Big
b
a
n
g
-
b
ig
c
ru
n
c
h
o
p
ti
m
iz
a
ti
o
n
f
o
r
p
a
ra
m
e
ter
e
sti
m
a
ti
o
n
i
n
str
u
c
tu
ra
l
s
y
ste
m
s,
”
M
e
c
h
a
n
ica
l
S
y
ste
ms
a
n
d
S
i
g
n
a
l
Pr
o
c
e
ss
in
g
,
v
o
l
.
2
4
,
n
o
.
8
,
p
p
.
2
8
8
8
-
2
8
9
7
,
2
0
1
0
.
[2
5
]
A
.
R.
Jo
rd
e
h
i,
“
A
c
h
a
o
ti
c
-
b
a
se
d
b
ig
b
a
n
g
-
b
ig
c
ru
n
c
h
a
lg
o
rit
h
m
f
o
r
so
lv
in
g
g
lo
b
a
l
o
p
ti
m
iza
ti
o
n
p
r
o
b
lem
s,
”
Ne
u
ra
l
Co
mp
u
t
in
g
a
n
d
A
p
p
li
c
a
ti
o
n
s
,
v
o
l
.
2
5
,
n
o
.
6
,
p
p
.
1
3
2
9
-
1
3
3
5
,
2
0
1
4
.
[2
6
]
B.
X
i
n
g
a
n
d
W
.
-
J.
G
a
o
,
In
n
o
v
a
ti
v
e
Co
m
p
u
tatio
n
a
l
In
telli
g
e
n
c
e
:
A
Ro
u
g
h
G
u
id
e
to
1
3
4
Clev
e
r
A
lg
o
rit
h
m
s.
Ne
w
Y
o
rk
,
NY
:
S
p
rin
g
e
r
,
2
0
1
4
e
d
it
io
n
e
d
.
,
D
e
c
.
2
0
1
3
.
[2
7
]
M
.
M
a
h
d
a
v
i,
M
.
F
e
sa
n
g
h
a
ry
,
a
n
d
E.
Da
m
a
n
g
ir
,
“
A
n
i
m
p
ro
v
e
d
h
a
r
m
o
n
y
se
a
rc
h
a
lg
o
rit
h
m
f
o
r
so
lv
in
g
o
p
ti
m
iza
ti
o
n
p
ro
b
lem
s,
”
Ap
p
li
e
d
M
a
t
h
e
ma
ti
c
s
a
n
d
Co
m
p
u
t
a
ti
o
n
,
v
o
l.
1
8
8
,
p
p
.
1
5
6
7
-
1
5
7
9
,
M
a
y
2
0
0
7
.
[2
8
]
Y
.
S
h
i
a
n
d
R
.
C
.
E
b
e
r
h
a
rt,
“
Emp
i
ric
a
l
stu
d
y
o
f
p
a
rticle
swa
rm
o
p
ti
miza
ti
o
n
,
”
i
n
P
ro
c
e
e
d
i
n
g
s
o
f
th
e
1
9
9
9
Co
n
g
re
ss
o
n
Ev
o
lu
ti
o
n
a
ry
Co
m
p
u
tatio
n
,
1
9
9
9
.
C
EC
9
9
,
v
o
l.
3
,
p
.
1
9
5
0
Vo
l.
3
,
1
9
9
9
.
[2
9
]
IEE
E,
“
T
h
e
IEE
E
3
0
-
b
u
s
tes
t
sy
ste
m
a
n
d
t
h
e
IEE
E
1
1
8
-
tes
t
sy
ste
m
”
,
(1
9
9
3
),
h
tt
p
:
//
ww
w
.
e
e
.
w
a
sh
in
g
to
n
.
e
d
u
/
trse
a
rc
h
/p
stc
a
/
.
[3
0
]
Jia
n
g
tao
Ca
o
,
F
u
li
W
a
n
g
a
n
d
P
i
n
g
L
i,
“
A
n
I
m
p
ro
v
e
d
Bio
g
e
o
g
ra
p
h
y
-
b
a
se
d
Op
ti
m
iza
ti
o
n
A
lg
o
rit
h
m
f
o
r
Op
ti
m
a
l
Re
a
c
ti
v
e
P
o
w
e
r
F
lo
w
”
,
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
C
o
n
tr
o
l
a
n
d
A
u
to
m
a
ti
o
n
V
o
l.
7
,
No
.
3
(
2
0
1
4
),
p
p
.
1
6
1
-
1
7
6
.
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