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m
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I
J
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Vo
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15
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.
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Decem
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er
20
25
,
p
p
.
5
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.
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5045
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TE
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ims
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ts.
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o
st
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th
e
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se
a
rc
h
in
th
e
p
a
s
t
so
lv
e
d
t
h
e
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p
ro
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u
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g
th
e
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c
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rre
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t
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m
o
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ti
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re
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c
ti
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n
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m
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ifi
e
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v
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o
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is
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ro
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se
d
i
n
t
h
i
s
p
a
p
e
r.
Th
e
m
a
in
id
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o
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h
e
m
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ti
o
n
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li
m
it
th
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ra
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d
o
m
n
e
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th
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m
u
tatio
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p
ro
c
e
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b
y
fo
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u
si
n
g
o
n
t
h
e
first,
se
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o
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d
,
a
n
d
th
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d
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b
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n
d
i
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ls.
To
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ti
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ro
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s s
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s sy
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se
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ti
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ize
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u
m
m
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g
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ize
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iza
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lt
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o
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th
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t
th
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ro
p
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se
d
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m
is
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re
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ffe
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ti
v
e
th
a
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m
b
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8
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so
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v
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e
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p
ro
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K
ey
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o
r
d
s
:
AC
tr
an
s
m
is
s
io
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ex
p
an
s
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n
p
lan
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g
Fu
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s
t
Me
tah
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r
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tic
alg
o
r
ith
m
s
Mo
d
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d
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er
e
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tial
ev
o
lu
ti
o
n
alg
o
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ith
m
Op
tim
izatio
n
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
T
h
an
h
L
o
n
g
Du
o
n
g
Facu
lty
o
f
E
lectr
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E
n
g
in
ee
r
in
g
T
ec
h
n
o
lo
g
y
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I
n
d
u
s
tr
ial
Un
iv
er
s
ity
o
f
Ho
C
h
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in
h
C
ity
Ho
C
h
i M
in
h
C
ity
,
Viet
n
am
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m
ail:
d
u
o
n
g
th
an
h
l
o
n
g
@
iu
h
.
ed
u
.
v
n
1.
I
NT
RO
D
UCT
I
O
N
T
r
an
s
p
o
r
tin
g
elec
tr
icity
f
r
o
m
th
e
p
r
o
d
u
cin
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to
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m
er
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th
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p
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im
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a
p
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tr
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s
m
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Ho
wev
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in
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th
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an
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m
is
s
io
n
n
etwo
r
k
i
n
r
ec
en
t y
ea
r
s
[
1
]
.
Nu
m
er
o
u
s
m
eth
o
d
s
h
av
e
b
ee
n
r
esear
ch
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to
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ess
th
is
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s
s
u
e.
Nev
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th
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f
o
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th
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lo
n
g
-
ter
m
p
lan
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i
n
g
h
o
r
izo
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,
tr
a
n
s
m
is
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ex
p
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s
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lan
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is
o
n
e
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f
th
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m
o
s
t
ap
p
r
o
p
r
iate
ap
p
r
o
ac
h
es.
T
h
e
p
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im
a
r
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g
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al
o
f
th
e
tr
an
s
m
is
s
io
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ex
p
an
s
io
n
p
lan
n
in
g
(
T
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P)
p
r
o
b
lem
is
to
d
eter
m
in
e
th
e
l
o
ca
tio
n
an
d
n
u
m
b
er
o
f
ad
d
itio
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al
lin
es
th
at
s
h
o
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ld
b
e
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ed
to
th
e
p
o
wer
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y
s
tem
w
ith
th
e
m
i
n
im
u
m
in
v
estme
n
t
co
s
t
wh
ile
m
ee
tin
g
th
e
p
o
we
r
s
y
s
tem
o
p
e
r
atio
n
co
n
s
tr
ain
ts
.
I
n
g
e
n
er
al,
t
h
er
e
a
r
e
two
m
ajo
r
m
o
d
els
u
s
ed
to
s
o
lv
e
th
e
T
E
P
p
r
o
b
lem
:
th
e
d
ir
ec
t
cu
r
r
en
t
(
DC
)
an
d
alter
n
atin
g
c
u
r
r
en
t
(
AC
)
m
o
d
els.
T
h
e
DC
p
o
we
r
f
l
o
w
(
PF
)
is
u
s
ed
i
n
th
e
DC
m
o
d
el
a
n
d
is
k
n
o
wn
as
a
lin
ea
r
ized
v
er
s
io
n
o
f
th
e
AC
PF
[
2
]
.
Sin
ce
th
e
T
E
P
p
r
o
b
lem
is
a
n
o
n
-
lin
ea
r
an
d
lar
g
e
-
s
ca
le
co
m
b
in
ato
r
ia
l
o
p
tim
izatio
n
p
r
o
b
lem
,
th
e
n
u
m
b
er
o
f
v
iab
le
s
o
lu
tio
n
s
g
r
o
w
s
with
th
e
s
y
s
tem
s
ize.
T
h
er
ef
o
r
e,
th
e
DC
m
o
d
el
h
as
b
ee
n
u
s
ed
as
a
s
im
p
le
v
er
s
io
n
o
f
th
e
AC
m
o
d
el
in
m
an
y
s
tu
d
ies
in
th
e
p
ast
[
3
]
–
[
8
]
to
d
ec
r
ea
s
e
th
e
co
m
p
lex
ity
o
f
th
e
T
E
P p
r
o
b
le
m
.
Ho
wev
er
,
t
h
er
e
ar
e
t
h
r
ee
f
a
cto
r
s
th
at
af
f
ec
t
th
e
ac
c
u
r
ac
y
o
f
th
e
T
E
P
p
r
o
b
le
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
6
,
Decem
b
e
r
20
25
:
5
0
4
5
-
5
0
5
4
5046
u
s
in
g
DC
m
o
d
el.
Firstl
y
,
th
e
s
y
s
tem
v
o
ltag
e
o
n
all
b
u
s
es
is
f
ix
ed
at
1
p
.
u
.
,
lea
d
in
g
t
o
an
u
n
ac
ce
p
tab
le
v
alu
e
f
o
r
th
e
AC
s
y
s
tem
.
Seco
n
d
ly
,
th
e
th
er
m
al
lim
it
o
f
t
h
e
tr
an
s
m
is
s
io
n
lin
e
m
ay
b
e
ex
ce
e
d
ed
b
ec
au
s
e
th
e
r
ea
ctiv
e
p
o
wer
f
lo
w
is
n
o
t
ta
k
en
in
to
ac
co
u
n
t.
T
h
ir
d
ly
,
it
is
h
ar
d
t
o
ev
alu
ate
th
e
p
o
wer
lo
s
s
o
f
a
s
y
s
tem
u
s
in
g
a
DC
m
o
d
el
[
9
]
.
I
n
o
r
d
er
to
in
cr
ea
s
e
th
e
ac
cu
r
ac
y
o
f
th
e
T
E
P
p
r
o
b
lem
,
m
an
y
s
tu
d
ies
h
av
e
s
o
lv
ed
th
e
T
E
P
p
r
o
b
lem
u
s
in
g
th
e
AC
m
o
d
el
in
r
ec
en
t
y
ea
r
s
.
T
h
e
m
u
ltis
tag
e
tech
n
iq
u
e
is
n
o
r
m
ally
ap
p
lie
d
f
o
r
s
o
lv
in
g
AC
tr
an
s
m
is
s
io
n
ex
p
an
s
io
n
p
lan
n
in
g
(
AC
T
E
P)
p
r
o
b
lem
[
9
]
–
[
1
3
]
.
Alth
o
u
g
h
t
h
ese
s
tu
d
ies
h
av
e
s
u
cc
ess
f
u
lly
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en
th
e
o
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tim
al
s
o
lu
tio
n
f
o
r
th
e
AC
T
E
P
p
r
o
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lem
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a
h
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g
e
am
o
u
n
t
o
f
s
im
u
latio
n
tim
e
is
r
e
q
u
ir
ed
.
M
o
r
eo
v
er
,
s
o
lv
in
g
th
e
AC
T
E
P
p
r
o
b
lem
u
s
in
g
a
m
u
ltis
tag
e
tech
n
i
q
u
e
r
eq
u
ir
ed
a
h
ig
h
ly
r
eliab
le
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o
r
ith
m
b
ec
a
u
s
e
th
e
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al
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o
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io
u
s
o
p
tim
al
s
o
lu
tio
n
.
T
h
er
ef
o
r
e,
f
i
n
d
in
g
an
e
f
f
ec
tiv
e
tech
n
iq
u
e
f
o
r
ad
d
r
ess
in
g
th
e
AC
T
E
P p
r
o
b
lem
is
an
im
p
o
r
ta
n
t g
o
al
f
o
r
r
esear
ch
g
r
o
u
p
s
.
O
n
th
e
o
th
er
h
an
d
,
t
h
e
ab
o
v
e
is
s
u
es
ca
n
b
e
s
o
lv
ed
b
y
ap
p
ly
i
n
g
th
e
AC
OPF
f
o
r
m
u
latio
n
,
wh
ich
is
allo
wed
to
s
o
lv
e
th
e
AC
T
E
P
p
r
o
b
lem
in
a
s
in
g
le
s
tag
e,
as
p
r
esen
ted
in
s
tu
d
y
[
1
4
]
.
T
h
e
lo
ad
-
s
h
ed
d
i
n
g
p
r
o
ce
s
s
is
co
n
s
id
er
ed
in
th
is
ap
p
r
o
ac
h
an
d
s
er
v
es
as
a
p
en
alty
v
alu
e
to
elim
in
ate
t
h
e
u
n
r
ea
lis
tic
tr
an
s
m
is
s
io
n
to
p
o
lo
g
ies.
B
ased
o
n
th
e
lo
ad
-
s
h
ed
d
i
n
g
s
tr
ateg
y
,
th
e
AC
o
p
tim
al
p
o
wer
f
lo
w
(
AC
OPF)
f
o
r
m
u
latio
n
is
wid
ely
a
p
p
lied
in
t
h
e
p
a
p
er
s
[
1
5
]
–
[
1
7
]
f
o
r
s
o
lv
in
g
th
e
AC
T
E
P
p
r
o
b
lem
.
Pap
e
r
[
1
6
]
co
m
p
ar
es
th
e
m
eta
-
h
e
u
r
is
tic
alg
o
r
ith
m
ap
p
r
o
ac
h
to
ad
d
r
ess
in
g
th
e
AC
T
E
P
p
r
o
b
lem
with
m
ath
em
atica
l
o
p
ti
m
izatio
n
-
b
ased
a
p
p
r
o
ac
h
es.
T
h
e
d
y
n
am
ic
T
E
P
p
r
o
b
lem
u
s
in
g
th
e
AC
OPF f
o
r
m
u
latio
n
is
ad
d
r
ess
ed
in
s
tu
d
y
[
1
7
]
u
tili
zin
g
a
m
eta
-
h
eu
r
is
tic
ap
p
r
o
ac
h
in
lar
g
e
-
s
ca
le
s
y
s
tem
s
.
T
h
e
o
p
tim
izatio
n
m
eth
o
d
s
f
o
r
s
o
lv
in
g
T
E
P
p
r
o
b
lem
ca
n
b
e
d
iv
id
e
d
in
to
two
b
asic
ap
p
r
o
ac
h
es:
m
ath
em
atica
l
an
d
m
eta
-
h
eu
r
i
s
tic.
I
n
a
m
ath
em
atica
l
ap
p
r
o
ac
h
,
th
e
T
E
P
p
r
o
b
lem
is
s
o
lv
ed
b
y
u
s
in
g
lin
ea
r
p
r
o
g
r
a
m
m
in
g
(
L
P)
[
1
8
]
,
b
r
an
c
h
an
d
b
o
u
n
d
(
B
&
B
)
[
1
9
]
,
an
d
b
en
d
er
d
ec
o
m
p
o
s
itio
n
(
B
D)
[
1
2
]
.
I
n
g
e
n
er
al,
th
e
s
o
lu
tio
n
is
s
u
cc
ess
f
u
lly
g
iv
e
n
b
y
u
s
in
g
a
m
ath
e
m
atica
l
ap
p
r
o
ac
h
i
n
a
s
h
o
r
t
tim
e.
Alth
o
u
g
h
th
is
a
p
p
r
o
ac
h
is
ef
f
ec
tiv
e
in
a
s
m
all
-
s
ca
le
p
r
o
b
lem
,
th
e
co
n
v
er
g
e
n
ce
p
r
o
ce
s
s
m
ay
b
e
a
wea
k
n
ess
in
a
lar
g
e
-
s
ca
le
p
r
o
b
lem
.
On
th
e
o
th
e
r
h
a
n
d
,
m
eta
-
h
eu
r
is
tic
alg
o
r
ith
m
s
ar
e
p
o
wer
f
u
l
at
s
o
lv
in
g
lar
g
e
-
s
ca
le
p
r
o
b
lem
s
.
Ho
wev
er
,
th
e
g
en
er
atio
n
,
e
v
alu
atio
n
,
an
d
s
elec
tio
n
o
f
ca
n
d
id
ates
in
th
e
p
o
p
u
latio
n
f
o
llo
w
a
lo
g
ical
r
u
le
[
1
5
]
.
T
h
u
s
,
a
h
u
g
e
s
im
u
latio
n
tim
e
is
r
eq
u
ir
e
d
ev
en
f
o
r
s
m
all
-
s
ca
le
p
r
o
b
le
m
s
.
An
o
th
er
c
h
allen
g
e
f
o
r
t
h
e
r
es
ea
r
ch
er
wh
e
n
u
s
in
g
m
eta
-
h
eu
r
is
tic
alg
o
r
ith
m
s
is
th
e
in
itial
p
ar
am
eter
s
.
So
m
e
p
a
p
er
s
ap
p
lied
m
eta
-
h
e
u
r
is
tic
alg
o
r
ith
m
s
with
in
itial
p
ar
am
eter
s
f
o
r
s
o
lv
in
g
th
e
T
E
P
p
r
o
b
lem
,
s
u
ch
as
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
[
1
4
]
,
im
p
r
o
v
ed
ze
b
r
a
o
p
tim
izatio
n
al
g
o
r
ith
m
(
I
Z
O
A)
[
2
0
]
,
an
d
s
o
cial
s
p
id
er
(
S
S)
[
7
]
.
B
esid
es,
th
e
T
E
P
p
r
o
b
lem
is
s
o
lv
ed
u
s
in
g
m
eta
-
h
eu
r
is
tic
alg
o
r
ith
m
s
with
o
u
t
i
n
itial
p
ar
am
eter
s
,
wh
ic
h
ca
n
b
e
lis
ted
as:
s
y
m
b
io
tic
o
r
g
a
n
is
m
s
s
ea
r
ch
(
SOS)
[
3
]
,
Kep
le
r
o
p
tim
izatio
n
alg
o
r
ith
m
(
KOA)
[
5
]
.
B
asically
,
th
e
ab
o
v
e
alg
o
r
ith
m
s
wer
e
s
u
cc
ess
f
u
lly
ap
p
lied
to
s
o
lv
in
g
th
e
s
im
p
lifi
ed
T
E
P
p
r
o
b
lem
.
On
th
e
o
th
e
r
h
an
d
,
m
an
y
s
tu
d
ies
m
o
d
if
ie
d
th
e
in
itial
m
eth
o
d
to
h
an
d
le
th
e
co
m
p
lex
T
E
P
p
r
o
b
lem
.
I
n
[
1
5
]
,
th
e
h
y
b
r
id
izati
o
n
b
etwe
en
d
if
f
er
en
tial
e
v
o
lu
t
io
n
alg
o
r
ith
m
a
n
d
p
o
p
u
latio
n
b
ased
i
n
cr
em
en
tal
lear
n
in
g
alg
o
r
ith
m
ca
lled
D
E
-
PB
I
L
c
is
p
r
o
p
o
s
ed
f
o
r
s
o
lv
in
g
th
e
AC
T
E
P
p
r
o
b
lem
,
co
n
s
id
er
in
g
t
h
e
f
u
e
l
co
s
t
o
f
g
en
er
atio
n
.
T
h
e
p
r
o
p
o
s
ed
al
g
o
r
ith
m
h
as
a
h
ig
h
co
n
v
e
r
g
en
c
y
r
ate.
Ho
wev
er
,
th
e
r
eq
u
ir
ed
co
n
tr
o
l
p
ar
am
eter
s
o
f
t
h
e
DE
-
PB
I
L
c
alg
o
r
ith
m
ar
e
v
er
y
h
u
g
e,
w
h
ile
th
e
d
if
f
er
en
tial
ev
o
lu
tio
n
(
DE
)
alg
o
r
ith
m
r
e
q
u
ir
es
o
n
ly
two
p
ar
am
eter
s
.
T
h
e
im
p
r
o
v
em
en
t
o
f
th
e
b
i
n
ar
y
b
at
al
g
o
r
ith
m
(
I
B
B
A)
is
p
r
o
p
o
s
ed
in
[
2
1
]
f
o
r
s
o
lv
in
g
b
o
th
s
tatic
an
d
d
y
n
a
m
ic
AC
T
E
P
p
r
o
b
lem
s
.
Ho
we
v
er
,
th
e
s
im
u
latio
n
tim
e
o
f
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
is
h
u
g
e,
ev
en
with
a
s
m
all
s
y
s
tem
.
B
ased
o
n
th
e
liter
atu
r
e
r
ev
iew,
th
e
ex
is
tin
g
o
p
tim
izatio
n
alg
o
r
ith
m
s
ar
e
ab
le
to
s
o
lv
e
th
e
AC
T
E
P
p
r
o
b
lem
.
Ho
wev
e
r
,
th
ey
r
e
q
u
ir
e
s
ev
er
al
co
n
tr
o
l
p
ar
am
eter
s
an
d
h
u
g
e
s
im
u
lat
io
n
tim
es,
wh
ich
in
cr
ea
s
e
th
e
alg
o
r
ith
m
’
s
co
m
p
lex
ity
an
d
co
m
p
u
tatio
n
co
s
t.
T
h
er
ef
o
r
e,
d
ev
elo
p
in
g
an
ef
f
i
cien
cy
o
p
tim
izatio
n
m
eth
o
d
f
o
r
s
o
lv
in
g
th
e
AC
T
E
P
p
r
o
b
lem
is
s
till
an
o
p
en
q
u
esti
o
n
f
o
r
m
an
y
s
tu
d
ies.
B
ased
o
n
th
e
ab
o
v
e
an
al
y
s
es
,
a
n
ew
m
o
d
i
f
icatio
n
o
f
th
e
d
if
f
er
en
tial
ev
o
lu
tio
n
alg
o
r
ith
m
c
alled
MD
E
is
p
r
o
p
o
s
ed
in
th
is
wo
r
k
to
h
an
d
le
th
e
AC
T
E
P
p
r
o
b
lem
in
th
e
s
ce
n
ar
io
o
f
f
u
el
co
s
t
co
n
s
id
er
atio
n
.
T
h
e
DE
alg
o
r
ith
m
is
k
n
o
wn
f
o
r
its
d
ir
ec
t
p
ar
allel
s
ea
r
ch
f
ea
tu
r
e
b
ased
o
n
m
u
tatio
n
an
d
cr
o
s
s
o
v
er
p
r
o
ce
s
s
es.
Mo
r
eo
v
er
,
th
e
e
f
f
icien
cy
o
f
th
e
DE
m
eth
o
d
in
s
o
l
v
in
g
t
h
e
T
E
P
p
r
o
b
lem
is
p
r
o
v
en
i
n
[
2
2
]
,
[
2
3
]
.
Ho
wev
er
,
th
e
o
p
tim
a
lity
an
d
co
n
v
e
r
g
en
c
y
s
p
ee
d
o
f
th
is
alg
o
r
ith
m
m
ay
b
e
a
p
r
o
b
lem
b
ec
au
s
e
o
f
th
e
r
an
d
o
m
n
ess
in
th
e
m
u
tatio
n
p
r
o
ce
s
s
,
wh
ich
ca
n
b
e
im
p
r
o
v
e
d
b
y
f
o
cu
s
in
g
o
n
t
h
e
b
est
in
d
iv
id
u
als
at
ea
ch
in
ter
ac
tio
n
.
T
h
er
e
f
o
r
e,
th
e
n
ew
i
n
d
iv
id
u
al
at
th
e
m
u
tatio
n
p
r
o
ce
s
s
is
cr
ea
ted
b
a
s
ed
o
n
th
e
c
h
ar
ac
ter
is
tics
o
f
th
e
b
est
in
d
iv
id
u
al
in
s
tead
o
f
th
r
ee
r
an
d
o
m
in
d
i
v
id
u
als
in
t
h
e
p
o
p
u
latio
n
i
n
th
is
m
o
d
if
icatio
n
.
T
h
e
ef
f
icien
c
y
o
f
th
e
p
r
o
p
o
s
ed
MD
E
alg
o
r
ith
m
is
p
r
o
v
ed
in
two
well
-
k
n
o
wn
m
o
d
els:
th
e
Gr
av
er
6
b
u
s
s
y
s
tem
an
d
th
e
I
E
E
E
2
4
b
u
s
s
y
s
tem
.
Mo
r
eo
v
er
,
th
e
r
esu
lts
o
f
th
e
MD
E
m
eth
o
d
ar
e
co
m
p
a
r
ed
with
th
e
o
r
ig
in
al
DE
[
2
4
]
an
d
f
iv
e
d
if
f
er
en
t m
et
h
o
d
s
:
th
e
one
-
to
-
one
-
b
ased
o
p
tim
i
ze
r
(
OOBO)
[
2
5
]
,
th
e
ar
tifi
cial
h
u
m
m
in
g
b
i
r
d
alg
o
r
ith
m
(
AHA)
[
2
6
]
,
th
e
d
an
d
elio
n
o
p
tim
izer
(
DO)
[
2
7
]
,
th
e
tu
n
a
s
war
m
o
p
tim
izatio
n
(
T
SO)
[
2
8
]
,
a
n
d
th
e
ch
ao
s
g
am
e
o
p
tim
izati
o
n
(
C
GO)
[
2
9
]
.
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:
2088
-
8
7
0
8
Mo
d
ified
d
iffer
en
tia
l e
vo
lu
tio
n
a
lg
o
r
ith
m
to
fin
d
in
g
o
p
tima
l
s
o
lu
tio
n
…
(
Th
a
n
h
Lo
n
g
Du
o
n
g
)
5047
2.
M
AT
H
E
M
AT
I
CA
L
F
O
RM
UL
A
T
I
O
N
2
.
1
.
O
bje
ct
iv
e
f
un
ct
io
n
T
h
e
o
b
jectiv
e
f
u
n
ctio
n
o
f
th
e
AC
T
E
P
p
r
o
b
lem
in
clu
d
ed
th
e
in
v
estme
n
t
co
s
ts
o
f
ad
d
itio
n
lin
es
an
d
g
en
er
atio
n
f
u
el
co
s
ts
as in
[
1
5
]
is
p
r
esen
ted
in
th
is
s
ec
tio
n
.
T
h
is
o
b
jectiv
e
f
u
n
ctio
n
ca
n
b
e
c
alcu
lated
as
(
1
)
:
:
=
∑
×
∈
+
8760
×
∑
(
×
)
∀
∈
×
;
∀
,
∈
;
≠
(
1
)
wh
er
e
an
d
ar
e
th
e
c
o
s
t
an
d
n
u
m
b
er
o
f
ad
d
itio
n
al
lin
es
th
at
n
ee
d
t
o
b
e
ad
d
ed
to
th
e
p
o
wer
s
y
s
tem
.
,
,
an
d
ar
e
th
e
g
en
er
atio
n
c
o
s
t
(
$
/MWh
)
,
th
e
to
tal
ac
tiv
e
p
o
wer
o
f
g
en
er
atio
n
,
an
d
th
e
ca
p
a
city
f
ac
to
r
o
f
th
e
g
en
e
r
ato
r
at
n
o
d
e
,
r
esp
e
ctiv
ely
.
,
,
an
d
ar
e
t
h
e
s
et
o
f
ca
n
d
id
ate
lin
es,
th
e
s
et
o
f
all
s
y
s
tem
b
u
s
es,
an
d
th
e
s
et
o
f
all
g
en
er
a
to
r
b
u
s
es,
r
esp
ec
tiv
ely
.
2
.
2
.
Co
ns
t
ra
ints
2
.
2
.
1
.
E
qu
a
t
io
n c
o
ns
t
ra
ints
T
h
e
AC
PF
eq
u
atio
n
co
n
s
tr
ai
n
ts
o
f
th
e
AC
T
E
P
p
r
o
b
lem
ar
e
d
escr
ib
ed
in
(
2
)
-
(
7
)
,
wh
ich
co
n
tain
th
e
p
o
wer
b
alan
cin
g
eq
u
atio
n
f
o
r
b
o
th
ac
tiv
e
an
d
r
ea
cti
v
e
p
o
wer
,
as
well
as
th
e
p
o
wer
f
lo
w
in
b
r
an
ch
es.
E
q
u
atio
n
s
(
2
)
an
d
(
3
)
p
r
o
v
id
e
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
b
alan
ce
s
(
,
)
+
=
(
2
)
(
,
)
+
=
+
(
3
)
T
h
e
eq
u
atio
n
(
4
)
p
r
esen
ts
th
e
ac
tiv
e
p
o
wer
f
l
o
w.
(
,
)
=
∑
[
c
os
+
]
,
(
4
)
T
h
e
r
ea
ctiv
e
p
o
wer
f
lo
w
is
s
h
o
wn
in
(
5
)
.
(
,
)
=
∑
[
s
in
+
]
,
(
5
)
T
h
e
co
m
p
le
x
p
o
we
r
f
lo
w
in
b
o
th
ter
m
in
als is
p
r
o
p
o
s
ed
in
(
6
)
an
d
(
7
)
.
=
√
(
)
2
+
(
)
2
(
6
)
=
√
(
)
2
+
(
)
2
(
7
)
2
.
2
.
2
.
I
nequ
a
t
io
n c
o
ns
t
ra
ints
E
q
u
atio
n
s
(
8
)
-
(
1
4
)
d
e
p
ict
th
e
AC
T
E
P
p
r
o
b
lem
'
s
in
eq
u
ality
co
n
s
tr
ain
ts
,
wh
ich
in
clu
d
e
ac
ti
v
e/r
ea
ctiv
e
g
en
er
atin
g
p
o
we
r
,
v
o
ltag
e,
s
h
u
n
t
c
o
m
p
e
n
s
atio
n
,
in
s
tallatio
n
cir
c
u
its
,
an
d
p
o
we
r
f
l
o
w
in
b
r
an
c
h
es.
T
h
e
allo
wed
ac
tiv
e
an
d
r
ea
ctiv
e
g
e
n
er
atio
n
s
ar
e
p
r
esen
ted
in
(
8
)
an
d
(
9
)
.
≤
≤
(
8
)
≤
≤
(
9
)
T
h
e
v
o
ltag
e
a
m
p
litu
d
e
is
p
r
esen
ted
in
(
1
0
)
.
≤
≤
(
1
0
)
T
h
e
lim
itatio
n
o
f
s
h
u
n
t c
o
m
p
e
n
s
atio
n
is
p
r
o
p
o
s
ed
in
(
1
1
)
.
≤
≤
(
1
1
)
T
h
e
m
ax
im
u
m
n
u
m
b
er
o
f
ad
d
i
tio
n
al
lin
es a
t e
ac
h
r
ig
h
t
-
of
-
wa
y
is
p
r
esen
ted
in
(
1
2
)
.
0
≤
≤
(
1
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
6
,
Decem
b
e
r
20
25
:
5
0
4
5
-
5
0
5
4
5048
T
h
e
eq
u
atio
n
s
(
1
3
)
an
d
(
1
4
)
in
tr
o
d
u
ce
th
e
tr
an
s
m
is
s
io
n
lin
e
c
ap
ac
ity
.
≤
(
1
3
)
≤
(
1
4
)
wh
er
e
,
,
,
,
,
,
,
an
d
ar
e
th
e
ex
itin
g
,
m
in
im
u
m
,
an
d
m
a
x
i
m
u
m
v
ec
to
r
s
o
f
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
o
f
th
e
g
en
er
ato
r
an
d
lo
a
d
d
em
a
n
d
,
r
esp
ec
tiv
ely
.
,
,
ar
e
th
e
ex
itin
g
,
m
in
im
u
m
,
an
d
m
a
x
im
u
m
o
f
s
h
u
n
t
co
m
p
en
s
atio
n
,
r
esp
ec
t
iv
ely
.
T
h
e
ca
lcu
latio
n
o
f
,
,
,
,
,
an
d
ca
n
b
e
f
o
u
n
d
in
[
1
3
]
.
,
,
an
d
ar
e
th
e
ex
itin
g
,
m
i
n
im
u
m
,
a
n
d
m
a
x
im
u
m
o
f
v
o
ltag
e,
r
esp
ec
tiv
ely
.
,
an
d
ar
e
th
e
ad
d
itio
n
,
m
a
x
im
u
m
n
u
m
b
er
o
f
n
ew
lin
es,
an
d
m
ax
im
u
m
ca
p
ac
ity
o
f
ea
c
h
b
r
a
n
ch
.
3.
O
P
T
I
M
I
Z
AT
I
O
N
M
E
T
H
O
D
3
.
1
.
M
o
dified
diff
er
ent
ia
l e
v
o
luti
o
n a
lg
o
rit
hm
T
h
e
d
i
f
f
er
en
tial
ev
o
lu
tio
n
al
g
o
r
ith
m
is
f
ir
s
t
p
r
esen
te
d
in
[
2
5
]
.
T
h
e
m
ain
id
ea
o
f
th
is
al
g
o
r
ith
m
is
b
ased
o
n
th
e
ev
o
lu
tio
n
p
r
o
ce
s
s
.
T
h
is
alg
o
r
ith
m
is
k
n
o
wn
as th
e
ef
f
ec
tiv
e
m
eth
o
d
f
o
r
s
o
lv
i
n
g
th
e
T
E
P p
r
o
b
lem
d
u
e
to
its
d
ir
ec
t
p
ar
allel
s
ea
r
c
h
s
tr
ateg
y
.
I
n
th
is
alg
o
r
ith
m
,
e
ac
h
ch
ar
ac
ter
is
tic
o
f
a
n
ew
in
d
iv
id
u
al
is
in
h
er
ited
f
r
o
m
t
h
e
p
r
ev
io
u
s
in
d
iv
id
u
al
o
r
f
r
o
m
th
e
in
d
iv
id
u
al
cr
ea
t
ed
f
r
o
m
th
e
m
u
tatio
n
p
r
o
ce
s
s
.
I
n
th
e
m
u
tatio
n
p
r
o
ce
s
s
,
a
n
ew
in
d
i
v
id
u
al
i
s
cr
ea
ted
b
ased
o
n
th
e
ch
a
r
ac
ter
is
tics
o
f
th
r
ee
r
an
d
o
m
in
d
iv
id
u
als
in
t
h
e
p
o
p
u
latio
n
.
T
h
is
p
r
o
ce
s
s
ca
n
b
e
d
escr
ib
ed
as:
=
+
×
(
−
)
(
1
5
)
wh
er
e
is
th
e
n
ew
in
d
iv
id
u
al
cr
ea
ted
in
th
e
m
u
tatio
n
p
r
o
ce
s
s
,
,
,
an
d
ar
e
th
e
th
r
ee
r
an
d
o
m
in
d
iv
id
u
als
in
th
e
in
itial
p
o
p
u
latio
n
.
is
th
e
m
u
tatio
n
f
ac
t
o
r
,
wh
ich
is
in
th
e
r
an
g
e
[
0
,
2
]
.
Alth
o
u
g
h
th
e
DE
alg
o
r
ith
m
s
u
cc
ess
f
u
lly
s
o
lv
es th
e
T
E
P
p
r
o
b
lem
[
2
2
]
,
[
2
3
]
,
th
e
o
p
tim
izatio
n
m
ay
n
o
t b
e
g
u
a
r
an
teed
b
ec
a
u
s
e
o
f
th
e
r
an
d
o
m
n
ess
o
f
th
e
m
u
tatio
n
p
r
o
ce
s
s
.
T
h
er
ef
o
r
e,
a
n
ew
eq
u
atio
n
b
ased
o
n
t
h
e
th
r
ee
b
est
in
d
iv
id
u
als
is
s
u
g
g
ested
in
th
is
s
tu
d
y
to
r
ep
l
ac
e
(
1
5
)
.
T
h
is
eq
u
atio
n
is
ex
p
r
ess
ed
as:
=
+
×
(
−
)
(
1
6
)
T
h
e
d
if
f
er
en
ce
b
etwe
en
(
1
5
)
a
n
d
(
1
6
)
is
th
e
,
wh
ich
is
th
e
r
an
d
o
m
ch
o
ice
o
f
th
e
f
ir
s
t,
s
ec
o
n
d
,
an
d
th
ir
d
elite
in
d
iv
id
u
als (
,
1
,
,
2
,
,
3
).
T
h
e
p
r
o
p
o
s
ed
eq
u
atio
n
n
o
t
o
n
ly
im
p
r
o
v
es
th
e
e
x
p
lo
itatio
n
s
tr
ateg
y
o
f
DE
alg
o
r
ith
m
s
b
u
t
a
ls
o
av
o
id
s
th
e
lo
ca
l
o
p
tim
al
s
o
lu
tio
n
b
y
r
an
d
o
m
ly
s
elec
tin
g
f
ir
s
t,
s
ec
o
n
d
,
an
d
th
ir
d
-
b
est
in
d
iv
i
d
u
a
ls
,
as
p
r
esen
ted
in
Fig
u
r
e
1
.
I
n
th
is
f
ig
u
r
e
,
th
e
s
ea
r
ch
s
p
ac
e
o
f
th
e
s
u
g
g
ested
al
g
o
r
ith
m
f
o
cu
s
es
o
n
th
e
th
r
ee
b
est
in
d
iv
id
u
als
wh
o
en
h
an
ce
th
e
ex
p
lo
itatio
n
p
r
o
c
ess
o
v
er
th
e
p
r
e
v
io
u
s
ap
p
r
o
a
ch
.
I
n
ad
d
itio
n
,
th
e
ex
p
lo
r
ati
o
n
m
eth
o
d
m
a
y
b
e
g
u
ar
an
teed
b
y
t
h
e
r
an
d
o
m
s
ele
ctio
n
o
f
th
ese
th
r
ee
b
est in
d
iv
i
d
u
als.
Ap
p
ly
in
g
th
e
p
r
o
p
o
s
ed
MD
E
t
o
s
o
lv
e
th
e
AC
T
E
P p
r
o
b
lem
c
an
b
e
d
escr
ib
e
d
in
th
e
s
tep
s
:
Step
1
:
R
ea
d
d
ata
f
r
o
m
th
e
ch
o
s
en
s
y
s
tem
an
d
ch
o
o
s
e
th
e
c
o
n
tr
o
l
s
p
ec
if
ied
p
a
r
am
eter
s
o
f
th
e
MD
E
m
eth
o
d
:
m
ax
iter
,
p
o
p
-
s
ize
(
)
,
,
an
d
.
Step
2
: G
en
er
atin
g
th
e
r
an
d
o
m
in
itial p
o
p
u
latio
n
(
1
7
)
:
=
+
×
(
−
)
,
=
1
,
…
(
1
7
)
wh
er
e
is
th
e
m
ax
im
u
m
n
u
m
b
er
o
f
in
d
iv
id
u
als
in
th
e
p
o
p
u
l
atio
n
.
an
d
ar
e
th
e
u
p
p
er
b
o
u
n
d
an
d
lo
wer
b
o
u
n
d
o
f
AC
T
E
P p
r
o
b
lem
.
T
h
ese
v
alu
es a
r
e
d
esc
r
ib
ed
in
(
1
8
)
-
(
1
9
)
.
=
[
1
,
…
,
,
1
,
…
,
,
1
,
…
,
]
(
1
8
)
=
[
1
,
…
,
,
1
,
…
,
,
1
,
…
,
]
(
1
9
)
wh
er
e
,
,
,
,
,
,
,
,
,
an
d
,
ar
e
th
e
l
o
wer
an
d
u
p
p
er
b
o
u
n
d
s
o
f
ca
n
d
i
d
ate
tr
an
s
m
is
s
io
n
lin
es v
o
ltag
es a
n
d
ac
tiv
e
g
en
er
ato
r
s
o
u
tp
u
t,
r
esp
ec
tiv
ely
.
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:
2088
-
8
7
0
8
Mo
d
ified
d
iffer
en
tia
l e
vo
lu
tio
n
a
lg
o
r
ith
m
to
fin
d
in
g
o
p
tima
l
s
o
lu
tio
n
…
(
Th
a
n
h
Lo
n
g
Du
o
n
g
)
5049
Step
3
:
R
u
n
th
e
AC
PF
f
o
r
all
in
itial
in
d
iv
id
u
als
an
d
c
h
ec
k
t
h
e
AC
co
n
s
tr
ain
ts
b
ased
o
n
th
e
f
itn
ess
v
alu
e.
T
h
e
f
itn
ess
v
alu
e
is
ca
lcu
lated
f
o
ll
o
win
g
(
2
0
)
:
=
+
×
∑
+
×
∑
+
×
∑
+
×
∑
(
2
0
)
wh
er
e
,
,
,
an
d
ar
e
th
e
p
en
alty
v
alu
es
o
f
th
e
g
en
er
atio
n
ac
tiv
e
p
o
wer
,
r
ea
ctiv
e
p
o
wer
,
p
o
wer
f
lo
w
i
n
b
r
a
n
ch
es,
an
d
v
o
lta
g
e,
r
esp
ec
tiv
ely
.
,
,
,
an
d
ar
e
th
e
p
e
n
alty
f
ac
to
r
s
,
r
esp
ec
tiv
ely
,
wh
ich
ar
e
s
et
o
f
10
6
.
S
t
e
p
4
:
E
v
a
l
u
at
e
t
h
e
p
o
p
u
l
a
ti
o
n
a
n
d
p
o
i
n
t
o
u
t
f
i
r
s
t
,
s
e
c
o
n
d
a
n
d
t
h
i
r
d
e
l
i
te
i
n
d
i
v
i
d
u
a
ls
(
,
1
,
,
2
,
,
3
)
.
Step
5
: Cre
ate
th
e
m
u
tatio
n
in
d
iv
id
u
al
b
ased
o
n
th
e
m
u
tatio
n
p
r
o
ce
s
s
u
s
in
g
th
e
p
r
o
p
o
s
ed
(
1
6
)
.
Ste
p
6
:
Ge
n
er
ate
t
h
e
n
ew
i
n
d
i
v
id
u
al
b
as
ed
o
n
t
h
e
c
r
o
s
s
o
v
er
(
)
f
ac
t
o
r
.
T
h
is
p
r
o
ce
s
s
ca
n
b
e
d
e
s
cr
i
b
ed
b
y
(
2
1
)
:
=
{
,
<
|
|
=
0
,
(
2
1
)
wh
er
e
is
th
e
cr
o
s
s
o
v
er
f
ac
t
o
r
,
wh
ich
is
th
e
r
a
n
d
o
m
v
alu
e
in
th
e
r
an
g
e
[
0
,
1
]
.
0
is
th
e
r
an
d
o
m
v
alu
e
in
th
e
r
an
g
e
[
1
,
].
Step
7
: Ru
n
AC
PF
an
d
ca
lcu
late
th
e
f
itn
ess
v
alu
e
o
f
t
h
e
n
e
w
in
d
iv
id
u
al
f
o
llo
win
g
th
e
(
2
0
)
.
Step
8
: Sele
cted
th
e
in
d
iv
id
u
al
f
o
r
th
e
n
ew
p
o
p
u
latio
n
b
y
(
2
2
)
:
+
1
=
{
,
(
)
<
(
)
,
(
2
2
)
Step
9
:
E
x
am
in
e
t
h
e
s
to
p
co
n
d
itio
n
.
I
f
th
e
m
ax
im
u
m
iter
atio
n
is
r
ea
ch
e
d
,
g
o
to
t
h
e
n
e
x
t
s
te
p
.
Oth
er
wis
e,
g
o
t
o
s
tep
4
.
Step
1
0
: Sto
p
an
d
p
r
i
n
t o
u
t th
e
o
p
tim
al
s
o
lu
tio
n
.
G
lo
b
a
l
O
p
ti
m
a
l
S
o
lu
ti
o
n
O
p
ti
m
a
l
S
o
lu
ti
o
n
O
p
ti
m
a
l
S
o
lu
ti
o
n
T
h
e
s
e
a
r
c
h
s
p
a
c
e
o
f
th
e
o
r
ig
in
a
l
e
q
u
a
ti
o
n
(
15
)
T
h
e
s
e
a
r
c
h
s
p
a
c
e
o
f
th
e
p
r
o
p
o
s
e
d
e
q
u
a
ti
o
n
(
16
)
T
h
e
s
e
a
r
c
h
s
p
a
c
e
o
f
th
e
p
r
o
p
o
s
e
d
e
q
u
a
t
i
o
n
(
16
)
T
h
e
s
e
a
r
c
h
s
p
a
c
e
o
f
th
e
p
r
o
p
o
s
ed
eq
u
ati
o
n
(
16
)
Fig
u
r
e
1
.
T
h
e
s
ea
r
ch
s
p
ac
e
o
f
th
e
p
r
o
p
o
s
ed
MD
E
alg
o
r
ith
m
4.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
T
h
e
ev
alu
atio
n
o
f
th
e
p
r
o
p
o
s
ed
MD
E
alg
o
r
ith
m
f
o
r
s
o
lv
in
g
th
e
AC
T
E
P
p
r
o
b
lem
is
p
er
f
o
r
m
ed
in
th
is
s
ec
tio
n
.
T
wo
s
y
s
tem
s
ar
e
u
s
ed
in
th
is
s
ec
tio
n
,
in
clu
d
in
g
th
e
Gr
av
er
6
b
u
s
s
y
s
tem
an
d
th
e
I
E
E
E
2
4
b
u
s
s
y
s
tem
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
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n
g
,
Vo
l.
15
,
No
.
6
,
Decem
b
e
r
20
25
:
5
0
4
5
-
5
0
5
4
5050
I
n
ea
ch
s
y
s
tem
,
th
e
s
tatic
A
C
T
E
P
p
r
o
b
lem
co
n
s
id
er
in
g
f
u
el
co
s
t
with
s
h
u
n
t
co
m
p
en
s
atio
n
in
teg
r
atio
n
is
s
o
lv
ed
u
s
in
g
th
e
MD
E
alg
o
r
it
h
m
.
Mo
r
eo
v
er
,
a
c
o
m
p
ar
is
o
n
o
f
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
with
o
th
er
m
eth
o
d
s
s
u
ch
as
DE
[
2
4
]
,
OOBO
[
2
5
]
,
A
HA
[
2
6
]
,
DO
[
2
7
]
,
T
SO
[
2
8
]
,
a
n
d
C
GO
[
2
9
]
is
p
e
r
f
o
r
m
ed
to
p
r
o
v
e
its
ef
f
ec
tiv
en
ess
f
o
r
s
o
lv
in
g
th
e
m
en
tio
n
ed
p
r
o
b
lem
.
T
h
e
p
r
o
g
r
am
is
p
er
f
o
r
m
ed
in
a
MA
T
L
AB
en
v
ir
o
n
m
e
n
t,
r
u
n
n
in
g
o
n
a
co
m
p
u
ter
with
an
I
n
tel®
C
o
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e
T
M
i5
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1
2
5
0
0
H
C
PU
at
3
.
1
0
GHz
an
d
1
6
GB
o
f
R
AM
.
T
h
e
A
C
p
o
wer
f
lo
w
is
ca
lcu
lated
u
s
in
g
th
e
MA
T
PO
W
E
R
[
3
0
]
to
o
lb
o
x
.
T
h
e
o
p
tim
al
s
o
lu
tio
n
o
f
all
m
eth
o
d
s
is
g
iv
en
af
ter
3
0
tr
ials
.
T
h
e
co
n
tr
o
l p
ar
am
eter
s
o
f
ea
ch
alg
o
r
ith
m
a
r
e
p
r
esen
ted
in
T
a
b
le
1
.
T
ab
le
1
.
T
h
e
o
p
e
r
atio
n
p
a
r
am
eter
s
o
f
u
s
ed
alg
o
r
ith
m
s
M
e
t
h
o
d
P
a
r
a
me
t
e
r
M
D
E
=
[
0
.
2
,
0
.
8
]
,
=
0
.
6
,
=
6
0
DE
=
[
0
.
2
,
0
.
8
]
,
=
0
.
6
,
=
6
0
O
O
B
O
=
6
0
AHA
=
6
0
AHA
=
6
0
TSO
=
0
.
7
,
=
0
.
0
5
,
=
6
0
C
G
O
=
6
0
4
.
1
.
T
he
G
ra
v
er
6
bu
s
s
y
s
t
em
T
h
is
s
y
s
tem
co
n
tain
s
6
b
u
s
es,
1
5
r
ig
h
ts
-
of
-
way
s
,
an
d
3
g
en
e
r
ato
r
s
,
with
m
ax
im
u
m
p
o
wer
g
en
er
atio
n
an
d
to
tal
lo
ad
d
em
a
n
d
o
f
1
1
0
0
MW,
7
6
0
MW,
an
d
1
5
2
MV
Ar
,
r
esp
ec
tiv
ely
.
T
h
e
allo
wed
n
u
m
b
er
o
f
ad
d
itio
n
lin
es
in
ea
ch
r
ig
h
ts
-
of
-
way
s
is
4
.
T
h
e
d
etail
d
ata
f
o
r
th
is
s
y
s
tem
ca
n
b
e
f
o
u
n
d
in
[
1
5
]
.
I
n
o
r
d
er
to
ca
lcu
late
th
e
f
u
el
co
s
t,
t
h
e
ca
p
ac
ity
f
ac
t
o
r
s
,
th
e
o
p
er
atin
g
c
o
s
ts
o
f
ea
c
h
g
en
er
ato
r
,
an
d
th
e
lim
it
o
f
s
h
u
n
t
co
m
p
e
n
s
atio
n
ar
e
s
et
as
in
[
1
5
]
.
T
h
e
m
a
x
im
u
m
in
ter
ac
tio
n
s
(
m
ax
iter
)
o
f
all
m
eth
o
d
s
in
th
is
s
y
s
tem
ar
e
1
5
0
.
T
h
e
s
im
u
latio
n
r
esu
lts
o
f
th
e
AC
T
E
P
p
r
o
b
le
m
o
f
th
is
s
y
s
tem
ar
e
g
iv
en
i
n
T
ab
le
2
.
Ob
s
er
v
ed
f
r
o
m
th
is
tab
le,
to
tal
co
s
t
o
b
tain
ed
b
y
u
s
in
g
th
e
p
r
o
p
o
s
ed
MD
E
alg
o
r
ith
m
is
3
0
,
3
9
5
.
3
6
×
10
3
$
,
in
clu
d
in
g
ad
d
itio
n
a
l
lin
e
in
v
estme
n
t
co
s
ts
(
2
5
0
×
10
3
$
)
an
d
g
en
er
at
o
r
f
u
el
co
s
ts
(
3
0
,
1
4
5
.
3
6
×
10
3
$
)
.
T
h
is
v
alu
e
is
lo
wer
th
an
th
e
s
o
l
u
tio
n
g
iv
en
b
y
OOBO
(
3
0
,
3
9
9
.
1
6
×
10
3
$
)
,
AHA
(
3
0
,
4
6
4
.
6
3
×
10
3
$
)
,
an
d
T
SO
(
3
0
,
3
9
9
.
7
9
×
10
3
$
)
,
r
esp
ec
tiv
ely
.
T
h
e
s
o
lu
tio
n
s
g
iv
en
b
y
th
e
MD
E
,
DE
,
DO
,
an
d
C
GO
m
eth
o
d
s
ar
e
eq
u
al.
Ho
wev
er
,
th
e
c
o
n
v
e
r
g
en
c
y
r
ate
o
f
t
h
e
DO
alg
o
r
ith
m
is
9
6
.
7
%,
wh
ich
is
lo
wer
th
an
th
e
MD
E
alg
o
r
it
h
m
.
Alth
o
u
g
h
th
e
s
o
lu
tio
n
g
iv
en
b
y
t
h
e
C
GO
m
eth
o
d
is
th
e
s
am
e
as
th
e
MD
E
m
eth
o
d
,
th
e
s
im
u
latio
n
tim
e
o
f
th
e
C
GO
m
eth
o
d
is
2
2
8
.
2
6
s
,
wh
ich
is
h
i
g
h
er
th
an
th
at
o
f
t
h
e
MD
E
m
eth
o
d
(
1
4
9
.
8
8
s
)
.
T
h
e
r
esu
lt
o
b
tain
ed
b
y
th
e
p
r
o
p
o
s
ed
MD
E
m
eth
o
d
is
n
o
t
m
u
c
h
d
if
f
er
en
t
co
m
p
ar
ed
to
th
e
o
r
ig
in
al
DE
m
et
h
o
d
b
ec
au
s
e
th
e
s
i
ze
an
d
th
e
s
ea
r
ch
s
p
ac
e
o
f
th
e
co
n
s
id
er
ed
s
y
s
tem
ar
e
q
u
ite
s
m
all.
I
n
ad
d
itio
n
,
th
e
co
n
v
er
g
e
n
ce
cu
r
v
e
o
f
all
u
s
ed
m
eth
o
d
s
an
d
th
e
r
esu
lts
o
f
th
e
AC
T
E
P p
r
o
b
lem
af
ter
3
0
tr
ials
ar
e
s
h
o
wn
in
Fig
u
r
es 2
.
Acc
o
r
d
i
n
g
to
Fig
u
r
e
2
(
a)
,
th
e
co
n
v
er
g
en
ce
s
p
ee
d
o
f
th
e
MD
E
tech
n
iq
u
e
is
f
aster
th
an
th
at
o
f
th
e
o
r
i
g
in
al
DE
tec
h
n
iq
u
e
b
ased
o
n
th
e
p
r
o
p
o
s
ed
eq
u
ati
o
n
.
M
o
r
eo
v
e
r
,
th
e
r
esu
lts
ac
h
iev
ed
a
f
ter
3
0
t
r
ials
o
f
th
e
MD
E
m
eth
o
d
ar
e
m
o
r
e
s
tab
le
th
a
n
o
th
er
m
eth
o
d
s
,
as
s
h
o
wn
in
Fig
u
r
e
2
(
b
)
.
T
h
e
n
ew
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D
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Lc
[
1
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]
A
d
d
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t
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l
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=
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Similar
ly
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h
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4
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M
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B
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C
G
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[
1
5
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A
d
d
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t
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l
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1
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3
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1
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1
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1
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−
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=
1
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−
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=
1
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−
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=
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=
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=
2
N
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a
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16
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
6
,
Decem
b
e
r
20
25
:
5
0
4
5
-
5
0
5
4
5052
T
ab
le
3
s
h
o
wn
th
at
th
e
n
ew
l
in
es
in
v
estme
n
t
co
s
t
f
o
u
n
d
b
y
DE
-
PB
I
L
c
(
5
8
0
×1
0
6
$
)
[
1
5
]
m
eth
o
d
is
s
m
aller
th
an
th
e
MD
E
(
6
2
7
×
1
0
6
$
)
m
eth
o
d
,
b
u
t
th
e
f
u
el
co
s
t
o
b
tain
ed
b
y
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E
m
eth
o
d
is
6
2
,
5
3
3
.
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3
×1
0
6
$
,
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ich
is
lo
wer
th
an
DE
-
PB
I
L
c
(
6
2
,
5
8
2
.
9
7
×1
0
6
$
)
[
1
5
]
m
eth
o
d
.
T
h
is
f
u
el
c
o
s
t
is
o
p
tim
ized
b
y
th
e
m
eta
-
h
eu
r
is
tic
alg
o
r
ith
m
(
MD
E
)
in
s
tead
o
f
th
e
in
te
r
io
r
p
o
in
t
m
eth
o
d
as
in
t
h
e
s
tu
d
y
[
1
5
]
.
T
h
er
ef
o
r
e
,
th
e
r
esu
lt
o
b
tain
ed
b
y
th
e
s
u
g
g
ested
M
DE
alg
o
r
ith
m
is
6
3
,
1
6
0
.
7
3
×
1
0
6
$
,
wh
ic
h
is
s
m
aller
th
an
th
e
DE
,
OOBO,
AHA
,
DO,
T
SO,
C
GO,
an
d
DE
-
PB
I
L
c
[
1
5
]
alg
o
r
ith
m
s
b
y
1
.
8
6
%,
0
.
9
%,
1
.
2
7
%,
1
.
5
8
%,
2
.
4
7
%,
1
.
0
8
%,
an
d
0
.
0
0
3
5
%,
r
esp
ec
tiv
ely
.
Mo
r
eo
v
er
,
th
e
MD
E
an
d
DE
ar
e
tw
o
tech
n
iq
u
es
th
at
h
av
e
a
1
0
0
%
co
n
v
er
g
e
n
cy
r
ate
af
ter
3
0
tr
ials
,
as
s
h
o
wn
in
Fig
u
r
e
3
.
T
h
e
co
n
v
er
g
en
ce
c
u
r
v
e
o
f
all
u
s
ed
m
eth
o
d
s
in
th
is
s
y
s
tem
is
p
r
esen
ted
in
Fig
u
r
e
3
(
a)
.
Ob
s
er
v
e
d
f
r
o
m
th
is
Fig
u
r
e,
th
e
co
n
v
er
g
e
n
ce
s
p
ee
d
o
f
th
e
p
r
o
p
o
s
ed
MD
E
alg
o
r
ith
m
is
h
ig
h
er
th
an
th
e
co
m
p
ar
ed
alg
o
r
ith
m
s
.
I
n
a
d
d
itio
n
,
th
e
r
esu
lts
g
iv
en
b
y
t
h
e
MD
E
m
eth
o
d
in
3
0
tr
ials
ac
h
iev
e
h
ig
h
s
tab
ilit
y
co
m
p
ar
ed
to
o
th
e
r
s
,
as sh
o
wn
in
Fig
u
r
e
3
(
b
)
.
(
a)
(
b
)
Fig
u
r
e
3
.
Simu
latio
n
r
esu
lts
:
(
a)
th
e
co
n
v
er
g
e
n
ce
cu
r
v
e
an
d
(
b
)
to
tal
co
s
t o
f
AC
T
E
P p
r
o
b
l
em
in
I
E
E
E
2
4
b
u
s
af
ter
3
0
r
u
n
s
5.
CO
NCLU
SI
O
N
I
n
th
is
r
esear
ch
,
th
e
m
o
d
if
i
ed
DE
alg
o
r
ith
m
is
p
r
esen
ted
f
o
r
s
o
lv
in
g
th
e
AC
T
E
P
p
r
o
b
lem
co
n
s
id
er
in
g
f
u
el
co
s
t.
T
h
e
ef
f
icien
cy
o
f
t
h
e
p
r
o
p
o
s
ed
tec
h
n
iq
u
e
is
p
r
o
v
en
b
y
s
o
lv
in
g
th
is
p
r
o
b
lem
u
s
in
g
th
e
Gr
av
er
6
b
u
s
s
y
s
tem
an
d
th
e
I
E
E
E
2
4
b
u
s
s
y
s
tem
.
Mo
r
e
o
v
er
,
th
e
r
esu
lts
f
o
u
n
d
b
y
t
h
e
MD
E
alg
o
r
ith
m
in
ea
ch
s
y
s
tem
ar
e
co
m
p
ar
ed
with
D
E
an
d
o
th
er
m
eta
-
h
eu
r
is
tics
.
I
n
th
e
G
r
av
er
6
b
u
s
s
y
s
tem
,
th
e
s
o
lu
tio
n
g
iv
en
b
y
th
e
MD
E
m
et
h
o
d
is
s
im
ilar
to
th
e
DE
,
DO,
an
d
C
GO
m
eth
o
d
s
.
Ho
wev
er
,
th
e
co
n
v
er
g
e
n
ce
s
p
ee
d
o
f
th
e
MD
E
m
eth
o
d
is
f
aster
th
an
t
h
at
o
f
t
h
e
o
th
er
m
eth
o
d
s
m
en
tio
n
ed
.
I
n
a
m
o
r
e
c
o
m
p
lex
s
y
s
tem
,
s
u
ch
as
th
e
I
E
E
E
2
4
b
u
s
s
y
s
tem
,
th
e
s
o
lu
tio
n
s
u
g
g
ested
b
y
th
e
MD
E
tech
n
iq
u
e
h
as
a
to
tal
co
s
t
lo
wer
b
y
1
.
8
6
%,
0
.
9
%,
1
.
2
7
%
,
1
.
5
8
%,
2
.
4
7
%,
a
n
d
1
.
0
8
%
c
o
m
p
ar
ed
t
o
o
th
e
r
tech
n
i
q
u
es.
I
n
ad
d
itio
n
,
th
e
im
p
r
o
v
e
m
en
t
o
f
th
e
p
r
o
p
o
s
ed
MD
E
alg
o
r
ith
m
is
co
n
f
ir
m
ed
b
y
th
e
co
m
p
ar
is
o
n
with
th
e
o
r
ig
in
al
DE
alg
o
r
ith
m
an
d
th
e
DE
-
PB
L
I
c
m
eth
o
d
in
liter
atu
r
e.
T
h
er
e
f
o
r
e,
th
is
alg
o
r
ith
m
ca
n
b
e
ap
p
lied
to
s
o
lv
e
t
h
e
AC
T
E
P
p
r
o
b
lem
in
lar
g
e
-
s
ca
le
s
y
s
tem
s
(
I
E
E
E
1
1
8
b
u
s
,
I
E
E
E
3
0
0
b
u
s
)
a
n
d
th
e
co
m
p
lex
T
E
P p
r
o
b
lem
s
in
o
u
r
f
u
tu
r
e
wo
r
k
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:
2088
-
8
7
0
8
Mo
d
ified
d
iffer
en
tia
l e
vo
lu
tio
n
a
lg
o
r
ith
m
to
fin
d
in
g
o
p
tima
l
s
o
lu
tio
n
…
(
Th
a
n
h
Lo
n
g
Du
o
n
g
)
5053
RE
F
E
R
E
NC
E
S
[
1
]
J.
M
.
C
a
r
r
a
sc
o
e
t
a
l
.
,
“
P
o
w
e
r
-
e
l
e
c
t
r
o
n
i
c
sy
s
t
e
ms
f
o
r
t
h
e
g
r
i
d
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n
t
e
g
r
a
t
i
o
n
o
f
r
e
n
e
w
a
b
l
e
e
n
e
r
g
y
s
o
u
r
c
e
s
:
a
su
r
v
e
y
,
”
I
E
EE
T
ra
n
s
a
c
t
i
o
n
s
o
n
I
n
d
u
st
r
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a
l
E
l
e
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c
s
,
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.
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3
,
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o
.
4
,
p
p
.
1
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–
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6
,
J
u
n
.
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,
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.
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1
0
9
/
TI
E.
2
0
0
6
.
8
7
8
3
5
6
.
[
2
]
B
.
G
j
o
r
g
i
e
v
,
A
.
E.
D
a
v
i
d
,
a
n
d
G
.
S
a
n
s
a
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,
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a
d
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r
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e
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f
A
C
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t
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p
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sy
st
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ms,
”
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l
e
c
t
ri
c
Po
w
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m
s R
e
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h
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v
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l
.
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.
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.
e
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8
5
.
[
3
]
S
.
V
e
r
ma
a
n
d
V
.
M
u
k
h
e
r
j
e
e
,
“
I
n
v
e
s
t
i
g
a
t
i
o
n
o
f
st
a
t
i
c
t
r
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n
s
mi
ss
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o
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e
x
p
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n
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o
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p
l
a
n
n
i
n
g
u
s
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n
g
t
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sy
mb
i
o
t
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c
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r
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a
n
i
sms
s
e
a
r
c
h
a
l
g
o
r
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t
h
m,
”
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n
g
i
n
e
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n
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O
p
t
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z
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1
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.
[
4
]
M
.
D
e
mi
r
b
a
s
,
M
.
K
e
n
a
n
D
o
s
o
g
l
u
,
a
n
d
S
.
D
u
ma
n
,
“
En
h
a
n
c
e
d
c
o
a
t
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o
p
t
i
mi
z
a
t
i
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n
a
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o
r
i
t
h
m
f
o
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st
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t
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c
a
n
d
d
y
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a
m
i
c
t
r
a
n
sm
i
ssi
o
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n
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t
w
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x
p
a
n
si
o
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p
l
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n
n
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n
g
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b
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e
ms
,
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EE
E
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c
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e
ss
,
v
o
l
.
1
3
,
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p
.
3
5
0
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8
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1
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2
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2
5
,
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o
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0
.
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9
/
A
C
C
ESS
.
2
0
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5
.
3
5
4
4
5
2
3
.
[
5
]
A
.
A
l
ma
l
a
q
,
K
.
A
l
q
u
n
u
n
,
R
.
A
b
b
a
ssi
,
Z.
M
.
A
l
i
,
M
.
M
.
R
e
f
a
a
t
,
a
n
d
S
.
H
.
E.
A
b
d
e
l
A
l
e
e
m
,
“
I
n
t
e
g
r
a
t
e
d
t
r
a
n
sm
i
ssi
o
n
e
x
p
a
n
si
o
n
p
l
a
n
n
i
n
g
i
n
c
o
r
p
o
r
a
t
i
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g
f
a
u
l
t
c
u
r
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n
t
l
i
m
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t
i
n
g
d
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v
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c
e
s
a
n
d
t
h
y
r
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st
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r
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c
o
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t
r
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d
seri
e
s
c
o
mp
e
n
sat
i
o
n
u
si
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met
a
-
h
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u
r
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t
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m
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z
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t
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o
n
t
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c
h
n
i
q
u
e
s
,
”
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c
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t
i
f
i
c
R
e
p
o
rt
s
,
v
o
l
.
1
4
,
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o
.
1
,
p
.
1
3
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4
6
,
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n
.
2
0
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4
,
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o
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:
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0
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1
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8
/
s
4
1
5
9
8
-
0
2
4
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6
3
3
3
1
-
1.
[
6
]
R
.
T.
Z
o
p
p
e
i
,
M
.
A
.
J.
D
e
l
g
a
d
o
,
L
.
H
.
M
a
c
e
d
o
,
M
.
J.
R
i
d
e
r
,
a
n
d
R
.
R
o
mero
,
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A
b
r
a
n
c
h
a
n
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m
.
His
re
se
a
rc
h
i
n
tere
sts
in
c
lu
d
e
p
o
we
r
sy
ste
m
o
p
e
ra
ti
o
n
,
p
o
we
r
sy
ste
m
o
p
ti
m
iza
ti
o
n
,
F
AC
TS
,
o
p
ti
m
iza
ti
o
n
a
l
g
o
ri
th
m
a
n
d
p
o
we
r
m
a
rk
e
ts.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
d
u
o
n
g
t
h
a
n
h
lo
n
g
@iu
h
.
e
d
u
.
v
n
.
Ng
u
y
e
n
Duc
H
u
y
Bu
i
re
c
e
iv
e
d
t
h
e
B.
E
n
g
.
a
n
d
M
.
E
n
g
.
d
e
g
re
e
s
in
e
lec
tri
c
a
l
e
n
g
in
e
e
rin
g
fr
o
m
I
n
d
u
strial
Un
iv
e
rsity
o
f
Ho
Ch
i
M
i
n
h
Cit
y
,
Ho
Ch
i
M
in
h
Cit
y
,
Vie
t
n
a
m
,
i
n
2
0
2
2
,
2
0
2
5
,
re
sp
e
c
ti
v
e
ly
.
C
u
rre
n
t
ly
,
h
e
is
a
P
h
.
D
.
st
u
d
e
n
t
a
t
F
a
c
u
lt
y
o
f
El
e
c
tri
c
a
l
En
g
i
n
e
e
rin
g
Tec
h
n
o
l
o
g
y
,
In
d
u
strial
Un
i
v
e
rsit
y
o
f
H
o
Ch
i
M
i
n
h
Cit
y
,
Ho
Ch
i
M
i
n
h
Cit
y
,
Vie
t
n
a
m
.
His
re
se
a
rc
h
in
tere
sts
in
c
lu
d
e
tran
s
m
issio
n
e
x
p
a
n
sio
n
p
lan
n
in
g
,
p
o
we
r
sy
ste
m
p
lan
n
i
n
g
,
p
o
we
r
sy
ste
m
o
p
e
ra
ti
o
n
,
F
ACTS
,
a
n
d
o
p
ti
m
iza
ti
o
n
a
lg
o
rit
h
m
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
b
u
i
2
h
u
y
@
g
m
a
il
.
c
o
m
.
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