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is
p
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(
E
L
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[
1
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p
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b
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s
an
al
y
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d
b
asicall
y
th
r
o
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g
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w
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3
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co
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MSGB
C
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I
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an
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ates
[
4
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5
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.
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esp
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[
6
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d
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t
t
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e
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ca
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e
f
o
u
n
d
i
n
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1
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.
I
n
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1
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tiv
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s
.
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ter
m
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(
1
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is
ad
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ed
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th
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co
s
t
r
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r
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lect
t
h
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v
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t.
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h
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co
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x
to
tal
co
s
t r
ate
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th
e
n
d
eter
m
i
n
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as:
(
)
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(
15
)
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F
p
in
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s
h
ii
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(
1
5
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2
.
2
.
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nv
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t
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lity
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ns
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ra
ints into
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lity
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ns
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ra
ints
Sin
ce
th
e
FMSG
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o
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it
h
m
r
e
q
u
ir
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t
h
at
all
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n
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ain
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h
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ai
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izat
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el
s
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n
to
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r
r
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n
d
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ain
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.
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h
e
m
et
h
o
d
d
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ib
ed
b
elo
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s
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ca
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n
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n
f
o
r
m
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f
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e
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in
eq
u
alitie
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
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ca
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o
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ain
t
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i
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i
i
ii
ii
ii
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hx
x
x
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f
x
x
x
i
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xx
x
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ain
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y
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a
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o
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le
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ain
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g
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5
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i
n
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n
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le
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ain
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n
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m
a
n
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er
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r
t
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a
m
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ain
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.
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in
1
1
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(
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in{
[
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(
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(
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a
x
0
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(
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18
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eq
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i
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i
i
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l
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u
i
i
ik
l
ik
nu
i
i
i
i
N
G
h
p
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p
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r
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k
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o
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itiv
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n
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e,
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ain
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at
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n
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ite
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ai
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3
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.
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5057
5054
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o
f
1
6
5
7
R
s
/h
r
.
Ov
er
a
s
o
lu
tio
n
ti
m
e
o
f
2
8
.
0
6
s
ec
o
n
d
s
w
h
ile
o
th
er
h
e
u
r
is
tic
m
et
h
o
d
s
lik
e
co
m
b
i
n
ed
c
y
cle
p
ar
ticle
s
w
ar
m
o
p
ti
m
izat
io
n
(
C
C
P
SO)
,
Gr
o
u
p
s
ea
r
ch
o
p
ti
m
izer
(
GSO)
,
C
o
n
s
tr
ain
t
tr
ea
t
m
e
n
t
s
tr
ateg
y
p
ar
ticle
s
w
ar
m
o
p
ti
m
izer
(
C
T
P
SO)
,
ch
ao
tic
s
eq
u
e
n
ce
s
a
n
d
cr
o
s
s
o
v
er
o
p
er
atio
n
al
g
o
r
ith
m
p
ar
ticl
e
s
w
ar
m
o
p
ti
m
izatio
n
(
C
C
P
SO)
,
co
n
tin
u
o
u
s
q
u
ic
k
g
r
o
u
p
s
ea
r
ch
o
p
ti
m
izer
(
C
QGS
O)
[
2
3
,
2
4
]
an
d
ev
o
lu
t
io
n
ar
y
p
r
o
g
r
am
m
i
n
g
(
E
P
)
m
et
h
o
d
etc.
y
ield
1
6
5
8
R
s
.
/
h
r
,
1
7
2
8
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s
.
/h
r
,
1
6
3
9
R
s
.
/h
r
,
1
6
5
8
R
s
.
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r
a
n
d
1
6
6
7
R
s
.
/h
r
f
o
r
s
o
lu
tio
n
ti
m
e
s
o
f
1
5
0
s
ec
o
n
d
s
,
5
3
.
8
0
s
ec
o
n
d
s
,
1
0
0
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ec
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n
d
s
,
1
5
0
s
ec
o
n
d
s
a
n
d
3
1
.
6
7
s
ec
o
n
d
s
r
esp
ec
ti
v
el
y
.
T
h
er
ef
o
r
e,
it
is
q
u
ite
co
n
s
p
icu
o
u
s
t
h
at
MSGB
C
A
E
P
m
e
th
o
d
o
u
tp
er
f
o
r
m
s
th
e
o
th
er
h
eu
r
i
s
tic
m
et
h
o
d
s
in
v
o
l
v
i
n
g
n
o
n
s
m
o
o
th
co
s
t
f
u
n
ctio
n
s
,
m
u
lt
i
-
o
b
j
ec
tiv
es
a
n
d
v
alv
e
p
o
in
t
lo
ad
in
g
[
2
5
-
2
7
]
in
ter
m
s
o
f
to
tal
co
s
t
r
ate
an
d
s
o
lu
tio
n
t
i
m
e
a
s
w
ell.
T
ab
le
5
.
R
ea
l p
o
w
er
an
d
e
m
is
s
io
n
le
v
el
f
o
r
th
e
p
r
o
p
o
s
ed
m
e
th
o
d
S
l
.
N
o
.
(
M
W
)
(
)
(
M
T
/
h
r
.
)
1
0
.
0
8
1
5
.
3
3
2
0
.
2
8
9
1
2
.
5
3
0
.
3
9
2
11
4
0
.
4
82
9
5
0
.
7
6
7
5
6
0
.
9
2
2
4.
RE
SU
L
T
ANAL
YSI
S
R
es
u
lts
f
o
r
Gen
er
atio
n
C
o
s
t
r
ate
v
s
.
ac
tiv
e
p
o
w
er
g
e
n
er
ati
o
n
an
d
e
m
is
s
io
n
lev
e
l
v
s
.
ac
t
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e
p
o
w
er
g
en
er
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n
f
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r
6
g
e
n
er
ato
r
I
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3
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u
s
te
s
t
ca
s
e
s
y
s
te
m
t
h
r
o
u
g
h
MSGB
C
A
E
P
ap
p
r
o
ac
h
w
er
e
tab
u
lated
i
n
T
ab
le
5
.
T
h
e
p
er
f
o
r
m
an
ce
o
f
MSGB
C
A
E
P
m
eth
o
d
f
o
r
co
s
t
r
ate
an
d
em
is
s
io
n
lev
e
l
r
ate
w
a
s
co
m
p
ar
ed
w
ith
o
th
er
h
e
u
r
is
tic
m
eth
o
d
s
a
n
d
t
h
e
r
es
u
lt
s
w
er
e
tab
u
lated
i
n
T
ab
le
6
.
C
lass
ical
m
e
th
o
d
s
lik
e
la
m
b
d
a
iter
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n
m
et
h
o
d
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d
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er
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e
u
r
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et
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d
s
co
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ld
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m
ee
t
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t
m
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ltip
le
co
n
s
tr
ain
ts
to
n
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g
lo
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al
s
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p
r
o
p
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ap
p
r
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b
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au
s
e
o
f
f
ast
j
u
d
icio
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s
m
o
d
if
ica
tio
n
o
f
in
iti
aliza
tio
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o
f
p
ar
en
t
p
o
p
u
latio
n
in
d
ep
en
d
en
t
o
f
cr
o
s
s
o
v
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m
ec
h
an
i
s
m
,
r
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l
te
d
g
lo
b
al
o
p
tim
al
s
o
lu
tio
n
w
it
h
les
s
co
m
p
u
tat
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n
al
ti
m
e
f
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r
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s
t
an
d
e
m
is
s
io
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o
b
j
ec
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f
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c
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s
.
T
h
e
p
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p
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m
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b
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ap
p
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in
to
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s
u
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m
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b
tain
in
g
g
lo
b
a
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tim
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lu
tio
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.
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5055
T
ab
le
6
.
C
o
m
p
ar
is
o
n
o
f
p
r
o
p
o
s
ed
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C
A
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m
et
h
o
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it
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r
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s
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p
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t
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l
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a
t
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(
R
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h
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1
5
5
7
9
6
1
.
3
4
5
1
5
5
8
8
6
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.
7
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1
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5
9
9
6
2
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1
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6
7
9
6
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Emi
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r
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1
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3
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1
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5
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se
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5.
P
E
RF
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RM
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ARA
CT
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RIS
T
I
CS
Fig
u
r
e
2
an
d
Fig
u
r
e
3
s
h
o
w
t
h
e
s
i
m
u
latio
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u
lt
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er
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is
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le
v
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v
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s
u
s
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ea
l
p
o
w
er
f
o
r
th
e
p
r
o
p
o
s
ed
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C
A
E
P
m
o
d
el
w
h
er
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f
o
r
in
cr
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en
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m
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r
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t
h
e
r
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y
o
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h
er
h
e
u
r
is
tic
m
et
h
o
d
s
s
u
c
h
as
C
C
P
SO,
C
T
P
SO,
GSO,
C
QGSO
a
n
d
E
P
etc.
an
d
ar
e
tab
u
late
d
in
T
ab
le
6
.
R
ea
l
p
o
w
er
P
(
i)
in
MW
R
ea
l
p
o
w
er
P
(
i)
in
MW
Fig
u
r
e
2
.
C
o
s
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g
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n
er
atio
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v
er
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Fig
u
r
e
3
.
E
m
is
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io
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er
s
u
s
r
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l
p
o
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er
6.
CO
NCLU
SI
O
N
T
h
e
o
p
tim
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f
u
el
co
s
t
s
o
f
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et
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ch
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th
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w
it
h
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ig
n
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ica
n
t
d
if
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er
e
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ce
.
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h
e
o
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tim
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e
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er
atio
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s
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h
e
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les
o
f
t
h
e
p
r
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E
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m
e
th
o
d
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d
t
h
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m
e
th
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ex
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tl
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m
atc
h
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ile
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h
e
s
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h
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le
o
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tain
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ith
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e
th
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s
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ica
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y
d
i
f
f
e
r
s
.
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h
e
n
u
m
b
er
o
f
iter
atio
n
s
o
f
t
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
is
r
ed
u
ce
d
g
r
ea
tl
y
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m
p
ar
ed
to
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e
o
th
er
m
eth
o
d
s
.
A
co
m
p
ar
ativ
e
s
t
u
d
y
o
f
th
e
co
m
p
u
ta
tio
n
ti
m
e
is
g
iv
e
n
i
n
th
e
last
r
o
w
o
f
T
ab
le
6
.
I
t
m
a
y
b
e
o
b
s
er
v
ed
th
at
o
n
an
av
er
a
g
e
co
m
p
u
tatio
n
ti
m
e
i
s
r
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u
ce
d
b
y
9
0
%
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h
ich
s
h
o
w
s
t
h
e
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m
p
u
tatio
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al
e
f
f
o
r
t
o
f
t
h
e
p
r
o
p
o
s
ed
m
eth
o
d
.
T
h
e
ab
o
v
e
f
ac
ts
v
al
id
ate
th
e
s
t
ate
m
e
n
t th
a
t th
e
p
r
o
p
o
s
ed
m
e
t
h
o
d
is
m
o
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e
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f
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n
t a
n
d
f
as
t c
o
n
v
er
g
in
g
as
w
el
l.
T
h
e
MSGB
C
A
E
P
ap
p
r
o
ac
h
d
ev
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ed
in
th
e
p
r
ese
n
t
s
tu
d
y
ca
n
b
e
u
til
ized
to
s
o
lv
e
a
s
in
g
le
o
b
j
ec
tiv
e
as
w
ell
as
co
n
f
lict
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n
g
m
u
lti
-
o
b
j
ec
tiv
e
p
o
w
er
d
i
s
p
atch
p
r
o
b
le
m
s
.
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h
e
h
ill
cli
m
b
in
g
alg
o
r
it
h
m
a
n
d
iter
ativ
e
g
r
ad
ie
n
t
m
et
h
o
d
s
g
e
t
tr
ap
p
ed
in
lo
ca
l
m
i
n
i
m
a
b
u
t
h
a
v
e
f
a
s
ter
co
n
v
e
r
g
en
ce
.
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SGB
C
A
E
P
ap
p
r
o
ac
h
h
as
g
lo
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al
s
ea
r
ch
ch
ar
ac
ter
is
tic
s
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n
d
r
o
b
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s
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n
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at
p
r
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e
n
t
t
h
e
m
f
r
o
m
g
e
tti
n
g
tr
ap
p
ed
in
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l
o
p
ti
m
a
u
n
li
k
e
h
ill
cli
m
b
in
g
alg
o
r
ith
m
.
Hen
ce
e
v
o
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tio
n
ar
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o
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h
m
s
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n
b
e
ap
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e
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ial
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ta
g
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o
f
t
h
e
s
o
l
u
ti
o
n
f
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g
lo
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al
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ch
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d
th
e
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m
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n
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al
g
o
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ith
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s
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e
ap
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h
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e
s
f
o
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e
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l
s
ea
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ch
.
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h
is
M
SGB
C
A
E
P
ap
p
r
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h
m
a
y
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.
RE
F
E
R
E
NC
E
S
[1
]
Y
.
M
a
,
e
t
a
l
.
,
“
Dy
n
a
m
ic
Eco
n
o
m
ic
Disp
a
tch
a
n
d
C
o
n
t
ro
l
o
f
a
sta
n
d
-
al
o
n
e
M
icr
o
g
rid
in
Do
n
g
A
o
Isla
n
d
,”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
E
lec
trica
l
En
g
in
e
e
rin
g
T
e
c
h
n
o
l
o
g
y
,
v
o
l.
1
0
,
n
o
.
4
,
p
p
.
1
4
3
2
-
1
4
4
0
,
2
0
1
5
.
[2
]
T.
Nik
n
a
m
,
e
t
a
l.
,
“
A
n
e
w
h
y
b
rid
a
lg
o
rit
h
m
f
o
r
o
p
ti
m
a
l
p
o
w
e
r
f
lo
w
c
o
n
sid
e
rin
g
p
r
o
h
i
b
it
e
d
z
o
n
e
s
a
n
d
v
a
lv
e
p
o
in
t
e
ffe
c
t,
”
En
e
r
g
y
Co
n
v
e
rs
io
n
a
n
d
M
a
n
a
g
e
me
n
t
,
v
o
l.
5
8
,
p
p
.
1
9
7
-
2
0
6
,
2
0
1
2
.
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
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n
g
,
Vo
l.
10
,
No
.
5
,
Octo
b
e
r
2
0
2
0
:
5
0
4
8
-
5057
5056
[3
]
S.
F
a
d
il
,
e
t
a
l
.
,
“
A
se
c
u
rit
y
-
c
o
n
stra
in
e
d
e
c
o
n
o
m
ic
d
isp
a
tch
tec
h
n
iq
u
e
u
si
n
g
m
o
d
if
ied
su
b
g
ra
d
ien
t
a
lg
o
rit
h
m
b
a
se
d
o
n
f
e
a
sib
le v
a
u
e
s a
n
d
p
se
u
d
o
sc
a
li
n
g
f
a
c
to
r
f
o
r
a
p
o
w
e
r
s
y
ste
m
a
re
a
i
n
c
lu
d
i
n
g
li
m
it
e
d
e
n
e
rg
y
su
p
p
ly
th
e
rm
a
l
u
n
it
s,
”
E
lec
tric p
o
we
r c
o
mp
o
n
e
n
t
sy
ste
m
,
v
o
l.
3
9
,
n
o
.
16
,
p
p
.
1
7
4
8
-
1
7
6
8
,
2
0
1
1
.
[4
]
S.
P
ra
b
a
k
a
ra
n
,
e
t
a
l.
,
“
Eco
n
o
m
ic
Disp
a
tch
Us
in
g
H
y
b
rid
P
a
rti
c
le
S
w
a
r
m
Op
ti
m
iza
ti
o
n
w
it
h
P
ro
h
ib
it
e
d
Op
e
ra
ti
n
g
Zo
n
e
s
a
n
d
Ra
m
p
Ra
te
L
i
m
it
Co
n
stra
in
ts
,
”
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
En
g
in
e
e
rin
g
T
e
c
h
n
o
lo
g
y
,
v
o
l.
10
,
n
o
.
4,
pp.
1
4
4
1
-
1
4
5
2
,
2
0
1
5
.
[5
]
P.
K.
Ho
ta
a
n
d
N.
C.
S
a
h
u
,
“
No
n
-
Co
n
v
e
x
Eco
n
o
m
ic
Disp
a
t
c
h
w
it
h
P
ro
h
ib
it
e
d
Op
e
ra
ti
n
g
Zo
n
e
s
th
r
o
u
g
h
G
ra
v
it
a
ti
o
n
a
l
S
e
a
rc
h
A
l
g
o
rit
h
m
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
El
e
c
tri
c
a
l
a
n
d
Co
mp
u
t
e
r
En
g
in
e
e
rin
g
(
IJ
ECE
)
,
v
o
l.
5
,
n
o
.
6
,
p
p
.
1
2
3
4
-
1
2
4
4
,
2
0
1
5
.
[6
]
Z.
L
.
G
a
in
g
,
“
P
a
rti
c
le
S
wa
r
m
Op
ti
m
iz
a
ti
o
n
f
o
r
s
o
lv
in
g
th
e
e
c
o
n
o
m
ic
d
isp
a
tch
c
o
n
sid
e
rin
g
th
e
g
e
n
e
ra
to
r
c
o
n
stra
in
ts
,
”
IE
EE
T
a
n
s
a
c
ti
o
n
o
n
Po
we
r S
y
st
e
ms
,
v
o
l.
1
8
,
n
o
.
3
,
p
p
.
1
1
8
7
-
1
1
9
5
,
2
0
0
3
.
[7
]
V.
K.
Ja
d
o
u
n
,
e
t
a
l.
,
“
Dy
n
a
m
ica
ll
y
c
o
n
tro
ll
e
d
p
a
rti
c
le
sw
a
r
m
o
p
ti
m
iza
ti
o
n
f
o
r
larg
e
-
s
c
a
le
n
o
n
c
o
n
v
e
x
e
c
o
n
o
m
i
c
d
isp
a
tch
p
ro
b
lem
s
,
”
In
ter
n
a
ti
o
n
a
l
T
ra
n
s
a
c
ti
o
n
s o
n
El
e
c
trica
l
En
e
rg
y
S
y
ste
ms
,
v
o
l.
2
5
,
n
o
.
1
1
,
p
p
.
3
0
6
0
-
3
0
7
4
,
2
0
1
4
.
[8
]
N.
G
h
o
rb
a
n
i,
e
t
a
l.
,
“
P
a
rti
c
le
sw
a
r
m
o
p
ti
m
iza
ti
o
n
w
it
h
sm
a
rt
in
e
rti
a
f
a
c
to
r
f
o
r
so
lv
in
g
n
o
n
-
c
o
n
v
e
x
e
c
o
n
o
m
ic
lo
a
d
d
isp
a
tch
p
ro
b
lem
s
,
”
In
ter
n
a
ti
o
n
a
l
T
ra
n
s
a
c
ti
o
n
s o
n
El
e
c
trica
l
En
e
rg
y
S
y
ste
ms
,
v
o
l.
2
4
,
n
o
.
8
,
p
p
.
1
1
2
0
-
1
1
3
3
,
2
0
1
4
.
[9
]
T
.
Nik
n
a
m
,
e
t
a
l.
,
“
A
n
e
w
p
a
rti
c
l
e
sw
a
r
m
o
p
ti
m
iza
ti
o
n
f
o
r
n
o
n
-
c
o
n
v
e
x
e
c
o
n
o
m
ic
d
isp
a
tch
,
”
Eu
r
o
p
e
a
n
T
ra
n
s
a
c
ti
o
n
s
o
n
E
lec
trica
l
Po
we
r
,
v
o
l.
2
1
,
n
o
.
1
,
p
p
.
6
5
6
-
6
7
9
,
2
0
1
1
.
[1
0
]
B
.
M
a
ll
ik
a
rju
n
a
,
e
t
a
l.
,
“
Eco
n
o
m
ic
L
o
a
d
Disp
a
tch
Do
w
n
sid
e
with
V
a
lv
e
-
P
o
i
n
t
Re
su
lt
Em
p
lo
y
in
g
a
Bin
a
r
y
Ba
t
F
o
rm
u
la
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
Co
m
p
u
ter
E
n
g
in
e
e
rin
g
(
IJ
ECE
)
,
v
o
l
.
4,
n
o
.
1,
p
p
.
1
0
1
-
1
0
7
,
F
e
b
.
2
0
1
4
.
[1
1
]
B
.
A
ll
a
o
u
a
a
n
d
A
.
L
a
o
f
i
,
“
Op
ti
m
a
l
P
o
w
e
r
F
lo
w
S
o
lu
t
io
n
Us
in
g
A
n
t
M
a
n
n
e
rs
f
o
r
El
e
c
tri
c
a
l
Ne
tw
o
rk
,
”
Ad
v
a
n
c
e
s
in
El
e
c
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
,
v
o
l.
0
9
,
n
o
.
1,
pp.
34
-
4
0
,
2
0
0
9
.
[1
2
]
S.
F
a
d
il
,
e
t
a
l.
,
“
A
S
o
lu
ti
o
n
to
se
c
u
rit
y
c
o
n
stra
in
e
d
n
o
n
-
c
o
n
v
e
x
e
c
o
n
o
m
ic
d
isp
a
tch
p
ro
b
lem
b
y
m
o
d
if
ied
su
b
g
ra
d
ien
t
a
lg
o
rit
h
m
b
a
se
d
o
n
f
e
a
sib
le
v
a
lu
e
s
,
”
In
t
e
rn
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
Po
we
r
a
n
d
En
e
rg
y
S
y
ste
m
,
v
o
l.
43
,
n
o
.
1
,
p
p
.
8
4
9
-
8
5
8
,
2
0
1
2
.
[1
3
]
S.
F
a
d
i
l
a
n
d
B.
U
ra
z
e
l,
“
S
o
lu
ti
o
n
to
se
c
u
rit
y
c
o
n
stra
in
e
d
n
o
n
c
o
n
v
e
x
p
u
m
p
e
d
–
sto
ra
g
e
h
y
d
ra
u
li
c
u
n
it
sc
h
e
d
u
li
n
g
p
ro
b
lem
b
y
m
o
d
if
ied
su
b
-
g
ra
d
ie
n
t
a
lg
o
rit
h
m
b
a
se
d
o
n
f
e
a
sib
le
v
a
lu
e
s
a
n
d
p
se
u
d
o
w
a
ter
p
rice
,
”
El
e
c
tric
Po
we
r
C
o
mp
o
n
e
n
ts
a
n
d
S
y
ste
ms
,
v
o
l.
41,
n
o
.
2,
p
p
.
1
1
1
-
1
3
5
,
20
1
3
.
[1
4
]
M
.
M
o
ra
d
i
-
Da
lv
a
n
d
,
e
t
a
l.
,
“
Co
n
ti
n
u
o
u
s
q
u
ick
g
ro
u
p
se
a
rc
h
o
p
ti
m
iz
e
r
f
o
r
so
lv
in
g
n
o
n
-
c
o
n
v
e
x
e
c
o
n
o
m
ic
d
isp
a
tch
p
ro
b
lem
s
,
”
El
e
c
tric P
o
we
r S
y
ste
m R
e
se
a
rc
h
,
v
o
l.
93,
p
p
.
93
-
1
0
5
,
2
0
1
2
.
[1
5
]
T
.
A
d
h
in
a
ra
y
a
n
a
n
a
n
d
M
.
S
y
d
u
l
u
,
“
Rse
rv
e
c
o
n
stra
in
e
d
e
c
o
n
o
m
ic
d
isp
a
tch
w
it
h
p
r
o
h
ib
it
e
d
o
p
e
ra
ti
n
g
z
o
n
e
s
u
sin
g
lo
g
ic
b
a
se
d
a
lg
o
rit
h
m
,
”
in
2007
IEE
E
Po
we
r
e
n
g
i
n
e
e
rin
g
S
o
c
iety
Ge
n
e
ra
l
M
e
e
ti
n
g
,
T
a
m
p
a
,
F
lo
rid
a
,
USA
,
p
p
.
1
-
7
,
2
0
0
7
.
[1
6
]
I.
A.
F
a
rh
a
t
a
n
d
M
.
E
.
E
l
-
H
a
w
a
r
y
,
“
In
terio
r
p
o
in
t
m
e
th
o
d
a
p
p
l
ica
ti
o
n
in
o
p
ti
m
u
m
o
p
e
ra
ti
o
n
a
l
sc
h
e
d
u
li
n
g
o
f
e
lec
tri
c
p
o
w
e
r
s
y
ste
m
s
,
”
IET
Ge
n
e
ra
ti
o
n
,
T
ra
n
sm
issio
n
a
n
d
Distrib
u
ti
o
n
,
v
o
l.
3
,
n
o
.
1
1
,
p
p
.
1
0
2
0
-
1
0
2
9
,
2
0
0
9
.
[1
7
]
Z.
L
.
G
a
in
g
a
n
d
R.
F
.
Ch
a
n
g
,
“
S
e
c
u
rit
y
-
Co
n
stra
in
e
d
o
p
ti
m
a
l
p
o
we
r
f
lo
w
b
y
m
ix
e
d
-
in
teg
e
r
g
e
n
e
ti
c
a
lg
o
rit
h
m
w
it
h
a
rit
h
m
e
ti
c
o
p
e
ra
to
rs
,
”
in
2006
IE
EE
Po
we
r
En
g
i
n
e
e
rin
g
S
o
c
iety
Ge
n
e
ra
l
M
e
e
ti
n
g
,
M
o
n
trea
l,
Qu
e
b
e
c
,
Ca
n
a
d
a
,
p
p
.
1
-
8
,
F
e
b
.
20
0
6.
[1
8
]
L
.
G
.
P
a
p
a
g
o
a
n
d
E.
S
.
F
ra
g
a
,
“
A
m
ix
e
d
in
teg
e
r
q
u
a
d
ra
ti
c
p
ro
g
ra
m
m
in
g
f
o
r
m
u
lat
io
n
f
o
r
th
e
e
c
o
n
o
m
ic
d
isp
a
tch
o
f
g
e
n
e
ra
to
rs w
it
h
p
ro
h
i
b
it
e
d
o
p
e
ra
ti
n
g
z
o
n
e
s
,
”
El
e
c
tr
ic
Po
w
e
r
S
y
st
e
m
s
Res
e
a
rh
,
v
o
l.
7
7
,
n
o
.
1
0
,
p
p
.
1
2
9
2
-
1
2
9
6
,
2
0
0
7
.
[1
9
]
S
.
Oz
y
o
n
a
n
d
D.
Ay
d
in
,
“
In
c
re
m
e
n
tal
a
rti
f
icia
l
b
e
e
c
o
lo
n
y
w
it
h
lo
c
a
l
se
a
rc
h
to
e
c
o
n
o
m
ic
d
isp
a
tch
p
ro
b
lem
w
it
h
ra
m
p
ra
te l
im
it
s a
n
d
p
ro
h
ib
it
e
d
o
p
e
ra
ti
n
g
z
o
n
e
s
,
”
En
e
rg
y
C
o
n
v
e
rs
io
n
a
n
d
M
a
n
a
g
e
me
n
t
,
v
o
l.
6
5
,
p
p
.
3
9
7
-
4
0
7
,
2
0
1
3
.
[2
0
]
L
.
d
o
s
S
.
C
o
e
lh
o
,
e
t
a
l.
,
“
Dif
fe
re
n
ti
a
l
e
v
o
lu
ti
o
n
b
a
se
d
o
n
tr
u
n
c
a
ted
L
é
v
y
-
t
y
p
e
f
li
g
h
ts
a
n
d
p
o
p
u
latio
n
d
iv
e
rsity
m
e
a
su
re
to
so
lv
e
e
c
o
n
o
m
ic
lo
a
d
d
isp
a
tch
p
ro
b
lem
s
,
”
In
t
e
rn
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
P
o
w
e
r
and
En
e
r
g
y
S
y
st
e
ms
,
v
o
l
.
5
7
,
p
p
.
1
7
8
-
1
8
8
,
2
0
1
4
.
[2
1
]
B.
M
a
h
d
a
d
a
n
d
K.
S
ra
iri
,
“
In
tera
c
ti
v
e
g
ra
v
it
a
ti
o
n
a
l
se
a
rc
h
a
l
g
o
rit
h
m
a
n
d
p
a
tt
e
rn
se
a
r
c
h
a
lg
o
rit
h
m
s
f
o
r
p
ra
c
ti
c
a
l
D
y
n
a
m
ic
Eco
n
o
m
ic
Disp
a
tch
,
”
In
ter
n
a
ti
o
n
a
l
T
r
a
n
sa
c
ti
o
n
s
o
n
El
e
c
trica
l
En
e
rg
y
S
y
ste
m
,
v
o
l.
2
5
,
n
o
.
1
0
,
p
p
.
2
2
8
9
-
2
3
0
9
,
2
0
1
4
.
[2
2
]
A
.
Ra
ja
g
o
p
a
lan
,
e
t
a
l.
,
“
S
o
lv
in
g
e
c
o
n
o
m
ic
lo
a
d
d
isp
a
tch
p
ro
b
lem
s
u
sin
g
c
h
a
o
ti
c
se
lf
–
a
d
a
p
ti
v
e
d
if
f
e
re
n
ti
a
l
h
a
rm
o
n
y
se
a
rc
h
a
lg
o
rit
h
m
,
”
In
ter
n
a
ti
o
n
a
l
T
ra
n
sa
c
ti
o
n
s
o
n
El
e
c
trica
l
E
n
e
rg
y
S
y
ste
ms
,
v
o
l.
2
5
,
n
o
.
5
,
p
p
.
8
4
5
-
8
5
8
,
2
0
1
5
.
[2
3
]
E.
A
fz
a
lan
a
n
d
M
.
Jo
o
ra
b
ian
,
“
A
n
i
m
p
ro
v
e
d
c
u
c
k
o
o
se
a
rc
h
a
lg
o
rit
h
m
f
o
r
p
o
w
e
r
e
c
o
n
o
m
ic
lo
a
d
d
isp
a
tch
,
”
In
ter
n
a
t
io
n
a
l
T
ra
n
sa
c
ti
o
n
s o
n
El
e
c
trica
l
En
e
rg
y
S
y
ste
ms
,
v
o
l.
2
5
,
n
o
.
6
,
p
p
.
9
5
8
-
9
7
5
,
2
0
1
5
.
[2
4
]
H.
Da
n
e
sh
i,
e
t
a
l.
,
“
M
ix
e
d
in
te
g
e
r
p
ro
g
ra
m
m
in
g
m
e
th
o
d
to
so
l
v
e
se
c
u
rit
y
c
o
n
stra
i
n
e
d
u
n
i
t
c
o
m
m
it
m
e
n
t
w
it
h
re
stricte
d
o
p
e
ra
ti
n
g
z
o
n
e
li
m
it
s
,
”
2
0
0
8
IE
EE
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
e
lec
tro
/i
n
f
o
rm
a
t
io
n
tec
h
n
o
lo
g
y
,
p
p
.
1
8
7
-
1
9
2
,
2
0
0
8
.
[2
5
]
W
.
Kh
a
m
se
n
,
e
t
a
l.
,
“
Hy
b
rid
m
e
th
o
d
f
o
r
so
lv
i
n
g
th
e
n
o
n
sm
o
o
th
c
o
st
f
u
n
c
ti
o
n
e
c
o
n
o
m
ic
d
isp
a
tch
p
r
o
b
lem
,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
E
lec
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
ECE
)
,
v
o
l.
1
0
,
n
o.
1
,
p
p
.
6
0
9
-
6
1
6
,
2
0
2
0
.
[2
6
]
R
.
Ha
b
a
c
h
i,
e
t
a
l.
,
“
Eco
n
o
m
ic
a
n
d
e
m
issio
n
d
isp
a
tch
u
si
n
g
c
u
c
k
o
o
se
a
rc
h
a
lg
o
rit
h
m
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
ECE
)
,
v
o
l.
9
,
n
o
.
5
,
p
p
.
3
3
8
4
-
3
3
9
0
,
2
0
1
9
.
[2
7
]
M.
Be
sth
a
,
e
t
a
l.
,
“
Eco
n
o
m
ic
L
o
a
d
Disp
a
tch
Do
w
n
sid
e
w
it
h
V
a
lv
e
-
P
o
in
t
Re
su
lt
Em
p
lo
y
in
g
a
Bin
a
ry
Ba
t
F
o
rm
u
la
,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
E
lec
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
ECE
)
,
v
o
l.
4
,
n
o.
1
,
p
p
.
1
0
1
-
1
0
7
,
2
0
1
4
.
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