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n
ch
ar
ac
ter
is
tic
[
4
]
w
it
h
a
n
d
w
it
h
o
u
t
tr
a
n
s
m
i
s
s
io
n
lo
s
s
[
1
2
]
in
co
r
p
o
r
atin
g
v
alv
e
p
o
in
t
an
al
y
s
is
h
as
b
ee
n
co
m
p
ar
ed
w
it
h
s
w
ar
m
o
p
ti
m
izatio
n
tech
n
iq
u
e[
2
]
in
v
o
l
v
in
g
MO
DB
C
[
9
]
.
I
n
th
i
s
d
is
s
er
ta
tio
n
th
e
i
m
p
ac
t
o
f
en
h
a
n
ce
d
p
o
w
er
d
e
m
an
d
i
n
v
o
lv
i
n
g
lo
ad
f
r
eq
u
en
c
y
co
n
t
r
o
l
lo
o
p
(
L
FC
)
an
d
au
to
m
ati
c
v
o
ltag
e
r
eg
u
lato
r
lo
o
p
(
A
VR
)
f
o
r
o
p
ti
m
izi
n
g
o
s
cillatio
n
s
in
f
r
eq
u
e
n
c
y
d
ev
ia
t
io
n
an
d
i
m
p
r
o
v
i
n
g
s
tead
y
s
ta
te
p
er
f
o
r
m
a
n
ce
,
h
as
b
ee
n
atte
m
p
ted
.
T
h
e
MO
DB
C
E
P
D
tech
n
iq
u
e
u
s
i
n
g
P
SO
[
6
]
b
ased
PID
co
n
tr
o
ller
p
er
tai
n
in
g
to
t
h
e
Z
e
ig
ler
Nich
o
ls
m
et
h
o
d
o
f
t
u
n
i
n
g
h
a
s
b
ee
n
ad
o
p
ted
in
th
is
d
i
s
s
er
tati
o
n
.
C
o
s
t
o
f
g
e
n
er
atio
n
v
er
s
u
s
e
m
is
s
io
n
le
v
el
o
f
a
th
er
m
a
l
p
o
w
er
p
la
n
t
w
it
h
a
n
d
w
it
h
o
u
t
tr
an
s
m
is
s
io
n
lo
s
s
in
co
r
p
o
r
atin
g
VP
L
,
MO
DB
C
an
d
MO
DB
C
E
P
D
o
p
tim
izatio
n
tech
n
iq
u
e
s
h
as
b
ee
n
an
al
y
ze
d
i
n
t
h
is
d
is
s
er
tatio
n
an
d
d
is
p
la
y
ed
v
id
e
FIG
-
3
a
n
d
FIG
-
4
r
esp
ec
tiv
el
y
.
2.
VALV
E
P
O
I
N
T
L
O
AD
I
N
G
T
h
er
m
al
p
o
w
er
p
lan
t
s
ar
e
ch
a
r
ac
ter
ized
b
y
m
u
ltip
le
s
tea
m
v
alv
es.
I
n
o
r
d
er
to
an
al
y
ze
t
h
e
f
u
e
l
co
s
t
f
u
n
ctio
n
t
h
e
v
al
v
e
p
o
in
t
lo
ad
in
g
[
1
1
]
ef
f
ec
t
i
s
d
escr
ib
ed
as
f
o
llo
w
s
,
L
et
N
b
e
th
e
n
u
m
b
er
o
f
u
n
it
s
.
T
h
e
g
en
er
atio
n
co
s
t
o
b
j
ec
tiv
e
f
u
n
c
tio
n
f
o
r
th
e
t
h
er
m
a
l
p
o
w
er
p
lan
t
in
t
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
ca
n
b
e
r
ep
r
esen
ted
b
y
th
e
co
s
t f
u
n
ctio
n
:
(
1
)
W
h
er
e,
i
a
,
i
b
an
d
i
c
ar
e
g
en
er
atio
n
co
s
t c
o
ef
f
icie
n
t
s
f
o
r
th
e
th
i
g
e
n
er
atin
g
u
n
it o
f
t
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
w
it
h
v
alv
e
p
o
in
t lo
ad
in
g
s
u
b
j
ec
ted
to
co
n
d
itio
n
:
(
2
)
W
h
e
r
e
i
=
1
,
2
,
3
.
.
.
.
.
.
.
.
n
,
i
pg
b
e
th
e
p
o
w
er
s
u
p
p
lied
b
y
th
e
i
th
u
n
it
a
n
d
P
D
b
e
th
e
lo
ad
d
e
m
an
d
i
n
MW
.
T
h
e
tr
an
s
m
is
s
io
n
lo
s
s
f
o
r
a
‘
n
’
u
n
it e
lectr
ic
p
o
w
er
s
y
s
te
m
i
s
ex
p
r
ess
ed
as:
(
3
)
(
4
)
W
h
er
e
m
pg
=
R
ea
l p
o
w
er
g
e
n
er
ated
b
y
m
t
h
p
o
w
er
p
lan
t,
n
pg
=
R
ea
l
p
o
w
er
g
e
n
er
ated
b
y
n
t
h
p
o
w
er
p
la
n
t;
mn
B
=T
r
a
n
s
m
i
s
s
io
n
lo
s
s
i
n
p
er
m
eg
a
w
att;
m
=B
u
s
v
o
ltag
e
an
g
le
o
f
m
t
h
p
o
w
er
p
lan
t;
n
=
B
u
s
v
o
lta
g
e
an
g
le
o
f
n
th
p
o
w
er
p
lan
t;
m
Mp
=C
u
r
r
en
t
d
is
tr
ib
u
t
io
n
f
a
cto
r
o
f
m
t
h
p
lan
t;
n
Mp
=
C
u
r
r
en
t
d
is
tr
ib
u
tio
n
f
ac
to
r
o
f
n
th
p
lan
t;
m
=P
h
ase
an
g
le
o
f
m
t
h
p
lan
t;
m
V
=V
o
ltag
e
a
t
th
e
m
th
b
u
s
;
n
V
=
Vo
ltag
e
at
th
e
t
h
b
u
s
;
l
R
=
L
o
ad
r
esis
ta
n
ce
,
an
d
n
=
p
h
ase
an
g
le
o
f
n
t
h
p
lan
t.
I
n
clu
d
i
n
g
v
al
v
e
p
o
i
n
t
lo
ad
i
n
g
an
d
i
n
co
r
p
o
r
atin
g
tr
an
s
m
is
s
io
n
lo
s
s
[
1
2
]
,
[
1
3
]
u
s
in
g
co
n
v
e
n
tio
n
a
l
m
et
h
o
d
th
e
co
s
t o
f
t
h
er
m
al
g
e
n
er
atio
n
is
e
x
p
r
ess
ed
as:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
5
,
Octo
b
er
2
0
1
7
:
2
3
8
2
–
2
3
9
1
2384
(
5
)
ii
S
u
b
j
e
c
t
e
d
t
o
c
o
n
d
i
t
i
o
n
g
m
i
n
g
m
a
x
i
p
p
g
p
2
.
1
.
Co
s
t
Crit
er
ia
f
o
r
E
co
no
m
i
c
L
o
a
d Dis
pa
t
ch
P
ro
ble
m
Usi
n
g
th
e
L
a
g
r
an
g
ian
m
u
ltip
l
ier
m
et
h
o
d
,
f
u
el
co
s
t
f
u
n
ctio
n
in
co
r
p
o
r
atin
g
tr
an
s
m
is
s
io
n
l
o
s
s
w
a
s
ex
p
r
ess
ed
in
eq
u
a
tio
n
(
5
)
,
b
y
d
if
f
er
e
n
tiati
n
g
th
e
eq
u
a
tio
n
(
5
)
w
e
g
et
:
(
6
)
(
7
)
(
8
)
E
q
u
a
tio
n
(
8
)
s
a
tis
f
ies th
e
eq
u
lity c
o
n
s
tr
a
in
t
i
d
l
p
g
p
p
,
(
7
)
2
i
D
i
v
i
d
i
n
g
e
q
u
a
t
i
o
n
b
y
a
(
9
)
(
1
0
)
T
h
e
em
i
s
s
io
n
eq
u
atio
n
i
s
ex
p
r
ess
ed
as
,
(
1
1
)
W
h
er
e,
i
,
i
an
d
,
i
i
i
a
n
d
K
ar
e
em
i
s
s
io
n
co
s
t
co
ef
f
icie
n
t
s
f
o
r
th
e
th
i
g
e
n
er
atin
g
u
n
it
o
f
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
.
3
.
M
O
D
B
C
3
.
1
.
Descript
io
n
I
n
t
h
is
p
ap
er
,
w
e
m
ak
e
u
s
e
o
f
MO
DB
C
[
9
]
f
o
r
m
u
lti
o
b
j
ec
tiv
e
p
r
o
b
le
m
s
w
h
ich
i
s
a
h
y
b
r
id
v
er
s
io
n
o
f
m
u
l
ti
a
g
e
n
t
s
y
s
te
m
(
M
A
S)
,
th
at
m
i
m
ics
its
s
tr
u
ctu
r
e
an
d
m
o
d
if
ied
Neld
er
–
Me
ad
[
5
]
m
et
h
o
d
to
f
i
n
d
a
n
o
p
tim
a
l
s
o
lu
t
io
n
b
ased
o
n
th
e
alg
o
r
ith
m
u
s
ed
b
y
b
ee
s
f
o
r
f
in
d
i
n
g
a
s
u
i
tab
le
p
lace
f
o
r
estab
lis
h
in
g
a
n
e
w
co
lo
n
y
.
T
h
e
ex
p
er
i
m
en
ta
l
r
esu
lts
s
h
o
w
th
e
r
o
b
u
s
t
n
e
s
s
an
d
ac
cu
r
ac
y
o
f
MO
DB
C
o
v
er
g
e
n
etic
alg
o
r
it
h
m
[
1
]
an
d
P
SO
[
2
]
.
Du
e
to
its
h
y
b
r
id
n
atu
r
e,
t
h
is
alg
o
r
it
h
m
p
r
o
v
id
es
o
n
l
y
d
eter
m
i
n
is
tic
s
o
l
u
ti
o
n
s
.
Ma
k
in
g
u
s
e
o
f
th
ese
a
g
en
t
–
a
g
en
t
[
5
]
in
ter
ac
tio
n
s
an
d
ev
o
l
u
tio
n
m
ec
h
a
n
i
s
m
o
f
b
ee
s
w
ar
m
s
in
a
lattice
-
li
k
e
en
v
ir
o
n
m
e
n
t,
th
e
p
r
o
p
o
s
ed
m
eth
o
d
ca
n
f
i
n
d
h
i
g
h
-
q
u
a
lit
y
s
o
l
u
tio
n
s
r
eliab
l
y
w
it
h
th
e
f
a
s
ter
co
n
v
er
g
e
n
ce
ch
ar
ac
ter
is
tic
s
i
n
a
r
ea
s
o
n
ab
l
y
g
o
o
d
co
m
p
u
tat
io
n
ti
m
e.
T
h
e
s
tar
tin
g
p
o
in
t
a
n
d
th
e
n
u
m
b
er
o
f
a
g
en
t
s
ar
e
i
m
p
o
r
tan
t
is
s
u
es
w
h
ile
h
a
n
d
li
n
g
s
u
c
h
alg
o
r
ith
m
s
.
T
h
e
ch
o
ice
o
f
th
e
n
u
m
b
er
o
f
ag
en
t
s
a
n
d
t
h
e
s
tar
tin
g
p
o
i
n
t
o
f
s
ea
r
c
h
ar
e
al
s
o
p
r
esen
ted
a
n
d
d
is
c
u
s
s
ed
in
th
i
s
p
ap
er
.
T
h
e
d
ec
is
io
n
m
ak
i
n
g
p
r
o
ce
s
s
in
th
e
h
o
n
e
y
b
ee
s
g
i
v
es
r
is
e
to
an
in
ter
esti
n
g
s
w
a
r
m
r
esear
ch
ar
ea
to
w
o
r
k
.
T
w
o
d
if
f
er
en
t
ca
s
es
w
it
h
d
i
f
f
er
e
n
t
co
n
d
itio
n
s
h
av
e
b
ee
n
co
n
s
id
er
ed
in
t
h
is
o
p
ti
m
izatio
n
p
r
o
ce
s
s
.
Af
o
r
esaid
r
ep
o
r
ted
tech
n
iq
u
es
w
er
e
ap
p
lied
to
th
e
s
tan
d
ar
d
I
E
E
E
3
0
-
b
u
s
[
1
]
s
ix
-
g
e
n
er
ato
r
test
ca
s
e
s
y
s
te
m
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
Mu
lti Ob
jective
Dir
ec
ted
B
ee
C
o
lo
n
y
Op
timiz
a
tio
n
fo
r
E
co
n
o
mic
Lo
a
d
Dis
p
a
tch
…
(
S
.
K
.
Ga
ch
h
a
y
a
t
)
2385
3.
2
.
M
O
DB
C
Alg
o
rit
h
m
1)
Set th
ep
ar
a
m
e
ter
,
p
.
Set th
e
len
g
t
h
o
f
s
tep
s
,
k
R
(
k
=
0
,
1
,
2
,
…,
p
),
2)
W
h
er
e
k
R
s
tan
d
s
f
o
r
s
tep
s
ize
f
o
r
th
e
k
t
h
p
ar
a
m
eter
.
3)
(
2
)
Set
th
e
r
an
g
e
f
o
r
ea
ch
p
ar
a
m
eter
as
,
i
k
f
k
TT
w
h
er
e
k
=
0
,
1
,
.
.
,
p
w
h
er
e
,
i
k
f
k
TT
r
ep
r
esen
t
th
e
in
itial a
n
d
f
i
n
al
v
alu
e
o
f
th
e
p
a
r
a
m
eter
.
4)
(
3
)
C
o
m
p
u
te
th
e
n
u
m
b
er
o
f
s
t
ep
s
in
ea
ch
s
tep
.
f
k
i
k
k
k
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ak
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,
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lo
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p
tim
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[
9
]
m
a
k
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g
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s
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f
th
e
Neld
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Me
ad
[
5
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m
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.
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[
6
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2
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p
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as
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F
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1
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av
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r
.
Sectio
n
-
4
.
1
r
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lect
s
t
h
e
f
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r
m
u
latio
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o
f
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tiv
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n
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eq
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at
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(
1
9
)
to
(
2
2
)
w
i
th
&
w
it
h
o
u
t tr
a
n
s
m
i
s
s
io
n
lo
s
s
[
1
2
]
as d
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b
elo
w
.
4
.
1
.
Wit
ho
ut
lo
s
s
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1
9
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2
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h lo
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2
1
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(
2
2
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T
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3
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test
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m
[
1
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co
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p
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6
g
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g
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n
its
s
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F
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-
2
f
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s
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m
p
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f
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lt
s
[
8
]
w
i
th
o
th
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s
o
f
t
co
m
p
u
ti
n
g
tec
h
n
iq
u
es.
T
h
ev
ar
io
u
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
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I
SS
N:
2
0
8
8
-
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Mu
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Dir
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B
ee
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Op
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[
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s
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f
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,
MO
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Dte
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P
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V
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[
1
0
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h
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tab
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v
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tab
le
-
1
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-
6
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Fig
u
r
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2
.
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0
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4
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2
Nelder
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A
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4
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[
5
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t [
3
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7
]
f
o
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f
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.
Sectio
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2
r
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4
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3
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atch
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atic
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h
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r
eq
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ir
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to
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ad
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tec
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m
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k
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h
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ate
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ca
p
ab
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eq
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alit
y
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n
s
tr
ai
n
t
s
.
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h
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m
e
th
o
d
s
ar
e
b
ased
o
n
th
e
eq
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in
cr
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m
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t
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esira
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th
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tio
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p
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p
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ld
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al,
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ch
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m
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th
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atica
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m
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n
o
r
m
all
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al.
T
h
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ac
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a
k
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it
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if
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icu
lt
to
d
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y
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it
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a
n
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p
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s
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te
m
p
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s
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tr
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at
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m
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tical
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m
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lati
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s
p
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k
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v
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n
ce
m
en
t
in
m
ath
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m
atica
l
o
p
ti
m
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tech
n
iq
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s
,
co
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v
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n
tio
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al
m
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m
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tical
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a
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n
d
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ap
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licatio
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i
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p
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te
m
s
.
C
o
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s
id
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ab
le
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f
o
r
ts
ar
e
r
eq
u
ir
ed
to
av
o
id
m
at
h
e
m
atic
al
tr
ap
s
s
u
c
h
as
ill
-
co
n
d
iti
o
n
in
g
an
d
co
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v
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n
ce
d
i
f
f
ic
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lties
.
Si
n
c
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m
o
s
t
clas
s
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m
et
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s
u
s
ed
th
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p
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b
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p
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in
t
ap
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h
w
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p
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ated
to
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n
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in
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e
iter
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,
p
ar
allel
p
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am
m
i
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tech
n
iq
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s
ca
n
n
o
t
b
e
ex
p
lo
ited
in
s
o
lv
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n
g
t
h
e
p
r
o
b
le
m
.
T
h
is
p
ap
er
f
o
cu
s
es
o
n
i
m
p
r
o
v
e
m
en
t
s
in
MO
DB
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ap
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ize
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g
lecti
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a
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m
is
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s
[
1
2
]
.
I
n
co
r
p
o
r
atin
g
tr
an
s
m
is
s
io
n
lo
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m
a
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er
MO
D
B
C
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P
D
tech
n
iq
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e
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ield
s
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est
o
p
ti
m
izat
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esu
lt
s
f
o
r
co
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t
o
f
g
en
er
atio
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an
d
em
is
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io
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le
v
el
as
w
ell.
P
ar
eto
-
o
p
tim
a
l
cu
r
v
e
s
[
8
]
u
tili
zi
n
g
VP
L
,
MO
DB
C
a
n
d
MO
DB
C
E
P
D
w
it
h
a
n
d
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o
u
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tr
an
s
m
i
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io
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o
w
n
in
FIG
-
3
&
FIG
-
4
j
u
s
tify
t
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e
f
f
icac
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o
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B
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D
tech
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iq
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v
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,
VP
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P
SO
[
6
]
an
d
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s
o
f
t
co
m
p
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t
in
g
tech
n
iq
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T
h
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m
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la
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r
eq
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ev
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b
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li
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tim
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C
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u
lated
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d
MO
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D
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p
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h
[
8
]
,
it is
f
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d
t
h
at
t
h
e
p
r
o
p
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s
ed
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es.T
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lts
o
b
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f
o
r
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p
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b
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s
.
RE
F
E
R
E
NC
E
S
[1
]
M
.
A
.
A
b
id
o
,
“
M
u
lt
i
o
b
jec
ti
v
e
e
v
o
lu
ti
o
n
a
ry
a
lg
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m
s
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le
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tri
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tch
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lem
”
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IEE
E
T
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sa
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Evo
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ry
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o
mp
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1
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,
p
p
.
3
1
5
-
3
2
9
,
2
0
0
6
.
[2
]
R.
A
lRas
h
id
i,
M
.
E.
El
-
Ha
w
a
r
y
,
“
Eco
n
o
m
ic
d
isp
a
tch
w
it
h
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n
v
ir
o
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m
e
n
tal
c
o
n
si
d
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ra
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o
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s
u
si
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g
p
a
rti
c
les
wa
r
m
o
p
ti
m
iza
ti
o
n
”
,
P
o
we
r E
n
g
in
e
e
rin
g
,
L
a
rg
e
E
n
g
i
n
e
e
rin
g
S
y
ste
ms
Co
n
fer
e
n
c
e
.
p
p
4
1
–
4
6
,
(
2
0
0
6
).
[3
]
R.
Ba
la
m
u
ru
g
a
n
a
n
d
S
.
S
u
b
ra
m
a
n
ian
,
“
A
si
m
p
li
f
ied
re
c
u
rsi
v
e
a
p
p
ro
a
c
h
to
c
o
m
b
in
e
d
e
c
o
n
o
m
ic
e
m
is
sio
n
d
is
p
a
tch
”
,
El
e
c
tric P
o
we
r Co
mp
o
n
e
n
t
S
y
ste
m
,
v
o
l.
3
6
,
p
p
.
1
7
–
2
7
,
2
0
0
8
.
[4
]
S
.
F
.
Bro
d
sk
y
,
R.
W
.
Ha
h
n
,
“
A
ss
e
ss
in
g
th
e
in
f
lu
e
n
c
e
o
f
p
o
w
e
r
p
o
o
ls
o
n
e
m
issio
n
c
o
n
stra
in
e
d
e
c
o
n
o
m
ic
d
isp
a
tch
”
,
IEE
E
T
ra
n
s P
o
we
r S
y
ste
m,P
W
R
S
-
v
o
l.
1
,
p
p
.
5
7
–
6
2
,
1
9
8
6
.
[5
]
K
P
it
c
h
a
i
V
ij
a
y
a
,
KK
M
a
h
a
p
a
tra,
"
A
d
a
p
ti
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-
f
u
z
z
y
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o
n
tro
ll
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b
a
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u
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ter
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li
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e
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o
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d
it
i
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rs,'
T
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KOM
NIKA
T
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lec
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mm
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ti
o
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,
C
o
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v
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l
.
9
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n
o
.
2
,
p
p
.
2
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1
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2
0
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1
.
[6
]
Ra
jes
h
Ku
m
a
r,
De
v
e
n
d
ra
S
h
a
rm
a
,
a
n
d
A
b
h
in
a
v
S
a
d
u
,
“
A
h
y
b
rid
m
u
lt
i
a
g
e
n
t
b
a
se
d
p
a
rti
c
le
sw
a
r
m
o
p
ti
m
iz
a
ti
o
n
a
lg
o
rit
h
m
f
o
r
e
c
o
n
o
m
ic p
o
w
e
r
d
is
p
a
tch
”
,
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
El
e
c
tric
Po
we
r E
n
e
rg
y
S
y
ste
m
,
v
o
l.
3
3
(
1
),
p
p
.
1
1
5
–
1
2
3
,
2
0
1
1
.
[7
]
S
.
M
u
ra
li
d
h
a
ra
n
,
K.
S
r
ik
rish
n
a
a
n
d
S
.
S
u
b
ra
m
a
n
ian
,
“
E
m
issio
n
c
o
n
stra
in
e
d
e
c
o
n
o
m
icd
isp
a
tch
–
a
n
e
w
r
e
c
u
rsiv
e
a
p
p
ro
a
c
h
”
,
El
e
c
tric P
o
we
r Co
mp
o
n
e
n
t
S
y
ste
m,
v
o
l.
3
4
,
p
p
.
3
4
3
–
3
5
3
,
2
0
0
6
.
[8
]
E.
Zi
tzle
r
a
n
d
L
.
T
h
iele
,
“
A
n
e
v
o
lu
ti
o
n
a
ry
a
lg
o
rit
h
m
f
o
r
m
u
lt
i
-
o
b
jec
ti
v
e
o
p
ti
m
iza
ti
o
n
,
T
h
e
stre
n
g
th
P
a
re
t
o
a
p
p
r
o
a
c
h
”
,
T
IK
-
Rep
.
,
4
3
,
1
9
9
8
.
[9
]
Ra
jes
h
Ku
m
a
r,
A
b
h
in
a
v
S
a
d
u
,
Ru
d
e
sh
Ku
m
a
r,
a
n
d
S
.
K.
P
a
n
d
a
,
“
A
No
v
e
l
m
u
lt
i
-
o
b
jec
ti
v
e
b
e
e
c
o
lo
n
y
o
p
ti
m
i
z
a
ti
o
n
a
lg
o
rit
h
m
f
o
r
m
u
lt
i
-
o
b
jec
ti
v
e
e
m
is
sio
n
c
o
n
stra
in
e
d
e
c
o
n
o
m
ic
p
o
w
e
r
d
isp
a
tch
,
El
e
c
trica
l
Po
w
e
r
a
n
d
En
e
rg
y
S
y
ste
ms
,
v
o
l.
4
3
p
p
.
1
2
4
1
–
1
2
5
0
,
2
0
1
2
.
[1
0
]
S
irap
a
ra
p
u
.
S
a
ty
a
n
a
ra
y
a
n
a
,
R.
K.
S
h
a
rm
a
,
M
u
k
ta,
a
n
d
M
u
t
u
a
l,
“
Eff
e
c
t
b
e
t
w
e
e
n
L
F
C
A
n
d
A
V
R
L
o
o
p
s
in
P
o
w
e
r
P
la
n
t”Elec
tri
c
a
l
a
n
d
El
e
c
tro
n
ics
En
g
in
e
e
rin
g
,
V
o
l
-
3
,
N
o
1
,
p
p
.
6
1
-
6
9
,
2
0
1
4
.
[1
1
]
De
ro
n
g
L
iu
,
Yin
g
Ca
i.
(
2
0
0
5
).
T
a
g
u
c
h
i
m
e
th
o
d
f
o
r
so
lv
in
g
e
c
o
n
o
m
ic
d
isp
a
tch
p
ro
b
lem
w
it
h
n
o
n
-
sm
o
o
th
c
o
st
f
u
n
c
ti
o
n
.
IEE
E
tra
n
s
a
c
ti
o
n
s o
n
p
o
we
r sy
ste
ms
,
V
o
l.
2
0
,
No
.
4
,
2
0
0
6
-
2
0
1
4
.
[1
2
]
N.
Ra
m
a
ra
jan
d
R.
Ra
ja
Ra
m
,
“
A
n
a
l
y
ti
c
a
l
a
p
p
ro
a
c
h
to
o
p
ti
m
iz
e
g
e
n
e
ra
ti
o
n
sc
h
e
d
u
le
o
f
p
lan
t
w
it
h
m
u
lt
ip
le
f
u
e
l
o
p
ti
o
n
s”
,
J
o
u
rn
a
l
o
f
i
n
stit
u
ti
o
n
o
f
e
n
g
in
e
e
rs
(
In
d
ia
),
Vo
l
6
8
.
p
t
EL
De
c
1
9
9
7
.
[1
3
]
M
a
ll
ik
rju
n
a
Be
sth
a
,
K.
Ha
rin
a
th
Re
d
d
y
,
O.
He
m
a
k
e
sh
a
v
u
lu
“
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
B
a
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
C
o
mp
u
t
e
r
En
g
i
n
e
e
rin
g
(
IJ
ECE
)
,
v
o
l
-
4
,
issu
e
-
1
,
p
p
.
1
0
1
-
1
0
7
,
2
0
1
4
.
[1
4
]
P
.
K.
H
o
ta
e
t.
a
l
‘No
n
-
Co
n
v
e
x
Eco
n
o
m
ic
Disp
a
tch
w
it
h
P
ro
h
ib
it
e
d
Op
e
ra
ti
n
g
Z
o
n
e
s
t
h
ro
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
te
rn
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
a
n
d
Co
mp
u
ter
En
g
i
n
e
e
rin
g
(
IJ
ECE
)
,
Vo
l.
5
,
No
.
6
,
p
p
.
1
2
3
4
-
1
2
4
4
,
2
0
1
5
.
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