I
nte
rna
t
io
na
l J
o
urna
l o
f
Adv
a
nces in Applie
d Science
s
(
I
J
AAS)
Vo
l.
9
,
No
.
4
,
Dec
em
b
e
r
2
0
2
0
,
p
p
.
265
~
269
I
SS
N:
2
2
5
2
-
8
8
1
4
,
DOI
: 1
0
.
1
1
5
9
1
/ijaas.v
9
.
i4
.
p
p
2
6
5
-
269
265
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
a
a
s
.
ia
esco
r
e.
co
m
Cha
o
tic
ba
sed
P
te
ro
pus a
lg
o
rithm f
o
r so
lv
ing
optima
l reactive
po
wer problem
L
en
in K
a
na
g
a
s
a
ba
i
De
p
a
rtme
n
t
o
f
EE
E
,
P
ra
sa
d
V.
P
o
tl
u
ri
S
id
d
h
a
rt
h
a
In
stit
u
te o
f
Tec
h
n
o
lo
g
y
,
In
d
ia
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
J
a
n
8
,
2
0
2
0
R
ev
is
ed
Ma
y
3
1
, 2
020
Acc
ep
ted
J
u
n
9
,
2
0
2
0
In
th
is
wo
rk
,
a
Ch
a
o
t
ic
b
a
se
d
P
t
e
ro
p
u
s
a
l
g
o
rit
h
m
(CP
A)
h
a
s
b
e
e
n
p
r
o
p
o
se
d
fo
r
so
l
v
i
n
g
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
we
r
p
ro
b
lem
.
P
tero
p
u
s
a
l
g
o
ri
th
m
imitate
s
d
e
e
d
s
o
f
th
e
P
ter
o
p
u
s.
No
rm
a
ll
y
P
tero
p
u
s
wh
il
e
f
ly
i
n
g
it
a
v
o
i
d
o
b
sta
c
les
b
y
u
sin
g
so
n
a
r
e
c
h
o
e
s,
p
a
rti
c
u
larl
y
u
ti
li
z
e
ti
m
e
d
e
lay
.
To
th
e
o
rig
in
a
l
P
tero
p
u
s
a
lg
o
rit
h
m
c
h
a
o
ti
c
d
istu
r
b
a
n
c
e
h
a
s
b
e
e
n
a
p
p
li
e
d
a
n
d
t
h
e
o
p
ti
m
a
l
c
a
p
a
b
il
it
y
o
f
th
e
a
lg
o
rit
h
m
h
a
s
b
e
e
n
imp
ro
v
e
d
in
se
a
rc
h
o
f
g
l
o
b
a
l
s
o
lu
t
io
n
.
I
n
o
r
d
e
r
t
o
a
u
g
m
e
n
t
t
h
e
p
o
p
u
latio
n
d
iv
e
rsit
y
a
n
d
p
re
v
e
n
t
e
a
rly
c
o
n
v
e
r
g
e
n
c
e
,
a
d
a
p
ti
v
e
l
y
c
h
a
o
ti
c
d
istu
r
b
a
n
c
e
is
a
d
d
e
d
a
t
th
e
ti
m
e
o
f
sta
g
n
a
ti
o
n
.
F
u
rth
e
rm
o
re
,
e
x
p
lo
ra
ti
o
n
a
n
d
e
x
p
lo
it
a
ti
o
n
c
a
p
a
b
il
it
y
o
f
th
e
p
r
o
p
o
se
d
a
l
g
o
rit
h
m
h
a
s
b
e
e
n
imp
ro
v
e
d
.
P
ro
p
o
se
d
C
P
A
tec
h
n
i
q
u
e
h
a
s
b
e
e
n
tes
ted
in
sta
n
d
a
r
d
IE
EE
1
4
,
3
0
0
b
u
s sy
ste
m
s &
re
a
l
p
o
we
r
lo
ss
h
a
s b
e
e
n
c
o
n
si
d
e
ra
b
ly
re
d
u
c
e
d
.
K
ey
w
o
r
d
s
:
C
h
ao
tic
P
ter
o
p
u
s
b
eh
av
i
o
u
r
Op
tim
al
r
e
ac
tiv
e
p
o
wer
T
r
an
s
m
is
s
io
n
lo
s
s
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
:
L
en
in
Kan
ag
asab
ai
,
Dep
ar
tm
en
t o
f
E
E
E
,
Pra
s
ad
V.
Po
tlu
r
i Sid
d
h
ar
th
a
I
n
s
titu
te
o
f
T
ec
h
n
o
lo
g
y
,
Kan
u
r
u
,
Vijay
awa
d
a
,
An
d
h
r
a
Pra
d
esh
,
5
2
0
0
0
7
,
I
n
d
ia.
E
m
ail: g
k
len
in
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
T
o
h
av
e
s
ec
u
r
e
&
ec
o
n
o
m
ic,
o
p
er
atio
n
s
o
f
th
e
p
o
wer
s
y
s
tem
o
p
tim
al
r
ea
ctiv
e
p
o
wer
p
r
o
b
lem
p
lay
s
a
p
r
im
e
r
o
le.
Nu
m
er
o
u
s
co
n
v
en
tio
n
al
m
eth
o
d
s
[
1
-
6
]
h
a
v
e
b
ee
n
s
u
cc
ess
f
u
lly
s
o
lv
ed
th
e
p
r
o
b
lem
.
B
u
t
d
if
f
icu
lty
f
o
u
n
d
in
h
an
d
lin
g
th
e
in
eq
u
ality
co
n
s
tr
ain
ts
.
Var
io
u
s
ty
p
es
o
f
ev
o
lu
tio
n
ar
y
alg
o
r
ith
m
s
[
7
-
1
8
]
ap
p
lied
to
s
o
lv
e
th
e
p
r
o
b
lem
.
T
h
is
p
ap
er
p
r
o
jects
ch
ao
tic
Pter
o
p
u
s
alg
o
r
ith
m
(
C
PA)
f
o
r
s
o
lv
in
g
r
ea
ctiv
e
p
o
wer
p
r
o
b
lem
.
Pter
o
p
u
s
alg
o
r
ith
m
is
d
esig
n
e
d
b
ased
o
n
th
e
ac
tio
n
s
o
f
Pter
o
p
u
s
.
wh
ile
f
ly
in
g
it
av
o
id
o
b
s
tacle
s
b
y
u
s
in
g
s
o
n
ar
ec
h
o
es,
p
ar
ticu
lar
ly
u
tili
ze
tim
e
d
elay
; h
ap
p
en
e
d
wh
ile
r
elea
s
e
an
d
r
ef
lectio
n
o
f
ec
h
o
wh
ich
h
as
b
ee
n
u
tili
ze
d
d
u
r
in
g
th
e
p
er
io
d
o
f
f
o
r
co
u
r
s
e
-
p
lo
t
tin
g
.
I
n
Pro
jecte
d
alg
o
r
ith
m
e
ch
o
lo
ca
tio
n
f
ea
t
u
r
e
is
u
tili
ze
d
in
th
e
alg
o
r
ith
m
an
d
ch
ao
s
th
e
o
r
y
in
ter
m
in
g
l
ed
in
th
e
f
lo
win
g
p
r
o
ce
s
s
.
I
n
o
r
d
e
r
to
au
g
m
en
t
th
e
p
o
p
u
latio
n
d
i
v
er
s
ity
an
d
p
r
ev
en
t
ea
r
ly
co
n
v
er
g
e
n
ce
,
ad
a
p
tiv
ely
ch
ao
tic
d
is
tu
r
b
an
ce
is
ad
d
ed
at
th
e
tim
e
o
f
s
tag
n
atio
n
.
Pro
jecte
d
C
PA
alg
o
r
ith
m
h
as
b
ee
n
t
ested
in
s
tan
d
ar
d
I
E
E
E
1
4
,
3
0
0
b
u
s
s
y
s
tem
s
&
s
im
u
latio
n
s
tu
d
y
s
h
o
w
th
e
b
est p
e
r
f
o
r
m
an
ce
o
f
th
e
p
r
o
jecte
d
al
g
o
r
ith
m
in
r
ed
u
ci
n
g
th
e
r
ea
l p
o
wer
lo
s
s
.
2.
P
RO
B
L
E
M
F
O
R
M
U
L
AT
I
O
N
T
h
e
k
ey
o
b
jectiv
e
o
f
th
e
r
ea
ctiv
e
p
o
wer
p
r
o
b
lem
is
to
m
in
im
ize
th
e
s
y
s
tem
r
ea
l
p
o
w
er
lo
s
s
&
g
iv
en
as,
P
l
o
s
s
=
∑
g
k
(
V
i
2
+
V
j
2
−
2
V
i
V
j
c
o
s
θ
ij
)
n
k
=
1
k
=
(
i
,
j
)
(
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
: 2
2
5
2
-
8
8
1
4
I
n
t J Ad
v
Ap
p
l Sci
,
Vo
l.
9
,
No
.
4
,
Dec
em
b
e
r
2
0
2
0
:
2
6
5
–
2
6
9
266
V
o
ltag
e
d
ev
iatio
n
m
ag
n
itu
d
es (
VD)
is
s
tated
as f
o
llo
ws
,
Min
im
ize
VD
=
∑
|
V
k
−
1
.
0
|
nl
k
=
1
(
2
)
L
o
ad
f
lo
w
e
q
u
ality
co
n
s
tr
ain
ts
:
P
Gi
–
P
Di
−
V
i
∑
V
j
nb
j
=
1
[
G
ij
c
os
θ
ij
+
B
ij
s
in
θ
ij
]
=
0
,
i
=
1
,
2
…
.
,
nb
(
3
)
Q
Gi
−
Q
Di
−
V
i
∑
V
j
nb
j
=
1
[
G
ij
s
in
θ
ij
+
B
ij
c
os
θ
ij
]
=
0
,
i
=
1
,
2
…
.
,
nb
(
4
)
I
n
eq
u
ality
c
o
n
s
tr
ain
t
s
ar
e:
V
Gi
m
i
n
≤
V
Gi
≤
V
Gi
m
ax
,
i
∈
ng
(
5
)
V
Li
m
i
n
≤
V
Li
≤
V
Li
m
ax
,
i
∈
nl
(
6
)
Q
Ci
m
i
n
≤
Q
Ci
≤
Q
Ci
m
ax
,
i
∈
nc
(
7
)
Q
Gi
m
i
n
≤
Q
Gi
≤
Q
Gi
m
ax
,
i
∈
ng
(
8
)
T
i
m
i
n
≤
T
i
≤
T
i
m
ax
,
i
∈
nt
(
9
)
S
Li
m
i
n
≤
S
Li
m
ax
,
i
∈
nl
(
10
)
3.
P
T
E
RO
P
U
S ALGO
RI
T
H
M
Pter
o
p
u
s
alg
o
r
ith
m
im
itates d
ee
d
s
o
f
th
e
Pter
o
p
u
s
.
No
r
m
ally
Pter
o
p
u
s
wh
ile
f
ly
in
g
it a
v
o
id
o
b
s
tacle
s
b
y
u
s
in
g
s
o
n
a
r
ec
h
o
es,
p
a
r
ticu
lar
ly
u
tili
ze
tim
e
d
elay
;
h
ap
p
en
ed
wh
ile
r
elea
s
e
an
d
r
e
f
le
ctio
n
o
f
ec
h
o
wh
ich
h
as b
ee
n
u
tili
ze
d
d
u
r
in
g
th
e
p
e
r
io
d
o
f
f
o
r
co
u
r
s
e
-
p
lo
ttin
g
.
Ge
n
er
alize
d
r
u
les f
o
r
Pter
o
p
u
s
alg
o
r
ith
m
a
r
e:
a.
T
o
s
en
s
e
th
e
d
is
tan
ce
-
all
Pter
o
p
u
s
u
s
e
ec
h
o
l
o
ca
tio
n
b.
I
n
ar
b
itra
r
ily
m
o
d
e
Pter
o
p
u
s
f
ly
with
v
elo
city
ϑ
i
at
p
o
s
itio
n
y
i
with
a
f
ix
ed
f
r
e
q
u
en
c
y
f
m
i
n
,
v
a
r
y
in
g
wav
elen
g
th
λ
an
d
lo
u
d
n
ess
A
0
to
s
ea
r
ch
f
o
r
p
r
e
y
.
T
h
ey
ca
n
r
o
b
o
tically
ad
j
u
s
t
th
e
f
r
e
q
u
en
cy
o
f
t
h
ei
r
r
elea
s
ed
p
u
ls
es
an
d
r
e
g
u
late
t
h
e
r
ate
o
f
p
u
ls
e
em
is
s
io
n
r
∈
[
0
;
1
]
,
with
r
ef
er
en
ce
to
th
e
p
r
o
p
in
q
u
it
y
o
f
th
e
g
o
al.
c.
L
o
u
d
n
ess
will v
ar
y
f
r
o
m
a
lar
g
e
(
p
o
s
itiv
e)
A
0
to
a
m
in
im
u
m
c
o
n
s
tan
t v
alu
e
A
m
i
n
.
P
tero
p
u
s
a
lg
o
r
ith
m
I
n
itialize
th
e
p
o
p
u
latio
n
Pu
ls
e
f
r
eq
u
en
cy
d
ef
in
e
d
in
th
e
r
an
g
e
o
f
G
i
∈
[
Q
m
i
n
,
G
m
ax
]
r
i
,
A
i
ar
e
d
e
f
in
ed
W
h
ile
(
t <
T
maximum
)
B
y
ad
ju
s
tm
en
t o
f
f
r
eq
u
e
n
cy
n
ew
s
o
lu
tio
n
s
ar
e
g
en
e
r
ated
Ob
tain
ed
So
lu
tio
n
&
v
elo
city
ar
e
u
p
d
ate
d
I
f
(
r
an
d
o
m
(
0
; 1
)
>
r
i
)
Fo
r
m
th
e
s
o
lu
tio
n
b
est o
n
e
is
s
elec
ted
Ar
o
u
n
d
th
e
b
est s
o
lu
tio
n
–
a
l
o
ca
l so
lu
tio
n
will b
e
en
g
en
d
e
r
ed
E
n
d
if
I
n
ar
b
itra
r
y
m
o
d
e
n
ew
s
o
lu
tio
n
s
ar
e
g
en
er
ate
d
I
f
(
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llo
win
g
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ad
v
Ap
p
l Sci
I
SS
N:
2
2
5
2
-
8
8
1
4
C
h
a
o
tic
b
a
s
ed
P
tero
p
u
s
a
lg
o
r
ith
m
fo
r
s
o
lvin
g
o
p
tima
l rea
ctive
p
o
w
er p
r
o
b
lem
(
Len
in
K
a
n
a
g
a
s
a
b
a
i
)
267
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t
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=
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G
m
ax
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m
i
n
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1
1
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t
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1
2
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t
+
1
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i
(
t
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l
i
(
t
)
(
1
3
)
E
x
is
tin
g
f
in
est s
o
lu
tio
n
h
as b
e
en
m
o
d
if
ie
d
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th
e
f
o
llo
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s
t
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A
i
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t
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1
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−
1
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1
4
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W
h
en
r
i
in
cr
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s
es,
Ai
will
d
ec
r
ea
s
e
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en
a
Pter
o
p
u
s
f
in
d
s
a
p
r
ey
&
it
m
ath
em
atica
lly
wr
itten
as f
o
llo
ws,
A
i
(
t
+
1
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=
α
A
i
(
t
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,
r
i
(
t
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=
r
i
(
0
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[
1
−
e
xp
(
−
γϵ
)
]
,
(
1
5
)
T
o
im
p
r
o
v
e
th
e
Pter
o
p
u
s
alg
o
r
ith
m
ch
ao
tic
d
is
tu
r
b
a
n
ce
[
1
9
-
2
1
]
is
in
tr
o
d
u
ce
d
.
Her
e,
v
a
r
ian
ce
2
d
em
o
n
s
tr
ates th
e
co
n
v
er
g
e
d
e
g
r
ee
o
f
all
p
ar
ticles.
2
=
∑
[
(
−
)
⁄
]
2
=
1
(
1
6
)
=
{
1
,
{
|
−
|
}
}
(
1
7
)
(
+
1
)
=
(
)
(
1
−
(
)
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(
1
8
)
I
n
o
r
d
er
to
au
g
m
en
t
t
h
e
p
o
p
u
latio
n
d
i
v
er
s
ity
an
d
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r
ev
e
n
t
ea
r
ly
co
n
v
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g
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n
ce
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d
ap
tiv
e
ly
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ao
tic
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is
tu
r
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an
ce
is
ad
d
ed
at
th
e
ti
m
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o
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s
tag
n
atio
n
.
T
h
u
s
,
′
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′
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+
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(
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P
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A
lg
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itialize
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ile
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t <
T
maximum
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ar
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ated
Ob
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So
lu
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&
v
elo
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ar
e
u
p
d
ate
d
Usi
n
g
th
e
eq
u
atio
n
s
u
p
d
ate
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v
elo
cities an
d
lo
ca
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Fo
r
m
th
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s
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est o
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e
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elec
ted
Ar
o
u
n
d
th
e
b
est s
o
lu
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a
l
o
ca
l so
lu
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will b
e
en
g
en
d
e
r
ed
E
n
d
if
I
n
ar
b
itra
r
y
m
o
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ar
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er
ate
d
I
f
(
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; 1
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<
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f
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New
s
o
lu
tio
n
s
ar
e
f
o
r
m
e
d
r
i
an
d
A
i
v
alu
es a
r
e
i
n
cr
ea
s
ed
E
n
d
if
C
u
r
r
en
t b
est is
f
o
u
n
d
b
y
r
an
k
in
g
th
e
Pter
o
p
u
s
in
o
r
d
er
E
n
d
wh
ile
Ou
tp
u
t th
e
o
p
tim
ized
r
esu
lts
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
: 2
2
5
2
-
8
8
1
4
I
n
t J Ad
v
Ap
p
l Sci
,
Vo
l.
9
,
No
.
4
,
Dec
em
b
e
r
2
0
2
0
:
2
6
5
–
2
6
9
268
4.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
Pro
p
o
s
ed
C
h
ao
tic
b
ased
Pter
o
p
u
s
alg
o
r
ith
m
(
C
PA)
h
as
b
e
en
test
ed
in
s
tan
d
ar
d
I
E
E
E
1
4
,
3
0
0
b
u
s
s
y
s
tem
s
an
d
co
m
p
ar
is
o
n
h
as
b
ee
n
d
o
n
e
with
s
tan
d
ar
d
alg
o
r
ith
m
s
.
Simu
latio
n
o
u
tp
u
t
clea
r
ly
in
d
icate
s
ab
o
u
t
th
e
ef
f
icien
cy
o
f
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
in
r
ed
u
ci
n
g
th
e
r
e
al
p
o
wer
lo
s
s
.
At
f
ir
s
t
in
s
tan
d
ar
d
I
E
E
E
1
4
b
u
s
s
y
s
tem
th
e
v
alid
ity
o
f
th
e
p
r
o
p
o
s
ed
C
PA
alg
o
r
ith
m
h
as
b
ee
n
test
ed
&
co
m
p
ar
is
o
n
r
esu
lts
ar
e
p
r
es
en
ted
in
T
ab
le
1
.
T
ab
le
1
.
C
o
m
p
a
r
is
o
n
r
esu
lts
C
o
n
t
r
o
l
v
a
r
i
a
b
l
e
s
A
B
C
O
[
2
2
]
I
A
B
C
O
[
2
2
]
P
r
o
j
e
c
t
e
d
C
P
A
V1
1
.
0
6
1
.
0
5
1
.
0
3
V2
1
.
0
3
1
.
0
5
1
.
0
0
V3
0
.
9
8
1
.
0
3
1
.
0
1
V6
1
.
0
5
1
.
0
5
1
.
0
0
V8
1
.
0
0
1
.
0
4
0
.
9
9
Q9
0
.
1
3
9
0
.
1
3
2
0
.
1
2
9
T5
6
0
.
9
7
9
0
.
9
6
0
0
.
9
6
9
T4
7
0
.
9
5
0
0
.
9
5
0
0
.
9
4
8
T4
9
1
.
0
1
4
1
.
0
0
7
1
.
0
0
2
P
l
o
ss
(
M
W
)
5
.
9
2
8
9
2
5
.
5
0
0
3
1
5
.
4
9
8
4
2
T
h
en
I
E
E
E
3
0
0
b
u
s
s
y
s
tem
[
2
3
]
is
u
s
ed
as
tes
t
s
y
s
tem
to
v
alid
ate
th
e
p
er
f
o
r
m
an
ce
o
f
t
h
e
p
r
o
p
o
s
ed
C
PA
alg
o
r
ith
m
.
T
ab
le
2
s
h
o
ws
th
e
co
m
p
ar
is
o
n
o
f
r
ea
l
p
o
wer
lo
s
s
o
b
tain
ed
af
ter
o
p
tim
izatio
n
.
R
ea
l
p
o
wer
lo
s
s
h
as b
ee
n
co
n
s
id
er
ab
l
y
r
ed
u
ce
d
wh
en
co
m
p
a
r
ed
to
t
h
e
o
t
h
er
s
tan
d
ar
d
r
ep
o
r
ted
alg
o
r
ith
m
s.
T
ab
le
2
co
m
p
ar
is
o
n
o
f
r
ea
l
p
o
wer
lo
s
s
P
a
r
a
me
t
e
r
M
e
t
h
o
d
EG
A
[
2
4
]
M
e
t
h
o
d
EEA
[
2
4
]
M
e
t
h
o
d
C
S
A
[
2
5
]
P
r
o
j
e
c
t
e
d
C
P
A
P
LO
S
S
(
M
W
)
6
4
6
.
2
9
9
8
6
5
0
.
6
0
2
7
6
3
5
.
8
9
4
2
6
2
7
.
1
5
6
4
5.
CO
NCLU
SI
O
N
I
n
th
is
p
ap
er
,
ch
ao
tic
b
ased
Pter
o
p
u
s
alg
o
r
ith
m
(
C
PA)
h
a
s
b
ee
n
s
u
cc
ess
f
u
lly
s
o
lv
ed
th
e
o
p
tim
al
r
ea
ctiv
e
p
o
wer
p
r
o
b
lem
.
Natu
r
al
ac
tio
n
s
o
f
Pter
o
p
u
s
h
as
b
ee
n
ef
f
ec
tiv
ely
i
m
itated
an
d
m
o
d
elled
to
s
o
lv
e
th
e
p
r
o
b
lem
.
An
ad
ap
tiv
e
c
h
ao
tic
d
is
tu
r
b
a
n
ce
is
ad
d
e
d
at
t
h
e
tim
e
o
f
s
tag
n
atio
n
Per
f
o
r
m
an
ce
o
f
th
e
Pter
o
p
u
s
alg
o
r
ith
m
h
as
b
ee
n
im
p
r
o
v
e
d
a
n
d
b
etter
-
q
u
ality
s
o
lu
tio
n
s
h
a
v
e
b
ee
n
o
b
tain
ed
.
I
n
ad
d
itio
n
,
ex
p
lo
r
atio
n
an
d
ex
p
lo
itatio
n
ca
p
ab
ilit
y
o
f
t
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
h
as
b
ee
n
e
n
h
an
c
ed
.
Pro
p
o
s
ed
C
PA
tech
n
iq
u
e
h
as
b
ee
n
test
ed
in
s
tan
d
ar
d
I
E
E
E
1
4
,
3
0
0
b
u
s
s
y
s
tem
s
&
r
ea
l
p
o
wer
lo
s
s
h
as
b
ee
n
co
n
s
id
er
ab
ly
r
ed
u
ce
d
.
RE
F
E
R
E
NC
E
S
[1
]
K.
Y.
Lee
,
e
t
a
l
,
“
F
u
e
l
-
c
o
st
m
in
i
m
isa
ti
o
n
fo
r
b
o
th
re
a
l
a
n
d
re
a
c
ti
v
e
-
p
o
we
r
d
isp
a
tch
e
s
,”
Pro
c
e
e
d
in
g
s
Ge
n
e
ra
ti
o
n
,
T
ra
n
sm
issio
n
a
n
d
Distrib
u
ti
o
n
C
o
n
fer
e
n
c
e
,
v
o
l.
1
3
1
,
n
o
.
3
,
p
p
.
8
5
-
9
3
,
1
9
8
4
.
[2
]
N.
I.
De
e
b
,
e
t
a
l
.
,
“
An
e
fficie
n
t
tec
h
n
iq
u
e
fo
r
re
a
c
ti
v
e
p
o
we
r
d
isp
a
tch
u
sin
g
a
re
v
ise
d
li
n
e
a
r
p
ro
g
ra
m
m
in
g
a
p
p
ro
a
c
h
,”
El
e
c
tric P
o
we
r S
y
ste
m R
e
se
a
rc
h
,
v
o
l.
1
5
,
n
o
.
2
,
p
p
.
1
2
1
-
1
3
4
,
1
9
8
8
.
[3
]
M
.
R.
Bjelo
g
r
li
c
,
M
.
S
.
Ca
l
o
v
ic,
B.
S
.
Ba
b
ic,
e
t.
a
l
.,
“
Ap
p
li
c
a
ti
o
n
o
f
Ne
wto
n
’s
o
p
ti
m
a
l
p
o
we
r
flo
w
in
v
o
lt
a
g
e
/rea
c
ti
v
e
p
o
we
r
c
o
n
tr
o
l
,”
I
EE
E
T
ra
n
s P
o
we
r S
y
ste
m
,
v
o
l.
5
,
n
o
.
4
,
p
p
.
1
4
4
7
-
1
4
5
4
,
1
9
9
0
.
[4
]
S
.
G
ra
n
v
il
le,
“
Op
ti
m
a
l
re
a
c
ti
v
e
d
isp
a
tch
t
h
ro
u
g
h
i
n
terio
r
p
o
i
n
t
m
e
th
o
d
s,”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r
S
y
ste
m
,
v
o
l/
iss
u
e
:
9
(
1
),
p
p
.
1
3
6
–
1
4
6
,
1
9
9
4
.
[5
]
N.
G
ru
d
in
in
,
“
Re
a
c
ti
v
e
p
o
we
r
o
p
ti
m
iza
ti
o
n
u
sin
g
su
c
c
e
ss
iv
e
q
u
a
d
ra
ti
c
p
ro
g
ra
m
m
in
g
m
e
th
o
d
,
”
IEE
E
T
ra
n
s
a
c
ti
o
n
s
o
n
P
o
we
r S
y
ste
m
,
v
o
l
.
1
3
,
n
o
.
4
,
p
p
.
1
2
1
9
-
1
2
2
5
,
1
9
9
8
.
[6
]
Wei
Ya
n
,
J.
Yu
,
D.
C.
Y
u
a
n
d
K.
Bh
a
tt
a
ra
i,
“
A
n
e
w
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
we
r
fl
o
w
m
o
d
e
l
in
re
c
tan
g
u
lar
fo
rm
a
n
d
i
ts
so
lu
ti
o
n
b
y
p
re
d
icto
r
c
o
rre
c
to
r
p
ri
m
a
l
d
u
a
l
in
teri
o
r
p
o
in
t
m
e
th
o
d
,
”
IEE
E
T
ra
n
s.
Pwr.
S
y
st
.
,
v
o
l
.
2
1
,
n
o
.
1,
pp.
61
-
6
7
,
2
0
0
6
.
[7
]
Ap
a
ra
ji
ta
M
u
k
h
e
rjee
,
Vi
v
e
k
a
n
a
n
d
a
M
u
k
h
e
rjee
,
“
S
o
l
u
ti
o
n
o
f
o
p
ti
m
a
l
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c
ti
v
e
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o
we
r
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isp
a
tch
b
y
c
h
a
o
ti
c
k
ril
l
h
e
rd
a
lg
o
rit
h
m
,
”
IET
Ge
n
e
r.
T
ra
n
sm
.
Distrib
,
v
o
l.
9
,
n
o
.
1
5
,
p
p
.
2
3
5
1
-
2
3
6
2
,
2
0
1
5
.
[8
]
Hu
,
Z.
,
Wa
n
g
,
X.
&
Tay
l
o
r,
G
.
“
S
to
c
h
a
stic
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
w
e
r
d
isp
a
tch
:
F
o
rm
u
latio
n
a
n
d
so
l
u
t
io
n
m
e
th
o
d
,
”
El
e
c
tr.
Po
we
r E
n
e
rg
y
S
y
st
.
,
v
o
l
.
3
2
,
n
o
.
6
,
p
p
.
6
1
5
-
6
2
1
,
2
0
1
0
.
[9
]
M
a
h
a
letc
h
u
m
i
A/P
M
o
r
g
a
n
,
No
r
Ru
l
Ha
sm
a
Ab
d
u
ll
a
h
,
M
o
h
d
He
rwa
n
S
u
laim
a
n
,
M
a
h
f
u
z
a
h
M
u
sta
fa
a
n
d
Ro
sd
iy
a
n
a
S
a
m
a
d
,
“
Co
m
p
u
tati
o
n
a
l
i
n
telli
g
e
n
c
e
tec
h
n
i
q
u
e
f
o
r
sta
ti
c
VA
R
c
o
m
p
e
n
sa
to
r
(S
VC)
in
sta
ll
a
ti
o
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J Ad
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Ap
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l Sci
I
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N:
2
2
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C
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a
o
tic
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a
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ed
P
tero
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u
s
a
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o
r
ith
m
fo
r
s
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lvin
g
o
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tima
l rea
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er p
r
o
b
lem
(
Len
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K
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g
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)
269
c
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ri
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g
m
u
lt
i
-
c
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t
in
g
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n
c
ies
(N
-
m)
,”
AR
PN
J
o
u
rn
a
l
o
f
E
n
g
i
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g
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.
1
0
,
no
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c
2
0
1
5
.
[1
0
]
M
o
h
d
He
rwa
n
S
u
laim
a
n
,
Z
u
ria
n
i
M
u
sta
ffa
,
Ha
m
d
a
n
Da
n
iy
a
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M
o
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R
u
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m
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a
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e
d
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d
Om
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r
Alima
n
,
“
S
o
lv
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ti
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c
ti
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e
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o
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lan
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g
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ro
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z
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n
a
tu
re
in
sp
ired
c
o
m
p
u
t
in
g
tec
h
n
iq
u
e
s
,”
AR
PN
J
o
u
rn
a
l
o
f
E
n
g
i
n
e
e
rin
g
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n
d
A
p
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ied
S
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s
,
vol
.
1
0
,
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o
.
2
1
,
p
p
.
9
7
7
9
-
9
7
8
5
,
No
v
2
0
1
5
.
[1
1
]
M
o
h
d
He
rwa
n
S
u
laim
a
n
,
W
o
n
g
Lo
In
g
,
Z
u
rian
i
M
u
s
taffa
a
n
d
M
o
h
d
Ru
sl
li
m
M
o
h
a
m
e
d
,
“G
re
y
wo
lf
o
p
ti
m
ize
r
fo
r
so
lv
i
n
g
e
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o
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ic
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a
tch
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r
o
b
lem
with
v
a
lv
e
-
l
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n
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ts
,”
AR
PN
J
o
u
rn
a
l
o
f
E
n
g
i
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e
rin
g
a
n
d
A
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1
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o
.
2
1
,
p
p
.
9
7
9
6
-
9
8
0
1
,
N
ov
2
0
1
5
.
[1
2
]
P
a
n
d
i
a
ra
jan
,
K.
&
Ba
b
u
lal,
C.
K.
,
“
F
u
z
z
y
h
a
rm
o
n
y
se
a
rc
h
a
l
g
o
rit
h
m
b
a
se
d
o
p
t
ima
l
p
o
we
r
f
lo
w
f
o
r
p
o
w
e
r
s
y
ste
m
se
c
u
rit
y
e
n
h
a
n
c
e
m
e
n
t,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
El
e
c
tric P
o
we
r E
n
e
rg
y
S
y
st.,
v
o
l.
7
8
,
p
p
.
7
2
-
7
9
.
2
0
1
6
.
[1
3
]
M
u
sta
ffa
,
Z.
,
S
u
laim
a
n
,
M
.
H.,
Y
u
so
f,
Y.,
Ka
m
a
ru
lza
m
a
n
,
S
.
F
.
,
“
A
n
o
v
e
l
h
y
b
ri
d
m
e
tah
e
u
risti
c
a
lg
o
rit
h
m
f
o
r
sh
o
rt
term
lo
a
d
fo
re
c
a
stin
g
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
S
imu
l
a
ti
o
n
:
S
y
ste
ms
,
S
c
ien
c
e
a
n
d
T
e
c
h
n
o
lo
g
y
,
v
o
l.
1
7
,
n
o
.
4
1
,
p
p
.
6
.
1
-
6
.
6
,
2
0
1
7
.
[1
4
]
S
u
laim
a
n
,
M
.
H.,
M
u
sta
ffa
,
Z.
,
M
o
h
a
m
e
d
,
M
.
R
.
,
A
li
m
a
n
,
O.
,
“
An
a
p
p
li
c
a
ti
o
n
o
f
m
u
lt
i
-
v
e
rse
o
p
ti
m
i
z
e
r
fo
r
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
we
r
d
isp
a
tch
p
r
o
b
le
m
s,”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
S
im
u
l
a
ti
o
n
:
S
y
ste
ms
,
S
c
ien
c
e
a
n
d
T
e
c
h
n
o
l
o
g
y
,
v
o
l.
1
7
,
no.
4
1
,
p
p
.
5
.
1
-
5
.
5
,
2
0
1
7
.
[1
5
]
M
a
h
a
letc
h
u
m
i
A/P
M
o
rg
a
n
,
No
r
Ru
l
Ha
sm
a
Ab
d
u
ll
a
h
,
M
o
h
d
He
rwa
n
S
u
laim
a
n
,
M
a
h
f
u
z
a
h
M
u
sta
fa
a
n
d
Ro
sd
i
y
a
n
a
S
a
m
a
d
,
“
M
u
lt
i
-
o
b
jec
ti
v
e
e
v
o
lu
ti
o
n
a
ry
p
ro
g
ra
m
m
in
g
(
M
OEP
)
u
sin
g
m
u
tati
o
n
b
a
se
d
o
n
a
d
a
p
ti
v
e
m
u
tatio
n
o
p
e
ra
to
r
(AMO)
a
p
p
li
e
d
f
o
r
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
we
r
d
isp
a
tch
,”
AR
PN
J
o
u
rn
a
l
o
f
En
g
in
e
e
rin
g
a
n
d
A
p
p
li
e
d
S
c
ien
c
e
s
,
vol
.
1
1
,
no
.
1
4
,
Ju
l
2
0
1
6
.
[1
6
]
Re
b
e
c
c
a
Ng
S
h
in
M
e
i,
M
o
h
d
He
rwa
n
S
u
laim
a
n
,
Zu
ria
n
i
M
u
sta
ffa
,
“
An
t
li
o
n
o
p
ti
m
ize
r
fo
r
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
we
r
d
isp
a
tch
s
o
lu
t
io
n
,”
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
S
y
ste
ms
,
S
p
e
c
ial
Iss
u
e
AM
P
E2
0
1
5
,
p
p
.
6
8
-
7
4
,
2
0
1
6
.
[1
7
]
M
a
h
a
letc
h
u
m
i
M
o
rg
a
n
,
No
r
Ru
l
Ha
sm
a
Ab
d
u
ll
a
h
,
M
o
h
d
He
rwa
n
S
u
laim
a
n
,
M
a
h
fu
z
a
h
M
u
sta
fa
,
R
o
sd
i
y
a
n
a
S
a
m
a
d
,
“
Be
n
c
h
m
a
rk
stu
d
ies
o
n
o
p
ti
m
a
l
r
e
a
c
ti
v
e
p
o
we
r
d
isp
a
tch
(ORPD)
b
a
se
d
m
u
lt
i
-
o
b
jec
ti
v
e
e
v
o
l
u
ti
o
n
a
r
y
p
r
o
g
ra
m
m
in
g
(M
OEP
)
u
sin
g
m
u
tati
o
n
b
a
se
d
o
n
a
d
a
p
ti
v
e
m
u
tatio
n
a
d
a
p
ter
(AMO)
a
n
d
p
o
ly
n
o
m
ial
m
u
tatio
n
o
p
e
ra
to
r
(P
M
O)
,”
J
o
u
rn
a
l
o
f
El
e
c
trica
l
S
y
ste
ms
,
v
o
l
.
1
2
,
n
o
.
1
,
p
p
.
1
2
1
-
1
3
2
,
2
0
1
6
.
[1
8
]
Re
b
e
c
c
a
Ng
S
h
in
M
e
i,
M
o
h
d
H
e
rwa
n
S
u
laim
a
n
,
Zu
rian
i
M
u
sta
f
fa
,
Ha
m
d
a
n
Da
n
iy
a
l,
“
Op
ti
m
a
l
re
a
c
ti
v
e
p
o
we
r
d
isp
a
tch
s
o
lu
ti
o
n
b
y
lo
ss
m
in
imiz
a
ti
o
n
u
sin
g
m
o
th
-
flam
e
o
p
ti
m
iza
ti
o
n
tec
h
n
i
q
u
e
,
”
A
p
p
li
e
d
S
o
f
t
Co
m
p
u
ti
n
g
,
v
o
l.
5
9
,
P
a
g
e
s 2
1
0
-
2
2
2
,
Oc
t
2
0
1
7
.
[1
9
]
X.S
.
Ya
n
g
.
,
“
Ba
t
a
lg
o
rit
h
m
fo
r
m
u
lt
i
-
o
b
jec
ti
v
e
o
p
ti
m
isa
ti
o
n
,”
I
n
t
e
rn
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
Bi
o
-
I
n
sp
ire
d
Co
m
p
u
t
a
ti
o
n
,
v
o
l.
3
,
n
o
.
5
,
p
p
.
2
6
7
-
2
7
4
,
2
0
1
1
.
[2
0
]
A.
H.
G
a
n
d
o
m
i,
G
.
J.
Y
u
n
,
X.
-
S
.
Ya
n
g
,
a
n
d
S
.
Tala
t
a
h
a
ri,
“
Ch
a
o
s
-
e
n
h
a
n
c
e
d
a
c
c
e
lera
t
e
d
p
a
rti
c
le
sw
a
rm
o
p
ti
m
iza
ti
o
n
,
”
C
o
mm
u
n
ic
a
ti
o
n
s i
n
No
n
li
n
e
a
r S
c
ien
c
e
a
n
d
Nu
me
ric
a
l
S
imu
l
a
ti
o
n
,
v
o
l.
1
8
,
n
o
.
2
,
p
p
.
3
2
7
-
3
4
0
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2
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.
[2
5
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,”
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ti
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p
p
.
2
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3
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6
,
2
0
1
7
.
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