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.
33
~
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N:
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er
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an
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23
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2
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f
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lv
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to
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v
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a
te
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o
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In
stit
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te o
f
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rin
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a
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.
Al
l
rig
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ts re
se
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d
.
C
o
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r
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p
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A
uth
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r
:
K.
L
en
in
Dep
ar
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tlu
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d
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ar
th
a
I
n
s
tit
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f
T
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h
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lo
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Kan
u
r
u
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Vij
a
y
a
w
ad
a,
An
d
h
r
a
P
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ad
esh
.
I
n
d
ia.
E
m
ail:
g
k
len
i
n
@
g
m
ai
l.c
o
m
1.
I
NT
RO
D
UCT
I
O
N
Op
ti
m
al
r
ea
cti
v
e
p
o
w
er
d
is
p
atch
p
r
o
b
lem
i
s
o
n
e
o
f
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p
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m
izatio
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lem
s
i
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te
m
.
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v
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tab
ili
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y
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te
m
.
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io
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m
at
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m
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tical
tech
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u
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h
a
v
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ee
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lv
e
th
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o
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ti
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al
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v
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p
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w
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d
i
s
p
atch
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b
le
m
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T
h
ese
i
n
cl
u
d
e
th
e
g
r
ad
ien
t
m
et
h
o
d
[
1
,
2
]
,
Ne
w
to
n
m
et
h
o
d
[
3
]
an
d
lin
ea
r
p
r
o
g
r
a
m
m
i
n
g
[
4
-
7
]
.
T
h
e
g
r
ad
ien
t
an
d
Ne
w
to
n
m
et
h
o
d
s
s
u
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t
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d
if
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in
h
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d
li
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g
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eq
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s
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to
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x
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r
ess
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s
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h
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a
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n
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b
al
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ti
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tech
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iq
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ith
m
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a
v
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h
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cti
v
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p
o
w
er
f
lo
w
p
r
o
b
le
m
[
8
,
9
]
.
I
n
r
ec
en
t
y
ea
r
s
,
t
h
e
p
r
o
b
le
m
o
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v
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as
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m
e
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co
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g
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.
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tab
i
lit
y
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v
o
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m
a
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e
w
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o
t
b
e
a
r
eliab
le
in
d
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o
f
h
o
w
f
ar
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o
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p
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in
t
is
f
r
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m
t
h
e
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p
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in
t
[
1
0
]
.
T
h
e
r
ea
ctiv
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p
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s
u
p
p
o
r
t
an
d
v
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ltag
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p
r
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b
lem
s
ar
e
in
tr
i
n
s
icall
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r
elate
d
.
Vo
ltag
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s
tab
ilit
y
ev
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u
atio
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u
s
i
n
g
m
o
d
a
l
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al
y
s
is
[
1
0
]
is
u
s
ed
as
th
e
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f
v
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tab
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.
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p
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o
f
t
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h
y
b
r
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d
if
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en
t a
l
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ith
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s
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b
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tr
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t
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h
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to
b
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f
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s
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f
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ate
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t
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k
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p
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[
1
1
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8
]
.
T
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p
ap
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p
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I
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A
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th
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in
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izat
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to
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m
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A
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f
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m
O
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(
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.
W
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th
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c
u
c
k
o
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b
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s
ex
p
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n
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w
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(
ar
b
itra
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walk
)
u
tili
zi
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g
f
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ef
l
y
al
g
o
r
ith
m
s
tr
ateg
y
i
n
s
tead
o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8938
IJ
-
AI
Vo
l.
7
,
No
.
1
,
Ma
r
ch
2
0
1
8
:
33
–
41
34
L
é
v
y
f
l
ig
h
t.
I
n
th
is
al
g
o
r
ith
m
cu
c
k
o
o
b
ir
d
s
w
il
l
also
b
e
a
war
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o
f
ea
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o
t
h
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p
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s
itio
n
s
u
t
ilizin
g
P
SO
s
w
ar
m
co
m
m
u
n
icatio
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tec
h
n
iq
u
e
to
s
ea
r
ch
f
o
r
a
b
etter
s
o
lu
tio
n
.
I
n
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d
er
to
ev
alu
ate
th
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e
f
f
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ith
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,
it
h
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tan
d
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1
1
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s
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Si
m
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o
w
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at
I
n
teg
r
ated
Alg
o
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m
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is
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2.
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p
o
w
er
lo
s
s
T
h
e
o
b
j
ec
tiv
e
o
f
t
h
e
r
ea
cti
v
e
p
o
w
er
d
is
p
atc
h
p
r
o
b
le
m
is
to
m
in
i
m
ize
t
h
e
ac
t
iv
e
p
o
w
er
lo
s
s
an
d
ca
n
b
e
d
ef
in
ed
i
n
eq
u
atio
n
s
as
f
o
llo
w
s
:
F
=
P
L
=
∑
g
k
k
∈
Nbr
(
V
i
2
+
V
j
2
−
2
V
i
V
j
c
os
θ
ij
)
(
1
)
W
h
er
e
F
-
o
b
j
ec
tiv
e
f
u
n
ctio
n
,
P
L
–
p
o
w
er
lo
s
s
,
g
k
-
co
n
d
u
ct
an
ce
o
f
b
r
an
c
h
,
Vi
a
n
d
Vj
ar
e
v
o
ltag
e
s
at
b
u
s
es
i,j
,
Nb
r
-
to
tal
n
u
m
b
er
o
f
tr
an
s
m
is
s
io
n
li
n
es i
n
p
o
w
er
s
y
s
te
m
s
.
Vo
ltag
e
p
r
o
f
ile
i
m
p
r
o
v
e
m
e
n
t
T
o
m
i
n
i
m
ize
t
h
e
v
o
lta
g
e
d
ev
ia
tio
n
in
P
Q
b
u
s
e
s
,
th
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
(
F)
ca
n
b
e
w
r
itte
n
as
:
F
=
P
L
+
ω
v
×
VD
(
2
)
W
h
er
e
VD
-
v
o
lta
g
e
d
ev
iat
io
n
,
ω
v
-
is
a
w
ei
g
h
t
in
g
f
ac
to
r
o
f
v
o
lt
ag
e
d
ev
iatio
n
.
An
d
th
e
Vo
lta
g
e
d
ev
iatio
n
g
i
v
en
b
y
:
VD
=
∑
|
V
i
−
1
|
N
p
q
i
=
1
(
3
)
W
h
er
e
Np
q
-
n
u
m
b
er
o
f
lo
ad
b
u
s
e
s
E
q
u
alit
y
C
o
n
s
tr
ain
t
T
h
e
eq
u
alit
y
co
n
s
tr
ain
t o
f
th
e
p
r
o
b
lem
is
i
n
d
icate
d
b
y
th
e
p
o
w
er
b
alan
ce
eq
u
a
tio
n
as
f
o
llo
w
s
:
P
G
=
P
D
+
P
L
(
4
)
W
h
er
e
P
G
-
to
tal
p
o
w
er
g
en
er
a
tio
n
,
P
D
-
to
tal
p
o
w
er
d
e
m
an
d
.
I
n
eq
u
alit
y
C
o
n
s
tr
ai
n
ts
T
h
e
in
eq
u
al
it
y
co
n
s
tr
ain
t
i
m
p
lies
th
e
li
m
its
o
n
co
m
p
o
n
en
ts
in
th
e
p
o
w
er
s
y
s
te
m
in
ad
d
itio
n
to
th
e
li
m
it
s
cr
ea
ted
to
m
ak
e
s
u
r
e
s
y
s
te
m
s
ec
u
r
it
y
.
Up
p
er
an
d
l
o
w
er
b
o
u
n
d
s
o
n
th
e
ac
tiv
e
p
o
w
e
r
o
f
s
lack
b
u
s
(
P
g
)
,
an
d
r
ea
ctiv
e
p
o
w
er
o
f
g
en
er
at
o
r
s
(
Qg
)
ar
e
w
r
itte
n
as f
o
llo
w
s
:
P
g
s
l
a
ck
m
i
n
≤
P
g
s
l
ack
≤
P
g
s
l
ack
m
ax
(
5
)
Q
gi
m
i
n
≤
Q
gi
≤
Q
gi
m
ax
,
i
∈
N
g
(
6
)
Up
p
er
an
d
lo
w
er
b
o
u
n
d
s
o
n
th
e
b
u
s
v
o
lta
g
e
m
a
g
n
it
u
d
es (
Vi)
ar
e
g
iv
e
n
b
y
:
V
i
m
i
n
≤
V
i
≤
V
i
m
ax
,
i
∈
N
(
7
)
Up
p
er
an
d
lo
w
er
b
o
u
n
d
s
o
n
th
e
tr
an
s
f
o
r
m
er
s
tap
r
atio
s
(
T
i)
a
r
e
g
iv
e
n
b
y
:
T
i
m
i
n
≤
T
i
≤
T
i
m
ax
,
i
∈
N
T
(
8
)
Up
p
er
an
d
lo
w
er
b
o
u
n
d
s
o
n
th
e
co
m
p
e
n
s
ato
r
s
(
Qc)
ar
e
g
iv
e
n
b
y
:
Q
c
m
i
n
≤
Q
c
≤
Q
C
m
ax
,
i
∈
N
C
(
9
)
W
h
er
e
N
is
th
e
to
tal
n
u
m
b
er
o
f
b
u
s
es,
N
g
i
s
t
h
e
to
tal
n
u
m
b
er
o
f
g
en
er
ato
r
s
,
NT
is
t
h
e
to
tal
n
u
m
b
er
o
f
T
r
an
s
f
o
r
m
er
s
,
Nc
is
t
h
e
to
tal
n
u
m
b
er
o
f
s
h
u
n
t r
ea
ctiv
e
co
m
p
en
s
ato
r
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
-
AI
I
SS
N:
2252
-
8938
I
n
teg
r
a
ted
A
lg
o
r
ith
m
fo
r
Dec
r
ea
s
in
g
A
ctive
P
o
w
er Lo
s
s
(
K
.
Len
in
)
35
3.
CUCK
O
O
SE
ARCH
AL
G
O
RIT
H
M
(
CS)
T
h
e
C
u
ck
o
o
Sear
ch
Alg
o
r
it
h
m
(
C
S)
w
as
i
n
s
p
ir
ed
b
y
t
h
e
o
b
lig
ate
b
r
o
o
d
p
a
r
asit
is
m
o
f
s
o
m
e
cu
c
k
o
o
s
p
ec
ies
b
y
la
y
in
g
t
h
eir
e
g
g
s
i
n
th
e
n
es
ts
o
f
h
o
s
t
b
ir
d
s
.
So
m
e
cu
ck
o
o
s
h
a
v
e
e
v
o
lv
ed
i
n
s
u
c
h
a
w
a
y
t
h
at
f
e
m
ale
p
ar
asit
ic
cu
ck
o
o
s
ca
n
i
m
ita
te
th
e
co
lo
u
r
s
an
d
p
atter
n
s
o
f
th
e
eg
g
s
o
f
a
f
e
w
c
h
o
s
en
h
o
s
t
s
p
ec
ies.
T
h
is
r
ed
u
ce
s
th
e
p
r
o
b
ab
ilit
y
o
f
th
e
e
g
g
s
b
ein
g
ab
a
n
d
o
n
ed
an
d
,
th
er
ef
o
r
e,
in
cr
ea
s
es
t
h
eir
r
e
-
p
r
o
d
u
ctiv
it
y
.
I
n
g
en
er
al,
t
h
e
cu
ck
o
o
eg
g
s
h
atc
h
s
li
g
h
tl
y
ea
r
lier
th
an
t
h
eir
h
o
s
t e
g
g
s
.
O
n
ce
th
e
f
ir
s
t c
u
c
k
o
o
ch
ick
is
h
atch
ed
,
h
is
f
ir
s
t i
n
s
ti
n
c
t
ac
tio
n
is
to
ev
ict
t
h
e
h
o
s
t
eg
g
s
b
y
b
li
n
d
l
y
p
r
o
p
ellin
g
t
h
e
e
g
g
s
o
u
t
o
f
t
h
e
n
e
s
t.
T
h
is
ac
tio
n
r
esu
lt
s
in
i
n
cr
ea
s
i
n
g
th
e
c
u
ck
o
o
c
h
ick
’
s
s
h
ar
e
o
f
f
o
o
d
p
r
o
v
id
ed
b
y
its
h
o
s
t
b
ir
d
.
Mo
r
eo
v
er
,
s
tu
d
ies
s
h
o
w
t
h
at
a
cu
c
k
o
o
ch
ic
k
ca
n
i
m
itate
t
h
e
ca
ll
o
f
h
o
s
t
ch
ick
s
to
g
ain
ac
ce
s
s
to
m
o
r
e
f
ee
d
in
g
o
p
p
o
r
tu
n
it
y
.
T
h
e
C
S
m
o
d
els
s
u
ch
b
r
ee
d
in
g
b
eh
av
io
r
an
d
,
th
u
s
,
ca
n
b
e
ap
p
lied
to
v
ar
io
u
s
o
p
ti
m
izat
io
n
p
r
o
b
lem
s
.
3
.
1
.
L
ev
y
F
lig
hts
I
n
n
atu
r
e,
an
i
m
als
s
ea
r
c
h
f
o
r
f
o
o
d
in
a
r
an
d
o
m
o
r
q
u
asi
r
an
d
o
m
m
an
n
er
.
Gen
er
all
y
,
t
h
e
f
o
r
ag
in
g
p
at
h
o
f
an
an
i
m
a
l
is
ef
f
ec
t
iv
el
y
a
r
an
d
o
m
w
al
k
b
ec
a
u
s
e
th
e
n
e
x
t
m
o
v
e
is
b
ased
o
n
b
o
th
t
h
e
c
u
r
r
en
t
lo
ca
tio
n
/
s
tate
a
n
d
th
e
tr
an
s
itio
n
p
r
o
b
ab
ilit
y
to
th
e
n
ex
t
lo
ca
tio
n
.
T
h
e
ch
o
s
e
n
d
i
r
ec
tio
n
i
m
p
lic
itl
y
d
ep
en
d
s
o
n
a
p
r
o
b
a
b
ilit
y
,
w
h
ich
ca
n
b
e
m
o
d
eled
m
ath
e
m
at
ical
l
y
.
Var
io
u
s
s
t
u
d
ies
h
a
v
e
s
h
o
w
n
th
at
t
h
e
f
li
g
h
t
b
eh
av
io
r
o
f
m
a
n
y
a
n
i
m
als
a
n
d
in
s
ec
t
s
d
e
m
o
n
s
tr
ate
s
th
e
t
y
p
ic
al
ch
ar
ac
ter
is
tic
s
o
f
L
é
v
y
f
li
g
h
ts
.
A
L
é
v
y
f
li
g
h
t
is
a
r
a
n
d
o
m
w
al
k
i
n
w
h
ich
t
h
e
s
tep
-
le
n
g
th
s
ar
e
d
is
tr
ib
u
ted
ac
co
r
d
in
g
to
a
h
ea
v
y
-
tailed
p
r
o
b
ab
ilit
y
d
is
tr
ib
u
tio
n
.
A
f
ter
a
lar
g
e
n
u
m
b
er
o
f
s
tep
s
,
th
e
d
is
ta
n
ce
f
r
o
m
th
e
o
r
ig
i
n
o
f
th
e
r
an
d
o
m
w
al
k
te
n
d
s
to
a
s
t
ab
le
d
is
tr
ib
u
tio
n
.
3
.
2
.
Cuck
o
o
Sea
rc
h I
m
ple
menta
t
io
n
E
ac
h
eg
g
i
n
a
n
est
r
ep
r
esen
ts
a
s
o
lu
tio
n
,
an
d
a
cu
ck
o
o
eg
g
r
ep
r
esen
ts
a
n
e
w
s
o
l
u
tio
n
.
T
h
e
aim
is
t
o
e
m
p
lo
y
t
h
e
n
e
w
an
d
p
o
ten
t
iall
y
b
etter
s
o
l
u
tio
n
s
(
c
u
ck
o
o
s
)
to
r
ep
lace
n
o
t
-
so
-
g
o
o
d
s
o
lu
tio
n
s
in
th
e
n
e
s
ts
.
I
n
t
h
e
s
i
m
p
le
s
t
f
o
r
m
,
ea
ch
n
est
h
as
o
n
e
eg
g
.
T
h
e
alg
o
r
ith
m
ca
n
b
e
ex
ten
d
ed
to
m
o
r
e
co
m
p
licated
c
ases
in
w
h
ic
h
ea
ch
n
est
h
as
m
u
ltip
le
eg
g
s
r
ep
r
ese
n
ti
n
g
a
s
e
t o
f
s
o
l
u
tio
n
s
T
h
e
C
S is
b
ased
o
n
th
r
ee
id
ea
lized
r
u
les:
1.
E
ac
h
cu
c
k
o
o
la
y
s
o
n
e
e
g
g
at
a
ti
m
e,
an
d
d
u
m
p
s
it i
n
a
r
an
d
o
m
l
y
c
h
o
s
e
n
n
e
s
t;
2.
T
h
e
b
est n
ests
w
it
h
h
ig
h
q
u
al
it
y
o
f
eg
g
s
(
s
o
lu
tio
n
s
)
w
ill ca
r
r
y
o
v
er
to
th
e
n
e
x
t
g
en
er
atio
n
s
;
3.
T
h
e
n
u
m
b
er
o
f
a
v
ailab
le
h
o
s
t
n
est
s
i
s
f
ix
ed
,
a
n
d
a
h
o
s
t
ca
n
d
i
s
co
v
er
an
alie
n
e
g
g
w
it
h
p
r
o
b
ab
ilit
y
p
a
ϵ
[
0
,
1
]
I
n
th
is
ca
s
e,
th
e
h
o
s
t
b
ir
d
ca
n
eith
er
th
r
o
w
t
h
e
eg
g
a
w
a
y
o
r
ab
an
d
o
n
th
e
n
est
to
b
u
ild
a
c
o
m
p
letel
y
n
e
w
n
est i
n
a
n
e
w
lo
ca
tio
n
.
Fo
r
s
i
m
p
lici
t
y
,
t
h
e
la
s
t
as
s
u
m
p
tio
n
ca
n
b
e
ap
p
r
o
x
i
m
ated
b
y
a
f
r
ac
tio
n
p
a
o
f
th
e
n
n
est
s
b
ein
g
r
ep
lace
d
b
y
n
e
w
n
est
s
,
h
a
v
in
g
n
e
w
r
an
d
o
m
s
o
l
u
tio
n
s
.
Fo
r
a
m
a
x
i
m
iz
atio
n
p
r
o
b
lem
,
t
h
e
q
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–
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36
w
h
ic
h
h
as a
n
i
n
f
in
ite
v
ar
ia
n
ce
.
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e,
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co
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tiv
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t
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4.
F
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r
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ated
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th
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tain
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t
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p
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latio
n
s
ize
co
n
s
tan
t.
T
h
e
o
p
er
atio
n
w
as p
er
f
o
r
m
ed
as
f
o
llo
w
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
-
AI
I
SS
N:
2252
-
8938
I
n
teg
r
a
ted
A
lg
o
r
ith
m
fo
r
Dec
r
ea
s
in
g
A
ctive
P
o
w
er Lo
s
s
(
K
.
Len
in
)
37
X
i
(
t
+
1
)
=
{
Y
i
(
t
)
if
f
(
Y
i
(
t
)
)
≤
f
(
X
i
(
t
)
)
X
i
(
t
)
if
f
(
Y
i
(
t
)
)
>
(
X
i
(
t
)
)
(
1
9
)
T
h
is
in
d
icate
s
t
h
at
t
h
e
o
r
ig
i
n
al
s
o
lu
tio
n
w
o
u
ld
b
e
r
ep
lace
d
b
y
th
e
o
f
f
s
p
r
in
g
s
o
l
u
tio
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i
f
t
h
e
f
it
n
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s
v
al
u
e
o
f
t
h
e
o
f
f
s
p
r
in
g
s
o
lu
tio
n
w
a
s
b
etter
t
h
an
th
e
o
r
ig
in
al
s
o
lu
t
io
n
.
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h
er
w
i
s
e,
th
e
o
r
ig
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al
s
o
lu
tio
n
w
o
u
ld
r
e
m
ai
n
i
n
th
e
p
o
p
u
latio
n
f
o
r
th
e
n
ex
t i
ter
atio
n
.
T
h
e
w
h
o
le
p
r
o
ce
d
u
r
e
w
a
s
r
ep
ea
ted
u
n
til t
h
e
s
to
p
p
in
g
cr
it
er
io
n
w
a
s
m
et.
Fire
f
l
y
A
l
g
o
r
ith
m
I
n
p
u
t:
R
a
n
d
o
mly
in
itia
liz
ed
p
o
s
itio
n
o
f
d
d
imen
s
io
n
p
r
o
b
lem:
Ou
tp
u
t:
P
o
s
itio
n
o
f th
e
a
p
p
r
o
x
ima
te
g
lo
b
a
l
o
p
tima
:
B
eg
in
I
n
itia
liz
e
p
o
p
u
la
tio
n
;
E
v
a
lu
a
te
fitn
ess
va
lu
e;
←
S
elec
t c
u
r
r
en
t b
est s
o
lu
tio
n
;
F
o
r
←
1
to
ma
x
S
o
r
t p
o
p
u
la
tio
n
b
a
s
ed
o
n
th
e
f
itn
ess
va
lu
e;
←
ℎ
(
)
;
←
_
ℎ
(
)
;
F
o
r
i
←
0
to
n
u
mb
er o
f
s
o
lu
t
io
n
s
F
o
r
j
←
0
to
n
u
mb
er o
f
s
o
lu
tio
n
s
I
f
(
(
)
>
(
)
)
th
en
C
a
lcu
la
te
d
is
ta
n
ce
a
n
d
a
ttr
a
ctive
n
ess
;
Up
d
a
te
p
o
s
itio
n
;
E
n
d
I
f
E
n
d
F
o
r
E
n
d
F
o
r
F
o
r
i
←
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to
n
u
mb
er o
f
s
o
lu
tio
n
s
C
r
ea
te
tr
iv
ia
l so
lu
tio
n
,
(
)
;
P
erfo
r
m
cro
s
s
o
ve
r
,
(
)
;
P
erfo
r
m
s
elec
tio
n
,
(
)
;
E
n
d
Fo
r
X
←
c
omb
in
e
(
X
g
o
o
d
,
X
w
o
r
s
t
)
;
X
G
←
Select
cu
r
r
en
t b
es
t so
lu
t
io
n
;
t
←
t
+
1
;
1;
E
n
d
Fo
r
E
n
d
B
eg
in
5.
P
ARTI
C
L
E
SWARM
O
P
T
I
M
I
Z
AT
I
O
N
(
P
SO
)
P
ar
ticle
S
w
ar
m
Op
ti
m
izatio
n
is
a
p
o
p
u
latio
n
-
b
ased
o
p
ti
m
izat
io
n
alg
o
r
ith
m
i
n
s
p
ir
ed
b
y
t
h
e
b
eh
av
io
u
r
o
f
f
lo
ck
s
o
f
b
ir
d
s
.
I
t
w
a
s
f
ir
s
tl
y
in
tr
o
d
u
ce
d
b
y
Ke
n
n
ed
y
a
n
d
E
b
er
h
ar
t
an
d
it
h
as
b
ee
n
lar
g
e
l
y
ap
p
lied
to
s
o
lv
e
o
p
tim
izatio
n
p
r
o
b
le
m
s
.
T
h
e
s
tan
d
ar
d
ap
p
r
o
ac
h
is
co
m
p
o
s
e
d
b
y
a
s
w
ar
m
o
f
p
ar
ticles,
wh
er
e
ea
ch
o
n
e
h
a
s
a
p
o
s
itio
n
w
ith
in
t
h
e
s
ea
r
ch
s
p
a
ce
x
i
⃗
⃗
⃗
⃗
an
d
e
ac
h
p
o
s
itio
n
r
ep
r
esen
ts
a
s
o
lu
tio
n
f
o
r
th
e
p
r
o
b
lem
.
T
h
e
p
ar
ticles
f
l
y
th
r
o
u
g
h
th
e
s
ea
r
c
h
s
p
ac
e
o
f
th
e
p
r
o
b
lem
s
ea
r
ch
i
n
g
f
o
r
th
e
b
est s
o
lu
tio
n
,
ac
co
r
d
in
g
to
th
e
cu
r
r
en
t v
elo
cit
y
v
i
⃗
⃗
⃗
th
e
b
est
p
o
s
itio
n
f
o
u
n
d
b
y
t
h
e
p
a
r
ticle
its
el
f
(
P
b
es
t
i
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
)
an
d
th
e
b
est
p
o
s
i
tio
n
f
o
u
n
d
b
y
t
h
ee
n
tire
s
w
ar
m
d
u
r
i
n
g
t
h
e
s
ea
r
ch
s
o
f
ar
(
G
b
es
t
i
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
)
.
A
cc
o
r
d
in
g
to
t
h
e
ap
p
r
o
ac
h
p
r
o
p
o
s
ed
b
y
Sh
i
a
n
d
E
b
er
h
ar
t
(
th
is
ap
p
r
o
ac
h
i
s
also
ca
lled
in
er
tia
P
SO)
,
th
e
v
elo
cit
y
o
f
a
p
ar
ticle
i
s
ev
al
u
ated
at
ea
ch
iter
atio
n
o
f
t
h
e
alg
o
r
ith
m
b
y
u
s
i
n
g
t
h
e
f
o
llo
w
in
g
eq
u
at
io
n
:
v
i
⃗
⃗
⃗
(
t
+
1
)
=
ω
v
i
⃗
⃗
⃗
(
t
)
+
r
1
c
1
|
P
b
es
t
i
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
−
x
i
⃗
⃗
⃗
(
t
)
|
+
r
2
c
2
|
G
b
es
t
i
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
−
x
i
⃗
⃗
⃗
(
t
)
|
(
2
0
)
W
h
er
e
r
1
an
d
r
2
ar
e
n
u
m
b
er
s
r
an
d
o
m
l
y
g
e
n
er
ated
in
th
e
i
n
ter
v
al
[
0
,
1
]
.
T
h
e
in
er
tia
w
ei
g
h
t
(
ω
)
co
n
tr
o
ls
th
e
in
f
lu
e
n
ce
o
f
th
e
p
r
ev
io
u
s
v
e
l
o
cit
y
an
d
b
alan
ce
s
th
e
ex
p
lo
r
atio
n
-
e
x
p
lo
i
tatio
n
b
eh
a
v
io
u
r
alo
n
g
th
e
p
r
o
ce
s
s
.
I
t
g
en
er
all
y
d
ec
r
ea
s
es
f
r
o
m
0
.
9
to
0
.
4
d
u
r
in
g
th
e
alg
o
r
it
h
m
e
x
ec
u
t
io
n
.
c
1
&
c
2
ar
e
ca
lled
co
g
n
it
iv
e
an
d
s
o
cial
ac
ce
ler
atio
n
co
n
s
tan
ts
,
r
esp
ec
tiv
el
y
,
an
d
w
ei
g
h
ts
th
e
in
f
l
u
en
ce
o
f
th
e
m
e
m
o
r
y
o
f
th
e
p
ar
ticle
an
d
th
e
in
f
o
r
m
ati
o
n
ac
q
u
ir
ed
f
r
o
m
t
h
e
n
eig
h
b
o
u
r
h
o
o
d
.
T
h
e
p
o
s
itio
n
o
f
ea
ch
p
ar
ticle
is
u
p
d
ated
b
ased
o
n
th
e
v
e
lo
cit
y
o
f
th
e
p
ar
ticle,
ac
co
r
d
in
g
to
th
e
f
o
llo
w
in
g
eq
u
atio
n
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8938
IJ
-
AI
Vo
l.
7
,
No
.
1
,
Ma
r
ch
2
0
1
8
:
33
–
41
38
x
i
⃗
⃗
⃗
(
t
+
1
)
=
x
i
⃗
⃗
⃗
(
t
)
+
v
i
⃗
⃗
⃗
(
t
+
1
)
(
2
1
)
T
h
e
co
m
m
u
n
icatio
n
to
p
o
lo
g
y
d
ef
in
es
t
h
e
n
ei
g
h
b
o
u
r
h
o
o
d
o
f
th
e
p
ar
ticles
a
n
d
,
as
a
co
n
s
eq
u
en
ce
,
t
h
e
f
lo
w
o
f
in
f
o
r
m
atio
n
t
h
r
o
u
g
h
t
h
e
p
ar
tic
les.
T
h
er
e
ar
e
t
w
o
b
asic
to
p
o
lo
g
ies:
g
lo
b
al
an
d
lo
ca
l.
I
n
t
h
e
f
o
r
m
er
,
ea
c
h
p
ar
ticle
s
h
ar
es
an
d
ac
q
u
ir
es
in
f
o
r
m
a
tio
n
d
ir
ec
tl
y
f
r
o
m
all
o
th
er
p
ar
ticles,
i.e
.
all
p
a
r
ticles
u
s
e
th
e
s
a
m
e
s
o
cial
m
e
m
o
r
y
,
ca
lled
G
best
.
I
n
th
e
lo
ca
l
to
p
o
lo
g
y
,
ea
ch
p
ar
ticle
o
n
l
y
s
h
ar
es
in
f
o
r
m
atio
n
w
it
h
t
w
o
n
ei
g
h
b
o
u
r
s
an
d
t
h
e
s
o
cial
m
e
m
o
r
y
is
n
o
t
th
e
s
a
m
e
w
it
h
in
t
h
e
w
h
o
le
s
w
ar
m
.
T
h
is
ap
p
r
o
ac
h
,
ca
lled
L
best
,
h
elp
s
to
av
o
id
a
p
r
em
at
u
r
e
attr
ac
tio
n
o
f
all
p
ar
ticles to
a
s
in
g
le
s
p
o
t p
o
in
t in
t
h
e
s
ea
r
c
h
s
p
ac
e.
5
.
1
.
I
nte
g
ra
t
ed
Alg
o
rit
h
m
(
I
A)
f
o
r
s
o
lv
ing
o
ptim
a
l r
ea
ct
i
v
e
po
w
er
pro
blem
I
n
th
i
s
p
r
o
p
o
s
ed
I
n
teg
r
ated
Al
g
o
r
ith
m
(
I
A
)
,
cu
c
k
o
o
b
ir
d
w
i
ll
b
e
ab
le
to
p
er
f
o
r
m
s
to
ch
a
s
tic
b
eh
av
io
u
r
(
r
an
d
o
m
w
al
k
)
u
s
i
n
g
th
e
s
tr
ate
g
y
o
f
f
ir
e
f
l
y
al
g
o
r
ith
m
,
i
n
s
tead
o
f
u
s
i
n
g
L
év
y
Fli
g
h
t
m
o
v
e
m
e
n
t.
A
l
s
o
th
e
cu
c
k
o
o
b
ir
d
s
w
il
l
b
e
ab
le
to
co
m
m
u
n
icate
t
h
e
m
to
i
n
f
o
r
m
ea
c
h
o
th
er
f
r
o
m
t
h
eir
p
o
s
itio
n
a
n
d
h
elp
ea
ch
o
th
er
to
i
m
m
i
g
r
ate
to
a
b
etter
p
lace
.
E
ac
h
c
u
ck
o
o
b
ir
d
w
ill r
ec
o
r
d
th
e
b
est p
er
s
o
n
al
e
x
p
er
ien
ce
as
p
b
est d
u
r
in
g
it
s
o
wn
lif
e.
I
n
ad
d
itio
n
,
th
e
b
est
p
b
est
a
m
o
n
g
all
th
e
b
ir
d
s
is
ca
lled
g
b
est.
T
h
e
cu
ck
o
o
b
i
r
d
s
’
co
m
m
u
n
icatio
n
is
estab
lis
h
ed
th
r
o
u
g
h
th
e
p
b
est
an
d
g
b
est.
T
h
ey
u
p
d
ate
th
eir
p
o
s
itio
n
u
s
in
g
th
ese
p
ar
a
m
et
er
s
alo
n
g
w
i
th
th
e
v
elo
cit
y
o
f
ea
c
h
s
w
ar
m
m
e
m
b
er
.
T
h
e
u
p
d
ate
r
u
le
f
o
r
cu
ck
o
o
(
i’
s
)
p
o
s
it
io
n
is
ca
r
r
ie
d
o
u
t
ac
co
r
d
in
g
to
eq
u
atio
n
s
(
2
0
,
2
1
)
.
1.
Star
t
2.
I
n
itiate
a
r
an
d
o
m
p
o
p
u
latio
n
o
f
n
h
o
s
t
3.
Get
a
cu
ck
o
o
r
an
d
o
m
l
y
i
4.
E
v
alu
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Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
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2252
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8938
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
2
2
5
2
-
8938
IJ
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AI
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7
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i
s
s
u
cc
ess
f
u
l
l
y
s
o
lv
ed
o
p
ti
m
al
r
ea
ct
iv
e
p
o
w
er
p
r
o
b
lem
.
Qu
ic
k
co
n
v
er
g
e
n
ce
o
f
th
e
C
u
c
k
o
o
Sear
ch
(
C
S),
th
e
v
ib
r
an
t
r
o
o
t
ch
an
g
e
o
f
th
e
Fire
f
l
y
A
l
g
o
r
ith
m
(
F
A
)
,
an
d
th
e
in
ce
s
s
a
n
t
p
o
s
itio
n
m
o
d
er
n
izatio
n
o
f
t
h
e
P
ar
ticle
S
w
ar
m
Op
ti
m
izatio
n
(
P
SO)
h
as
b
ee
n
co
m
b
in
ed
to
f
o
r
m
th
e
I
n
te
g
r
ated
A
l
g
o
r
ith
m
(
I
A
)
.
I
n
o
r
d
er
to
ev
alu
ate
th
e
e
f
f
icie
n
c
y
o
f
t
h
e
p
r
o
p
o
s
ed
I
n
teg
r
ated
A
l
g
o
r
ith
m
(
I
A
)
,
it
h
as
b
ee
n
test
ed
in
s
tan
d
ar
d
I
E
E
E
5
7
,
1
1
8
b
u
s
s
y
s
te
m
s
a
n
d
co
m
p
ar
ed
to
o
th
er
s
tan
d
ar
d
r
ep
o
r
ted
alg
o
r
ith
m
s
.
Si
m
u
latio
n
r
es
u
lt
s
s
h
o
w
t
h
at
I
n
teg
r
ated
Alg
o
r
it
h
m
(
I
A
)
is
co
n
s
id
er
ab
l
y
r
ed
u
ce
d
th
e
r
ea
l
p
o
w
er
lo
s
s
a
n
d
v
o
lta
g
e
p
r
o
f
ile
w
it
h
i
n
t
h
e
li
m
its
.
RE
F
E
R
E
NC
E
S
[1
]
O.A
lsa
c
,
a
n
d
B.
S
c
o
tt
,
“
Op
ti
m
a
l
lo
a
d
f
lo
w
w
it
h
ste
a
d
y
sta
te se
c
u
rit
y
”
,
IEE
E
T
ra
n
sa
c
ti
o
n
.
P
A
S
-
1
9
7
3
,
p
p
.
7
4
5
-
7
5
1
.
[2
]
L
e
e
K
Y,
P
a
r
u
Y
M
,
Oritz
J
L
–
A
u
n
it
e
d
a
p
p
r
o
a
c
h
t
o
o
p
ti
m
a
l
re
a
l
a
n
d
re
a
c
ti
v
e
p
o
w
e
r
d
isp
a
tch
,
IE
EE
T
r
a
n
sa
c
ti
o
n
s
o
n
p
o
we
r A
p
p
a
ra
t
u
s a
n
d
sy
ste
ms
1
9
8
5
:
P
A
S
-
1
0
4
:
1
1
4
7
-
1
1
5
3
[3
]
A
.
M
o
n
ti
c
e
ll
i,
M
.
V.F
P
e
re
ira,
a
n
d
S
.
G
ra
n
v
il
le,
“
S
e
c
u
rit
y
c
o
n
stra
in
e
d
o
p
ti
m
a
l
p
o
w
e
r
f
lo
w
w
it
h
p
o
st
c
o
n
ti
n
g
e
n
c
y
c
o
rre
c
ti
v
e
re
sc
h
e
d
u
li
n
g
”
,
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r S
y
st
e
ms
:
P
W
RS
-
2
,
No
.
1
,
p
p
.
1
7
5
-
1
8
2
.
,
1
9
8
7
.
[4
]
De
e
b
N,
S
h
a
h
i
d
e
h
p
u
r
S
.
M
,
L
in
e
a
r
re
a
c
ti
v
e
p
o
w
e
r
o
p
ti
m
iza
ti
o
n
in
a
larg
e
p
o
w
e
r
n
e
tw
o
rk
u
sin
g
th
e
d
e
c
o
m
p
o
siti
o
n
a
p
p
ro
a
c
h
.
IEE
E
T
ra
n
sa
c
ti
o
n
s o
n
p
o
we
r sy
ste
m
1
9
9
0
:
5
(2
)
:
4
2
8
-
4
3
5
[5
]
Ho
b
so
n
,
“
Ne
tw
o
rk
c
o
n
sra
in
e
d
re
a
c
ti
v
e
p
o
w
e
r
c
o
n
tro
l
u
sin
g
li
n
e
a
r
p
r
o
g
ra
m
m
in
g
,
”
IEE
E
T
ra
n
s
a
c
ti
o
n
s
o
n
p
o
we
r
sy
ste
ms
P
A
S
-
9
9
(
4
)
,
p
p
8
6
8
=
8
7
7
,
1
9
8
0
[6
]
K.Y
L
e
e
,
Y.M
P
a
rk
,
a
n
d
J.L
Oritz,
“
Fu
e
l
–
c
o
st
o
p
ti
miz
a
ti
o
n
f
o
r
b
o
t
h
re
a
l
a
n
d
re
a
c
ti
v
e
p
o
we
r
d
isp
a
tch
e
s
”
,
IEE
P
ro
c
;
1
3
1
C
,
(3
),
p
p
.
8
5
-
9
3
.
[7
]
M
.
K.
M
a
n
g
o
li
,
a
n
d
K.Y.
L
e
e
,
“
Op
ti
m
a
l
re
a
l
a
n
d
re
a
c
ti
v
e
p
o
w
e
r
c
o
n
tro
l
u
sin
g
li
n
e
a
r
p
r
o
g
ra
m
m
in
g
”
,
El
e
c
tr.P
o
we
r
S
y
st.R
e
s
,
Vo
l.
2
6
,
p
p
.
1
-
1
0
,
1
9
9
3
.
[8
]
K.A
n
b
u
ra
ja,
“
Op
ti
m
a
l
p
o
w
e
r
f
lo
w
u
sin
g
re
f
in
e
d
g
e
n
e
ti
c
a
lg
o
rit
h
m
”
,
El
e
c
tr.P
o
we
r
Co
mp
o
n
.
S
y
st
,
V
o
l.
3
0
,
1
0
5
5
-
1
0
6
3
,
2
0
0
2
.
[9
]
De
v
a
r
a
j,
a
n
d
B.
Ye
g
a
n
a
ra
y
a
n
a
,
“
Ge
n
e
ti
c
a
lg
o
rith
m
b
a
se
d
o
p
t
ima
l
p
o
we
r fl
o
w
fo
r se
c
u
rity e
n
h
a
n
c
e
m
e
n
t”
,
IEE
p
r
o
c
-
G
e
n
e
r
a
ti
o
n
.
T
ra
n
sm
issio
n
a
n
d
.
Di
strib
u
ti
o
n
;
1
5
2
,
6
No
v
e
m
b
e
r
2
0
0
5
.
[1
0
]
C.
A
.
Ca
n
iza
re
s
,
A
.
C.
Z.
d
e
S
o
u
z
a
a
n
d
V.H.
Qu
in
tan
a
,
“
Co
m
p
a
riso
n
o
f
p
e
rf
o
r
m
a
n
c
e
in
d
ice
s
f
o
r
d
e
tec
ti
o
n
o
f
p
r
o
x
im
it
y
to
v
o
lt
a
g
e
c
o
ll
a
p
se
,
’’
v
o
l
.
1
1
.
n
o
.
3
,
p
p
.
1
4
4
1
-
1
4
5
0
,
A
u
g
1
9
9
6
.
[1
1
]
Eb
e
rh
a
rt,
R.
C.
a
n
d
J.
Ke
n
n
e
d
y
,
1
9
9
5
.
A
n
e
w
o
p
ti
mize
r
u
sin
g
p
a
rticle
swa
rm
th
e
o
ry
.
P
ro
c
e
e
d
i
n
g
o
f
th
e
6
th
In
tern
a
ti
o
n
a
l
S
y
m
p
o
siu
m
o
n
M
icro
M
a
c
h
i
n
e
a
n
d
Hu
m
a
n
S
c
ien
c
e
,
p
p
:
3
9
-
4
3
.
[1
2
]
A
b
d
u
ll
a
h
,
A
.
e
t
a
l.
2
0
1
2
.
A
n
e
w
h
y
b
rid
f
ire
f
l
y
a
l
g
o
rit
h
m
f
o
r
c
o
m
p
lex
a
n
d
n
o
n
li
n
e
a
r
p
r
o
b
lem
.
Distrib
u
ted
Co
m
p
u
ti
n
g
a
n
d
A
rti
f
icia
l
In
telli
g
e
n
c
e
.
S
p
rin
g
e
r
.
6
7
3
–
6
8
0
.
[1
3
]
Bra
tt
o
n
,
D.
a
n
d
Ke
n
n
e
d
y
,
J.
2
0
0
7
.
De
fi
n
in
g
a
sta
n
d
a
rd
f
o
r
p
a
rticle
swa
rm
o
p
ti
miza
ti
o
n
.
S
w
a
r
m
In
telli
g
e
n
c
e
S
y
m
p
o
siu
m
,
2
0
0
7
.
S
IS
2
0
0
7
.
IEE
E
(2
0
0
7
)
,
1
2
0
–
1
2
7
.
[1
4
]
El
-
S
a
wy
,
A
.
A
.
e
t
a
l.
2
0
1
2
.
A
No
v
e
l
Hy
b
rid
A
n
t
Co
lo
n
y
Op
ti
m
iza
ti
o
n
a
n
d
F
iref
l
y
A
l
g
o
rit
h
m
f
o
r
S
o
lv
in
g
Co
n
stra
in
e
d
En
g
in
e
e
rin
g
De
sig
n
P
ro
b
lem
s.
J
o
u
rn
a
l
o
f
Na
t
u
ra
l
S
c
ien
c
e
s a
n
d
M
a
th
e
ma
ti
c
s
.
6
,
(2
0
1
2
).
[1
5
]
F
a
ro
o
k
,
S
.
a
n
d
Ra
ju
,
P
.
S
.
Ev
o
l
u
ti
o
n
a
ry
H
y
b
rid
G
e
n
e
ti
c
-
F
ire
f
l
y
A
lg
o
rit
h
m
f
o
r
G
lo
b
a
l
Op
ti
m
iza
ti
o
n
.
[1
6
]
G
a
n
d
o
m
i,
A
.
H.
e
t
a
l.
2
0
1
3
.
Cu
c
k
o
o
se
a
rc
h
a
lg
o
rit
h
m
:
a
m
e
t
a
h
e
u
risti
c
a
p
p
r
o
a
c
h
to
so
lv
e
stru
c
tu
ra
l
o
p
ti
m
iza
ti
o
n
p
ro
b
lem
s.
En
g
in
e
e
rin
g
wit
h
Co
m
p
u
ter
s
.
2
9
,
(
2
0
1
3
),
1
7
–
3
5
.
[1
7
]
G
h
o
d
ra
ti
,
A
.
a
n
d
L
o
tf
i,
S
.
2
0
1
2
.
A
h
y
b
rid
CS
/
P
S
O
a
lg
o
rit
h
m
f
o
r
g
lo
b
a
l
o
p
ti
m
iza
ti
o
n
.
I
n
telli
g
e
n
t
I
n
f
o
rm
a
ti
o
n
a
n
d
Da
tab
a
se
S
y
ste
m
s.
S
p
rin
g
e
r
.
8
9
–
9
8
.
[1
8
]
Ha
ss
a
n
z
a
d
e
h
,
T
.
a
n
d
M
e
y
b
o
d
i,
M
.
R.
2
0
1
2
.
A
n
e
w
h
y
b
rid
a
lg
o
rith
m
b
a
se
d
o
n
Fi
re
fl
y
Al
g
o
rit
h
m
a
n
d
c
e
ll
u
la
r
le
a
rn
i
n
g
a
u
t
o
ma
t
a
.
2
0
t
h
Ira
n
ia
n
Co
n
f
e
re
n
c
e
o
n
E
lec
tri
c
a
l
En
g
in
e
e
rin
g
(ICE
E)
(2
0
1
2
)
,
6
2
8
–
6
3
3
.
[1
9
]
He
z
a
m
,
I.
M
.
a
n
d
A
b
d
e
lRao
u
f
,
O.
2
0
1
3
.
P
a
rti
c
le
S
w
a
r
m
Op
ti
m
iza
ti
o
n
A
p
p
ro
a
c
h
f
o
r
S
o
lv
in
g
Co
m
p
lex
V
a
riab
le
F
ra
c
ti
o
n
a
l
P
r
o
g
ra
m
m
in
g
P
ro
b
lem
s.
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
En
g
in
e
e
rin
g
.
2
,
(
2
0
1
3
).
[2
0
]
He
z
a
m
,
I.
M
.
a
n
d
A
b
d
e
lRao
u
f
,
O.M
.
M
.
H.
2
0
1
3
.
S
o
lv
in
g
F
ra
c
ti
o
n
a
l
P
ro
g
ra
m
m
in
g
P
ro
b
lem
s
Us
in
g
M
e
tah
e
u
risti
c
A
l
g
o
rit
h
m
s
u
n
d
e
r
Un
c
e
rtain
ty
.
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Ad
v
a
n
c
e
d
Co
mp
u
t
in
g
.
4
6
,
(2
0
1
3
),
1
2
6
1
–
1
2
7
0
.
[2
1
]
He
z
a
m
,
I.
M
.
a
n
d
Ra
o
u
f
,
O.A
.
2
0
1
3
.
Em
p
lo
y
in
g
T
h
re
e
S
w
a
r
m
In
telli
g
e
n
t
A
lg
o
rit
h
m
s
f
o
r
S
o
lv
in
g
I
n
t
e
g
e
r
F
ra
c
ti
o
n
a
l
P
r
o
g
ra
m
m
in
g
P
ro
b
lem
s.
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
S
c
ien
ti
fi
c
a
n
d
E
n
g
in
e
e
rin
g
Res
e
a
rc
h
(
IJ
S
ER
)
.
4
,
I
ss
u
e
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Evaluation Warning : The document was created with Spire.PDF for Python.