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l
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A
b
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Dep
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m
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co
m
1.
I
NT
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lectr
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tili
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to
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D
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[
1
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2
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,
c
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3
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d
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P
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R
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w
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f
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is
co
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s
id
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as
a
m
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x
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in
te
g
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n
o
n
-
li
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ea
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p
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m
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p
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o
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lem
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T
h
er
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ar
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m
a
n
y
t
y
p
e
s
o
f
o
p
ti
m
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n
tech
n
iq
u
es:
‒
C
las
s
ical
o
p
ti
m
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io
n
:
D
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d
s
o
n
s
o
m
e
m
ath
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m
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ical
m
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p
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s
s
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ch
a
s
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p
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r
a
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m
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m
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.
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s
ca
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p
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u
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th
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p
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b
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m
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(
r
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f
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)
,
th
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clas
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eth
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co
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m
e
m
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h
ti
m
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d
m
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tr
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tim
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m
s
o
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tio
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o
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lo
b
al.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2252
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8792
Dis
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p
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fig
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(
Ma
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mo
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49
‒
Heu
r
is
tic
o
p
ti
m
iza
tio
n
:
T
h
is
t
y
p
e
d
ep
en
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s
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n
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b
eh
a
v
io
r
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f
s
o
m
eth
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g
i
n
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e
n
at
u
r
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s
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ch
as
an
t
co
lo
n
y
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g
r
a
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w
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m
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h
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d
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w
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m
et
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…
etc.
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h
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m
ain
ad
v
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tag
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.
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d
is
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ta
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in
it
is
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at
it
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less
ac
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.
‒
A
r
ti
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tel
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ce
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s
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n
p
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in
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d
m
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ch
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ticle
s
w
a
r
m
.
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h
e
n
et
w
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k
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f
ig
u
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f
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p
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w
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s
s
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ctio
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w
as
f
ir
s
tl
y
i
n
tr
o
d
u
ce
d
b
y
Me
r
lin
an
d
B
ac
k
in
1
9
7
5
[
1
]
.
T
h
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y
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s
ed
h
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is
tic
a
p
p
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b
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tech
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co
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f
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u
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w
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o
p
tim
iza
tio
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g
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r
ith
m
(
W
OA
)
[
4
]
p
r
esen
ted
in
th
is
s
t
u
d
y
m
i
m
ic
s
t
h
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b
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lo
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in
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p
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.
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h
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if
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m
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.
W
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A
h
a
s
p
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f
f
icien
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n
s
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lv
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2
9
m
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m
atica
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p
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m
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n
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b
lem
s
a
n
d
6
s
tr
u
ct
u
r
al
o
p
tim
izatio
n
p
r
o
b
lem
s
[
4
]
.
A
t
s
ec
t
io
n
2
in
t
h
is
ar
ticle,
r
ec
o
n
f
i
g
u
r
atio
n
p
r
o
b
lem
w
i
l
l
b
e
f
o
r
m
u
lated
in
m
at
h
e
m
atica
l
f
o
r
m
.
T
h
e
w
h
ale
o
p
ti
m
iza
tio
n
alg
o
r
ith
m
w
ill
b
e
ex
p
r
ess
ed
in
a
m
at
h
e
m
atica
l
f
o
r
m
at
s
ec
tio
n
3
,
s
ec
tio
n
4
is
d
ed
icate
d
f
o
r
th
e
i
m
p
le
m
e
n
tatio
n
o
f
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
to
m
i
n
i
m
ize
p
o
w
er
lo
s
s
o
f
3
3
,
6
9
,
an
d
1
1
8
b
u
s
s
y
s
te
m
s
.
T
h
en
th
e
o
b
tain
ed
r
es
u
lt
s
ar
e
co
m
p
ar
ed
to
p
r
ev
io
u
s
l
y
ap
p
li
ed
h
eu
r
is
tic
m
et
h
o
d
s
to
p
r
o
v
e
its
ef
f
icie
n
c
y
a
t sectio
n
5
.
I
n
th
e
last
f
e
w
y
ea
r
s
,
m
a
n
y
r
esear
ch
er
s
tr
ied
to
s
o
lv
e
th
e
r
ec
o
n
f
i
g
u
r
atio
n
p
r
o
b
lem
u
s
i
n
g
d
if
f
er
e
n
t
m
et
h
o
d
s
tr
y
i
n
g
to
r
ea
ch
les
s
ti
m
e
-
co
n
s
u
m
i
n
g
m
et
h
o
d
s
an
d
l
o
o
k
in
g
f
o
r
th
e
g
lo
b
al
o
p
ti
m
u
m
.
Au
th
o
r
s
o
f
[
5
]
u
s
e
g
r
e
y
w
o
l
f
o
p
ti
m
izat
io
n
al
g
o
r
ith
m
w
h
ich
i
s
in
s
p
ir
ed
f
r
o
m
h
u
n
ti
n
g
s
tr
ate
g
y
o
f
g
r
e
y
w
o
l
v
es
to
s
o
l
v
e
r
ec
o
n
f
i
g
u
r
atio
n
p
r
o
b
lem
f
o
r
(
3
3
b
u
s
s
y
s
te
m
,
6
9
b
u
s
s
y
s
te
m
,
a
n
d
1
1
8
b
u
s
s
y
s
te
m
)
.
Au
t
h
o
r
s
o
f
[
6
]
u
s
e
f
ir
e
w
o
r
k
s
alg
o
r
ith
m
f
o
r
s
o
lv
in
g
r
ec
o
n
f
i
g
u
r
atio
n
p
r
o
b
lem
o
n
3
3
an
d
1
1
9
b
u
s
s
y
s
te
m
.
T
h
e
f
ir
e
w
o
r
k
s
al
g
o
r
ith
m
d
ep
en
d
s
o
n
th
e
s
p
ar
k
s
g
e
n
er
ated
in
th
e
e
x
p
lo
s
io
n
.
T
h
is
al
g
o
r
ith
m
s
elec
t
s
s
o
m
e
q
u
ali
t
y
p
o
i
n
ts
a
t
ea
ch
g
en
er
atio
n
a
n
d
th
e
s
ea
r
ch
p
r
o
ce
s
s
co
n
ti
n
u
e
s
u
n
t
il
a
s
p
ar
k
r
ea
ch
es
t
h
e
o
p
ti
m
u
m
.
T
h
e
au
t
h
o
r
s
also
m
e
n
t
io
n
ed
th
at
t
h
e
m
ai
n
d
is
ad
v
an
ta
g
e
o
f
th
e
p
r
e
v
io
u
s
m
et
h
o
d
s
is
r
ep
r
esen
ted
i
n
t
h
e
co
m
p
u
tatio
n
al
ti
m
e
a
n
d
w
o
r
k
d
o
n
e
u
n
d
er
n
o
r
m
al
co
n
d
itio
n
s
.
Au
t
h
o
r
s
o
f
[
7
]
u
s
e
a
b
in
ar
y
g
r
o
u
p
s
ea
r
ch
al
g
o
r
ith
m
to
s
o
l
v
e
th
e
r
ec
o
n
f
i
g
u
r
atio
n
p
r
o
b
lem
o
n
I
E
E
E
3
3
an
d
6
9
b
u
s
s
y
s
te
m
s
.
T
h
is
alg
o
r
ith
m
d
ep
en
d
s
o
n
an
i
m
al
s
ea
r
ch
in
g
b
eh
a
v
io
r
an
d
s
ca
n
n
in
g
m
et
h
o
d
o
lo
g
y
to
g
et
th
e
o
p
ti
m
u
m
s
ea
r
c
h
in
g
s
tr
at
eg
y
.
Au
th
o
r
s
o
f
[
8
]
u
s
e
g
r
av
itatio
n
al
s
ea
r
ch
alg
o
r
it
h
m
(
GS
A
)
to
ap
p
ly
o
n
r
ec
o
n
f
i
g
u
r
atio
n
p
r
o
b
lem
3
3
an
d
6
9
b
u
s
s
y
s
te
m
.
T
h
is
al
g
o
r
ith
m
d
ep
en
d
s
o
n
th
e
la
w
o
f
g
r
av
it
y
an
d
m
a
s
s
in
ter
ac
tio
n
d
u
e
to
Ne
w
to
n
’
s
la
w
.
Au
t
h
o
r
s
o
f
[
9
]
u
s
e
a
n
t c
o
lo
n
y
o
p
ti
m
izatio
n
a
n
d
m
u
s
ician
’
s
b
eh
a
v
io
r
in
s
p
ir
ed
to
ap
p
ly
o
n
3
3
an
d
1
1
8
b
u
s
s
y
s
te
m
r
ec
o
n
f
ig
u
r
atio
n
p
r
o
b
le
m
s
.
T
h
e
an
t
co
lo
n
y
o
p
ti
m
izatio
n
m
et
h
o
d
d
ep
en
d
s
o
n
th
e
b
eh
av
io
r
o
f
an
t
to
f
in
d
t
h
e
s
h
o
r
test
p
ath
b
et
w
ee
n
f
o
o
d
an
d
n
est
v
ia
p
h
er
o
m
o
n
e
as
in
d
ir
ec
t
co
m
m
u
n
icatio
n
.
T
h
e
h
ar
m
o
n
ic
s
ea
r
c
h
o
p
ti
m
i
za
tio
n
d
ep
en
d
s
o
n
th
e
h
ar
m
o
n
y
b
et
w
ee
n
m
u
s
icia
n
s
to
c
o
m
e
u
p
w
ith
a
n
ice
h
ar
m
o
n
y
.
Au
t
h
o
r
s
o
f
[
1
0
]
u
s
e
a
m
o
d
if
ied
p
ar
ticle
s
w
ar
m
as
a
m
et
a
h
eu
r
i
s
tic
o
p
ti
m
izatio
n
al
g
o
r
ith
m
to
s
o
l
v
e
th
e
r
ec
o
n
f
i
g
u
r
atio
n
p
r
o
b
lem
o
n
3
2
n
o
d
es
an
d
6
9
n
o
d
es
s
y
s
te
m
.
T
h
is
al
g
o
r
ith
m
d
ev
elo
p
ed
b
y
Ke
n
n
ed
y
an
d
E
b
er
h
ar
t
in
1
9
9
5
an
d
it is
in
s
p
ir
ed
b
y
th
e
s
o
cial
b
eh
av
io
r
o
f
b
ir
d
f
lo
ck
s
an
d
f
i
s
h
s
ch
o
o
ls
.
Au
t
h
o
r
s
o
f
[
1
1
]
u
s
e
b
ac
ter
ia
f
o
r
ag
in
g
b
eh
av
io
r
o
p
tim
izatio
n
alg
o
r
ith
m
to
s
o
l
v
e
th
e
r
ec
o
n
f
ig
u
r
at
io
n
p
r
o
b
lem
.
T
h
is
o
p
tim
izatio
n
t
ec
h
n
iq
u
e
is
in
s
p
ir
ed
f
r
o
m
s
o
cial
f
o
r
ag
i
n
g
b
eh
a
v
io
r
o
f
E
s
ch
erich
ia
co
li
an
d
it
h
as
h
i
g
h
ab
ili
t
y
to
s
o
l
v
e
r
e
al
o
p
ti
m
izatio
n
ap
p
licatio
n
s
.
T
h
is
m
et
h
o
d
w
a
s
ap
p
lied
to
3
3
b
u
s
s
y
s
te
m
.
Au
t
h
o
r
s
o
f
[
1
2
]
u
s
e
b
ee
co
l
o
n
y
o
p
ti
m
iza
tio
n
alg
o
r
it
h
m
w
h
ich
is
in
s
p
ir
ed
f
r
o
m
i
n
telli
g
e
n
t
f
o
r
ag
in
g
b
eh
av
io
r
o
f
h
o
n
e
y
b
ee
s
w
ar
m
to
s
o
lv
e
r
ec
o
n
f
i
g
u
r
atio
n
p
r
o
b
le
m
o
n
3
3
an
d
1
1
9
b
u
s
s
y
s
te
m
.
Au
t
h
o
r
s
o
f
[
1
3
]
u
s
e
c
u
ck
o
o
s
ea
r
ch
o
p
ti
m
izatio
n
al
g
o
r
ith
m
w
h
ic
h
is
in
s
p
ir
ed
f
r
o
m
b
r
o
o
d
p
ar
asit
is
m
o
f
cu
ck
o
o
s
p
ec
ies
to
lay
th
eir
eg
g
s
in
th
e
n
est
s
o
f
th
e
o
th
er
s
p
ec
ies
o
f
b
ir
d
s
f
o
r
o
p
tim
izatio
n
p
r
o
b
le
m
s
.
T
h
is
alg
o
r
ith
m
is
ap
p
lied
o
n
th
r
ee
d
if
f
er
e
n
t
p
o
w
er
s
y
s
te
m
s
an
d
it p
r
o
v
es it
s
ef
f
icie
n
c
y
.
I
n
t
h
is
p
ap
er
,
a
n
ew
h
eu
r
i
s
tic
o
p
ti
m
izat
io
n
tech
n
iq
u
e
is
u
s
ed
w
h
ic
h
is
ca
lled
w
h
ale
o
p
ti
m
izat
io
n
al
g
o
r
ith
m
(
W
OA
)
.
T
h
is
alg
o
r
it
h
m
is
i
n
s
p
ir
ed
f
r
o
m
t
h
e
w
h
ale
h
u
n
t
in
g
b
eh
a
v
io
r
.
I
t
is
w
as
p
r
o
v
e
n
it
s
ef
f
icie
n
c
y
i
n
s
o
l
v
in
g
m
a
n
y
m
at
h
e
m
atica
l
o
p
ti
m
izatio
n
m
o
d
els
a
n
d
its
h
ig
h
ab
ili
t
y
to
a
v
o
id
lo
ca
l
o
p
ti
m
al
an
d
it
s
f
ast
co
n
v
er
g
en
ce
.
I
n
t
h
is
ar
tic
le,
at
s
ec
tio
n
2
t
h
e
r
ec
o
n
f
i
g
u
r
atio
n
p
r
o
b
lem
is
b
ei
n
g
f
o
r
m
u
la
ted
i
n
m
ath
e
m
atica
l
m
o
d
el.
A
t
s
ec
t
io
n
3
,
t
h
e
W
O
A
i
s
b
ein
g
ill
u
s
tr
ated
in
d
etail
i
n
a
m
at
h
e
m
a
tical
f
o
r
m
.
A
t
s
ec
tio
n
4
,
th
e
al
g
o
r
ith
m
o
f
ap
p
l
y
in
g
t
h
e
W
O
A
o
n
t
h
e
r
ec
o
n
f
i
g
u
r
atio
n
p
r
o
b
lem
is
b
ei
n
g
s
tated
.
A
t
s
ec
tio
n
5
,
th
e
r
es
u
lt
s
ar
e
d
is
cu
s
s
ed
an
d
co
m
p
ar
ed
to
o
th
er
h
eu
r
is
t
ic
m
et
h
o
d
s
.
2.
P
RO
B
L
E
M
F
O
R
M
UL
AT
I
O
N
F
O
R
NE
T
WO
RK
R
E
C
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NF
I
G
U
RAT
I
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N
Ob
j
ec
tiv
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f
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n
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:
m
in
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m
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p
o
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lo
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lo
s
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P
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f
o
r
all
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tio
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.
C
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s
tr
ain
t
s
:
Vo
ltag
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co
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tr
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t
:
m
i
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2
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4
8
–
57
50
T
o
p
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s
tr
ain
t
: th
e
s
y
s
te
m
m
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t b
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r
ad
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t
er
r
ec
o
n
f
ig
u
r
atio
n
No
te:
P
loss
: to
tal
p
o
w
er
lo
s
s
in
t
h
e
s
y
s
te
m
I
i
: th
e
m
a
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it
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b
u
s
i
T
h
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
is
ca
lc
u
lated
f
r
o
m
th
e
s
o
lu
tio
n
o
f
p
o
w
er
f
lo
w
eq
u
atio
n
s
s
u
c
h
as
th
e
Ne
w
to
n
R
ap
h
s
o
n
m
et
h
o
d
.
T
o
ch
ec
k
s
y
s
te
m
r
ad
ialit
y
,
i
n
cid
e
n
ce
m
atr
i
x
A
i
s
f
o
r
m
ed
w
it
h
d
i
m
en
s
io
n
s
eq
u
al
.
N
u
m
b
er
o
f
b
r
an
ch
es (
M
)
*
n
u
m
b
er
o
f
b
u
s
es
(
N
)
an
d
th
e
ele
m
e
n
ts
o
f
t
h
i
s
m
atr
ix
ca
n
b
e
f
o
r
m
e
d
as
f
o
llo
w
s
:
0
in
c
a
s
e
o
f
th
e
b
r
a
n
c
h
n
o
t
c
o
n
n
e
c
t
e
d
to
b
u
s
1
in
c
a
s
e
o
f
th
e
b
r
a
n
c
h
f
r
o
m
b
u
s
1
in
c
a
s
e
o
f
th
e
b
r
a
n
c
h
is
to
b
u
s
ij
ij
A
i
j
ij
T
h
en
th
e
co
l
u
m
n
r
e
f
er
r
in
g
to
th
e
r
e
f
er
en
ce
n
o
d
e
(
u
s
u
all
y
f
ir
s
t
co
l
u
m
n
)
m
u
s
t
b
e
o
m
itted
.
I
f
d
eter
m
in
a
n
t
(
A
)
eq
u
als
1
o
r
-
1
th
e
n
th
e
s
y
s
te
m
is
r
ad
ial.
I
f
d
et
(
A
)
eq
u
als
ze
r
o
,
th
en
th
e
s
y
s
te
m
is
n
o
t
r
ad
ial,
an
d
s
o
m
e
lo
ad
s
m
a
y
b
e
d
is
co
n
n
ec
ted
.
3.
WH
AL
E
O
P
T
I
M
I
Z
A
T
I
O
N
AL
G
O
RI
T
H
M
I
t
is
a
h
eu
r
i
s
tic
m
eth
o
d
d
is
co
v
er
ed
in
2
0
1
6
an
d
it
m
i
m
ic
s
h
u
m
p
b
ac
k
w
h
ale
h
u
n
ti
n
g
s
tr
a
teg
y
.
I
t
h
as
m
an
y
ad
v
a
n
tag
e
s
s
u
c
h
as
lo
ca
l
o
p
tim
u
m
a
v
o
id
an
ce
an
d
f
ast
co
n
v
er
g
e
n
ce
.
Sear
ch
ag
e
n
ts
ar
e
in
itial
ized
f
ir
s
tl
y
to
s
ea
r
ch
f
o
r
th
e
o
p
ti
m
u
m
(
p
r
e
y
)
(
ex
p
lo
r
atio
n
p
h
ase)
a
n
d
t
h
en
u
p
d
ate
t
h
eir
p
o
s
itio
n
s
to
w
ar
d
t
h
e
b
est
s
ea
r
ch
ag
en
t
n
ea
r
th
e
o
p
ti
m
u
m
.
W
e
ca
n
m
at
h
e
m
atica
l
l
y
e
x
p
r
ess
t
h
a
t b
y
(
1
)
.
3
.
1
.
E
x
plo
ra
t
io
n pha
s
e
*
|
(
)
(
)
|
D
C
x
t
x
t
(
1
)
*
(
1
)
(
)
A
.
D
x
t
x
t
A
2
.
r
a
a
2
Cr
W
h
er
e
t
is
th
e
cu
r
r
en
t
iter
atio
n
,
A
,
C
ar
e
th
e
co
ef
f
icie
n
t
v
ec
to
r
s
,
*
()
xt
is
t
h
e
p
o
s
itio
n
o
f
b
est
s
ea
r
ch
ag
en
t,
()
xt
is
th
e
p
o
s
itio
n
v
ec
to
r
,
a
is
lin
ea
r
d
ec
r
ea
s
e
f
r
o
m
2
to
0
an
d
r
is
r
an
d
o
m
v
ec
to
r
in
[
0
,
1
]
.
3
.
2
.
E
x
plo
it
a
t
io
n pha
s
e
I
n
ex
p
lo
itatio
n
p
h
ase,
w
h
ale
s
u
s
e
a
b
u
b
b
le
n
et
attac
k
in
g
m
et
h
o
d
to
ca
tch
th
e
p
r
e
y
.
T
h
er
e
ar
e
2
m
ec
h
a
n
i
s
m
s
f
o
r
b
u
b
b
le
n
et
as sh
o
w
n
in
F
ig
u
r
e
1
.
‒
Sh
r
i
n
k
i
n
g
en
cir
cli
n
g
m
ec
h
a
n
is
m
*
(
1
)
(
)
A
.
D
x
t
x
t
(
2
)
‒
Sp
ir
al
u
p
d
atin
g
p
o
s
itio
n
*
(
1
)
c
o
s
(
2
)
(
)
bl
x
t
D
e
l
x
t
(
3
)
w
h
er
e
*
|
(
)
(
)
|
D
x
t
x
t
is
t
h
e
d
is
ta
n
ce
b
et
w
ee
n
s
ea
r
ch
ag
e
n
t a
n
d
th
e
p
r
e
y
.
b
: c
o
n
s
tan
t (
u
s
u
all
y
1
)
l
: r
an
d
o
m
n
u
m
b
er
i
n
[
0
,
1
]
Usu
al
l
y
,
h
u
m
p
b
ac
k
u
s
es
e
ac
h
m
ec
h
an
is
m
w
it
h
p
r
o
b
ab
ilit
y
5
0
%
s
o
w
e
ca
n
s
u
m
m
ar
iz
e
th
e
ex
p
lo
itatio
n
p
h
ase
i
n
t
h
e
f
o
llo
w
i
n
g
eq
u
a
tio
n
s
:
*
*
(
)
A
.
D
i
f
0
.
5
;
(
1
)
c
o
s
(
2
)
(
)
i
f
0
.
5
,
bl
x
t
p
xt
D
e
l
x
t
p
w
h
er
e
p
is
r
an
d
o
m
n
u
m
b
er
in
[
0
,
1]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
A
p
p
l P
o
w
er
E
n
g
I
SS
N:
2252
-
8792
Dis
tr
ib
u
tio
n
p
o
w
er sys
tem
r
ec
o
n
fig
u
r
a
tio
n
u
s
in
g
w
h
a
le
o
p
timiz
a
tio
n
a
lg
o
r
ith
m
(
Ma
h
mo
u
d
S
o
lima
n
)
51
(
a)
(
b
)
Fig
u
r
e
1
.
B
u
b
b
le
-
n
et
s
ea
r
c
h
m
ec
h
an
i
s
m
i
m
p
le
m
e
n
ted
in
W
O
A
(
X
∗
i
s
th
e
b
est
s
o
lu
tio
n
o
b
tain
ed
s
o
f
ar
)
,
(
a)
s
h
r
in
k
i
n
g
e
n
cir
cli
n
g
m
ec
h
a
n
is
m
,
(
b
)
s
p
ir
al
u
p
d
atin
g
p
o
s
it
io
n
T
h
e
W
OA
alg
o
r
ith
m
ca
n
b
e
s
u
m
m
ar
ized
i
n
th
e
f
o
llo
w
in
g
p
s
eu
d
o
co
d
e:
Initialize the whales population Xi (i = 1, 2, ..., n)
Calculate the fitness of each search agent
X*=the best search agent
while (t < maximum number of iterations)
for each search agent
Update
a, A, C, l, and p
if1 (p<0.5)
if2 (|A| < 1)
Update the position of the current search agent by the Eq. (1)
else if2 (|A|
Select a random search agent (
X
rand
)
Update the position of the current search agent by the Eq. (2)
end if2
else if1 (p> 0.5)
Update
the position of the current search by the Eq. (3)
end if1
end for
Check if any search agent goes beyond the search space and amend it
Calculate the fitness of each search agent
Update X* if there is a better solution
t=t+1
end while
return X*
4.
F
O
R
M
U
L
A
T
I
O
N
O
F
W
O
A
F
O
R
S
O
L
VI
NG
M
I
N
I
M
U
M
P
O
W
E
R
L
O
S
S
RE
C
O
NF
I
G
U
RA
T
I
O
N
P
RO
B
L
E
M
T
h
e
d
is
tr
ib
u
tio
n
s
y
s
te
m
s
ca
n
b
e
d
escr
ib
e
d
as
a
m
atr
i
x
w
it
h
d
i
m
en
s
io
n
s
Mx
L
.
W
h
er
e
M
is
n
u
m
b
er
o
f
b
r
an
ch
es
a
n
d
L
i
s
n
u
m
b
er
o
f
b
u
s
es.
I
t
ca
n
b
e
as
s
u
m
ed
th
a
t
w
h
ales
m
o
v
e
b
et
w
ee
n
b
r
an
c
h
es
an
d
s
elec
t
w
h
ic
h
o
n
e
is
to
b
e
o
p
en
.
Step
(
1
)
:
I
n
itializin
g
th
e
p
o
s
it
i
o
n
o
f
s
ea
r
ch
a
g
en
ts
I
n
itial
r
an
d
o
m
p
o
s
itio
n
s
f
o
r
ea
ch
s
ea
r
ch
a
g
en
t
ar
e
s
et
an
d
s
elec
ti
n
g
r
an
d
o
m
s
w
itc
h
es
to
b
e
o
p
en
ed
(
tie
s
w
itc
h
es).
T
h
en
th
e
in
itia
l
co
n
f
ig
u
r
atio
n
is
ch
ec
k
ed
w
h
e
th
er
it
is
a
r
a
d
ial
s
y
s
te
m
o
r
n
o
t.
I
f
th
e
s
y
s
te
m
is
r
ad
ial,
w
e
ca
n
r
u
n
a
p
o
w
er
f
l
o
w
a
n
al
y
s
i
s
o
n
it
to
ca
lc
u
late
to
tal
p
o
w
er
lo
s
s
i
n
t
h
e
s
y
s
te
m
an
d
m
i
n
i
m
u
m
b
u
s
v
o
ltag
e.
No
w
,
w
e
ca
n
a
s
s
u
m
e
th
at
t
h
e
b
est
co
n
f
ig
u
r
atio
n
is
t
h
e
in
i
tial
co
n
f
i
g
u
r
atio
n
an
d
t
h
en
s
tar
t
t
h
e
n
e
x
t
s
tep
to
ch
an
g
e
th
e
r
ec
o
n
f
i
g
u
r
atio
n
o
f
th
e
s
y
s
te
m
.
Step
(
2
)
:
U
p
d
atin
g
p
o
s
itio
n
s
o
f
s
ea
r
ch
a
g
e
n
ts
I
n
ea
ch
iter
atio
n
(
i)
,
a
n
e
w
co
n
f
ig
u
r
atio
n
is
p
r
o
d
u
ce
d
u
s
i
n
g
(
W
OA
)
b
y
s
elec
ti
n
g
s
o
m
e
s
w
i
tch
es
to
b
e
o
p
en
.
T
h
e
co
n
f
ig
u
r
atio
n
m
u
s
t
b
e
e
v
alu
ated
b
y
3
i
m
p
o
r
tan
t a
ctio
n
s
:
1.
C
h
ec
k
s
y
s
te
m
r
ad
ialit
y
:
b
y
f
o
r
m
in
g
i
n
cid
en
ce
m
a
tr
ix
(
A
)
,
t
h
e
s
y
s
te
m
is
c
h
ec
k
ed
i
f
it
is
r
ad
ial
o
r
n
o
t
i
f
th
e
s
y
s
te
m
is
n
o
t
r
ad
ial,
th
e
co
n
f
ig
u
r
atio
n
i
s
d
is
ca
r
d
ed
an
d
th
e
f
itn
e
s
s
f
u
n
ctio
n
(
p
o
w
er
lo
s
s
)
is
s
et
to
eq
u
al
in
f
in
it
y
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8792
I
n
t J
A
p
p
l P
o
w
er
E
n
g
,
Vo
l.
9
,
No
.
1
,
A
p
r
il 2
0
2
0
:
4
8
–
57
52
2.
R
u
n
p
o
w
er
f
lo
w
an
a
l
y
s
is
:
“
N
e
w
to
n
R
ap
h
s
o
n
m
et
h
o
d
”
is
t
h
e
m
et
h
o
d
u
s
ed
f
o
r
lo
ad
f
lo
w
o
f
t
h
e
s
y
s
te
m
an
d
ch
ec
k
t
h
e
b
u
s
v
o
lta
g
e
li
m
it.
m
i
n
m
a
x
0
.
9
1
a
n
d
1
.
VV
I
f
th
e
s
y
s
te
m
d
o
es
n
o
t
s
ati
s
f
y
v
o
lta
g
e
li
m
it
co
n
d
itio
n
,
th
e
co
n
f
i
g
u
r
atio
n
i
s
d
is
ca
r
d
ed
also
,
an
d
th
e
f
itn
e
s
s
f
u
n
ctio
n
is
s
et
to
eq
u
al
i
n
f
i
n
it
y
.
3.
E
v
alu
a
te
f
it
n
e
s
s
f
u
n
ctio
n
(
l
o
s
s
P
)
Step
(
3
)
:
D
eter
m
i
n
atio
n
o
f
b
es
t c
o
n
f
i
g
u
r
atio
n
to
g
et
m
i
n
i
m
u
m
p
o
w
er
lo
s
s
T
h
e
p
r
o
ce
s
s
co
n
tin
u
es
u
n
til
r
e
ac
h
in
g
t
h
e
m
a
x
i
m
u
m
n
u
m
b
er
o
f
iter
atio
n
s
.
A
t
ea
ch
iter
atio
n
,
if
f
it
n
es
s
f
u
n
ctio
n
<i
n
itial
f
it
n
es
s
f
u
n
ctio
n
,
th
e
n
th
e
c
u
r
r
en
t c
o
n
f
i
g
u
r
ati
o
n
is
s
et
to
b
e
th
e
b
est co
n
f
i
g
u
r
atio
n
5.
RE
SU
L
T
S AN
D
CO
M
P
ARING
W
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I
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1
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ar
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etit
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S
[1
]
R.
S
.
Ra
o
,
K.
Ra
v
in
d
ra
,
K
.
S
a
ti
s
h
a
n
d
S
.
V
.
L
.
Na
ra
sim
h
a
m
,
“
P
o
w
e
r
lo
ss
m
in
im
iza
ti
o
n
in
d
istri
b
u
ti
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n
sy
ste
m
u
sin
g
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e
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ra
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n
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o
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istri
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ted
g
e
n
e
ra
ti
o
n
,
”
IEE
E
T
ra
n
sa
c
ti
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n
s
o
n
Po
we
r
S
y
ste
ms
,
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l.
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8
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o
.
1
,
p
p
.
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5
,
2
0
1
3
.
[2
]
A
.
S
.
A
lv
a
n
i
a
n
d
S
.
M
.
M
a
h
a
e
i,
“
Re
c
o
n
f
ig
u
ra
ti
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o
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d
istri
b
u
ti
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e
o
f
DG
s
to
im
p
ro
v
in
g
th
e
r
e
li
a
b
il
it
y
,
”
In
d
o
n
e
sia
n
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
E
n
g
i
n
e
e
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n
d
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o
mp
u
ter
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c
ien
c
e
,
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l.
2
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o
.
2
,
p
p
.
2
4
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-
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4
7
,
2
0
1
6
[3
]
R
.
S
i
r
j
a
n
i
,
A
.
M
o
h
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m
e
d
,
a
n
d
H
.
S
h
a
r
e
e
f
,
“
H
e
u
r
i
s
t
i
c
o
p
t
i
m
i
z
a
t
i
o
n
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e
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h
n
i
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e
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k
s
:
A
c
o
m
p
r
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e
n
s
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v
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r
e
v
i
e
w
,
”
P
r
z
e
g
l
a
d
E
l
e
k
t
r
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t
e
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i
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y
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l
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8
,
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o
.
7
a
,
p
p
.
1
-
7
,
2
0
1
2
.
[4
]
S
.
M
irj
a
li
li
a
n
d
A
.
L
e
w
is,
“
T
h
e
w
h
a
le
o
p
ti
m
iza
ti
o
n
a
lg
o
rit
h
m
,
”
Ad
v
a
n
c
e
s
in
En
g
i
n
e
e
rin
g
S
o
ft
w
a
re
,
v
o
l.
9
5
,
p
p
.
5
1
-
6
7
,
2
0
1
6
.
[5
]
R.
D
.
M
o
h
a
m
m
e
d
i,
R.
Zi
n
e
,
M
.
M
o
sb
a
h
,
a
n
d
S
.
A
rif
,
“
Op
ti
m
u
m
n
e
t
w
o
rk
re
c
o
n
f
ig
u
ra
ti
o
n
u
si
n
g
g
re
y
w
o
lf
o
p
ti
m
i
z
e
r,
”
T
e
lec
o
mm
u
n
.
C
o
mp
u
t.
E
l
.
Co
n
tro
l
,
v
o
l.
1
6
,
n
o
.
5
,
p
.
2
4
2
8
,
2
0
1
8
.
[6
]
A
.
M
.
I
m
r
a
n
a
n
d
M
.
K
o
w
s
a
l
y
a
,
“
A
n
e
w
p
o
w
e
r
s
y
s
t
e
m
r
e
c
o
n
f
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g
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r
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t
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o
n
s
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h
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m
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n
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v
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g
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n
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m
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t
u
s
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g
f
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r
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w
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r
k
s
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l
g
o
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t
h
m
,
”
I
n
t
.
J
.
o
f
E
l
e
c
.
P
o
w
e
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a
n
d
E
n
e
r
g
y
S
y
s
t
e
m
s
,
v
o
l
.
6
2
,
p
p
.
3
1
2
-
3
2
2
,
2
0
1
4
.
[7
]
S
.
T
e
im
o
u
rz
a
d
e
h
a
n
d
K.
Zare
,
“
A
p
p
li
c
a
ti
o
n
o
f
b
in
a
ry
g
ro
u
p
se
a
rc
h
o
p
ti
m
iza
ti
o
n
t
o
d
istri
b
u
ti
o
n
n
e
tw
o
rk
re
c
o
n
f
ig
u
ra
ti
o
n
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
P
o
we
r
&
En
e
rg
y
S
y
ste
ms
,
v
o
l.
6
2
,
p
p
.
4
6
1
-
4
6
8
,
2
0
1
4
.
[8
]
Y.
M
.
S
h
u
a
i
b
,
M
.
S
.
Ka
lav
a
th
i,
a
n
d
C.
C.
A
sir
Ra
jan
,
“
Op
ti
m
a
l
re
c
o
n
f
ig
u
ra
ti
o
n
i
n
ra
d
ial
d
istri
b
u
ti
o
n
sy
ste
m
u
sin
g
g
ra
v
it
a
ti
o
n
a
l
se
a
rc
h
a
lg
o
rit
h
m
,
”
in
El
e
c
tric P
o
we
r Co
m
p
o
n
e
n
ts
a
n
d
S
y
ste
ms
,
v
o
l.
4
2
,
n
o
.
7
,
p
p
.
7
0
3
-
7
1
5
,
2
0
1
4
.
[9
]
A
.
Y.
A
b
d
e
laz
iz,
R.
A
.
Os
a
m
a
,
a
n
d
S
.
M
.
El
k
h
o
d
a
ry
,
“
Distrib
u
ti
o
n
sy
ste
m
s
re
c
o
n
f
ig
u
ra
ti
o
n
u
s
in
g
a
n
t
c
o
l
o
n
y
o
p
ti
m
iza
ti
o
n
a
n
d
h
a
rm
o
n
y
se
a
rc
h
a
lg
o
rit
h
m
s,”
El
e
c
tric P
o
we
r Co
mp
o
.
a
n
d
S
y
st
.
,
v
o
l
.
4
1
,
n
o
.
5
,
p
p
.
5
3
7
-
5
5
4
,
2
0
1
3
.
[1
0
]
A
.
Y
.
A
b
d
e
l
a
z
i
z
,
F
.
M
.
M
o
h
a
m
m
e
d
,
S
.
F
.
M
e
k
h
a
m
e
r
,
a
n
d
M
.
A
.
L
.
B
a
d
r
,
“
D
i
s
t
r
i
b
u
t
i
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n
s
y
s
t
e
m
s
r
e
c
o
n
f
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g
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r
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o
n
u
s
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n
g
a
m
o
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i
f
ie
d
p
a
r
t
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le
sw
a
rm
o
p
t
im
iza
t
i
o
n
a
l
g
o
r
i
t
h
m
,
”
E
le
c
t
r
ic
P
o
w
.
S
y
s
t
.
R
e
s
e
a
rc
h
,
v
o
l
.
7
9
,
n
o
.
1
1
,
p
p
.
1
5
2
1
-
1
5
3
0
,
2
0
0
9
.
[1
1
]
K
.
S
.
K
u
m
a
r
a
n
d
T
.
J
a
y
a
b
a
r
a
t
h
i
,
“
P
o
w
e
r
s
y
s
t
e
m
r
e
c
o
n
f
i
g
u
r
a
t
i
o
n
a
n
d
l
o
s
s
m
i
n
i
m
i
z
a
t
i
o
n
f
o
r
a
n
d
i
s
t
r
i
b
u
t
i
o
n
s
y
s
t
e
m
s
u
s
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n
g
b
a
c
t
e
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a
l
f
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g
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n
g
o
p
t
i
m
i
z
a
t
i
o
n
a
l
g
o
r
i
t
h
m
,
”
I
n
t
.
J
.
o
f
E
l
e
c
t
r
i
c
a
l
P
o
w
e
r
&
E
n
e
r
g
y
S
y
s
t
e
m
s
,
v
o
l
.
3
6
,
n
o
.
1
,
p
p
.
1
3
-
1
7
,
2
0
1
2
.
[1
2
]
R.
S
.
Ra
o
,
S
.
V
.
L
.
Na
ra
sim
h
a
m
,
a
n
d
M
.
Ra
m
a
li
n
g
a
ra
ju
,
“
Op
ti
m
i
z
a
t
io
n
o
f
d
istri
b
u
ti
o
n
n
e
tw
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rk
c
o
n
f
ig
u
ra
ti
o
n
f
o
r
lo
ss
re
d
u
c
ti
o
n
u
sin
g
a
rti
f
icia
l
b
e
e
c
o
lo
n
y
a
lg
o
rit
h
m
,
”
In
t
.
J
.
o
f
El
e
c
trica
l,
Co
m
p
u
ter
,
En
e
rg
e
ti
c
,
El
e
c
tro
n
ic
a
n
d
Co
mm
u
n
ica
ti
o
n
E
n
g
i
n
e
e
rin
g
,
v
o
l.
2
,
n
o
.
9
,
p
p
.
1
9
6
4
-
1
9
7
0
,
2
0
0
8
.
[1
3
]
T
.
T
.
Ng
u
y
e
n
a
n
d
A
.
V
.
T
ru
o
n
g
,
“
Distrib
u
t
io
n
n
e
tw
o
rk
re
c
o
n
f
ig
u
ra
ti
o
n
f
o
r
p
o
w
e
r
lo
ss
m
in
im
iza
ti
o
n
a
n
d
v
o
lt
a
g
e
p
r
o
f
i
l
e
im
p
r
o
v
e
m
e
n
t
u
s
i
n
g
c
u
c
k
o
o
s
e
a
rc
h
a
lg
o
r
i
t
h
m
,
”
I
n
t
.
J
.
o
f
E
l
e
c
.
P
o
w
.
&
E
n
e
r
.
S
y
s
t
.
,
v
o
l
.
6
8
,
p
p
.
2
3
3
-
2
4
2
,
2
0
1
5
.
[1
4
]
M
.
P
.
S
e
lv
a
n
a
n
d
K.
S
.
S
w
a
ru
p
,
“
Distrib
u
ti
o
n
sy
ste
m
lo
a
d
f
l
o
w
u
sin
g
o
b
jec
t
-
o
rien
ted
m
e
th
o
d
o
l
o
g
y
,
”
2
0
0
4
In
ter
n
a
t
io
n
a
l
C
o
n
fer
e
n
c
e
o
n
P
o
w
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r S
y
ste
m T
e
c
h
n
o
l
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y
,
P
o
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rCo
n
2
0
0
4
,
S
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n
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p
o
re
,
v
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.
2
,
p
p
.
1
1
6
8
-
1
1
7
3
,
2
0
0
4
.
[1
5
]
A
.
Waz
ir
a
n
d
N.
A
rb
a
b
,
“
A
n
a
l
y
s
is
a
n
d
o
p
ti
m
iza
ti
o
n
o
f
IEE
E
3
3
b
u
s
ra
d
ial
d
istri
b
u
ted
sy
ste
m
u
si
n
g
o
p
t
im
iza
ti
o
n
a
lg
o
rit
h
m
,
”
J
o
u
rn
a
l
o
f
Eme
rg
in
g
T
re
n
d
s i
n
Ap
p
li
e
d
En
g
i
n
e
e
rin
g
,
v
o
l.
1
,
n
o
.
2
,
p
p
.
1
7
-
2
1
,
2
0
1
6
.
[1
6
]
R
.
D
.
Z
i
m
m
e
rm
a
n
,
C
.
E
.
M
u
r
i
l
l
o
-
S
á
n
c
h
e
z
,
a
n
d
R
.
J
.
T
h
o
m
a
s
,
“
M
A
T
P
O
W
E
R
:
S
t
e
a
d
y
-
s
t
a
te
o
p
e
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a
t
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o
n
s
,
p
l
a
n
n
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n
g
,
a
n
d
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l
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s
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o
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s
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s
e
a
r
c
h
a
n
d
e
d
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c
a
t
i
o
n
,
”
I
E
E
E
T
r
a
n
s
.
o
n
P
o
w
e
r
S
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s
t
e
m
s
,
v
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l
.
2
6
,
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