I
nte
rna
t
io
na
l J
o
urna
l o
f
I
nfo
rm
a
t
ics a
nd
Co
m
m
un
ica
t
io
n T
ec
hn
o
lo
g
y
(
I
J
-
I
CT
)
Vo
l.
1
4
,
No
.
3
,
Dec
em
b
er
20
2
5
,
p
p
.
7
8
3
~
7
9
0
I
SS
N:
2252
-
8
7
7
6
,
DOI
:
1
0
.
1
1
5
9
1
/iji
ct
.
v
1
4
i
3
.
pp
783
-
7
9
0
783
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o
ur
na
l ho
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e
:
h
ttp
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//ij
ict.
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esco
r
e.
co
m
Unit
co
mm
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tmen
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problem
so
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ed
with
a
da
ptive
par
ticle
swa
rm
o
ptimiza
tion
Ra
m
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B
a
bu
M
uthu,
Venk
a
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r
Cha
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Art
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ticle
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to
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y:
R
ec
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J
u
l 1
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2
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2
4
R
ev
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ed
Ma
r
1
5
,
2
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2
5
Acc
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ted
J
u
n
9
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5
Th
is
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c
le
p
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se
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ts
a
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iv
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a
p
p
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a
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a
t
so
l
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h
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r
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b
lem
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g
e
n
e
ra
ti
o
n
sc
h
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d
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li
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g
b
y
s
u
p
p
ly
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n
g
a
ll
p
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ss
ib
le
o
p
e
ra
ti
n
g
sta
tes
fo
r
g
e
n
e
ra
ti
n
g
u
n
it
s
fo
r
t
h
e
g
i
v
e
n
ti
m
e
sc
h
e
d
u
le
o
v
e
r
th
e
d
a
y
.
T
h
e
sc
h
e
d
u
li
n
g
v
a
riab
les
a
re
se
t
u
p
to
c
o
d
e
th
e
lo
a
d
d
e
m
a
n
d
a
s
a
n
in
te
g
e
r
e
a
c
h
d
a
y
.
T
h
e
p
ro
p
o
se
d
a
d
a
p
ti
v
e
p
a
rti
c
le
sw
a
rm
o
p
t
imiz
a
ti
o
n
(A
P
S
O)
tec
h
n
iq
u
e
is
u
se
d
t
o
so
lv
e
t
h
e
g
e
n
e
ra
ti
o
n
sc
h
e
d
u
li
n
g
issu
e
b
y
a
m
e
th
o
d
o
f
o
p
t
imiz
a
ti
o
n
c
o
n
sid
e
ri
n
g
p
r
o
d
u
c
ti
o
n
a
s
we
ll
a
s
tran
sit
o
ry
c
o
sts.
Th
e
s
y
ste
m
a
n
d
g
e
n
e
ra
to
r
c
o
n
stra
in
ts
a
re
c
o
n
sid
e
re
d
w
h
e
n
so
l
v
in
g
t
h
e
p
r
o
b
lem
,
w
h
ich
in
c
lu
d
e
s
m
in
imu
m
a
n
d
m
a
x
imu
m
u
p
ti
m
e
a
n
d
d
o
wn
ti
m
e
a
s
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ll
a
s
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e
a
m
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n
t
o
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e
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e
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u
c
e
d
b
y
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a
c
h
p
ro
d
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c
i
n
g
u
n
it
(li
k
e
c
a
p
a
c
it
y
re
se
rv
e
s).
Th
is
p
a
p
e
r
d
e
sc
rib
e
s
th
e
su
g
g
e
ste
d
a
l
g
o
ri
th
m
th
a
t
c
a
n
b
e
a
p
p
l
ied
f
o
r
u
n
it
c
o
m
m
it
m
e
n
t
p
ro
b
lem
s
with
wi
n
d
a
n
d
h
e
a
t
u
n
it
s.
Tes
t
sy
ste
m
s
with
2
6
a
n
d
1
0
u
n
i
ts
a
re
u
se
d
to
v
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li
d
a
te t
h
e
su
g
g
e
ste
d
a
lg
o
rit
h
m
.
K
ey
w
o
r
d
s
:
Ad
ap
tiv
e
PS
O
Pro
h
ib
ited
zo
n
e
R
am
p
r
ate
Sto
ch
asti
c
o
p
tim
izatio
n
Un
it c
o
m
m
itm
en
t
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
:
R
am
esh
B
ab
u
Mu
th
u
Dep
ar
tm
en
t o
f
E
lectr
ical
an
d
E
lectr
o
n
ics E
n
g
in
ee
r
i
n
g
,
St.
J
o
s
ep
h
’
s
C
o
lleg
e
o
f
E
n
g
in
ee
r
i
n
g
Sh
o
lin
g
an
allu
r
,
OM
R
,
C
h
en
n
ai,
T
am
iln
ad
u
,
I
n
d
ia
E
m
ail:
r
am
esh
b
ab
u
m
@
s
tjo
s
ep
h
s
.
ac
.
in
1.
I
NT
RO
D
UCT
I
O
N
Gen
er
atio
n
s
ch
ed
u
lin
g
is
also
ca
lled
as
u
n
it
co
m
m
itm
en
t
(
UC
)
is
a
n
o
n
-
lin
ea
r
co
m
p
l
ex
m
ix
ed
-
in
teg
er
o
p
tim
izatio
n
p
r
o
b
lem
th
at
aim
s
t
o
d
is
tr
ib
u
te
th
e
to
tal
d
em
an
d
ac
r
o
s
s
all
g
e
n
e
r
atin
g
u
n
its
wh
ile
m
in
im
izin
g
o
p
er
atin
g
ex
p
e
n
s
es,
in
clu
d
in
g
b
o
th
p
r
o
d
u
ctio
n
c
o
s
t
an
d
tr
an
s
itio
n
co
s
t.
T
h
e
UC
p
r
o
ce
s
s
in
v
o
lv
es
m
ee
tin
g
ti
m
e
s
p
ec
if
ic
co
n
s
tr
ain
ts
,
b
alan
cin
g
lo
ad
d
em
an
d
,
a
cc
o
u
n
tin
g
f
o
r
s
y
s
tem
lo
s
s
es,
a
n
d
en
s
u
r
in
g
r
eser
v
e
ca
p
ac
ity
.
A
cr
u
cial
s
tep
in
s
o
lv
in
g
th
e
UC
p
r
o
b
lem
in
d
eter
m
in
in
g
th
e
h
o
u
r
ly
o
p
er
ati
o
n
al
s
tatu
s
o
f
ea
ch
g
en
er
atin
g
u
n
it,
wh
ich
th
e
n
g
u
id
es
th
e
allo
ca
tio
n
o
f
p
o
w
er
an
d
r
eser
v
e
ca
p
ac
ity
th
r
o
u
g
h
o
u
t
th
e
p
lan
n
in
g
h
o
r
izo
n
.
T
h
e
m
ain
ten
an
ce
o
f
elec
tr
ica
l
n
etwo
r
k
f
u
n
ctio
n
ality
is
m
o
s
tly
th
e
r
esp
o
n
s
ib
ilit
y
o
f
UC
[
1]
-
[
5
]
.
Po
wer
s
y
s
tem
s
o
lu
tio
n
b
ec
o
m
es
m
o
r
e
d
if
f
icu
lt
as
th
e
n
u
m
b
er
o
f
p
r
o
d
u
cin
g
u
n
its
in
c
r
ea
s
es
an
d
th
e
UC
p
r
o
b
lem
s
g
et
e
x
p
o
n
en
tially
m
o
r
e
co
m
p
lex
.
Nu
m
e
r
o
u
s
s
tr
ateg
ies
h
av
e
b
ee
n
p
u
t
f
o
r
th
to
ad
d
r
ess
th
e
UC
is
s
u
e
with
th
e
lo
west
o
p
er
atin
g
co
s
t
f
ea
s
ib
le,
in
cr
ea
s
in
g
p
o
ten
ti
al
s
av
in
g
s
f
r
o
m
th
e
elec
tr
icit
y
n
etwo
r
k
o
p
er
ato
r
.
Ho
wev
er
,
th
e
r
e
ar
e
d
if
f
er
en
c
es
in
th
e
ac
c
u
r
ac
y
an
d
s
p
ee
d
o
f
th
eir
ca
lcu
latio
n
s
.
T
h
ese
m
eth
o
d
s
ca
n
b
e
s
ep
ar
ated
in
to
two
ca
teg
o
r
ies:
s
to
ch
asti
c
an
d
d
eter
m
in
is
tic
s
ea
r
ch
alg
o
r
ith
m
s
.
B
o
u
n
d
a
n
d
b
r
a
n
ch
m
et
h
o
d
s
(
B
&
B
)
,
d
eter
m
in
is
tic
ap
p
r
o
a
ch
es
in
clu
d
e
la
g
r
an
g
ia
n
r
ela
x
atio
n
d
if
f
er
en
tial
e
v
o
lu
tio
n
(
L
R
DE
)
,
lag
r
an
g
ian
r
elax
atio
n
(
L
R
)
,
a
n
d
im
p
r
o
v
e
d
lag
r
an
g
ian
r
elax
atio
n
(
I
L
R
)
a
n
d
d
y
n
am
ic
p
r
o
g
r
am
m
in
g
(
DP)
[
6]
-
[
1
2
]
.
Fo
r
p
o
wer
s
y
s
tem
s
o
f
m
o
d
er
ate
s
ize,
th
ese
m
eth
o
d
s
h
a
n
d
l
e
p
r
o
b
lem
s
f
ast,
ac
cu
r
ately
,
a
n
d
s
im
p
ly
.
Fo
r
th
em
,
th
e
ch
allen
g
es
a
r
e
i
n
co
n
v
er
g
e
n
ce
,
q
u
ality
o
f
s
o
lu
tio
n
,
an
d
in
t
r
icac
y
.
So
m
e
ex
a
m
p
les
o
f
h
eu
r
is
tic
o
r
s
to
ch
asti
c
s
ea
r
ch
m
eth
o
d
s
ar
e
an
t
co
lo
n
y
o
p
tim
izatio
n
,
ev
o
lu
tio
n
ar
y
p
r
o
g
r
am
m
in
g
,
tab
u
s
ea
r
ch
,
an
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
7
6
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
,
Vo
l.
1
4
,
No
.
3
,
Dec
em
b
er
20
2
5
:
783
-
7
9
0
784
s
im
u
lated
an
n
ea
lin
g
,
f
u
zz
y
ad
ap
tiv
e
PS
O
(
FAP
SO)
,
h
y
b
r
id
PS
O
(
HP
SO)
,
d
is
cr
ete
PS
O
(
DPSO),
g
en
etic
alg
o
r
ith
m
s
,
an
d
m
u
lti
-
ob
jecti
v
e
PS
O.
Usi
n
g
th
e
two
ca
teg
o
r
ies
o
f
alg
o
r
ith
m
s
o
u
tlin
ed
a
b
o
v
e,
a
f
ew
h
y
b
r
id
alg
o
r
ith
m
s
ar
e
also
p
r
o
p
o
s
ed
[
1
3
]
-
[
2
5
]
.
T
h
ese
m
eth
o
d
s
p
r
o
d
u
ce
h
ig
h
ly
o
p
tim
al
o
u
tco
m
es
wh
ile
h
an
d
lin
g
d
if
f
icu
lt
lin
ea
r
an
d
n
o
n
lin
ea
r
r
estrictio
n
s
.
All
th
e
s
e
ap
p
r
o
ac
h
es,
h
o
wev
er
,
s
u
f
f
er
f
r
o
m
th
e
a
cc
u
r
ac
y
is
s
u
e.
T
h
e
co
m
p
u
tatio
n
al
tim
e
an
d
s
o
lu
tio
n
q
u
ality
ar
e
b
o
th
ad
v
er
s
ely
af
f
ec
ted
b
y
t
h
e
lar
g
er
p
r
o
b
lem
an
d
m
o
r
e
g
en
er
atin
g
u
n
its
.
T
h
is
wo
r
k
p
r
o
p
o
s
es
n
ew
ap
p
r
o
ac
h
b
y
g
en
e
r
atin
g
u
n
it
with
all
p
o
s
s
ib
le
s
tates
o
f
co
m
b
in
atio
n
of
ea
ch
p
ar
ticle
at
each
tim
e
s
tep
.
B
y
u
s
in
g
th
e
p
r
o
p
o
s
ed
APSO
to
o
p
tim
ize
th
ese
p
ar
ticle
s
tates
in
s
tead
o
f
an
y
o
th
e
r
tech
n
iq
u
e
m
en
ti
o
n
e
d
ab
o
v
e,
th
e
p
o
wer
s
y
s
tem
o
p
er
ato
r
ca
n
ac
h
iev
e
ex
ce
llen
t
r
e
s
u
lts
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
2
.
1
.
P
r
o
blem
f
o
rm
ula
t
io
n
T
h
e
p
r
im
ar
y
g
o
al
o
f
th
e
g
e
n
er
atio
n
s
ch
ed
u
lin
g
p
r
o
b
lem
is
to
ascer
tain
th
e
co
m
m
itm
en
t
s
tatu
s
o
f
th
e
av
ailab
le
th
er
m
al
u
n
its
to
r
ed
u
ce
th
e
to
tal
o
p
er
atio
n
al
ex
p
en
s
es,
wh
ich
co
m
p
r
is
e
s
tar
tu
p
,
s
h
u
td
o
wn
a
n
d
p
r
o
d
u
ctio
n
co
s
ts
.
T
h
is
f
u
n
cti
o
n
ca
n
b
e
o
p
tim
ized
wh
ile
tak
in
g
in
to
ac
co
u
n
t
all
g
e
n
er
ato
r
a
n
d
s
y
s
tem
co
n
s
tr
ain
ts
.
2
.
1
.
1
.
Co
s
t
o
f
pro
du
ct
io
n
Min
im
izin
g
th
e
o
v
er
all
p
r
o
d
u
ctio
n
co
s
t
th
r
o
u
g
h
o
u
t
th
e
s
ch
e
d
u
lin
g
p
e
r
io
d
wh
ile
a
d
h
er
in
g
to
a
s
et
o
f
g
en
er
ato
r
lim
itatio
n
s
is
th
e
m
ain
g
o
al
o
f
th
e
UC
p
r
o
b
le
m
.
In
(
1
)
p
r
o
v
id
es
PC
i
f
o
r
u
n
it
i,
th
e
q
u
ad
r
atic
p
r
o
d
u
ctio
n
c
o
s
.
W
h
er
e,
,
an
d
ar
e
th
e
co
ef
f
icien
ts
o
f
c
o
s
t
a
n
d
is
th
e
ac
tiv
e
p
o
wer
o
u
tp
u
t
in
MW
o
f
th
e
co
m
m
itted
u
n
it
i
.
=
+
+
2
(1
)
2
.
1
.
2
.
I
nitia
l o
utla
y
T
h
e
in
itial
co
n
tr
ib
u
tio
n
is
th
e
n
ex
t
p
ar
t
o
f
th
e
f
u
n
ctio
n
th
at
is
th
e
g
o
al
.
Dep
en
d
in
g
o
n
th
e
T
Off
tim
e
(
OFF),
th
e
s
tar
tin
g
co
s
t
ca
n
b
e
d
eter
m
in
ed
b
y
ex
p
o
n
en
tial
s
tar
tin
g
co
s
t
an
d
b
eg
in
n
in
g
(
c
o
ld
/h
o
t)
co
s
ts
.
T
h
e
s
tar
tin
g
co
s
t
is
r
ef
er
r
ed
to
as
a
war
m
s
tar
t
if
th
e
co
l
d
s
tar
t
t
im
e
is
less
th
an
t
h
e
to
tal
o
f
f
-
e
ak
p
e
r
io
d
(T
Off
)
.
I
f
n
o
t,
th
ey
ar
e
co
n
s
id
er
ed
a
c
o
ld
s
tar
t.
T
h
e
in
itial
co
s
t SC
i f
o
r
ea
ch
p
er
io
d
t is
o
b
tain
ed
f
r
o
m
(
2
)
.
,
=
+
{
1
−
e
xp
(
)
}
(
2
)
=
{
ℎ
≥
ℎ
≤
(
3)
=
{
|
|
+
`1
1
(
3
)
T
h
e
s
u
b
s
eq
u
en
t
p
ar
am
ete
r
s
ar
e
em
p
lo
y
ed
in
th
is
f
o
r
m
u
latio
n
,
i
d
en
o
tes
th
e
co
o
lin
g
tim
e
co
n
s
tan
t;
D
i
off
d
en
o
tes
th
e
o
f
f
tim
e
b
ef
o
r
e
u
n
it
i
co
m
es
in
to
co
m
m
itm
en
t;
HSC
i
s
tan
d
s
f
o
r
h
o
t
s
tar
t
u
p
ex
p
en
s
es;
C
SC
i
f
o
r
ch
ill
s
tar
t
-
u
p
ex
p
en
s
es;
an
d
C
T
i
s
tan
d
s
f
o
r
ch
ill
-
s
tar
t
tim
e.
L
im
itatio
n
o
n
th
e
eq
u
ilib
r
iu
m
o
f
p
o
wer
.
C
ap
ac
ity
b
alan
ce
co
n
s
tr
ain
ts
en
s
u
r
e
th
at
th
e
to
t
al
p
o
wer
p
r
o
d
u
ce
d
by
ea
c
h
ty
p
e
of
g
e
n
er
at
in
g
u
n
it
eq
u
als
th
e
p
o
wer
lo
ad
f
o
r
ea
ch
tim
e
p
e
r
i
o
d
.
∑
,
,
=
1
=
,
+
,
=
1
,
2
,
3
…
…
(
4
)
T
h
e
v
ar
iab
les P
L,
t
an
d
P
D,
t
r
e
p
r
esen
t th
e
to
tal
lo
s
s
es a
n
d
p
o
w
er
d
em
an
d
at
h
o
u
r
t in
MW.
2
.
1
.
3
.
T
he
ro
llin
g
re
s
er
v
e
lim
it
A
r
o
llin
g
r
eser
v
e
is
th
e
u
n
d
er
u
s
ed
ca
p
ac
ity
o
f
g
r
id
en
e
r
g
y
ass
ets
th
at
ca
n
m
o
m
e
n
tar
ily
o
f
f
s
et
f
r
eq
u
e
n
cy
ch
a
n
g
es
o
r
p
o
wer
o
u
tag
es.
His
to
r
ically
,
h
u
g
e
s
y
n
ch
r
o
n
o
u
s
g
en
er
at
o
r
s
wer
e
eq
u
ip
p
ed
with
r
o
tatin
g
r
eser
v
es.
P
RR
r
ep
r
esen
t
s
th
e
r
o
llin
g
r
eser
v
e
at
tim
e
t
an
d
t
h
e
i
th
g
en
er
ato
r
'
s
u
p
p
er
b
o
u
n
d
lim
it
is
d
en
o
ted
b
y
P
max
.
∑
,
≥
,
+
,
+
,
=
1
,
2
,
3
,
…
=
1
(
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
I
SS
N:
2252
-
8
7
7
6
Un
it c
o
mmitmen
t p
r
o
b
lem
s
o
lved
w
ith
a
d
a
p
tive
p
a
r
ticle
s
w
a
r
m
o
p
timiz
a
tio
n
(
R
a
mesh
B
a
b
u
Mu
th
u
)
785
2
.
1
.
4
.
Z
o
ne
o
f
pro
hib
it
ed
o
pera
t
io
n
C
er
tain
o
p
er
atin
g
zo
n
es
p
r
ev
en
t
th
e
g
en
er
ato
r
s
f
r
o
m
p
r
o
d
u
cin
g
r
ea
l
p
o
wer
b
ec
au
s
e
o
f
m
ec
h
an
ical
s
tr
ess
o
r
s
u
b
s
y
n
ch
r
o
n
o
u
s
o
s
cillatio
n
s
,
wh
ich
ca
u
s
e
th
e
u
n
it
to
co
m
p
letely
s
h
u
t
d
o
wn
.
T
h
e
r
ea
s
o
n
b
eh
in
d
th
e
d
is
co
n
tin
u
ity
in
th
e
f
u
el
-
c
o
s
t
cu
r
v
e
is
th
ese
r
eg
io
n
s
,
also
r
ef
er
r
ed
to
as
p
r
o
h
ib
ited
o
p
er
atin
g
zo
n
es
.
I
n
z
o
n
e
o
f
p
r
o
h
ib
ited
o
p
er
atio
n
(
POZ
)
,
g
en
er
ato
r
s
ar
e
p
r
o
h
ib
ited
in
r
ea
l
tim
e.
W
h
ile
p
o
z
i
an
d
n
poz
s
ta
n
d
f
o
r
u
n
its
h
av
in
g
f
o
r
b
id
d
en
zo
n
es
a
n
d
th
e
n
u
m
b
er
o
f
r
estricte
d
o
p
er
atin
g
zo
n
es,
r
esp
ec
tiv
ely
,
P
i
u
an
d
P
i
l
d
en
o
te
th
e
m
ax
im
u
m
an
d
m
in
im
u
m
v
alu
es o
f
th
e
ith
g
en
er
ato
r
with
in
th
e
p
r
o
h
i
b
ited
o
p
er
atin
g
ar
ea
s
.
,
∈
{
,
≤
≤
,
−
1
≤
≤
,
≤
≤
,
1
(
6
)
m
=
2
,
3
,
…,
wh
en
,
,
=1
i =
1
,
2
,
….
.
,
2
.
1
.
5
.
B
o
un
da
ry
co
ns
t
ra
int
o
f
t
he
g
ener
a
t
o
r
T
h
e
lim
itatio
n
s
o
f
t
h
e
u
p
p
e
r
an
d
l
o
wer
b
o
u
n
d
s
s
p
ec
if
ied
h
er
e
m
u
s
t
b
e
o
p
er
ate
d
b
y
th
e
co
m
m
itted
g
en
er
ato
r
s
.
≥
,
≥
ℎ
,
=
1
(
7
)
2
.
1
.
6
.
M
ini
m
um
up
t
im
e/do
wnt
im
e
lim
it
Acc
o
r
d
in
g
to
(
8
)
th
e
g
en
e
r
ato
r
s
n
ee
d
a
m
in
im
u
m
am
o
u
n
t
o
f
tim
e
to
s
tar
t
d
u
r
in
g
th
e
co
o
l
in
g
p
h
ase
an
d
s
to
p
d
u
r
in
g
th
e
r
u
n
n
in
g
co
n
d
itio
n
.
}
(
,
−
,
−
1
)
(
(
−
1
)
−
)
≥
0
(
,
−
,
−
1
)
(
(
−
1
)
−
)
≤
0
(
8
)
T
o
n
i
n
d
icate
s
th
e
tim
e
th
e
u
n
i
t
was
tu
r
n
e
d
o
n
b
ef
o
r
e
t
h
e
h
o
u
r
,
an
d
MU
T
i
an
d
MD
T
i
is
th
e
l
o
west
u
p
p
er
/lo
we
r
tim
e
lim
it in
h
o
u
r
s
f
o
r
th
e
i
th
u
n
it.
T
o
n
/
T
o
f
f
'
s
v
alu
e
is
r
ep
r
esen
ted
as
,
}
(
)
=
(
1
+
(
−
1
)
(
1
−
,
)
(
)
=
(
1
+
(
−
1
)
,
(
9
)
2
.
1
.
7
.
L
im
it
a
t
io
n o
n r
a
m
p r
a
t
e
I
n
m
ath
em
atics,
a
g
e
n
er
ato
r
'
s
r
am
p
u
p
/
d
o
wn
lim
it is
ex
p
r
ess
e
d
as,
}
[
,
−
1
−
(
1
+
,
−
1
)
(
,
+
1
)
]
≤
,
[
,
−
1
−
(
1
+
,
)
(
,
−
1
)
]
≤
,
(1
0
)
2
.
2
.
So
lutio
n
us
ing
AP
SO
T
h
e
r
o
b
u
s
tn
ess
an
d
ad
ap
tab
il
ity
o
f
s
to
ch
asti
c
o
p
tim
izatio
n
m
eth
o
d
s
ar
e
m
ak
in
g
th
em
in
cr
ea
s
in
g
ly
attr
ac
tiv
e
f
o
r
s
o
lv
i
n
g
n
o
n
-
lin
ea
r
o
p
tim
izatio
n
is
s
u
es.
A
p
o
p
u
lar
s
war
m
-
b
ased
,
b
i
o
-
in
s
p
ir
ed
tech
n
iq
u
e
f
o
r
s
o
lv
in
g
o
p
tim
izatio
n
is
s
u
es
is
ca
lled
PS
O.
I
t
is
ea
s
y
t
o
u
s
e
an
d
h
ig
h
ly
ef
f
icien
t.
Usi
n
g
v
elo
cities
s
im
ilar
to
b
ir
d
s
,
th
e
p
o
p
u
latio
n
-
b
ased
PS
O
alg
o
r
ith
m
m
o
d
if
ies th
e
s
tar
tin
g
p
o
p
u
latio
n
to
d
eter
m
in
e
th
e
b
est r
o
u
te
to
tak
e
in
o
r
d
er
to
ar
r
i
v
e
at
th
e
tar
g
e
t.
Similar
to
o
th
er
p
o
p
u
latio
n
-
b
ased
tech
n
iq
u
es,
th
e
co
n
v
e
n
tio
n
al
PS
O
ca
n
b
e
lim
ited
to
lo
ca
l m
in
im
a.
T
h
e
in
er
tia
weig
h
t
an
d
th
e
r
an
d
o
m
v
a
r
iab
les
C
1
a
n
d
C
2
ar
e
th
e
p
r
im
ar
y
d
eter
m
in
a
n
ts
o
f
th
e
o
r
ien
tatio
n
o
f
th
e
s
o
lu
tio
n
s
ea
r
ch
s
p
ac
e
in
PS
O.
I
t
is
p
o
s
s
ib
le
f
o
r
th
e
u
p
d
ated
p
a
r
ticles
to
b
ec
o
m
e
s
tu
ck
i
n
th
e
lo
ca
l
o
p
tim
al
s
o
lu
tio
n
wh
en
th
ey
f
ail
to
f
o
llo
w
th
e
l
ea
d
e
r
.
I
n
th
is
w
o
r
k
,
th
e
q
u
asi
-
o
p
p
o
s
itio
n
al
lear
n
i
n
g
tech
n
iq
u
e
p
r
o
p
o
s
ed
b
y
K
u
m
a
r
an
d
B
ab
u
[
7
]
is
in
teg
r
ated
with
th
e
m
u
tatio
n
o
p
er
ato
r
.
I
t
was
in
tr
o
d
u
ce
d
to
in
cr
ea
s
e
PS
O
'
s
s
ea
r
ch
ca
p
ab
ilit
ies an
d
p
o
p
u
latio
n
v
a
r
iety
.
T
h
e
f
o
r
m
u
la
p
r
o
v
id
es th
e
q
u
asimu
tatio
n
o
p
e
r
ato
r
,
X
i
q0
=
r
a
n
d
(
X
i
C
,
X
i
0
)
(1
1
)
X
i
C
=
X
i
m
ax
+
X
i
m
in
2
(1
2
)
0
=
+
−
(1
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
7
6
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
,
Vo
l.
1
4
,
No
.
3
,
Dec
em
b
er
20
2
5
:
783
-
7
9
0
786
wh
er
e
ar
e
th
e
m
in
im
u
m
an
d
m
ax
im
u
m
b
o
u
n
d
lim
its
o
f
ith
in
d
iv
id
u
al’
s
s
ea
r
ch
s
p
ac
e;
is
t
h
e
in
d
iv
id
u
al
a
n
d
0
is
th
e
o
p
p
o
s
ite
in
d
iv
id
u
al;
X
iq
0
is
a
u
n
if
o
r
m
l
y
d
is
tr
ib
u
ted
r
an
d
o
m
n
u
m
b
er
b
etwe
en
X
i
C
an
d
X
i
0
.
T
h
e
g
en
er
atio
n
o
f
q
u
asi
-
o
p
p
o
s
ite
in
d
iv
id
u
als
is
b
ased
o
n
th
e
leap
r
ate
(
L
r
)
.
Alth
o
u
g
h
th
e
tech
n
iq
u
e
d
o
es
n
o
t
en
tire
ly
co
n
v
er
g
e
to
th
e
g
lo
b
al
o
p
tim
u
m
,
it
d
o
es
co
n
v
er
g
e
r
a
p
id
ly
to
s
m
aller
v
alu
es
o
f
L
r
.
Similar
ly
,
b
ec
au
s
e
o
f
th
e
wid
e
r
s
ea
r
ch
s
p
ac
e,
alg
o
r
ith
m
s
with
lar
g
er
L
r
v
alu
es
m
ay
tak
e
a
lo
n
g
tim
e
to
co
n
v
er
g
e.
T
h
e
ju
m
p
r
ate
s
elec
tio
n
s
h
o
u
l
d
p
r
ev
en
t
ea
r
l
y
co
n
v
er
g
e
n
ce
a
n
d
o
f
f
er
s
u
f
f
icien
t
n
o
tab
le
c
h
an
g
es
at
b
aselin
e.
As a
r
esu
lt,
th
e
ad
ap
tiv
e
h
o
p
r
ate
th
at
th
is
s
tu
d
y
em
p
lo
y
ed
to
ac
co
u
n
t f
o
r
th
ese
is
s
u
es is
s
tat
ed
as:
L
r
=
L
r
,
m
ax
−
L
r
,
m
ax
−
L
r
,
m
in
i
t
er
m
ax
×
ite
r
(1
4
)
wh
er
e,
L
r,
min
=0
.
0
1
,
L
r,
max
=0
.
5
,
iter
is
th
e
cu
r
r
en
t
iter
atio
n
,
an
d
iter
m
ax
is
th
e
m
a
x
im
u
m
iter
atio
n
.
T
o
av
o
id
p
r
em
atu
r
e
co
n
v
er
g
en
ce
L
r
is
h
ig
h
at
th
e
s
tar
tin
g
an
d
it
is
p
r
o
g
r
ess
iv
ely
r
ed
u
ce
d
to
im
p
r
o
v
e
th
e
co
n
v
e
r
g
en
ce
r
ate.
T
h
e
s
u
g
g
ested
alg
o
r
ith
m
u
s
e
s
th
e
co
n
v
en
tio
n
al
PS
O
wit
h
th
e
in
teg
r
atio
n
o
f
q
u
asi
-
o
p
p
o
s
itio
n
al
lear
n
in
g
-
b
ased
m
u
tatio
n
alo
n
g
with
th
e
ad
ap
tiv
e
leap
r
ate,
h
en
ce
,
it
is
ca
lled
A
PS
O.
T
h
e
p
s
eu
d
o
co
d
e
o
f
th
e
p
r
o
p
o
s
ed
APSO is
g
iv
en
in
Ps
eu
d
o
co
d
e
1.
Ps
eu
d
o
co
d
e
1
.
APSO p
s
eu
d
o
c
o
d
e
Pseudo code: Adaptive Particle Swarm Algorithm
1.
Initialize X
i,
V
i
, iteration, pbest, gbest
2.
Generate random particles(P)
3.
For each particle (i)
4.
Calculate fitness function (f
i
)
5.
Update pbest, gbest
6.
End for
7.
While iteration
8.
For each particle I
9.
Update X
i
, V
i
10.
If X
i
> limit, then X
i
= limit
11.
Calculate fitness function f
i
12.
Update pbest, gbest
13.
End for
14.
End while
15.
Check if any search agent goes beyond the search space and amend it
16.
Calculate the leap rate L
r
by equation 15
17.
If rand (0, l) < L
r
18.
Compute quasi
-
opposite individual for integer variable by Equation 12
19.
End
20.
Calculate the fitness of each search agent
21.
Update X* if there is a better solution
22.
Update the value of F and Return
23.
End
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
MA
T
L
AB
9
.
4
(
R
2
0
1
8
a)
co
n
t
ain
s
th
e
s
o
f
twar
e
f
o
r
th
e
s
u
g
g
ested
ap
p
r
o
ac
h
to
ad
d
r
ess
in
g
th
e
UC
p
r
o
b
lem
.
I
t
r
u
n
s
o
n
an
I
n
tel
C
o
r
e
i5
with
a
C
PU
s
p
ee
d
o
f
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.
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an
d
8
GB
o
f
R
AM
r
u
n
n
in
g
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in
d
o
ws
1
0
.
T
h
e
s
u
g
g
ested
ap
p
r
o
ac
h
is
test
ed
o
n
two
test
ca
s
es,
an
d
th
e
o
u
tco
m
es
ar
e
co
n
tr
asted
with
a
n
u
m
b
er
o
f
ex
is
tin
g
m
eth
o
d
s
f
r
o
m
th
e
liter
atu
r
e.
T
est
c
ase
1
is
a
r
ath
er
co
n
v
en
tio
n
al
1
0
-
u
n
it
s
y
s
tem
with
a
q
u
ad
r
atic
c
o
s
t
f
u
n
ctio
n
a
n
d
a
r
o
tatin
g
r
eser
v
e
.
T
est
c
ase
2
u
s
es a
2
6
-
u
n
it R
T
S sy
s
tem
with
a
r
o
tatin
g
r
eser
v
e.
3
.
1
.
T
est
c
a
s
e
1
T
h
e
d
ata
f
o
r
th
e
1
0
-
u
n
it
s
y
s
t
em
is
p
r
esen
ted
in
r
ef
er
e
n
ce
[
7
]
.
A
s
p
in
n
in
g
r
ese
r
v
e
o
f
1
0
%
o
f
th
e
s
y
s
tem
d
em
an
d
is
estab
lis
h
ed
f
o
r
th
at
h
o
u
r
,
wh
ile
ad
h
e
r
in
g
to
th
e
MU
T
/MDT
co
n
s
tr
ai
n
t.
Sin
ce
th
e
v
alv
e
-
p
o
in
t
an
d
r
am
p
r
ate
co
n
s
tr
ain
ts
ar
e
n
o
t
tak
en
in
to
ac
co
u
n
t
in
th
is
in
s
tan
ce
,
th
e
o
u
tco
m
es
ca
n
b
e
co
n
tr
asted
with
th
o
s
e
f
r
o
m
p
r
ev
io
u
s
r
es
ea
r
ch
.
T
est
ca
s
e
1
em
p
lo
y
s
a
1
0
-
u
n
it
s
y
s
tem
th
at
c
o
n
s
is
ten
tly
ac
co
m
m
o
d
ates
a
v
ar
iety
o
f
lo
ad
s
.
T
h
e
test
s
y
s
te
m
d
ata
is
s
o
u
r
ce
d
f
r
o
m
t
h
e
liter
atu
r
e
r
ef
e
r
en
ce
s
[
7
]
an
d
[
1
2
]
.
T
h
e
s
to
ch
asti
c
n
atu
r
e
o
f
t
h
e
m
eta
-
h
eu
r
is
tic
alg
o
r
ith
m
s
n
ec
es
s
itates
s
tati
s
tical
an
al
y
s
is
f
o
r
v
alid
atio
n
.
T
ab
le
1
p
r
esen
ts
th
e
av
er
ag
e,
s
tan
d
ar
d
d
ev
iatio
n
,
b
est,
an
d
wo
r
s
t
r
esu
lts
f
r
o
m
2
5
s
ep
ar
ate
ex
p
er
im
en
ts
.
T
h
e
tab
le
s
h
o
ws
h
o
w
clo
s
e
to
th
e
o
p
tim
al
c
o
s
t
th
e
a
v
er
ag
e
co
s
t
ac
h
iev
ed
f
o
r
s
ev
er
al
test
ca
s
es
is
.
T
h
e
s
o
lu
tio
n
p
r
ec
is
io
n
wo
u
ld
b
e
m
o
r
e
ad
v
an
tag
eo
u
s
f
o
r
a
co
m
p
licated
s
y
s
tem
with
m
o
r
e
u
n
its
th
an
f
o
r
a
s
y
s
tem
with
f
ewe
r
u
n
its
.
T
h
e
T
ab
le
1
also
s
h
o
ws
th
e
co
m
p
a
r
is
o
n
o
f
th
e
r
esu
lts
with
o
th
er
o
p
tim
izatio
n
alg
o
r
ith
m
s
.
R
am
p
-
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
I
SS
N:
2252
-
8
7
7
6
Un
it c
o
mmitmen
t p
r
o
b
lem
s
o
lved
w
ith
a
d
a
p
tive
p
a
r
ticle
s
w
a
r
m
o
p
timiz
a
tio
n
(
R
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mesh
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a
b
u
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th
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)
787
r
ate
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itatio
n
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ca
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u
tatio
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p
ar
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le
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er
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et
h
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d
s
d
o
cu
m
e
n
ted
in
th
e
liter
atu
r
e,
th
e
av
er
a
g
e
co
m
p
u
t
in
g
tim
e
in
cr
ea
s
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ea
r
ly
with
th
e
n
u
m
b
er
o
f
u
n
its
.
T
h
e
s
tatis
tical
an
aly
s
i
s
is
p
r
esen
ted
in
T
a
b
le
1
.
T
h
e
co
n
v
er
g
en
ce
c
h
ar
a
cter
is
tics
o
f
th
e
p
r
o
p
o
s
ed
m
eth
o
d
is
p
lo
tted
in
Fig
u
r
e
1
.
Fig
u
r
e
2
s
h
o
ws
th
e
v
a
r
iatio
n
o
f
s
p
in
n
i
n
g
r
eser
v
e
an
d
lo
a
d
d
em
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d
.
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t'
s
ev
id
en
t
th
at
s
p
in
n
i
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r
eser
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e
will
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e
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s
s
ib
le
f
o
llo
win
g
th
e
u
n
it
co
m
m
itm
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t p
r
o
ce
d
u
r
e.
A
v
ar
iatio
n
o
f
to
tal
co
s
t
with
r
esp
ec
t
to
iter
atio
n
is
p
lo
tted
in
Fig
u
r
e
3
,
wh
ich
s
h
o
ws th
e
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p
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ter
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o
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ith
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.
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t
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itted
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r
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d
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Fig
u
r
e
4
.
I
t
m
ak
es
it
ev
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th
at
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h
e
eq
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n
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ain
t
is
s
atis
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ied
f
o
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e
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o
u
r
s
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Fig
u
r
e
4
p
r
o
v
i
d
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f
o
r
m
atio
n
r
eg
a
r
d
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e
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tal
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r
r
ed
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o
r
e
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n
.
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ab
le
1
.
An
a
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is
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m
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ar
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e
1
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l
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A
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u
r
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Fig
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r
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ir
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Fig
u
r
e
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.
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o
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p
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n
s
e
in
cu
r
r
ed
in
a
ten
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u
n
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s
y
s
tem
Fig
u
r
e
4
.
Po
wer
o
u
tp
u
t in
a
s
y
s
tem
with
ten
u
n
its
3
.
2
.
T
est
ca
s
e
2
A
2
6
u
n
it
s
y
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tem
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n
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e
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s
ec
o
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s
e.
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est
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y
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tem
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ata
f
o
r
2
6
u
n
it
s
y
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tem
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tak
en
f
r
o
m
[
7
]
.
Usi
n
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2
6
-
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y
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em
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e
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en
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ed
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lin
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r
o
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o
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tim
ized
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s
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g
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e
APSO
m
eth
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d
.
T
ab
le
2
tab
u
lates
th
e
a
v
er
ag
e
,
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r
s
t,
an
d
b
est
r
esu
lts
f
r
o
m
th
e
2
5
tr
ail
r
u
n
s
.
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t
i
s
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id
e
n
t
f
r
o
m
th
e
r
esu
lts
th
at
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
7
6
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
,
Vo
l.
1
4
,
No
.
3
,
Dec
em
b
er
20
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5
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ested
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le
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o
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u
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ased
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to
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tech
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e
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ch
as
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al
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ar
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r
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e
o
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r
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alt
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ativ
e
s
to
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o
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tim
izatio
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m
eth
o
d
s
.
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r
th
e
r
m
o
r
e,
t
h
e
u
s
e
o
f
s
p
ec
ial
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n
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g
e
n
ce
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alu
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n
ex
p
e
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ite
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o
r
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g
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e
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ality
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e
m
an
d
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n
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ain
t
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d
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v
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er
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r
r
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d
y
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g
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ests
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o
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o
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m
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o
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ith
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h
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ch
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ick
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f
u
r
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s
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en
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t
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u
g
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ested
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o
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m
p
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ts
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n
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in
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s
to
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u
n
it
c
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m
m
itm
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t
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ltip
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ictio
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ar
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s
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e
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g
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ested
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m
itm
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B
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r
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le
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lar
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d
)
,
we
ca
n
p
r
o
d
u
ce
a
s
to
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m
m
i
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o
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lled
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tem
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s
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m
itm
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s
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g
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g
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ested
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o
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wer
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o
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p
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y
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ls
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is
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m
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s
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f
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[
1
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G
.
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G
RAP
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AUTH
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RS
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m
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sh
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b
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th
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d
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tro
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m
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a
d
ra
s
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i
v
e
rsity
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e
n
n
a
i,
In
d
ia,
in
1
9
9
8
,
a
n
d
a
n
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.
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d
e
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re
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o
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sy
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s
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g
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ra
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ll
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g
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n
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g
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a
d
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ra
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n
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in
2
0
0
0
.
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re
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e
iv
e
d
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h
.
D
.
in
p
o
we
r
sy
ste
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e
n
g
in
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e
rin
g
fro
m
An
n
a
Un
i
v
e
rsit
y
i
n
2
0
1
3
.
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is
c
u
rre
n
tl
y
a
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ro
fe
ss
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r
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n
th
e
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p
a
rtme
n
t
o
f
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lec
tri
c
a
l
a
n
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tro
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ics
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g
in
e
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rin
g
,
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t
.
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o
se
p
h
’s
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o
ll
e
g
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o
f
En
g
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n
e
e
rin
g
,
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e
n
n
a
i.
His
re
se
a
r
c
h
in
tere
sts
in
c
lu
d
e
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p
p
li
c
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ti
o
n
s
o
f
c
o
m
p
u
tati
o
n
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l
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n
telli
g
e
n
c
e
tec
h
n
iq
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e
s
to
p
o
we
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sy
ste
m
s
,
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istri
b
u
te
d
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n
e
rg
y
re
so
u
rc
e
s
a
n
d
sm
a
rt
g
rid
.
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c
a
n
b
e
c
o
n
tac
ted
at
e
m
a
il
:
ra
m
e
sh
b
a
b
u
m
@s
tj
o
se
p
h
s.a
c
.
in
.
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n
k
a
te
shk
u
m
a
r
Ch
a
n
d
r
a
se
k
a
r
a
n
re
c
e
iv
e
d
h
is
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a
c
h
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r’s
d
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re
e
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tri
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l
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n
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g
i
n
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e
rin
g
a
n
d
M
a
ste
rs
in
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o
we
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sy
ste
m
s
E
n
g
i
n
e
e
rin
g
fr
o
m
A
n
n
a
U
n
iv
e
rsit
y
,
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e
n
n
a
i
in
th
e
y
e
a
rs
2
0
0
6
a
n
d
2
0
1
0
.
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re
c
e
iv
e
d
P
h
.
D
.
i
n
p
o
we
r
s
y
ste
m
e
n
g
i
n
e
e
rin
g
f
ro
m
An
n
a
Un
iv
e
rsity
in
2
0
2
3
.
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is
c
u
rre
n
tl
y
a
As
sista
n
t
P
r
o
fe
ss
o
r
i
n
th
e
De
p
a
rtme
n
t
o
f
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e
c
tri
c
a
l
a
n
d
El
e
c
tro
n
ics
En
g
in
e
e
rin
g
,
S
t
.
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s
e
p
h
’s
Co
ll
e
g
e
o
f
E
n
g
in
e
e
rin
g
,
C
h
e
n
n
a
i.
His
field
s
o
f
in
tere
st
in
c
lu
d
e
p
o
we
r
sy
ste
m
d
e
re
g
u
lati
o
n
,
sm
a
rt
g
ri
d
,
a
n
d
p
o
we
r
sy
ste
m
p
lan
n
i
n
g
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
v
e
n
k
a
tes
h
k
u
m
a
rc
@s
tj
o
se
p
h
s.a
c
.
in
.
Bh
a
r
a
th
r
a
j
Mu
n
u
sa
m
y
fro
m
Th
ir
u
v
a
n
n
a
m
a
lai,
Ch
e
n
g
a
m
,
a
n
u
n
d
e
rg
ra
d
u
a
te
stu
d
e
n
t
a
t
S
t.
Jo
se
p
h
’s
Co
ll
e
g
e
o
f
En
g
in
e
e
rin
g
sp
e
c
ialize
s
in
th
e
n
ich
e
field
o
f
p
o
we
r
s
y
ste
m
s
a
n
d
o
p
ti
m
iza
ti
o
n
.
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h
a
s
a
c
ti
v
e
ly
e
n
g
a
g
e
d
i
n
a
ra
n
g
e
o
f
tec
h
n
ica
l
t
a
sk
s
a
n
d
h
a
s
a
stro
n
g
in
tere
st
in
m
a
c
h
in
e
lea
rn
i
n
g
.
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c
o
n
tri
b
u
ti
o
n
s
a
re
in
ten
d
e
d
t
o
o
ffe
r
imp
o
rtan
t
n
e
w
u
n
d
e
rsta
n
d
in
g
s
a
n
d
d
e
v
e
lo
p
m
e
n
ts
i
n
th
e
se
q
u
ic
k
ly
d
e
v
e
lo
p
in
g
d
o
m
a
in
s
o
f
st
u
d
y
.
H
e
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
b
h
a
ra
th
ra
jm1
9
@g
m
a
il
.
c
o
m
.
Dha
sa
g
r
e
e
v
a
n
S
a
n
k
a
r
a
n
a
r
a
y
a
n
a
n
a
n
u
n
d
e
rg
ra
d
u
a
te
stu
d
e
n
t
a
t
S
t.
Jo
se
p
h
'
s
Co
ll
e
g
e
o
f
En
g
i
n
e
e
rin
g
,
is
sp
e
c
ializin
g
in
t
h
e
n
ich
e
field
o
f
e
m
b
e
d
d
e
d
p
r
o
g
ra
m
m
in
g
a
n
d
th
e
o
re
ti
c
a
l
e
m
b
e
d
d
e
d
lo
g
ic
wit
h
i
n
t
h
e
De
p
a
rtme
n
t
o
f
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e
c
tri
c
a
l
a
n
d
El
e
c
tr
o
n
ic
En
g
in
e
e
rin
g
.
He
h
a
s
a
p
ro
fo
u
n
d
i
n
tere
st
in
t
h
e
o
re
ti
c
a
l
p
h
y
sic
s
a
n
d
m
a
c
h
i
n
e
lea
rn
in
g
a
n
d
h
a
s
a
c
ti
v
e
ly
p
a
rti
c
ip
a
te
d
in
a
v
a
riety
o
f
p
ro
jec
ts.
T
h
e
se
e
x
p
e
rien
c
e
s
h
a
v
e
a
ll
o
we
d
h
im
to
e
x
p
lo
re
t
h
e
fa
sc
in
a
ti
n
g
in
ters
e
c
ti
o
n
o
f
m
a
c
h
in
e
lea
rn
in
g
,
t
h
e
o
re
ti
c
a
l
p
h
y
sic
s,
a
n
d
e
lec
tri
c
a
l
e
n
g
i
n
e
e
rin
g
.
He
c
a
n
b
e
c
o
n
tac
ted
at
e
m
a
il
:
d
a
sh
a
g
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