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7
]
.
S
w
ar
m
I
n
telli
g
e
n
ce
cla
s
s
o
f
o
th
er
m
eth
o
d
s
,
clo
s
e
to
t
h
e
G
A
a
n
d
s
h
o
w
in
g
h
i
g
h
ef
f
icien
c
y
to
o
p
tim
izin
g
th
e
o
p
er
atio
n
o
f
p
o
w
er
s
y
s
te
m
s
.
A
s
in
t
h
e
ab
o
v
e
-
m
en
t
io
n
ed
r
esear
ch
[
7
]
,
Stat
ic
Var
C
o
m
p
e
n
s
ato
r
ar
e
u
s
ed
in
[
8
]
,
b
u
t
f
o
r
th
e
ir
o
p
tim
izatio
n
t
h
e
P
ar
ticle
S
w
a
r
m
Op
ti
m
izatio
n
(
P
SO)
alg
o
r
i
th
m
is
ap
p
lied
.
T
h
e
r
esear
ch
es
[
6
]
s
h
o
w
s
s
lig
h
t
s
u
p
er
io
r
ity
o
f
t
h
e
P
ar
ticle
S
w
ar
m
Op
ti
m
izatio
n
al
g
o
r
ith
m
o
v
e
r
th
e
G
A
in
s
o
l
v
i
n
g
th
e
p
r
o
b
lem
o
f
o
p
ti
m
al
allo
ca
t
io
n
o
f
r
ea
ctiv
e
p
o
w
er
s
o
u
r
ce
s
d
is
tr
ib
u
tio
n
i
n
n
e
t
w
o
r
k
n
o
d
es.
I
n
th
e
ar
ticle
[
9
]
a
m
o
d
i
f
icat
io
n
o
f
t
h
e
P
SO
to
o
p
ti
m
ize
s
ize
o
f
d
is
tr
ib
u
t
ed
g
e
n
er
atio
n
.
I
n
t
h
e
s
t
u
d
y
[
1
0
]
it
is
p
r
o
v
ed
th
at
f
o
r
t
h
e
r
ea
ctiv
e
p
o
w
er
u
n
i
ts
o
p
er
atio
n
al
co
n
tr
o
l
t
h
e
A
r
ti
f
icia
l
B
ee
C
o
lo
n
y
Op
ti
m
izatio
n
(
A
B
C
O
)
alg
o
r
ith
m
is
m
o
r
e
ef
f
ec
tiv
e
t
h
a
n
th
e
G
A
a
n
d
th
e
P
SO,
b
ec
au
s
e
in
th
e
A
B
C
O
p
r
o
cc
es
n
ev
er
co
n
v
er
g
e
s
in
t
h
e
n
eig
h
b
o
r
h
o
o
d
o
f
s
in
g
le
s
o
lu
tio
n
.
T
h
i
s
ar
ticle
p
r
o
p
o
s
es
to
ap
p
ly
a
m
u
ch
le
s
s
co
m
m
o
n
l
y
u
s
ed
S
w
ar
m
I
n
te
llig
e
n
ce
al
g
o
r
ith
m
,
n
a
m
e
l
y
th
e
alg
o
r
it
h
m
t
h
e
F
ir
ef
l
y
Op
ti
m
izatio
n
al
g
o
r
ith
m
(
F
FO)
[
1
1
]
.
I
t
w
as
m
o
d
i
f
icatio
n
to
s
o
lv
i
n
g
a
t
w
o
-
cr
iter
io
n
o
p
ti
m
izatio
n
p
r
o
b
le
m
.
A
ls
o
,
t
h
e
FF
O
al
g
o
r
ith
m
w
a
s
m
o
d
if
ied
b
y
u
s
i
n
g
a
g
r
ad
ien
t
d
escen
t.
1
.
1
.
Sta
t
e
m
ent
o
f
t
he
pro
ble
m
T
h
e
m
at
h
e
m
atica
l
m
o
d
el
o
f
th
e
o
p
tim
izatio
n
p
r
o
b
lem
in
v
o
l
v
es
r
ea
l
p
o
w
er
lo
s
s
es
m
i
n
i
m
izi
n
g
as
w
ell
as
co
s
ts
f
o
r
co
m
p
en
s
atin
g
u
n
it
s
’
(
C
U)
i
n
s
tallatio
n
.
T
h
e
s
i
m
p
lest
w
a
y
o
f
r
ed
u
ci
n
g
t
h
e
m
u
lti
cr
iter
ia
p
r
o
b
lem
to
o
n
e
-
cr
iter
io
n
o
n
e
i
s
a
lin
ea
r
c
o
n
v
o
l
u
tio
n
.
A
cti
v
e
p
o
w
er
lo
s
s
es
an
d
co
s
ts
r
elate
d
to
C
U
c
an
b
e
co
n
n
ec
ted
in
o
n
e
cr
iter
io
n
o
f
f
in
a
n
cial
lo
s
s
e
s
ta
k
in
g
i
n
to
ac
co
u
n
t
th
e
co
s
t
p
er
u
n
it
f
o
r
p
o
w
er
lo
s
s
e
s
(
1
k
W
)
an
d
th
e
co
s
t
p
er
u
n
i
t
f
o
r
C
U
p
o
w
er
(
1
k
V
A
r
)
.
T
h
e
p
o
w
er
lo
s
s
es
co
s
t i
s
d
ef
in
ed
b
y
th
e
tar
if
f
b
ei
n
g
ch
ar
g
ed
f
r
o
m
t
h
e
c
u
s
to
m
er
s
.
Ma
th
e
m
atica
l
f
o
r
m
u
latio
n
o
f
o
p
tim
izatio
n
ca
n
b
e
s
tated
as f
o
llo
w
s
[6
]:
W
(
Q
)
=
c
cu
·
Q
sum
+
c
p
·
Δ
P·t
→
m
i
n
Q
sum
=
(
Q
1
+ Q
2
+
…
+
Q
n
)
(
1
)
W
ith
r
estrictio
n
s
:
Q
min
i
≤
Q
i
≤
Q
max
i
,
w
h
er
e
a.
Q
is
a
C
U
’
s
p
o
w
er
v
ec
to
r
;
b.
i
is
C
U
’
s
p
o
w
er
in
n
o
d
e
(
if
it i
s
0
,
th
en
n
o
d
e
d
o
es n
o
t r
eq
u
ir
e
C
U’
s
in
s
tallat
io
n
)
;
c.
n
is
a
n
u
m
b
er
o
f
n
o
d
es
w
h
er
e
C
Us ca
n
b
e
in
s
ta
lled
;
d.
c
cu
is
co
s
t o
f
t
h
e
C
U
s
(
$
p
er
v
o
lt
-
a
m
p
er
e)
;
e.
c
p
is
co
s
t o
f
ac
ti
v
e
p
o
w
er
(
$
p
er
w
att
-
h
o
u
r
)
;
f.
Δ
P
is
to
tal
lo
s
s
e
s
o
f
r
ea
l p
o
w
e
r
in
n
et
w
o
r
k
;
g.
t
is
esti
m
ated
p
er
io
d
in
h
o
u
r
s
.
As
a
g
en
er
al
r
u
le,
t
h
is
p
r
o
b
lem
i
s
co
n
s
id
er
ed
as
o
n
e
-
cr
iter
i
o
n
b
y
co
n
v
o
l
u
tio
n
i
n
to
o
n
e
o
r
tr
an
s
f
er
r
in
g
o
f
o
n
e
o
f
t
h
e
cr
iter
ia
i
n
to
r
e
s
tr
ictio
n
s
.
Ho
w
e
v
er
,
th
e
m
o
d
el
ap
p
licatio
n
w
ith
t
w
o
cr
i
ter
ia
al
l
o
w
s
a
d
ec
is
io
n
m
ak
er
to
h
av
e
m
o
r
e
in
f
o
r
m
at
io
n
ab
o
u
t
s
y
s
te
m
i
m
p
r
o
v
e
m
e
n
t
o
p
tio
n
s
.
I
t
is
o
f
p
ar
ticu
lar
i
m
p
o
r
tan
ce
to
u
s
e
m
u
lti
-
cr
iter
ia
o
p
ti
m
iza
tio
n
w
h
en
a
m
o
n
g
cr
iter
ia
t
h
e
p
ar
t
o
f
w
h
ic
h
i
n
f
lu
e
n
ce
s
th
e
s
h
o
r
t
-
ter
m
i
n
d
icato
r
s
a
n
d
th
e
o
th
er
p
ar
t
in
f
l
u
en
ce
s
t
h
e
lo
n
g
-
ter
m
o
n
e
s
.
T
h
u
s
,
t
h
e
o
p
ti
m
izat
io
n
p
r
o
b
lem
E
q
u
atio
n
(
1
)
m
a
y
n
o
t
b
e
r
ed
u
ce
d
to
o
n
e
-
cr
iter
io
n
b
u
t n
ee
d
s
to
b
e
s
o
lv
ed
u
s
i
n
g
t
w
o
cr
iter
ia
s
ep
ar
a
tel
y
w
it
h
r
estrictio
n
th
e
s
a
m
e
as in
E
q
u
a
tio
n
(
1
)
:
c
cu
·
t·
Δ
P
→
m
i
n
c
cu
·Q
sum
→
m
i
n
(
2
)
1
.
2
.
F
iref
ly
a
lg
o
rit
hm
T
h
e
Fire
f
l
y
al
g
o
r
ith
m
[
1
1
]
as
all
S
w
ar
m
I
n
telli
g
en
ce
al
g
o
r
ith
m
s
i
s
b
ased
o
n
th
e
a
g
en
t
s
(
f
ir
ef
lie
s
)
m
o
v
e
m
e
n
t
in
t
h
e
d
ec
is
io
n
s
e
ar
ch
in
g
s
p
ac
e.
L
et
’
s
co
n
s
id
er
th
e
o
b
j
ec
tiv
e
f
u
n
ct
io
n
m
in
i
m
u
m
p
r
o
b
le
m
o
f
th
e
f
o
llo
w
in
g
t
y
p
e
f
(
X
)
,
w
h
er
e
X
is
a
v
ec
to
r
o
f
v
ar
ied
p
ar
a
m
et
er
s
w
h
ic
h
ca
n
g
et
th
e
v
al
u
es
f
r
o
m
s
o
m
e
D
ar
ea
.
E
ac
h
ag
e
n
t
is
s
p
ec
if
ied
b
y
th
e
v
al
u
e
o
f
X
p
ar
a
m
eter
an
d
v
al
u
e
o
f
a
n
o
p
ti
m
ized
f
u
n
ctio
n
f
(
X
)
.
T
h
u
s
,
th
e
a
g
e
n
t
is
a
f
ea
s
ib
le
s
o
lu
tio
n
o
f
t
h
e
co
n
s
id
er
ed
o
p
ti
m
izatio
n
p
r
o
b
le
m
.
As
t
h
e
al
g
o
r
ith
m
is
b
ased
o
n
w
atc
h
i
n
g
f
o
r
f
l
y
’
s
b
eh
a
v
io
r
,
ea
ch
a
g
en
t
is
co
n
s
id
er
ed
to
s
ee
th
e
“
li
g
h
t
”
f
r
o
m
t
h
eir
n
ei
g
h
b
o
r
s
,
b
u
t
t
h
e
b
r
ig
h
t
n
ess
o
f
th
e
“
li
g
h
t”
d
ep
en
d
s
o
n
th
e
d
is
ta
n
ce
b
et
w
e
en
ag
e
n
ts
.
Fo
r
th
e
p
r
o
ce
s
s
o
f
s
o
lu
tio
n
f
i
n
d
in
g
to
b
e
co
n
v
er
g
ed
to
t
h
e
o
p
ti
m
u
m
,
ea
c
h
a
g
en
t
i
n
i
ts
m
o
v
e
m
e
n
t
ta
k
es
i
n
to
ac
co
u
n
t
o
n
l
y
th
o
s
e
n
eig
h
b
o
r
s
h
av
i
n
g
a
b
etter
v
al
u
e
o
f
f
(
X
)
cr
iter
io
n
.
B
u
t
f
o
r
t
h
e
alg
o
r
it
h
m
n
o
t
to
d
eg
en
er
ate
in
to
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
3
,
J
u
n
e
201
8
:
1
7
5
8
–
1765
1760
g
r
ee
d
y
h
eu
r
i
s
tics
,
it
is
n
ec
e
s
s
a
r
y
to
h
a
v
e
a
g
en
ts
’
s
to
ch
as
tic
m
o
v
e
m
e
n
t.
T
h
is
p
ec
u
liar
it
y
is
also
s
p
ec
i
f
ic
f
o
r
all
S
w
ar
m
al
g
o
r
ith
m
s
.
T
h
e
FF
O
alg
o
r
ith
m
o
p
er
atio
n
s
ch
e
m
e
ca
n
b
e
d
escr
ib
ed
as f
o
llo
w
s
:
Step
1
.
T
o
d
is
tr
ib
u
te
th
e
a
g
en
t
s
r
an
d
o
m
l
y
in
t
h
e
s
o
l
u
tio
n
s
ea
r
ch
in
g
s
p
ac
e.
Step
2
.
T
o
ca
lcu
late
v
alu
e
s
o
f
th
e
o
p
ti
m
ized
f
u
n
ctio
n
p
er
ea
c
h
ag
e
n
t.
I
f
t
h
e
ag
e
n
t
h
as a
b
ett
er
v
alu
e,
it
w
il
l
h
av
e
m
o
r
e
o
p
p
o
r
tu
n
ity
to
s
er
v
e
it.
Step
3
.
E
ac
h
ag
en
t
n
ee
d
s
to
h
a
v
e
a
n
e
w
p
o
s
itio
n
b
ased
o
n
th
e
f
o
r
m
u
las
g
iv
e
n
b
elo
w
.
Step
4
.
T
o
ca
r
r
y
o
u
t t
h
e
m
o
v
e
m
en
t o
f
ea
ch
a
g
e
n
t in
to
a
n
e
w
p
o
s
itio
n
.
Step
5
.
I
f
th
e
co
n
d
itio
n
o
f
co
m
p
letio
n
is
i
m
p
le
m
e
n
ted
,
th
e
al
g
o
r
ith
m
n
ee
d
s
to
b
e
f
i
n
i
s
h
ed
o
r
o
th
er
w
i
s
e
n
ee
d
s
to
b
e
p
ass
ed
to
th
e
Step
2
.
T
h
e
r
esu
lt
o
f
al
g
o
r
it
h
m
p
er
f
o
r
m
an
ce
is
t
h
e
b
est
-
s
av
ed
s
o
lu
ti
o
n
.
T
h
e
s
t
u
d
y
[
1
0
]
p
r
o
v
id
es
a
u
n
i
v
er
s
a
l
s
ch
e
m
e
o
f
S
w
ar
m
I
n
telli
g
en
ce
alg
o
r
ith
m
d
e
s
cr
ip
tio
n
.
A
cc
o
r
d
in
g
to
it,
t
h
e
Fire
f
l
y
al
g
o
r
it
h
m
s
h
o
u
ld
b
e
w
r
i
tte
n
as f
o
llo
w
s
:
FF
= {
S
,
M,
A
,
P
,
I
,
O
}.
1
.
Set o
f
ag
en
t
s
(
f
ir
e
f
lie
s
)
S
= {
s
1
,
s
2
,
…,
s
|
S
|
},
|
S
|
i
s
a
n
u
m
b
er
o
f
a
g
en
ts
.
A
t it
er
atio
n
j
th
e
i
th
a
g
e
n
t is
s
p
ec
if
i
ed
b
y
t
h
e
s
tate
s
ij
= {
X
ij
},
w
h
er
e
X
ij
= {
x
1
ij
, x
2
ij
, …,
x
lij
}
is
a
v
ec
to
r
o
f
th
e
v
ar
ied
p
ar
a
m
eter
s
(
ag
e
n
t
’
s
p
o
s
itio
n
)
,
l
is
a
n
u
m
b
er
o
f
t
h
e
v
ar
ied
p
ar
am
eter
s
.
2
.
Vec
to
r
M
is
ag
en
t
s
’
b
r
ig
h
t
n
ess
.
M
= {
f
(
X
1
j
)
,
f
(
X
2
j
)
,
f
(
X
|
s
|
j
)}
B
r
ig
h
t
n
es
s
is
d
eter
m
i
n
ed
b
y
t
h
e
o
p
ti
m
a
lit
y
cr
iter
io
n
.
T
h
is
v
ec
to
r
en
s
u
r
es
th
e
in
d
ir
ec
t
e
x
p
er
ien
ce
ex
c
h
an
g
e
a
m
o
n
g
ag
e
n
t
s
.
3
.
T
h
e
alg
o
r
ith
m
A
d
escr
ib
es S
w
ar
m
f
u
n
ctio
n
in
g
m
ec
h
a
n
i
s
m
s
.
T
h
er
e
ar
e
d
if
f
er
en
t
m
o
d
if
i
ca
tio
n
s
o
f
t
h
i
s
alg
o
r
ith
m
.
T
h
is
is
f
o
llo
w
ed
b
y
t
h
e
d
escr
ip
tio
n
o
f
b
asic a
l
g
o
r
ith
m
.
a)
Gen
er
atio
n
o
f
i
n
itial p
o
s
itio
n
s
i
s
:
X
i
1
←
r
a
n
d
o
m
(
G
(
X
)
)
,
i
=
1
,
…,
|
S
|,
w
h
er
e
r
an
d
o
m
(
G
(
X
)
)
is
a
v
ec
t
o
r
o
f
eq
u
all
y
d
i
s
tr
ib
u
ted
r
an
d
o
m
v
ar
iab
les
m
ee
ti
n
g
t
h
e
r
e
s
t
r
ictio
n
s
o
f
s
ea
r
ch
i
n
g
s
p
ac
e.
b
)
C
r
iter
io
n
ca
lcu
latio
n
p
er
ag
en
t is b
ei
n
g
i
m
p
le
m
en
ted
b
y
:
m
ij
=
f
(
X
ij
)
,
i
=
1
,
…,
|
S
|
X
j
best
←
X
ij
|
f
(
X
ij
)
≤
f
(
X
j
best
)
(
3
)
T
h
e
cr
iter
io
n
ca
lcu
latio
n
tak
es
p
lace
in
th
e
m
a
th
e
m
atica
l
m
o
d
el
o
f
th
e
p
r
o
b
lem
w
h
er
e
X
ij
v
ec
to
r
s
ar
e
en
ter
ed
f
r
o
m
al
g
o
r
ith
m
s
a
n
d
th
e
r
es
u
lt
s
ar
e
r
etu
r
n
ed
to
th
e
alg
o
r
it
h
m
th
r
o
u
g
h
t
h
e
in
ter
f
ac
e
{
I
,
O
}.
c)
A
g
e
n
t
s
’
m
o
v
e
m
e
n
t:
X
ij+
1
←
X
ij
+
v
(
X
ij
,
X
kj
)
·
(
X
ij
–
X
kj
)
+
α
·
r
a
n
d
o
m
|
m
kj
≤
m
ij
,
i
,
k
=
1
,
…,
|
S
|
,
i
≠
k
,
if
G
(
X
ij
+1
)
=
0
,
X
ij
+1
←
X
ij
,
i
=
1
,
…,
|
S
|,
(
4
)
W
h
er
e
r
a
n
d
∈
[
0
,
1
]
,
an
d
G
(
X
)
is
u
s
ed
in
t
h
i
s
ca
s
e
as
t
h
e
p
r
ed
icate
s
h
o
w
i
n
g
i
f
X
b
elo
n
g
s
th
e
ar
ea
o
f
ad
m
is
s
ib
le
s
o
lu
t
io
n
s
.
T
h
e
f
u
n
c
tio
n
v
(
X
ij
,
X
kj
)
d
ef
in
e
s
th
e
attr
ac
tiv
e
n
e
s
s
o
f
k
a
g
en
t
f
o
r
i a
g
en
t
w
it
h
j
alg
o
r
it
h
m
iter
atio
n
:
v
(
X
ij
,
X
kj
)
=
β
·
(
1
+
γ
·
r
(
X
ij
,
X
kj
))
-
1
(
5
)
w
h
er
e
r
(
X
ij
, X
kj
)
is
C
ar
tesi
a
n
d
is
tan
ce
b
et
w
ee
n
ag
e
n
t
s
.
d
)
I
f
w
it
h
j
iter
atio
n
t
h
e
co
m
p
letio
n
co
n
d
itio
n
is
i
m
p
le
m
e
n
ted
,
th
e
v
al
u
e
h
as
th
e
o
u
tp
u
t
O
.
Ot
h
er
w
is
e,
t
h
e
tr
an
s
itio
n
to
iter
atio
n
b
)
is
tak
en
p
lace
.
4
.
Vec
to
r
P
=
{α
,
β,
γ
}
ar
e
co
e
f
f
icien
ts
o
f
t
h
e
al
g
o
r
ith
m
.
C
o
ef
f
icie
n
t
α
d
eter
m
in
e
s
th
e
i
n
f
lu
e
n
ce
d
eg
r
ee
o
f
s
to
c
h
asti
c
alg
o
r
ith
m
n
atu
r
e.
C
o
e
f
f
icien
t
β
s
ets
t
h
e
d
eg
r
ee
o
f
attr
ac
tio
n
b
et
w
ee
n
ag
e
n
t
s
with
ze
r
o
d
is
ta
n
ce
b
et
w
ee
n
t
h
e
m
i.e
.
d
ef
i
n
es
th
e
ag
e
n
t
’
s
m
u
t
u
al
i
n
f
lu
e
n
ce
.
C
o
ef
f
icie
n
t γ
co
n
tr
o
ls
t
h
e
d
ep
en
d
en
ce
o
f
attr
ac
tio
n
o
n
t
h
e
d
is
tan
ce
b
et
w
ee
n
a
g
en
ts
.
5
.
I
d
en
tif
ier
s
I
an
d
O
ar
e
alg
o
r
ith
m
’
i
n
p
u
ts
an
d
o
u
tp
u
ts
(
to
b
e
in
ter
co
n
n
ec
ted
)
f
o
r
th
e
in
ter
co
n
n
ec
tio
n
w
ith
t
h
e
p
r
o
b
lem
s
o
lv
ed
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
F
ir
efly
A
lg
o
r
ith
m
t
o
Op
mima
l D
is
tr
ib
u
tio
n
o
f R
ea
ctive
P
o
w
er C
o
mp
en
s
a
tio
n
Un
its
(
V
.
Z.
Ma
n
u
s
o
v)
1761
2.
RE
S
E
ARCH
M
E
T
H
O
D
2
.
1
.
A
pp
ly
ing
t
he
FFO
a
lg
o
rit
h
m
f
o
r
t
w
o
-
c
rit
er
ia
o
ptim
iza
t
io
n
Ou
r
p
r
eli
m
in
ar
y
e
x
p
er
i
m
e
n
ts
,
as
w
ell
as
ex
p
er
i
m
en
t
s
[
1
2
]
s
h
o
w
s
th
at
i
f
o
p
ti
m
izatio
n
p
r
o
b
le
m
h
as
a
s
in
g
le
cr
iter
io
n
,
t
h
e
n
m
o
s
t
f
ir
e
f
lies
co
n
v
er
g
es r
ap
id
l
y
(
ab
o
u
t
af
ter
1
0
0
iter
atio
n
s
)
to
a
n
ei
g
h
b
o
r
h
o
o
d
o
f
th
e
o
n
e
s
o
lu
tio
n
.
Ho
w
e
v
er
,
ea
ch
FF
O
ag
en
t
i
s
d
ir
ec
tl
y
in
f
l
u
en
ce
d
b
y
all
o
th
er
ag
en
ts
,
w
h
ich
h
a
s
a
be
tter
f
itn
es
s
v
al
u
e.
I
t
f
u
n
d
a
m
e
n
tall
y
d
i
f
f
er
e
n
tiate
s
t
h
e
F
FO
al
g
o
r
it
h
m
f
r
o
m
o
t
h
er
p
o
p
u
latio
n
-
b
ased
alg
o
r
it
h
m
s
.
Fo
r
e
x
a
m
p
le,
i
n
th
e
G
A
,
a
n
e
w
s
o
l
u
tio
n
i
s
o
b
tain
ed
f
r
o
m
th
e
cr
o
s
s
o
v
er
o
f
a
s
m
all
n
u
m
b
er
(
u
s
u
all
y
t
w
o
)
o
f
p
ar
en
t
s
o
lu
tio
n
s
.
I
n
th
e
P
SO
al
g
o
r
ith
m
,
t
h
e
ag
e
n
t
is
in
f
l
u
e
n
ce
d
b
y
t
h
e
b
est
s
o
l
u
t
io
n
a
m
o
n
g
its
n
ei
g
h
b
o
r
s
o
r
ev
en
a
m
o
n
g
all
a
g
en
t
o
f
th
e
s
w
ar
m
.
I
n
t
h
e
A
B
C
O
alg
o
r
ith
m
,
o
n
l
y
a
f
e
w
o
f
t
h
e
b
est
s
o
l
u
t
io
n
s
ar
e
s
elec
ted
,
wh
ich
af
f
ec
t
th
e
n
e
x
t
s
tep
s
.
T
h
is
f
ea
tu
r
e
allo
w
s
a
p
p
ly
i
n
g
th
e
FF
O
a
lg
o
r
it
h
m
ea
s
il
y
f
o
r
p
r
o
b
lem
s
to
b
e
s
o
lv
ed
w
i
th
s
ev
er
al
co
n
f
lic
tin
g
cr
iter
ia
r
eq
u
ir
in
g
f
in
d
in
g
t
h
e
alter
n
at
iv
e
it
s
el
f
.
E
ac
h
ag
e
n
t
is
i
n
f
l
u
en
ce
d
b
y
all
ag
en
t
s
,
w
h
ic
h
ar
e
m
u
c
h
b
etter
b
y
o
n
e
cr
iter
io
n
(
m
i
n
i
m
u
m
lo
s
s
es o
r
m
i
n
i
m
u
m
co
m
p
e
n
s
at
io
n
p
o
w
er
)
.
Fo
r
ex
a
m
p
le,
in
Fi
g
u
r
e
1
,
f
o
u
r
ag
en
t
s
w
ill
b
e
in
f
l
u
e
n
ce
d
b
y
all
ag
en
ts
e
x
ce
p
t
2
an
d
9
.
I
n
th
is
ca
s
e,
f
ir
s
t,
s
ix
t
h
,
a
n
d
eig
h
th
a
g
e
n
ts
’
in
f
lu
e
n
ce
w
il
l
b
e
less
t
h
a
n
th
ir
d
,
f
if
t
h
,
an
d
s
e
v
e
n
t
h
ag
e
n
ts
i
n
f
lu
en
ce
a
s
t
h
e
y
ar
e
at
th
e
r
e
m
o
te
d
is
tan
ce
f
r
o
m
t
h
e
f
o
u
r
t
h
o
n
e.
T
h
e
f
i
f
t
h
ag
e
n
t
w
il
l
h
a
v
e
m
o
r
e
i
n
f
lu
e
n
ce
.
T
h
e
s
ix
t
h
a
g
en
t
w
ill
n
o
t
b
e
in
f
l
u
e
n
ce
d
b
y
a
n
y
o
f
th
e
a
g
en
ts
m
e
n
tio
n
ed
as it i
s
in
t
h
e
b
est p
o
s
itio
n
ac
co
r
d
in
g
to
b
o
th
cr
iter
ia.
Fig
u
r
e
1
.
Fire
f
l
y
a
lg
o
r
it
h
m
i
n
f
lu
en
ce
w
i
th
in
t
w
o
-
cr
iter
io
n
p
r
o
b
lem
2
.
2
.
I
nte
ra
ct
io
n
t
he
F
F
O
a
lg
o
rit
hm
a
n
d o
pti
m
iza
t
io
n p
ro
ble
m
T
h
e
in
ter
ac
tio
n
o
f
t
h
e
F
FO
al
g
o
r
ith
m
a
n
d
th
e
o
p
ti
m
izat
io
n
p
r
o
b
lem
i
s
p
er
f
o
r
m
ed
ac
co
r
d
in
g
to
t
h
e
f
o
llo
w
in
g
s
c
h
e
m
e:
a.
T
h
e
alg
o
r
ith
m
g
e
n
er
ates n
e
w
ag
en
t
s
et
(
s
o
lu
tio
n
s
)
.
b.
E
ac
h
ag
e
n
t p
o
s
itio
n
X
is
m
ap
p
ed
to
p
r
o
b
lem
s
o
l
u
tio
n
(
v
ec
to
r
Q
)
,
as sh
o
w
n
b
y
E
q
u
atio
n
(
6
)
.
c.
C
r
iter
io
n
E
q
u
atio
n
(
1
)
is
ca
lcu
lated
f
o
r
ea
ch
s
o
lu
t
io
n
an
d
cr
it
er
io
n
v
al
u
es a
r
e
s
et
to
Fire
f
l
y
alg
o
r
ith
m
.
d.
T
h
e
FF
O
alg
o
r
ith
m
u
p
d
ates a
g
en
t p
o
s
itio
n
u
s
i
n
g
E
q
u
atio
n
s
(
3
)
-
(
5
)
.
e.
T
h
ese
s
tep
s
ar
e
p
er
f
o
r
m
ed
u
n
t
il th
e
n
u
m
b
er
o
f
iter
atio
n
s
is
e
x
h
a
u
s
ted
.
Ag
e
n
t
p
o
s
itio
n
X
is
u
s
ed
as
th
e
co
ef
f
ic
ien
t
s
v
ec
to
r
,
s
o
th
e
p
o
w
er
o
f
i
th
C
U
w
as
d
eter
m
i
n
ed
as
th
e
p
r
o
d
u
ct
o
f
th
e
x
i
th
e
ca
lc
u
lated
m
ax
i
m
u
m
allo
w
ab
le
p
o
w
er
o
f
C
U
in
t
h
e
i
th
n
o
d
e
Q
i
= x
i
∙
Q
m
ax
i
.
(
6
)
2
.
3
.
L
o
ca
l
s
ea
rc
h
T
h
e
FF
O
ag
en
t
s
ar
e
m
o
v
ed
to
th
e
cr
iter
ia
im
p
r
o
v
e
m
e
n
t
s
i
d
e,
b
u
t
ca
n
n
o
t
ch
an
g
e
p
o
s
itio
n
s
p
er
s
tep
f
o
r
a
b
ig
g
er
d
is
tan
ce
s
i
n
ce
th
e
r
e
m
o
te
a
g
e
n
ts
’
i
n
f
lu
e
n
ce
is
n
o
t
s
o
m
u
c
h
.
T
h
e
in
f
lu
en
ce
is
d
ec
r
ea
s
ed
ex
p
o
n
en
t
iall
y
w
i
th
d
is
ta
n
ce
i
n
cr
ea
s
in
g
.
Du
e
to
it,
th
e
p
r
o
b
a
b
ilit
y
o
f
th
e
a
g
en
t
w
ill
“
p
ass
o
v
er
”
s
o
m
e
ex
tr
e
m
e
p
o
in
t
o
n
its
w
a
y
.
O
n
t
h
e
o
th
e
r
h
an
d
,
it
w
ill
n
o
t
allo
w
all
t
h
e
ag
en
t
s
to
q
u
ick
l
y
ap
p
ea
r
in
o
n
e
ex
tr
e
m
e
p
o
in
t
ev
en
i
f
it
is
a
g
lo
b
al
o
n
e.
Sin
ce
th
e
al
g
o
r
ith
m
f
i
n
d
s
n
o
t
a
n
ex
ac
t
ex
tr
e
m
e
p
o
in
t
b
u
t
f
in
d
s
s
o
m
e
ar
ea
u
p
o
n
co
m
p
let
io
n
o
f
FF
O
alg
o
r
it
h
m
o
p
er
atio
n
,
it
is
ex
p
e
d
ien
t
to
ca
r
r
y
o
u
t
lo
ca
l
s
ea
r
ch
in
g
in
t
h
e
s
p
ac
e
o
f
th
e
b
es
t
s
o
lu
tio
n
f
o
u
n
d
s
u
ch
a
s
th
e
g
r
a
d
ien
t d
escen
t.
T
o
in
cr
ea
s
e
th
e
th
e
FF
O
al
g
o
r
ith
m
ef
f
ec
ti
v
e
n
es
s
,
it
is
p
o
s
s
i
b
le
to
ca
r
r
y
o
u
t
i
ts
ad
j
u
s
t
m
e
n
t
w
i
th
t
h
e
g
r
ad
ien
t
d
esce
n
t.
I
n
it
iall
y
,
t
h
e
F
FO
a
l
g
o
r
ith
m
is
la
u
n
ch
ed
o
u
t,
an
d
it
p
er
f
o
r
m
s
s
ea
r
c
h
i
n
g
w
it
h
i
n
t
h
e
s
p
ac
e
o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
3
,
J
u
n
e
201
8
:
1
7
5
8
–
1765
1762
ac
ce
p
tab
ilit
y
.
Ho
w
e
v
er
,
in
t
h
is
ca
s
e,
t
h
e
alg
o
r
it
h
m
ca
n
f
i
n
d
th
e
s
p
ac
e
o
f
g
lo
b
al
e
x
t
r
e
m
u
m
b
u
t
n
o
t
t
h
e
ex
tr
e
m
u
m
it
s
el
f
d
u
e
to
its
d
iv
er
s
i
f
ica
tio
n
f
ea
tu
r
e
allo
w
i
n
g
n
o
t
“to
b
e
s
t
u
ck
”
in
lo
ca
l
ar
ea
s
.
Gr
ad
ien
t
alg
o
r
ith
m
s
,
o
n
t
h
e
co
n
tr
ar
y
,
f
r
eq
u
en
tl
y
ar
e
n
o
t
ab
le
to
g
et
o
u
t
f
r
o
m
lo
ca
l
e
x
tr
e
m
u
m
s
.
S
u
ch
a
lg
o
r
it
h
m
s
ar
e
co
m
p
u
ter
-
in
te
n
s
iv
e,
i
n
p
ar
tic
u
lar
,
w
it
h
a
lar
g
e
q
u
a
n
tit
y
o
f
o
p
ti
m
ized
v
ar
iab
les
b
ein
g
av
ailab
le.
Ho
w
ev
e
r
,
g
r
ad
ien
t
d
esce
n
t
allo
w
s
f
i
n
d
i
n
g
t
h
e
ex
tr
e
m
u
m
in
t
h
at
r
e
g
io
n
w
h
er
e
it
h
as
s
tar
ted
its
o
p
er
atio
n
.
Du
e
to
it,
th
e
m
o
r
e
ef
f
ec
t
iv
e
alg
o
r
it
h
m
co
m
b
in
atio
n
at
w
h
ic
h
th
e
FF
O
al
g
o
r
ith
m
ca
r
r
ies
o
u
t
s
p
ac
e
ap
p
r
o
x
i
m
atio
n
(
o
n
e
o
r
s
o
m
e)
r
elati
v
el
y
f
a
s
t
w
it
h
i
n
t
h
e
w
h
o
le
s
p
ac
e
o
f
s
o
l
u
tio
n
s
b
ein
g
u
s
ed
af
ter
w
ar
d
as
t
h
e
i
n
i
tial
p
o
s
itio
n
f
o
r
th
e
g
r
ad
ien
t d
esce
n
t.
2.
4
.
P
o
w
er
s
up
ply
s
y
s
t
e
m
us
ed
T
h
e
ex
p
er
im
e
n
t
s
w
er
e
p
er
f
o
r
m
ed
b
y
u
s
i
n
g
th
e
f
r
ag
m
e
n
t
o
f
T
a
j
ik
is
tan
d
is
tr
ib
u
tio
n
elec
tr
ic
al
n
et
w
o
r
k
o
f
elec
tr
ic
p
o
w
er
s
y
s
te
m
s
h
o
wn
in
Fig
u
r
e
2
.
T
h
e
s
elec
tio
n
o
f
n
o
d
es
f
o
r
t
h
e
C
U
s
lo
ca
tio
n
i
s
ca
r
r
ied
o
u
t
b
y
f
u
zz
y
lo
g
ic.
Fo
r
t
h
is
v
o
lta
g
e
d
ev
ia
tio
n
in
t
h
e
n
o
d
es
a
n
d
r
ea
l
p
o
w
er
lo
s
s
es
in
b
r
an
c
h
es
h
a
v
e
b
ee
n
co
n
s
id
er
ed
as
li
n
g
u
i
s
tic
v
ar
i
ab
les.
T
h
e
v
o
lta
g
e
d
ev
i
atio
n
ca
n
b
e
“lo
w
”,
“
b
elo
w
a
v
er
ag
e”
,
“
a
v
er
ag
e”
o
r
“h
ig
h
”.
T
h
e
r
ea
l
p
o
w
er
lo
s
s
es
in
b
r
an
ch
e
s
ca
n
b
e
“
b
elo
w
a
v
er
a
g
e”
o
r
“
ab
o
v
e
av
er
ag
e”
.
T
h
e
n
o
d
e
is
s
elec
ted
a
s
p
o
ten
tiall
y
s
u
itab
le
f
o
r
th
e
C
U
if
t
h
e
v
o
lta
g
e
d
ev
iatio
n
is
“
lo
w
”
o
r
“
b
elo
w
a
v
er
a
g
e”
an
d
r
ea
l
p
o
w
er
l
o
s
s
es
ar
e
“
ab
o
v
e
a
v
er
a
g
e”
.
T
h
e
n
u
m
b
er
s
o
f
t
h
e
s
elec
ted
n
o
d
es f
o
r
th
e
co
n
s
id
e
r
ed
cir
cu
it (
s
ch
e
m
e)
ar
e
ci
r
cled
as it is sh
o
w
n
i
n
Fi
g
u
r
e
2
.
Fig
u
r
e
2
.
E
lectr
ical
Net
w
o
r
k
F
r
ag
m
e
n
t
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
3
.
1
.
O
ne
-
cr
it
er
io
n pro
ble
m
s
o
luti
o
n
T
h
e
FF
O
a
l
g
o
r
ith
m
u
s
ed
5
0
a
g
en
t
s
,
p
ar
a
m
e
ter
v
al
u
es
P
=
{
α
,
β,
γ
}
=
{0
.
5
,
0
.
0
1
,
1
0
0
.
0
}.
T
h
en
it
w
a
s
ap
p
lied
w
ith
u
s
in
g
t
h
e
lo
ca
l
s
ea
r
ch
,
as
d
escr
ib
ed
in
Sectio
n
2
.
A
ls
o
,
th
e
o
p
ti
m
izatio
n
p
r
o
b
le
m
E
q
u
atio
n
(
1
)
w
a
s
s
o
l
v
ed
b
y
g
r
ad
ie
n
t d
escen
t
w
ith
s
ev
er
al
ar
b
itra
r
y
i
n
it
ial
co
n
d
itio
n
s
.
T
o
co
m
p
ar
e
th
e
e
f
f
icie
n
c
y
o
f
t
h
e
FF
O
alg
o
r
ith
m
s
,
w
e
also
ap
p
lied
th
e
P
SO
alg
o
r
ith
m
i
n
eq
u
al
co
n
d
itio
n
s
.
T
h
e
w
o
r
s
t
a
n
d
th
e
b
est
r
esu
lts
o
f
t
h
e
g
r
ad
ien
t
d
esce
n
t,
r
esu
lt
s
o
f
th
e
FF
O
an
d
th
e
F
FO
w
it
h
th
e
g
r
ad
ien
t
d
escen
t
ar
e
lis
ted
in
T
ab
le
1
.
T
a
b
le
1
u
s
es
f
o
llo
w
in
g
n
o
tatio
n
s
:
a.
I
n
it
is
r
esu
lt
s
w
it
h
o
u
t a
n
y
o
p
ti
m
izatio
n
;
b.
FFO
is
r
esu
lt
s
o
f
t
h
e
Fire
f
l
y
al
g
o
r
ith
m
;
c.
Gra
d
ien
t B
is
r
esu
lt
s
o
f
th
e
g
r
ad
ien
t d
escen
t
w
i
th
b
ad
in
it
ial
co
n
d
itio
n
s
;
d.
Gra
d
ien
t G
is
r
esu
lt
s
o
f
t
h
e
g
r
ad
ien
t d
escen
t
w
i
th
g
o
o
d
in
itia
l c
o
n
d
itio
n
s
;
e.
FF
O
+ G
D
is
r
esu
lts
o
f
t
h
e
Fi
r
ef
l
y
al
g
o
r
ith
m
w
i
th
u
s
i
n
g
th
e
g
r
ad
ien
t d
esce
n
t;
f.
P
S
O
i
s
r
esu
lt
s
o
f
t
h
e
P
ar
ticle
Sw
ar
m
Op
ti
m
izatio
n
al
g
o
r
ith
m
;
g.
W
is
cr
iter
io
n
as
s
h
o
w
n
b
y
E
q
u
atio
n
(
1
)
:
co
s
t
o
f
ac
ti
v
e
p
o
w
er
lo
s
s
es
f
o
r
4
y
ea
r
s
p
lu
s
co
s
ts
f
o
r
co
m
p
e
n
s
at
io
n
u
n
it
s
;
h.
Δ
P
is
ac
ti
v
e
p
o
w
er
lo
s
s
e
s
;
i.
Q
sum
is
to
tal
p
o
w
er
o
f
C
Us.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
C
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p
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N:
2088
-
8708
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ith
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izatio
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T
wo
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cr
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r
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m
S
o
lutio
n
Usi
n
g
t
h
e
FF
O
al
g
o
r
ith
m
f
o
r
th
e
t
w
o
-
cr
iter
io
n
p
r
o
b
le
m
as
it
w
a
s
d
escr
ib
ed
in
Sec
ti
o
n
3
.
2
th
e
f
o
llo
w
in
g
s
et
o
f
o
p
ti
m
al
s
o
lu
tio
n
s
ac
co
r
d
in
g
to
P
ar
eto
co
u
ld
b
e
o
b
tain
ed
as
it
w
a
s
s
h
o
w
n
i
n
T
ab
le
3
an
d
Fig
u
r
e
3
.
T
ab
le
3
.
A
lter
n
ate
So
l
u
tio
n
o
f
T
w
o
C
r
iter
io
n
P
r
o
b
le
m
S
o
l
u
t
i
o
n
i
n
d
e
x
Δ
P
,
k
W
Q
s
um
,
M
V
A
r
1
1
1
3
4
2
.
8
6
2
1
1
3
8
2
.
7
0
3
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1
4
4
2
.
6
4
4
1
1
6
0
2
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6
0
5
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2
0
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2
.
1
7
6
1
2
9
3
0
.
3
8
0
7
1
2
9
8
0
.
0
Fig
u
r
e
3
.
So
lu
tio
n
o
f
t
w
o
-
cr
ite
r
io
n
o
p
ti
m
izatio
n
p
r
o
b
le
m
3
.
3
.
Dis
cu
s
s
io
n
Fo
r
th
e
On
e
-
cr
iter
io
n
p
r
o
b
lem
,
th
e
g
r
ad
ien
t
d
esce
n
t
u
n
d
er
b
ad
in
itia
l
co
n
d
itio
n
s
h
a
s
f
o
u
n
d
th
e
w
o
r
s
e
s
o
lu
tio
n
t
h
an
it
h
ad
w
it
h
t
h
e
o
r
ig
in
al
o
n
e
(
w
it
h
o
u
t
co
m
p
e
n
s
atio
n
)
.
E
v
en
th
e
b
est
s
o
lu
tio
n
i
s
f
o
u
n
d
b
y
t
h
e
g
r
ad
ien
t d
esce
n
t
s
i
g
n
i
f
ica
n
tl
y
co
n
ce
d
es th
e
FF
O
’
s
s
o
l
u
tio
n
a
n
d
th
e
P
SO
’
s
s
o
l
u
tio
n
.
T
h
e
t
wo
b
est s
o
lu
tio
n
s
ar
e
o
b
tain
ed
b
y
t
h
e
F
FO
al
g
o
r
ith
m
w
i
th
th
e
g
r
ad
ien
t
d
esce
n
t
a
n
d
th
e
P
SO
al
g
o
r
ith
m
.
E
x
p
er
im
en
ts
h
a
v
e
s
h
o
wn
th
at
t
h
e
g
r
ad
ien
t
d
escen
t
s
h
o
u
ld
b
e
u
s
ed
to
i
m
p
r
o
v
e
t
h
e
e
f
f
icien
c
y
o
f
t
h
e
F
FO
al
g
o
r
ith
m
.
I
n
t
h
is
ca
s
e,
th
e
r
esu
lt
s
ar
e
clo
s
e
to
th
e
r
es
u
lt
s
o
f
th
e
P
SO
al
g
o
r
ith
m
,
i
n
wh
ich
t
h
e
id
ea
o
f
t
h
e
g
r
ad
ien
t
d
escen
t
i
s
alr
ea
d
y
i
m
p
licitl
y
e
m
b
ed
d
ed
s
in
ce
t
h
e
ag
en
t
s
te
n
d
to
d
iv
id
e
to
th
e
p
o
in
t o
f
t
h
e
b
est s
o
l
u
tio
n
.
W
h
il
e
th
e
FF
O
alg
o
r
it
h
m
ass
u
m
e
s
a
m
o
r
e
co
m
p
lex
p
r
o
ce
s
s
o
f
s
e
lectin
g
t
h
e
n
e
x
t s
tep
d
ir
ec
tio
n
o
f
ea
ch
a
g
en
t.
A
ll
s
o
l
u
tio
n
s
o
f
th
e
o
n
e
-
cr
iter
io
n
p
r
o
b
lem
ex
ce
p
t
th
e
s
o
l
u
ti
o
n
b
ein
g
f
o
u
n
d
b
y
th
e
g
r
ad
ie
n
t
d
escen
t
b
ased
o
n
b
ad
i
n
itial
ap
p
r
o
x
i
m
atio
n
s
tr
ateg
ical
l
y
p
r
o
v
id
e
t
h
e
s
a
m
e
o
u
tco
m
e
b
u
t
th
e
s
o
l
u
ti
o
n
b
ein
g
f
o
u
n
d
b
y
th
e
FF
O
co
m
b
in
at
io
n
an
d
t
h
e
g
r
ad
ien
t r
eq
u
ir
es
f
e
w
er
ca
p
ital
in
v
e
s
t
m
en
ts
i
n
to
C
U
s
.
Fo
r
th
e
t
w
o
-
cr
iter
io
n
o
p
ti
m
i
za
tio
n
p
r
o
b
lem
,
t
h
e
p
r
esen
te
d
r
esu
lts
d
e
m
o
n
s
tr
ate
t
h
at
a
m
o
n
g
an
y
co
u
p
le
o
f
s
o
lu
tio
n
s
o
n
e
s
o
lu
ti
o
n
is
m
u
c
h
b
etter
f
r
o
m
lo
s
s
es
(
m
o
r
e
p
r
o
f
i
tab
le
in
th
e
lo
n
g
-
ter
m
p
er
s
p
ec
tiv
e)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
3
,
J
u
n
e
201
8
:
1
7
5
8
–
1765
1764
T
h
e
s
ec
o
n
d
o
n
e,
o
n
t
h
e
o
th
er
h
a
n
d
,
w
it
h
t
h
e
r
eq
u
ir
ed
C
Us
p
o
w
er
(
r
eq
u
ir
es
f
e
w
er
ca
p
ita
l
in
v
es
t
m
e
n
t
s
i
n
to
C
Us).
T
h
e
m
o
d
el
ap
p
licatio
n
w
it
h
t
w
o
cr
iter
ia
allo
w
ed
to
d
etec
t
th
at
af
ter
th
e
ce
r
tain
lev
e
l
th
e
co
m
p
en
s
atio
n
ef
f
ec
tiv
e
n
e
s
s
is
d
ec
r
ea
s
ed
as
i
t
is
s
ee
n
in
Fig
u
r
e
3
.
Fo
r
in
s
ta
n
ce
,
th
e
s
o
lu
tio
n
№1
is
m
u
ch
b
etter
th
an
s
o
l
u
tio
n
№
2
f
r
o
m
lo
s
s
es
’
d
ec
r
ea
s
e
b
u
t
r
eq
u
ir
es
s
i
g
n
i
f
ican
tl
y
m
o
r
e
ex
p
en
s
es
f
o
r
t
h
e
s
tar
t
-
u
p
in
v
est
m
e
n
t
s
i
n
to
C
U.
T
h
u
s
,
t
h
e
s
ec
o
n
d
o
p
tio
n
ap
p
lied
w
ill
g
i
v
e
m
o
r
e
i
n
f
o
r
m
ati
o
n
to
t
h
e
d
ec
i
s
io
n
m
a
k
er
a
n
d
allo
w
s
m
a
k
i
n
g
a
ch
o
ice
b
ased
o
n
th
e
r
elatio
n
o
f
tactica
l a
n
d
s
tr
ate
g
ic
p
r
io
r
ities
.
T
h
e
FF
O
al
g
o
r
ith
m
h
as
a
co
n
ce
p
tu
al
d
if
f
er
en
ce
f
r
o
m
s
u
c
h
li
k
e
m
o
r
e
w
id
e
s
p
r
ea
d
S
w
ar
m
a
lg
o
r
ith
m
s
as
th
e
P
ar
ticle
S
w
ar
m
Op
t
i
m
izatio
n
,
t
h
e
A
r
ti
f
icial
B
e
e
C
o
lo
n
y
Op
ti
m
izatio
n
,
a
n
d
th
e
An
t
C
o
lo
n
y
Op
ti
m
izatio
n
.
I
n
th
e
P
ar
ticle
S
w
ar
m
Op
ti
m
izatio
n
al
g
o
r
ith
m
,
ea
ch
p
ar
ticle
tak
es
th
e
n
e
x
t
s
tep
b
ein
g
o
r
ien
ted
at
its
s
elf
-
b
est
s
o
l
u
tio
n
as
w
ell
as
at
o
n
e
o
f
th
e
b
est
s
o
lu
tio
n
a
m
o
n
g
all
p
ar
ticles.
I
n
th
e
A
r
t
if
icial
B
ee
C
o
lo
n
y
Op
ti
m
izatio
n
al
g
o
r
ith
m
,
ea
c
h
b
ee
tak
es
t
h
e
s
tep
b
ein
g
o
r
ien
t
ed
at
s
in
g
le
s
o
lu
t
io
n
a
m
o
n
g
s
o
m
e
s
o
l
u
tio
n
s
.
An
d
in
t
h
e
F
ir
ef
l
y
al
g
o
r
ith
m
,
ea
c
h
ag
en
t
p
er
f
o
r
m
s
t
h
e
s
tep
o
r
ie
n
t
ed
at
all
a
g
en
t
s
b
ei
n
g
in
th
e
b
est
p
o
s
itio
n
th
a
n
it
its
el
f
.
T
h
u
s
,
ea
c
h
a
g
e
n
t
h
as
i
t
s
o
w
n
s
u
b
s
et
a
g
en
t
s
a
n
d
is
in
f
l
u
en
ce
d
b
y
th
e
s
e
s
u
b
s
et
ag
e
n
ts
at
a
ce
r
tai
n
s
tep
.
Su
c
h
p
ec
u
liar
it
y
,
o
n
th
e
o
n
e
h
an
d
,
s
lo
w
s
d
o
w
n
th
e
p
r
o
ce
s
s
o
f
alg
o
r
it
h
m
co
n
v
er
g
en
ce
a
n
d
o
n
th
e
o
th
er
h
a
n
d
–
allo
w
s
th
e
al
g
o
r
ith
m
to
tak
e
i
n
to
ac
co
u
n
t
t
h
e
r
eg
io
n
o
f
s
p
a
ce
o
f
s
o
lu
tio
n
s
ea
r
ch
i
n
g
(
d
ec
is
io
n
m
ak
i
n
g
)
w
h
ic
h
ca
n
b
e
ca
lled
as a
n
alter
n
at
iv
e
b
et
w
ee
n
d
if
f
er
en
t
v
ar
ian
ts
o
f
p
r
o
b
lem
s
o
l
u
tio
n
.
T
o
in
cr
ea
s
e
th
e
Fire
f
l
y
al
g
o
r
ith
m
e
f
f
ec
ti
v
en
e
s
s
,
it
is
p
o
s
s
ib
l
e
to
ca
r
r
y
o
u
t
its
ad
j
u
s
t
m
e
n
t
w
it
h
a
lo
ca
l
s
ea
r
ch
,
s
u
c
h
a
s
t
h
e
g
r
ad
ien
t
d
escen
t.
T
h
e
Fire
f
l
y
alg
o
r
it
h
m
g
et
s
t
h
e
s
p
ac
e
o
f
ex
tr
e
m
u
m
,
a
n
d
t
h
e
g
r
ad
ien
t
d
escen
t
s
ea
r
ch
es
th
e
ex
tr
e
m
u
m
i
n
t
h
at
r
e
g
io
n
w
h
er
e
it
h
a
s
s
tar
ted
its
o
p
er
atio
n
.
I
n
o
th
er
w
o
r
d
s
,
t
h
e
Fire
f
l
y
alg
o
r
ith
m
ca
r
r
ies o
u
t a
p
p
r
o
x
i
m
atio
n
s
,
th
e
n
t
h
e
g
r
ad
ien
t d
es
ce
n
t u
s
es t
h
ese
s
o
lu
tio
n
s
as t
h
e
in
itial p
o
s
itio
n
s
.
4.
CO
NCLU
SI
O
N
T
h
e
m
u
lti
-
cr
iter
io
n
p
r
o
b
lem
o
f
r
ea
ctiv
e
p
o
w
er
o
p
ti
m
iz
atio
n
in
a
p
o
w
er
g
r
id
u
s
in
g
h
e
u
r
is
ti
c
alg
o
r
ith
m
s
w
as
co
n
s
id
er
ed
.
T
w
o
cr
iter
ia
w
er
e
co
n
s
id
er
ed
:
m
i
n
i
m
izatio
n
o
f
ac
ti
v
e
p
o
w
er
lo
s
s
es
i
n
t
h
e
p
o
w
er
tr
an
s
m
is
s
io
n
li
n
e
s
an
d
m
in
i
m
a
l c
o
s
ts
o
f
i
n
s
talled
r
ea
cti
v
e
p
o
w
er
co
m
p
e
n
s
atio
n
u
n
it
s
.
T
h
e
Fu
zz
y
lo
g
ic
r
u
le
w
as
d
es
i
g
n
ed
a
n
d
ap
p
lied
to
d
ec
r
ea
s
e
t
h
e
d
i
m
en
s
io
n
o
f
t
h
e
p
r
o
b
le
m
.
T
h
e
f
u
zz
y
lo
g
ic
allo
w
ed
s
elec
ti
n
g
th
e
m
o
r
e
ap
p
r
o
p
r
iate
n
o
d
es
f
o
r
th
e
lo
ca
tio
n
o
f
co
m
p
e
n
s
at
in
g
u
n
it
s
t
ak
in
g
i
n
to
ac
co
u
n
t
th
e
v
o
lta
g
e
d
ev
iat
io
n
s
i
n
t
h
e
n
o
d
e
an
d
ac
tiv
e
p
o
w
er
lo
s
s
es i
n
n
ea
r
b
y
b
r
an
ch
e
s
.
Fire
f
l
y
o
p
ti
m
izat
io
n
al
g
o
r
ith
m
w
as
m
o
d
if
ied
to
ap
p
ly
to
m
u
l
ti
-
cr
iter
io
n
o
p
ti
m
izatio
n
p
r
o
b
le
m
an
d
to
i
m
p
r
o
v
e
e
f
f
ec
ti
v
en
e
s
s
b
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m
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ap
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as c
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State
Ass
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n
t o
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t
h
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Min
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o
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E
d
u
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tio
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Scien
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o
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th
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R
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Fed
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,
P
r
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j
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t 8
.
6
8
0
9
.
2
0
1
7
/8
.
9
.
RE
F
E
R
E
NC
E
S
[1
]
A
.
A
u
g
u
stin
e
,
e
t.
a
l.
,
“
Vo
lt
a
g
e
re
g
u
latio
n
o
f
S
TA
T
C
OM
u
s
in
g
f
u
z
z
y
se
l
f
tu
n
i
n
g
P
I
c
o
n
tr
o
ll
e
r,
”
i
n
Pro
c
.
Circ
u
it
,
Po
we
r a
n
d
C
o
mp
u
ti
n
g
T
e
c
h
n
o
l
o
g
ies
(
ICCPCT
)
,
Na
g
e
r
c
o
il
,
2
0
1
6
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
F
ir
efly
A
lg
o
r
ith
m
t
o
Op
mima
l D
is
tr
ib
u
tio
n
o
f R
ea
ctive
P
o
w
er C
o
mp
en
s
a
tio
n
Un
its
(
V
.
Z.
Ma
n
u
s
o
v)
1765
[2
]
R.
S
.
Ra
o
,
e
t
.
a
l
.
“
P
o
w
e
r
lo
ss
m
in
im
iz
a
ti
o
n
in
d
istri
b
u
ti
o
n
sy
ste
m
u
sin
g
n
e
tw
o
rk
re
c
o
n
f
ig
u
ra
ti
o
n
in
th
e
p
re
se
n
c
e
o
f
d
istri
b
u
ted
g
e
n
e
ra
ti
o
n
,
”
IEE
E
T
r
a
n
sa
c
ti
o
n
s o
n
P
o
we
r S
y
ste
ms
,
v
o
l.
2
8
,
n
o
.
1
,
p
p
.
3
1
7
-
3
2
5
,
2
0
1
3
.
[3
]
C.
A
.
Ra
jan
a
n
d
M
.
R.
M
o
h
a
n
,
“
A
n
Ev
o
lu
ti
o
n
a
ry
P
ro
g
ra
m
m
in
g
Ba
se
d
Tab
u
S
e
a
rc
h
M
e
th
o
d
f
o
r
S
o
lv
in
g
th
e
Un
i
t
Co
m
m
it
m
e
n
t
P
ro
b
lem
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r S
y
ste
ms
,
v
o
l.
1
9
,
n
o
.
1
,
p
p
.
5
7
7
-
5
8
5
,
2
0
0
4
.
[4
]
A
.
H.
M
a
n
ta
wy
,
e
t
a
l.
,
"
In
teg
ra
t
in
g
G
e
n
e
ti
c
A
l
g
o
rit
h
m
s,
T
a
b
u
S
e
a
rc
h
,
a
n
d
S
im
u
late
d
A
n
n
e
a
li
n
g
f
o
r
th
e
Un
it
Co
m
m
it
m
e
n
t
P
ro
b
lem
,
"
in
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r
S
y
ste
ms
,
v
o
l
.
1
4
,
n
o
.
3
,
p
p
.
8
2
9
-
8
3
6
,
1
9
9
9
.
[5
]
D.
De
rv
a
n
i
a
n
d
J.
P
.
R
o
se
ly
n
,
“
Ge
n
e
ti
c
a
lg
o
rit
h
m
b
a
se
d
re
a
c
ti
v
e
p
o
w
e
r
d
isp
a
tch
f
o
r
v
o
lt
a
g
e
sta
b
il
it
y
i
m
p
ro
v
e
m
e
n
t,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
E
lec
trica
l
Po
we
r
&
En
e
rg
y
S
y
ste
ms
,
v
o
l.
3
2
,
n
o
.
1
0
,
p
p
.
1
1
5
1
-
1
1
5
6
,
2
0
1
0
.
[6
]
V
.
Z
.
M
a
n
u
so
v
,
e
t.
a
l.
,
“
Im
p
lem
e
n
tatio
n
o
f
P
o
p
u
lati
o
n
A
lg
o
rit
h
m
s
to
M
i
n
im
ize
P
o
w
e
r
L
o
ss
e
s
a
n
d
Ca
b
le
Cro
ss
-
S
e
c
ti
o
n
i
n
P
o
w
e
r
S
u
p
p
ly
S
y
ste
m
,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
t
ric
a
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
,
v
o
l.
6
,
n
o
.
6
,
p
p
.
2
9
5
5
-
2
9
6
1
,
2
0
1
6
.
[7
]
M
d
.
Im
ra
n
A
z
i
m
a
n
d
M
d
.
F
a
y
z
u
r
Ra
h
m
a
n
,
"
G
e
n
e
ti
c
A
lg
o
rit
h
m
Ba
se
d
Re
a
c
ti
v
e
P
o
w
e
r
M
a
n
a
g
e
m
e
n
t
b
y
S
V
C"
,
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
E
lec
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
,
v
o
l.
4
,
n
o
.
2
,
p
p
.
2
0
0
-
2
0
6
,
2
0
1
4
[8
]
M
.
N.
Da
z
a
h
ra
,
e
t.
a
l.
“
Op
ti
m
a
l
L
o
c
a
ti
o
n
o
f
S
V
C
u
si
n
g
P
a
rti
c
le
S
w
a
r
m
Op
ti
m
i
z
a
ti
o
n
a
n
d
V
o
lt
a
g
e
S
tab
il
it
y
In
d
e
x
e
s,”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
Co
mp
u
ter
E
n
g
i
n
e
e
rin
g
,
v
o
l
.
6
,
n
o
.
6
,
p
p
.
2
5
8
1
-
2
5
8
8
,
2
0
1
6
.
[9
]
J.
J.
Ja
m
i
a
n
,
e
t
a
l.
,
“
A Ne
w P
a
rti
c
le S
wa
r
m
O
p
ti
m
iza
ti
o
n
Tec
h
n
iq
u
e
in
Op
ti
m
izin
g
S
iz
e
o
f
Distrib
u
ted
G
e
n
e
ra
ti
o
n
,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
E
lec
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
,
v
o
l.
1
,
n
o
.
1
,
p
p
.
1
3
7
-
1
4
6
,
2
0
1
2
.
[1
0
]
V
.
Z
.
M
a
n
u
s
o
v
,
e
t.
a
l.
,
“
S
w
a
rm
in
telli
g
e
n
c
e
a
lg
o
rit
h
m
s
f
o
r
th
e
p
ro
b
lem
o
f
th
e
o
p
ti
m
a
l
p
lac
e
m
e
n
t
a
n
d
o
p
e
ra
ti
o
n
c
o
n
tro
l
o
f
re
a
c
ti
v
e
p
o
w
e
r
so
u
rc
e
s
in
to
p
o
w
e
r
g
rid
s,”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
De
sig
n
a
n
d
Na
tu
re
a
n
d
Eco
d
y
n
a
mic
s
,
v
o
l.
1
2
,
n
o
.
1
,
p
p
.
1
0
1
-
1
0
2
,
2
0
1
7
.
[1
1
]
X
.
Ya
n
g
,
“
F
iref
l
y
a
lg
o
rit
h
m
,
S
to
c
h
a
stic
Tes
t
F
u
n
c
ti
o
n
a
n
d
De
sig
n
Op
ti
m
iza
ti
o
n
,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
Bi
o
-
In
sp
ire
d
C
o
mp
u
ta
t
io
n
,
v
o
l.
2
,
n
o
.
2
,
p
p
.
7
8
-
8
4
,
2
0
1
0
.
[1
2
]
Ba
g
h
o
u
ri
M
o
sta
f
a
,
Ch
a
k
k
o
r
S
a
a
d
,
Ha
jrao
u
i
A
b
d
e
rra
h
m
a
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,
“
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ir
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a
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m
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p
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ff
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tero
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e
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s
”
,
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ter
n
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ti
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a
l
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o
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rn
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f
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trica
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r E
n
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g
,
v
o
l.
6
,
n
o
.
3
,
p
p
.
9
1
-
9
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,
2
0
1
7
.
B
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G
RAP
H
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S
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AUTH
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RS
Va
d
i
m
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i
n
o
v
iev
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c
h
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a
n
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so
v
re
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d
th
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B.
S
.
a
n
d
t
h
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h
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d
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re
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tri
c
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l
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e
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rin
g
f
ro
m
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v
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sib
irsk
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e
c
tri
c
Tec
h
n
ica
l
In
stit
u
te,
No
v
o
sib
irsk
,
Ru
ss
ia i
n
1
9
6
3
a
n
d
1
9
8
6
,
re
sp
e
c
ti
v
e
ly
.
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i
s
a
P
r
o
f
e
ss
o
r
o
f
th
e
De
p
a
rtm
e
n
t
o
f
In
d
u
strial
P
o
w
e
r
S
u
p
p
ly
S
y
ste
m
s
in
N
o
v
o
sib
irsk
S
tate
T
e
c
h
n
ica
l
Un
iv
e
rsit
y
,
Ru
ss
ia.
His
c
u
rre
n
t
re
se
a
rc
h
a
re
a
is
a
rti
f
i
c
ial
in
telli
g
e
n
c
e
tec
h
n
o
lo
g
ies
a
n
d
p
ro
b
a
b
il
ist
ic
m
e
th
o
d
s i
n
e
lec
tri
c
p
o
w
e
r
s
y
ste
m
s.
Pa
v
e
l
V
i
k
t
o
r
o
v
ic
h
M
a
tr
e
n
i
n
re
c
e
iv
e
d
th
e
B.
S
.
a
n
d
M
.
S
.
d
e
g
re
e
s
in
f
o
rm
a
ti
o
n
tec
h
n
o
lo
g
ies
f
ro
m
No
v
o
sib
irsk
S
tate
Tec
h
n
ica
l
Un
iv
e
rsit
y
,
No
v
o
sib
irsk
,
Ru
ss
ia
in
2
0
1
2
a
n
d
2
0
1
4
,
re
sp
e
c
ti
v
e
l
y
.
He
is
a
P
h
D
st
u
d
e
n
t
i
n
No
v
o
si
b
irsk
S
tate
T
e
c
h
n
ica
l
Un
iv
e
rsit
y
.
His
m
a
in
in
tere
sts
a
re
re
late
d
to
s
to
c
h
a
stic
o
p
ti
m
iza
ti
o
n
m
e
th
o
d
s
,
d
e
sig
n
a
n
d
d
e
v
e
lo
p
m
e
n
t
in
f
o
r
m
a
ti
o
n
sy
ste
m
s
,
a
n
d
a
rti
f
icia
l
in
telli
g
e
n
c
e
tec
h
n
o
lo
g
ies
in
e
lec
tr
ic p
o
w
e
r
s
y
ste
m
s.
Lo
la
S
h
.
At
a
b
a
e
v
a
re
c
e
iv
e
d
th
e
B.
S
f
ro
m
T
a
ji
k
S
tate
P
e
d
a
g
o
g
ica
l
Un
iv
e
rsit
y
,
Du
sh
a
n
b
e
,
Re
p
u
b
li
c
o
f
T
a
ji
k
sta
n
,
in
1
9
8
2
.
S
h
e
is
a
S
e
n
io
r
L
e
c
tu
re
r,
F
o
re
ig
n
L
a
n
g
u
a
g
e
s
De
p
a
rtm
e
n
t,
No
v
o
sib
irsk
S
tate
T
e
c
h
n
ica
l
Un
iv
e
r
sit
y
(NS
T
U).
He
r
c
u
rre
n
t
d
irec
ti
o
n
o
f
re
se
a
r
c
h
a
c
ti
v
it
ies
:
T
e
a
c
h
in
g
f
o
re
ig
n
lan
g
u
a
g
e
s (E
n
g
li
sh
)
to
T
e
c
h
n
ica
l
Un
iv
e
rsit
y
S
tu
d
e
n
ts.
P
r
o
v
id
i
n
g
t
ra
n
sla
ti
o
n
p
ra
c
ti
c
e
c
l
a
ss
e
s
.
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