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Dec
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201
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29
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1
I
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
6
,
No
.
6
,
Dec
em
b
er
201
6
:
29
5
5
–
29
6
1
2956
2.
P
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p
p
l
y
s
y
s
te
m
s
is
n
ec
ess
ar
y
b
ec
a
u
s
e
tr
an
s
m
is
s
i
o
n
o
f
th
e
r
ea
ctiv
e
cu
r
r
e
n
t
f
r
o
m
ac
ti
v
e
p
o
w
er
s
o
u
r
ce
s
(
g
e
n
er
ato
r
s
)
to
p
o
w
er
co
n
s
u
m
er
s
i
s
u
n
p
r
o
f
ita
b
le.
I
t
is
d
u
e
to
t
h
e
f
ac
t
th
a
t
th
e
r
ea
ctiv
e
c
u
r
r
en
t
o
cc
u
p
ies
p
ar
t
o
f
th
e
cr
o
s
s
s
e
ctio
n
o
f
a
co
n
d
u
cto
r
o
f
elec
tr
ic
p
o
w
er
li
n
es
a
n
d
cr
ea
tes
th
er
ei
n
t
h
e
s
a
m
e
lo
s
s
es
o
f
ac
tiv
e
p
o
w
er
(
I
2
R
)
a
s
t
h
e
ac
ti
v
e
c
u
r
r
en
t
in
cr
ea
s
in
g
s
i
m
u
lta
n
eo
u
s
l
y
t
h
e
cu
r
r
en
t d
en
s
it
y
in
to
t
h
e
co
n
d
u
cto
r
(
A
∙
m
m
2
)
.
I
n
t
h
is
p
ap
er
,
th
e
ca
lcu
la
tio
n
s
w
er
e
m
ad
e
f
o
r
a
p
o
w
er
s
u
p
p
l
y
g
r
ip
o
f
o
n
e
s
ec
tio
n
o
f
i
n
ter
n
a
l
co
n
s
u
m
p
tio
n
s
u
b
s
tatio
n
o
f
an
in
d
u
s
tr
ial
e
n
ter
p
r
is
e,
w
h
er
e
t
h
e
cli
m
atic
co
n
d
itio
n
s
f
o
r
E
q
u
atio
n
u
ip
m
en
t
ar
e
s
tr
ictl
y
r
e
g
u
la
ted
.
Mo
to
r
s
o
f
p
u
m
p
s
,
f
a
n
s
an
d
co
m
p
r
es
s
o
r
ar
e
th
e
m
ai
n
co
n
s
u
m
er
s
,
an
d
a
l
en
g
t
h
o
f
ca
b
le
li
n
es
ar
e
s
ev
er
al
h
u
n
d
r
ed
s
o
f
m
eter
s
.
T
h
e
g
eo
g
r
ap
h
ical
ar
r
an
g
e
m
e
n
t o
f
g
r
id
’
s
ele
m
e
n
ts
d
ep
en
d
s
o
n
th
e
ar
r
an
g
e
m
e
n
t
o
f
th
e
p
r
o
ce
s
s
i
n
g
E
q
u
a
tio
n
u
ip
m
en
t,
s
o
,
it is
i
m
p
o
s
s
ib
le
to
r
ed
u
ce
th
e
le
n
g
t
h
o
f
t
h
e
s
u
p
p
l
y
.
I
n
th
i
s
s
t
u
d
y
,
t
h
e
p
o
w
er
s
u
p
p
l
y
s
y
s
te
m
o
f
a
u
r
an
i
u
m
p
r
o
d
u
ctio
n
p
la
n
t
i
n
th
e
to
w
n
o
f
An
g
ar
s
k
i
s
co
n
s
id
er
ed
.
T
h
e
p
o
w
er
s
u
p
p
ly
s
y
s
te
m
r
ep
r
ese
n
ts
4
0
0
Vo
ltag
es
s
u
b
s
tat
io
n
co
m
p
r
is
i
n
g
4
s
ec
tio
n
s
,
an
d
th
e
ar
r
an
g
e
m
en
t o
f
ea
ch
s
ec
tio
n
i
s
r
ad
ial.
T
h
e
p
o
w
er
-
s
u
p
p
l
y
s
y
s
te
m
o
f
th
e
ea
ch
s
ec
tio
n
h
as
1
0
p
o
w
er
d
is
tr
ib
u
tio
n
p
o
in
ts
,
2
p
u
m
p
s
E
q
u
atio
n
u
ip
p
ed
w
ith
m
o
to
r
s
o
f
1
3
2
k
W
an
d
2
s
u
p
p
l
y
l
in
e
s
f
o
r
th
e
co
m
p
r
e
s
s
o
r
s
.
E
v
er
y
s
u
p
p
ly
li
n
e
co
n
s
i
s
ts
o
f
1
3
co
m
p
r
ess
o
r
s
(
9
k
W
)
th
a
t
ar
e
s
u
p
p
lied
w
ith
a
r
ib
b
o
n
ca
b
le.
A
cti
v
e
p
o
w
er
lo
s
s
es
i
n
tr
an
s
m
i
s
s
io
n
lin
e
s
o
f
th
is
n
e
t
w
o
r
k
ar
e
h
i
g
h
d
u
e
to
t
h
e
n
et
w
o
r
k
h
a
v
i
n
g
a
lo
t
o
f
b
r
a
n
ch
e
s
a
n
d
lar
g
e
d
is
ta
n
ce
s
b
etw
ee
n
t
h
e
n
o
d
es
.
I
t
i
s
s
u
g
g
e
s
ted
to
i
n
s
tall
R
P
C
U
s
c
lo
s
e
to
t
h
e
p
o
w
er
d
is
tr
ib
u
tio
n
p
o
in
ts
,
c
lo
s
e
to
co
n
tr
o
l
ca
b
in
ets
o
f
p
u
m
p
s
a
n
d
clo
s
e
to
th
e
co
n
tr
o
l
r
ac
k
o
f
th
e
f
ir
s
t
co
m
p
r
es
s
o
r
at
th
e
s
u
p
p
l
y
lin
es.
T
h
e
ca
lcu
latio
n
o
f
m
a
x
i
m
u
m
lo
ad
s
h
o
w
ed
th
at
n
o
w
r
atio
o
f
co
n
s
u
m
p
tio
n
o
f
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
w
er
s
o
f
th
e
s
y
s
te
m
(
tg
φ)
is
0
.
5
5
.
T
h
is
f
ac
t
in
d
icate
s
th
e
lo
w
e
n
er
g
y
e
f
f
icie
n
c
y
o
f
s
u
p
p
l
y
s
y
s
te
m
u
n
d
er
co
n
s
id
er
atio
n
.
2
.
2
.
T
he
m
a
t
he
m
a
t
ica
l
m
o
del
A
p
p
licatio
n
o
f
t
h
e
f
ir
s
t
w
a
y
r
esu
lt
s
in
to
u
n
lo
ad
th
e
n
et
w
o
r
k
b
y
r
ea
cti
v
e
p
o
w
er
an
d
co
n
s
E
q
u
atio
n
u
e
n
tl
y
to
i
n
cr
e
asin
g
ac
ti
v
e
p
o
w
er
lo
s
s
e
s
i
n
t
h
e
n
et
w
o
r
k
b
y
r
ea
s
o
n
o
f
r
ea
ctiv
e
p
o
w
er
tr
an
s
m
is
s
io
n
in
t
h
e
ca
b
le
li
n
es
.
T
h
e
s
ec
o
n
d
m
et
h
o
d
lead
s
u
s
to
f
o
r
m
u
late
a
n
o
p
ti
m
izat
io
n
p
r
o
b
lem
.
T
o
cr
ea
te
a
m
a
th
e
m
atica
l
m
o
d
el
o
f
th
e
o
p
tim
izatio
n
p
r
o
b
lem
,
it
is
n
ec
ess
ar
y
to
d
ef
i
n
e,
an
o
p
ti
m
izatio
n
cr
iter
io
n
,
co
n
tr
o
lled
v
ar
iab
les,
a
n
d
co
n
s
tr
ain
ts
.
T
h
e
m
ai
n
ai
m
o
f
t
h
e
o
p
tim
izatio
n
is
to
m
i
n
i
m
ize
a
ctiv
e
p
o
w
er
lo
s
s
e
s
.
T
h
e
d
ep
en
d
en
t v
ar
iab
les ar
e
th
e
v
alu
e
s
o
f
t
h
e
R
P
C
U
p
o
w
er
in
th
e
n
o
d
es.
Z
1
(
Q
x
)
=
c
Q
Q
∑
(
Q
x
)
+
c
P
T
Δ
P
(
Q
x
)
→
m
in
,
(
1
)
0
≤
Q
xi
≤
Q
max
i
,
i
=
1
,
…
,
n
.
(
2
)
T
h
e
co
m
p
o
n
e
n
ts
i
n
th
e
E
q
u
ati
o
n
1
ar
e
d
eter
m
in
ed
as
f
o
llo
ws:
a.
Q
x
= {
Q
x
1
,
Q
x
2
,
…,
Q
xn
};
b.
Q
xi
p
o
w
er
o
f
th
e
R
P
C
U
in
i
-
th
j
u
n
ctio
n
;
c.
Q
max
i
is
r
ea
ctiv
e
p
o
w
er
o
f
lo
a
d
in
i
-
t
h
j
u
n
ct
io
n
;
d.
n
is
a
q
u
an
tit
y
o
f
co
n
s
id
er
ed
ju
n
ct
io
n
s
a
v
ailab
le
f
o
r
in
s
tal
lat
io
n
o
f
th
e
R
P
C
Us
;
e.
c
Q
is
co
s
t o
f
t
h
e
R
P
C
Us (
p
er
v
o
lt
-
a
m
p
er
e)
;
f.
Q
∑
(
Q
x
)
is
s
u
m
Q
xi
,
i
=
1
,
…
,
n
;
g.
с
P
i
s
co
s
t o
f
elec
tr
ic
lo
s
s
e
s
;
h.
Δ
P
(
Q
x
)
is
to
tal
lo
s
s
e
s
o
f
ac
ti
v
e
p
o
w
er
w
it
h
i
n
a
n
et
w
o
r
k
u
s
in
g
p
o
w
er
s
o
f
R
P
C
U
d
e
f
in
ed
b
y
Q
x
.
i.
T
is
a
co
n
s
id
er
ed
o
p
er
atio
n
in
t
er
v
al
ex
p
r
ess
ed
i
n
h
o
u
r
s
at
m
a
x
i
m
u
m
lo
ad
.
I
n
ad
d
itio
n
,
th
e
a
llo
ca
tio
n
o
f
th
e
R
P
C
U
s
clo
s
e
to
t
h
e
d
is
tr
ib
u
tio
n
p
o
i
n
ts
al
lo
w
s
r
ed
u
cin
g
cr
o
s
s
-
s
ec
tio
n
s
o
f
th
e
s
u
p
p
l
y
c
ab
les.
Ob
v
io
u
s
l
y
,
t
h
e
c
u
r
r
en
t
d
en
s
it
y
i
n
t
h
e
p
o
w
er
li
n
es
is
r
ed
u
ce
d
b
y
t
h
e
d
ee
p
co
m
p
e
n
s
at
io
n
.
T
h
e
co
n
d
u
cto
r
cr
o
s
s
-
s
ec
tio
n
is
s
elec
ted
o
n
th
e
b
asis
o
f
r
elatio
n
s
h
ip
F
=
I
/
j
econ
(
j
econ
is
a
ce
r
tain
ec
o
n
o
m
ic
cu
r
r
e
n
t
d
e
n
s
it
y
.
As
t
h
e
cu
r
r
en
t
d
ec
r
ea
s
es,
t
h
e
cr
o
s
s
-
s
ec
tio
n
o
f
t
h
e
co
n
d
u
cto
r
s
ca
n
b
e
d
ec
r
ea
s
ed
to
o
.
A
t th
e
s
a
m
e
ti
m
e,
cu
r
r
en
ts
i
n
s
w
itc
h
i
n
g
d
ev
i
ce
s
ar
e
r
ed
u
ce
d
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T
h
e
m
ain
co
n
s
u
m
er
s
o
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t
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p
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m
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Z
2
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x
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c
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Q
x
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P
T
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Q
x
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T
h
e
v
alu
e
Z
2
(
Q
x
)
ar
e
ev
al
u
ate
d
b
y
t
h
e
f
o
llo
w
i
n
g
s
ch
e
m
e:
1.
C
alcu
late
th
e
c
u
r
r
en
t
s
,
v
o
lta
g
e
s
in
t
h
e
g
r
id
,
an
d
ac
ti
v
e
p
o
w
er
lo
s
s
es
Δ
P
(
Q
x
)
u
s
in
g
t
h
e
in
i
tial
cr
o
s
s
-
s
ec
t
io
n
s
2.
Su
m
m
ar
ize
p
o
w
er
s
o
f
t
h
e
R
P
C
Us
Q
∑
(Q
x
)
3.
De
ter
m
i
n
e
m
in
i
m
al
p
o
s
s
ib
le
cr
o
s
s
-
s
ec
tio
n
o
f
t
h
e
m
ain
ca
b
le
lin
es o
f
th
e
g
r
id
an
d
f
i
n
d
th
e
t
o
tal
v
o
lu
m
e
V
(Q
x
).
4.
R
ec
alcu
late
th
e
v
al
u
e
o
f
Δ
P
(
Q
x
)
ag
ain
u
s
i
n
g
th
e
n
e
w
cr
o
s
s
-
s
ec
tio
n
s
,
s
i
n
ce
ac
ti
v
e
p
o
w
er
lo
s
s
es c
h
a
n
g
e
af
ter
ch
a
n
g
in
g
o
f
cr
o
s
s
-
s
ec
tio
n
s
.
5.
Fin
all
y
,
d
eter
m
i
n
e
t
h
e
Z
2
(Q
x
)
u
s
i
n
g
E
q
u
atio
n
3.
6.
T
h
e
co
n
n
ec
tio
n
b
et
w
ee
n
th
e
al
g
o
r
ith
m
s
a
n
d
th
e
o
p
ti
m
izatio
n
p
r
o
b
lem
3.
E
VO
L
U
T
I
O
N
ARY
AND
S
WARM
O
P
T
I
M
I
Z
AT
I
O
N
3
.
1
.
E
v
o
lutio
na
ry
a
nd
Sw
a
rm
o
p
t
i
m
iza
t
io
n
T
h
e
p
o
p
u
latio
n
-
b
ased
alg
o
r
it
h
m
s
u
s
i
n
g
p
r
i
n
cip
les
o
f
n
at
u
r
e
d
em
o
n
s
tr
ate
t
h
e
h
i
g
h
est
p
er
f
o
r
m
an
ce
a
m
o
n
g
t
h
e
o
th
er
s
to
c
h
asti
c
o
p
tim
izatio
n
m
et
h
o
d
s
.
E
v
o
lu
tio
n
ar
y
a
n
d
s
w
ar
m
m
et
h
o
d
s
ar
e
class
if
ied
as
so
-
ca
lled
p
o
p
u
latio
n
-
b
ased
m
eth
o
d
s
s
i
n
ce
t
h
e
y
u
s
e
s
y
s
te
m
s
o
f
a
g
en
ts
.
T
h
e
ter
m
ag
e
n
t
c
an
b
e
d
ef
i
n
ed
as
a
p
o
in
t
X
in
to
th
e
d
ec
is
io
n
s
p
ac
e
o
f
th
e
o
p
tim
izat
io
n
p
r
o
b
lem
d
ef
in
ed
as
f
(
X
)
→
ex
tr
.
W
e
d
iv
id
e
E
v
o
lu
t
io
n
ar
y
an
d
S
w
ar
m
m
et
h
o
d
s
s
i
n
ce
th
e
o
p
ti
m
izatio
n
p
r
o
ce
s
s
m
a
y
b
e
ev
o
lu
tio
n
ar
y
o
r
s
w
ar
m
i
n
g
[
8
]
.
T
h
e
ev
o
lu
t
io
n
ar
y
p
r
o
ce
s
s
is
b
a
s
ed
o
n
th
e
cr
ea
ti
o
n
t
h
e
n
e
w
p
o
p
u
lat
io
n
s
at
e
v
e
r
y
n
e
w
s
tep
ta
k
i
n
g
i
n
to
ac
co
u
n
t
t
h
e
ex
p
er
ien
ce
(
a
n
u
m
b
er
o
f
last
s
o
l
u
tio
n
s
o
f
t
h
e
o
p
tim
izat
io
n
p
r
o
b
lem
a
n
d
th
e
s
o
lu
t
io
n
s
’
q
u
al
ities
)
o
b
tain
ed
b
y
th
e
p
r
ev
io
u
s
s
tep
s
,
s
o
th
i
s
p
r
o
ce
s
s
s
i
m
ilar
to
th
e
n
at
u
r
a
l
s
elec
tio
n
.
T
h
e
S
w
ar
m
p
r
o
ce
s
s
is
b
ased
o
n
th
e
m
o
v
e
m
en
ts
o
f
t
h
e
ag
en
t
s
i
n
to
th
e
d
ec
is
io
n
s
p
ac
e
u
s
i
n
g
a
n
u
m
b
er
o
f
r
u
le
s
an
d
t
h
e
in
ter
ac
t
io
n
s
b
et
w
ee
n
th
e
a
g
en
ts
.
I
n
co
n
tr
ast
to
ev
o
lu
tio
n
ar
y
al
g
o
r
ith
m
s
,
t
h
e
ag
en
t
s
ar
e
n
o
t
cr
ea
ted
an
d
n
o
t
d
estro
y
ed
an
d
th
e
s
w
a
r
m
p
o
p
u
latio
n
h
as
n
o
t
an
y
ce
n
tr
alize
d
co
n
tr
o
l s
y
s
te
m
.
T
h
e
co
m
p
ar
is
o
n
ev
o
l
u
tio
n
ar
y
an
d
s
w
ar
m
m
et
h
o
d
s
ar
e
p
r
esen
te
d
in
T
ab
le
1
.
T
ab
le
1
.
E
v
o
lu
tio
n
ar
y
a
n
d
S
war
m
Op
ti
m
izatio
n
F
e
a
t
u
r
e
Ev
o
l
u
t
i
o
n
a
r
y
S
w
a
r
m
I
n
sp
i
r
a
t
i
o
n
N
a
t
u
r
a
l
se
l
e
c
t
i
o
n
C
o
l
l
e
c
t
i
v
e
b
e
h
a
v
i
o
r
o
f
b
e
e
s,
f
l
o
c
k
s,
a
n
t
s
,
f
i
s
h
e
s,
e
t
c
.
Ea
c
h
s
t
e
p
C
r
e
a
t
i
n
g
n
e
w
p
o
p
u
l
a
t
i
o
n
s
a
t
e
v
e
r
y
n
e
w
st
e
p
M
o
v
e
me
n
t
s u
s
i
n
g
a
n
u
mb
e
r
o
f
r
u
l
e
s a
n
d
a
n
i
n
d
i
r
e
c
t
e
x
c
h
a
n
g
e
o
f
d
a
t
a
b
e
t
w
e
e
n
t
h
e
a
g
e
n
t
s
C
o
n
t
r
o
l
C
e
n
t
r
a
l
i
z
e
d
c
o
n
t
r
o
l
sy
st
e
m
D
e
c
e
n
t
r
a
l
i
z
e
d
c
o
n
t
r
o
l
sy
st
e
m
Ex
a
mp
l
e
s
G
e
n
e
t
i
c
a
l
g
o
r
i
t
h
m
G
e
n
e
t
i
c
p
r
o
g
r
a
mm
i
n
g
D
i
f
f
e
r
e
n
t
i
a
l
e
v
o
l
u
t
i
o
n
P
a
r
t
i
c
l
e
sw
a
r
m o
p
t
i
mi
z
a
t
i
o
n
A
r
t
i
f
i
c
i
a
l
b
e
e
c
o
l
o
n
y
o
p
t
i
m
i
z
a
t
i
o
n
A
n
t
c
o
l
o
n
y
o
p
t
i
mi
z
a
t
i
o
n
B
a
t
a
l
g
o
r
i
t
h
m
T
h
e
m
ai
n
ad
v
a
n
ta
g
e
o
f
th
e
p
o
p
u
latio
n
alg
o
r
ith
m
s
is
t
h
e
ab
ilit
y
to
ex
p
lo
r
e
th
e
d
ec
is
io
n
s
p
ac
e
au
to
m
at
icall
y
r
e
g
ar
d
less
o
f
it
s
d
im
e
n
s
io
n
an
d
to
p
o
lo
g
y
,
it
r
esu
lt
s
at
r
ath
er
q
u
ic
k
l
y
f
i
n
d
in
g
g
o
o
d
s
o
lu
tio
n
s
.
I
n
th
is
p
ap
er
,
th
e
Gen
etic
alg
o
r
ith
m
an
d
th
e
P
ar
ticle
S
war
m
Op
ti
m
izat
io
n
alg
o
r
it
h
m
s
ar
e
ap
p
lied
.
T
h
e
d
escr
ip
tio
n
s
d
etailed
o
f
th
e
s
e
alg
o
r
ith
m
s
ar
e
ea
s
y
to
f
i
n
d
b
y
t
h
e
liter
at
u
r
e
(
G
A
[
9
]
,
[
1
0
]
,
S
w
ar
m
I
n
telli
g
e
n
ce
[
1
1
]
,
P
SO [
1
2
-
1
3
]
)
,
th
er
ef
o
r
e,
th
is
p
ap
er
g
i
v
es t
h
e
b
r
ief
d
escr
ip
tio
n
w
ith
o
u
t t
h
e
m
at
h
e
m
atic
al
m
o
d
els.
3
.
2
.
T
he
G
enet
ic
a
lg
o
rit
h
m
T
h
e
GA
s
tar
ted
to
b
e
u
s
ed
f
o
r
s
o
lv
in
g
o
p
ti
m
izatio
n
p
r
o
b
le
m
s
i
n
1
9
6
0
-
70
af
ter
r
esear
ch
es
o
f
I
n
g
o
R
ec
h
e
n
b
er
g
an
d
J
o
h
n
Ho
llan
d
[
1
0
]
.
GA
is
b
ased
o
n
th
e
p
r
in
cip
les
o
f
t
h
e
n
at
u
r
al
s
elec
ti
o
n
:
in
h
er
itan
ce
(
th
e
tr
an
s
itio
n
c
h
ar
ac
ter
is
tics
f
r
o
m
p
ar
en
t
to
p
r
o
g
en
y
)
,
m
u
tatio
n
(
th
e
s
u
d
d
en
c
h
an
g
e
c
h
ar
ac
ter
is
tics
)
,
s
elec
tio
n
(
th
e
ch
o
ice
o
f
m
o
r
e
s
u
i
tab
le
u
n
its
)
an
d
cr
o
s
s
in
g
o
v
er
(
th
e
in
ter
c
h
an
g
e
o
f
co
r
r
esp
o
n
d
in
g
ch
ar
a
cter
is
tics
)
[
9
-
1
0
]
.
I
t
is
th
e
e
v
o
lu
t
io
n
ar
y
al
g
o
r
ith
m
.
So
lu
tio
n
s
o
f
t
h
e
o
p
ti
m
izatio
n
p
r
o
b
lem
ar
e
r
ec
o
r
d
ed
as
v
ec
to
r
s
o
f
v
al
u
es
an
d
ca
lled
ch
r
o
m
o
s
o
m
e
s
.
Ho
w
e
v
e
r
,
w
e
s
u
g
g
est
u
s
i
n
g
th
e
ter
m
a
g
en
t
f
o
r
u
n
if
o
r
m
it
y
.
T
h
e
ter
m
ag
en
t
i
s
co
m
m
o
n
l
y
u
s
ed
in
t
h
e
f
ield
o
f
th
e
S
war
m
I
n
telli
g
en
ce
,
b
u
t
it
ca
n
also
b
e
ap
p
lied
in
d
escr
ib
in
g
th
e
ev
o
l
u
tio
n
ar
y
alg
o
r
ith
m
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
6
,
No
.
6
,
Dec
em
b
er
201
6
:
29
5
5
–
29
6
1
2958
T
h
e
p
r
o
ce
s
s
o
f
o
p
ti
m
iza
tio
n
s
i
m
u
late
s
t
h
e
n
at
u
r
al
s
elec
tio
n
.
E
v
er
y
a
g
en
t
X
i
n
t
h
e
p
o
p
u
latio
n
i
s
ev
alu
a
ted
b
y
th
e
v
al
u
e
o
f
o
p
ti
m
izatio
n
cr
iter
io
n
,
ca
lcu
lated
as
f
(
X
)
.
First,
th
e
r
a
n
d
o
m
p
o
p
u
latio
n
is
g
en
er
ated
an
d
f
o
r
ea
c
h
X
v
al
u
e
f
(
X
)
is
ca
lcu
lated
.
T
h
en
th
e
a
lg
o
r
it
h
m
s
elec
ts
t
h
e
a
g
en
ts
f
o
r
th
e
n
e
x
t
it
er
atio
n
,
tak
i
n
g
i
n
to
ac
co
u
n
t t
h
e
f
(
X
)
o
f
ea
c
h
ag
e
n
t.
Selecte
d
ag
e
n
ts
ar
e
co
m
b
i
n
ed
an
d
ch
a
n
g
ed
r
an
d
o
m
l
y
,
s
o
th
e
n
e
w
p
o
p
u
latio
n
is
cr
ea
ted
an
d
f
o
r
ea
ch
n
e
w
a
g
en
t
f
(
X
)
is
ev
alu
a
ted
.
W
h
ile
th
e
s
to
p
cr
iter
io
n
is
n
o
t
m
et,
t
h
e
s
el
ec
tio
n
,
co
m
b
in
i
n
g
,
etc.
ar
e
r
e
-
s
tar
t.
3
.
3
.
T
he
P
a
rt
icle
Sw
a
r
m
O
pti
m
i
za
t
io
n a
l
g
o
ri
t
h
m
T
h
e
P
ar
ticle
S
w
ar
m
Op
ti
m
izat
io
n
al
g
o
r
ith
m
i
s
a
o
n
e
o
f
th
e
m
o
s
t c
o
m
m
o
n
l
y
u
s
ed
S
w
ar
m
I
n
telli
g
e
n
c
e
alg
o
r
ith
m
s
.
P
SO
b
ased
o
n
a
b
ir
d
f
lo
ck
s
b
eh
a
v
io
r
an
d
it
w
as
d
ev
elo
p
ed
b
y
J
.
Ken
n
ed
y
a
n
d
R
.
E
b
er
h
ar
t
[
1
2
]
.
B
ir
d
f
lo
ck
ac
ts
co
o
r
d
in
ated
ac
co
r
d
in
g
to
a
n
u
m
b
er
o
f
s
i
m
p
l
e
r
u
les.
E
v
er
y
b
ir
d
(
p
ar
ticle)
c
o
o
r
d
in
ates
th
e
o
w
n
m
o
v
e
m
e
n
ts
w
i
th
t
h
e
f
lo
ck
s
.
I
n
th
e
P
SO a
lg
o
r
it
h
m
,
e
v
er
y
p
ar
t
icle
is
d
en
o
ted
b
y
co
o
r
d
in
ates
X
an
d
b
y
t
h
e
v
alu
e
o
f
t
h
e
cr
iter
io
n
f
(
X
)
.
T
h
e
v
ec
t
o
r
X
is
t
h
e
p
o
s
itio
n
o
f
a
p
ar
ticl
e,
an
d
a
v
ec
to
r
V
is
a
v
elo
cit
y
o
f
a
p
ar
ticle.
I
n
itial
v
alu
e
s
o
f
X
a
n
d
V
ar
e
r
an
d
o
m
.
T
h
e
v
ec
to
r
s
X
an
d
V
o
f
all
p
ar
ticles ar
e
u
p
d
ated
ac
co
r
d
in
g
to
a
n
u
m
b
er
o
f
r
u
le
s
u
s
i
n
g
th
e
b
est
p
o
s
itio
n
o
f
a
p
ar
ticle,
th
e
b
est
p
o
s
itio
n
o
f
th
e
w
h
o
le
s
w
ar
m
,
t
h
e
in
er
tia
w
ei
g
h
ts
o
f
t
h
e
p
ar
ticle
s
an
d
th
e
s
to
c
h
asti
c
d
e
v
iatio
n
s
.
3
.
4
.
P
SO
pa
ra
m
et
er
s
elec
t
io
n
T
h
e
P
SO
alg
o
r
ith
m
s
h
a
s
3
n
u
m
b
er
o
f
b
e
h
av
io
u
r
al
p
ar
a
m
e
ter
s
α
1
,
α
2
,
ω
an
d
v
max
,
w
h
ic
h
allo
w
to
co
n
tr
o
l
s
p
ee
d
,
p
er
f
o
r
m
a
n
ce
an
d
o
th
er
f
ea
tu
r
es
o
f
t
h
e
p
r
o
ce
s
s
o
f
th
e
P
SO
o
p
er
atio
n
[
1
3
-
1
4
]
T
h
e
n
ec
ess
it
y
o
f
tu
n
in
g
t
h
e
v
al
u
es
o
f
t
h
e
p
ar
am
eter
s
f
o
r
a
ta
s
k
s
o
lv
ed
i
s
a
s
ig
n
i
f
ica
n
t
i
m
p
er
f
ec
tio
n
o
f
th
e
P
SO
f
o
r
its
h
i
g
h
ef
f
ec
tiv
e
r
ea
liza
tio
n
[
1
3
]
,
[
1
5
]
.
Ma
n
u
al
c
h
a
n
g
i
n
g
o
f
t
h
e
p
ar
am
eter
s
a
n
d
u
s
a
g
e
o
f
s
ev
er
al
p
r
ed
ef
in
ed
s
et
s
o
f
t
h
e
p
ar
am
eter
s
ar
e
t
h
e
ea
s
ie
s
t
an
d
th
e
m
o
s
t
p
r
ev
ale
n
t
w
a
y
s
to
th
e
p
ar
a
m
eter
s
s
elec
ti
o
n
.
T
h
e
f
ir
s
t
w
a
y
r
E
q
u
atio
n
u
ir
e
s
a
lo
w
o
f
ti
m
e
a
n
d
d
o
es
n
o
t
e
n
s
u
r
e
t
h
e
e
f
f
ec
ti
v
e
s
o
lu
tio
n
.
T
h
e
s
ec
o
n
d
w
a
y
c
o
n
s
is
ts
in
ch
o
o
s
i
n
g
th
e
b
est
p
ar
a
m
eter
s
a
m
o
n
g
t
h
e
s
ev
er
al
u
s
ab
le
s
ets
b
y
ex
p
er
i
m
e
n
ts
.
T
h
is
w
a
y
also
li
m
it
s
d
o
es
n
o
t
en
s
u
r
e
th
e
ef
f
ec
tiv
e
s
o
lu
tio
n
s
i
n
ce
it
is
li
m
ited
b
y
s
et
s
e
ts
o
f
t
h
e
p
ar
a
m
eter
u
s
ed
.
T
h
e
r
esear
ch
[
1
3
]
p
r
o
v
id
es
an
o
v
er
v
ie
w
o
f
s
t
u
d
ies
th
a
t
d
ea
l
w
i
th
t
u
n
in
g
P
SO
p
ar
am
e
ter
s
.
I
t
p
o
in
ts
o
u
t
a
p
r
i
m
iti
v
e
n
es
s
an
d
lo
w
e
f
f
icien
c
y
o
f
m
an
u
al
tu
n
in
g
,
b
u
t
at
t
h
e
s
a
m
e
ti
m
e,
i
t
cr
iticizes
m
o
r
e
co
m
p
le
x
m
et
h
o
d
s
f
o
r
t
h
eir
r
a
n
g
e
o
f
ap
p
lic
atio
n
li
m
ita
tio
n
a
n
d
ex
ce
s
s
iv
e
alg
o
r
it
h
m
co
m
p
lica
t
io
n
.
T
h
er
ef
o
r
e,
in
th
i
s
r
esear
c
h
,
a
tec
h
n
ic
o
f
t
h
e
m
eta
-
o
p
ti
m
izatio
n
[
1
3
-
1
4
]
w
as
ap
p
lied
.
T
h
e
m
eta
-
o
p
ti
m
izatio
n
allo
w
s
t
u
n
in
g
t
h
e
b
eh
av
io
u
r
al
p
ar
am
eter
s
au
to
m
atica
ll
y
.
4.
E
XP
E
R
I
M
E
NT
AND
A
NAL
YSI
S
4
.
1
.
Appl
ica
t
io
n o
f
t
he
po
pu
la
t
io
n
-
ba
s
ed
o
pti
m
iza
t
io
n
T
h
e
in
ter
ac
tio
n
o
f
t
h
e
alg
o
r
it
h
m
an
d
t
h
e
m
o
d
els
o
f
th
e
o
p
ti
m
izatio
n
p
r
o
b
lem
s
(
E
q
u
atio
n
1
-
3
)
ca
n
b
e
d
escr
ib
ed
b
y
th
e
s
i
m
p
le
s
c
h
e
m
e.
Fo
r
ea
ch
alg
o
r
ith
m
iter
atio
n
an
d
ea
ch
ag
e
n
t o
f
p
o
p
u
latio
n
:
1.
T
h
e
alg
o
r
ith
m
g
i
v
es t
h
e
n
e
w
a
g
en
t
’
s
p
o
s
itio
n
X
.
2.
T
h
e
m
o
d
el
o
f
a
p
o
w
er
g
r
id
g
et
s
th
e
X
a
n
d
m
ap
p
in
g
it
to
t
h
e
v
ec
to
r
Q
x
an
d
th
e
v
al
u
e
o
f
t
h
e
cr
iter
io
n
Z
1
(
Q
x
)
o
r
Z
2
(
Q
x
)
is
d
eter
m
i
n
ed
.
3.
T
h
e
alg
o
r
ith
m
g
i
v
es t
h
e
v
al
u
e
th
e
cr
iter
io
n
as
f
(
X
).
4.
W
h
en
t
h
e
s
tep
s
1
-
3
ar
e
ca
r
r
ie
d
o
u
t
f
o
r
all
ag
en
ts
,
t
h
e
p
o
s
iti
o
n
s
o
f
t
h
e
ag
e
n
t
s
ar
e
ch
an
g
ed
b
y
P
SO
o
r
th
e
n
e
w
p
o
p
u
latio
n
o
f
t
h
e
a
g
en
t
s
a
r
e
g
en
er
ated
b
y
G
A
; a
n
d
t
h
e
p
r
o
ce
s
s
is
r
ep
ea
ted
.
T
h
u
s
,
th
e
m
eth
o
d
o
f
ca
lcu
la
ti
o
n
o
f
Z
1
(
Q
x
)
an
d
Z
2
(
Q
x
)
ca
n
b
e
an
y
o
n
e,
r
eg
ar
d
les
s
o
f
th
e
o
p
ti
m
izat
io
n
alg
o
r
ith
m
an
d
th
e
o
p
ti
m
izati
o
n
alg
o
r
ith
m
is
i
n
d
ep
en
d
en
t
o
f
it.
T
h
is
ap
p
r
o
ac
h
allo
w
s
u
s
to
ap
p
ly
d
if
f
er
en
t
o
p
tim
izatio
n
m
et
h
o
d
s
ea
s
il
y
an
d
q
u
ick
l
y
.
T
h
er
e
ar
e
n
o
t
clo
s
e
r
elatio
n
s
h
ip
s
b
et
w
ee
n
th
e
m
o
d
el
o
f
t
h
e
op
tim
izatio
n
p
r
o
b
lem
a
n
d
t
h
e
o
p
tim
izatio
n
alg
o
r
it
h
m
s
.
I
t
i
s
p
o
s
s
ib
le
d
u
e
to
t
h
e
f
le
x
ib
ilit
y
an
d
ad
ap
tab
ilit
y
o
f
p
o
p
u
latio
n
-
b
ased
al
g
o
r
ith
m
s
t
o
th
e
co
n
d
itio
n
s
o
f
t
h
e
o
p
ti
m
i
za
tio
n
p
r
o
b
le
m
s
.
T
h
u
s
,
t
h
e
ca
l
cu
latio
n
o
f
a
p
o
w
er
g
r
id
ca
n
b
e
ca
r
r
ied
o
u
t
m
ea
n
s
a
s
p
ec
i
alize
d
s
o
f
t
w
ar
e
a
s
th
e
a
n
al
y
s
i
s
o
f
r
elatio
n
s
h
ip
s
b
et
w
e
en
k
e
y
i
n
d
icato
r
s
o
f
th
e
g
r
id
an
d
v
alu
e
s
o
f
v
ar
iab
l
es
an
d
f
in
d
i
n
g
th
e
o
p
ti
m
al
m
o
d
e
o
f
th
e
g
r
id
ca
n
b
e
p
er
f
o
r
m
ed
b
y
a
s
ep
ar
ate
ar
tif
icial
i
n
tell
ig
e
n
ce
s
o
f
t
w
ar
e
lib
r
ar
y
.
I
n
th
e
ca
s
e
co
n
s
id
er
ed
,
it
is
n
ec
e
s
s
ar
y
to
m
ap
t
h
e
v
ec
to
r
X
an
d
th
e
v
ec
to
r
Q
x
to
ap
p
l
y
t
h
e
in
ter
f
ac
e
d
escr
ib
ed
ab
o
v
e.
I
n
o
r
d
er
to
m
ak
e
ap
p
licatio
n
an
d
d
escr
ip
t
io
n
o
f
t
h
e
alg
o
r
it
h
m
s
,
it
i
s
p
o
s
ited
th
at
t
h
e
s
ea
r
c
h
s
p
ac
e
o
f
th
e
al
g
o
r
ith
m
s
i
s
li
m
ited
b
et
w
ee
n
0
.
0
an
d
1
.
0
f
o
r
e
ac
h
ax
i
s
.
T
h
e
v
ec
t
o
r
X
is
u
s
ed
n
o
t
as
th
e
R
P
C
Us
p
o
w
er
v
ec
to
r
Q
x
,
b
u
t
as
t
h
e
c
o
ef
f
icie
n
t
s
v
ec
to
r
to
ta
k
e
i
n
to
ac
co
u
n
t
th
e
m
a
x
i
m
u
m
allo
w
a
b
le
p
o
w
er
o
f
R
P
C
U
in
th
e
n
o
d
es.
Q
xi
=
X
i
∙
Q
max
i
,
0
≤
X
i
≤
1
,
i
=
1
,
…
,
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
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C
E
I
SS
N:
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-
8708
I
mp
leme
n
ta
tio
n
o
f
P
o
p
u
la
tio
n
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lg
o
r
ith
ms to
Min
imiz
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P
o
w
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r
Lo
s
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.
.
.
.
(
V
.
Z.
Ma
n
u
s
o
v)
2959
T
h
u
s
,
t
h
e
o
p
ti
m
izatio
n
al
g
o
r
ith
m
i
s
i
n
d
ep
en
d
en
t
o
f
cr
i
ter
ia
ca
lcu
latio
n
.
D
u
e
it,
ch
a
n
g
es
in
th
e
p
o
w
e
r
g
r
id
d
o
n
o
t
ca
u
s
e
t
h
e
n
ec
es
s
it
y
o
f
c
h
an
g
i
n
g
a
n
y
th
i
n
g
i
n
th
e
o
p
tim
izatio
n
m
eth
o
d
i
m
p
le
m
e
n
tatio
n
.
T
o
co
n
s
id
er
th
e
l
i
m
itatio
n
s
o
f
t
g
φ
t
h
e
p
e
n
alt
y
v
al
u
es
ar
e
u
s
ed
.
I
f
t
h
e
v
alu
e
o
f
t
g
φ
d
o
es
n
o
t
f
it
t
h
e
li
m
itatio
n
s
,
th
e
n
t
h
e
v
alu
e
o
f
th
e
o
p
ti
m
izatio
n
cr
ite
r
io
n
(
Z
1
(
Q
x
)
o
r
Z
2
(
Q
x
)
)
is
ad
d
e
d
to
an
ex
tr
a
-
lar
g
e
p
en
alt
y
v
al
u
e.
4
.
1
.
E
x
peri
m
e
nt
des
cr
iptio
n
T
h
e
o
p
tim
izatio
n
p
r
o
b
le
m
s
(
E
q
u
atio
n
1
&
2
an
d
E
q
u
atio
n
2
&
3
)
w
er
e
s
o
lv
ed
b
y
G
A
an
d
P
SO.
W
e
u
s
ed
G
A
w
ith
t
h
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[1
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A.
H.
M
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]
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.
R
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[4
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.
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8708
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2961
[7
]
J.
J.
Ja
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n
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t
a
l.
,
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A Ne
w P
a
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k
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]
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.
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0
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1
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2
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C.
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rh
a
rt,
“
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3
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4
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P.
V
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M
a
tren
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n
a
n
d
V.
G
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S
e
k
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e
v
,
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P
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rti
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