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I
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5
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4
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at
n
ee
d
s
etti
n
g
s
.
Als
o
,
th
e
ac
cu
r
ac
y
o
f
r
esu
lts
an
d
ti
m
e
o
f
co
n
v
er
g
e
n
ce
o
f
C
S
A
i
s
b
etter
t
h
an
th
e
o
t
h
er
al
g
o
r
ith
m
s
li
k
e
G
A
a
n
d
P
SO,
w
h
ic
h
m
o
tiv
a
tes i
t to
f
i
n
d
t
h
e
s
o
lu
tio
n
o
f
m
an
y
o
p
ti
m
izatio
n
p
r
o
b
le
m
s
in
th
e
p
o
w
er
s
y
s
te
m
[
1
7
]
.
T
h
e
p
u
r
p
o
s
e
o
f
th
e
p
ap
er
is
t
o
ap
p
ly
t
h
e
C
S
A
to
f
i
n
d
th
e
s
o
lu
tio
n
to
th
e
n
o
n
-
co
n
v
e
x
c
o
n
s
tr
ain
e
d
E
P
D
p
r
o
b
lem
.
T
h
e
m
u
ltip
le
f
u
e
l
o
p
tio
n
s
,
p
r
o
h
ib
ited
o
p
er
atin
g
zo
n
e
s
,
an
d
tr
a
n
s
m
i
s
s
io
n
p
o
w
er
lo
s
s
e
s
ar
e
co
n
s
id
er
ed
in
t
h
e
p
r
o
b
le
m
f
o
r
m
u
latio
n
o
f
E
P
D.
A
ls
o
,
a
co
n
s
tr
ain
t
h
a
n
d
li
n
g
tec
h
n
iq
u
e
is
p
r
o
p
o
s
ed
to
s
atis
f
y
th
e
d
i
f
f
er
e
n
t
s
y
s
te
m
co
n
s
tr
ai
n
ts
s
u
cc
es
s
f
u
l
l
y
.
T
o
s
h
o
w
t
h
e
e
f
f
icien
c
y
o
f
t
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
,
it
is
ap
p
lied
to
th
r
ee
v
as
tl
y
-
u
s
ed
tes
t
s
y
s
te
m
s
w
i
th
d
i
f
f
er
en
t
ec
o
n
o
m
ic
l
o
ad
d
is
p
atch
co
n
f
i
g
u
r
atio
n
s
,
an
d
th
e
r
es
u
lt
s
ar
e
co
m
p
ar
ed
to
o
th
er
r
ele
v
an
t
r
ep
o
r
ted
alg
o
r
ith
m
s
.
T
h
e
o
th
e
r
s
ec
tio
n
s
o
f
t
h
e
p
ap
er
ar
e
ar
r
an
g
ed
as
f
o
llo
w
s
:
T
h
e
m
at
h
e
m
atica
l
m
o
d
el
o
f
th
e
n
o
n
-
co
n
v
e
x
E
P
D
p
r
o
b
l
e
m
is
g
iv
e
n
i
n
s
ec
tio
n
2
.
T
h
e
d
escr
ip
tio
n
o
f
th
e
p
r
o
p
o
s
ed
C
S
A
i
s
p
r
ese
n
te
d
in
s
ec
tio
n
3
.
Sec
tio
n
4
ex
p
l
ain
s
t
h
e
p
r
o
p
o
s
ed
co
n
s
tr
ai
n
t
h
an
d
lin
g
tech
n
iq
u
e.
T
h
e
s
i
m
u
latio
n
r
es
u
lts
,
s
tati
s
ti
ca
l
an
a
l
y
s
i
s
a
n
d
co
m
p
ar
is
o
n
r
esu
lt
s
ar
e
d
is
c
u
s
s
ed
in
s
ec
tio
n
5
.
Sectio
n
6
s
h
o
w
s
th
e
co
n
cl
u
s
io
n
o
f
t
h
e
p
ap
er
.
2.
P
RO
B
L
E
M
F
O
R
M
UL
AT
I
O
N
T
h
e
E
P
D
w
it
h
M
FO
is
a
n
o
p
ti
m
izatio
n
p
r
o
b
lem
th
at
o
b
j
ec
ts
to
m
i
n
i
m
ize
t
h
e
to
tal
f
u
el
c
o
s
t
a
m
o
n
g
th
e
m
u
ltip
le
f
u
els
o
f
ea
ch
u
n
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t
w
h
il
e
s
atis
f
y
i
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th
e
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if
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n
t
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n
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ai
n
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s
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T
o
m
o
d
el
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MFO,
t
h
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s
e
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ad
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atic
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ctio
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s
ed
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o
r
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e
f
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s
t
f
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ctio
n
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T
h
e
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P
D
w
it
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M
F
O
p
r
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b
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ca
n
b
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m
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m
a
ticall
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r
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r
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ted
as
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o
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w
s
:
min
=
∑
(
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=
1
(
1
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(
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=
{
1
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1
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1
2
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2
2
1
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2
.
.
.
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1
≤
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(2
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w
h
er
e
α
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, β
iL
an
d
γ
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ar
e
th
e
co
s
t c
o
ef
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t
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o
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it f
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L
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T
h
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p
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b
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lv
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s
u
b
j
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t to
th
e
f
o
llo
w
in
g
co
n
s
tr
ain
ts
:
1
)
P
o
w
er
b
alan
ce
co
n
s
tr
ai
n
t:
T
h
e
to
tal
g
en
er
ated
p
o
w
er
m
u
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t
s
at
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f
y
th
e
lo
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d
em
an
d
(
P
D
)
an
d
tr
an
s
m
is
s
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lo
s
s
es (
P
loss
)
[
1
]
.
Hen
ce
,
NG
i
l
o
s
s
D
Gi
P
P
P
1
(
3
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T
h
e
p
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ca
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co
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p
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Kr
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(
B
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co
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t)
as
f
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w
s
[
2
0
]
:
=
∑
∑
+
∑
+
=
1
=
1
=
1
(
4
)
2
)
Gen
er
atio
n
li
m
i
ts
co
n
s
tr
ain
t:
T
h
e
r
ea
l
o
u
tp
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t
p
o
w
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f
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m
g
e
n
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m
u
s
t
b
e
w
it
h
i
n
li
m
its
a
s
f
o
llo
w
s
[
1
]
:
NG
i
P
P
P
Gi
Gi
Gi
,.......,
1
,
m
a
x
m
i
n
(
5
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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4471
3
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P
r
o
h
ib
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o
p
er
atin
g
zo
n
es
co
n
s
tr
ai
n
t:
T
h
e
t
h
er
m
a
l
u
n
i
ts
ca
n
h
av
e
P
O
Z
s
w
h
er
e
th
e
o
p
er
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n
is
u
n
d
es
ir
ab
le
d
u
e
to
i
n
s
tab
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is
s
u
es
o
r
p
h
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s
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al
li
m
itatio
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s
o
n
m
ac
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in
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co
m
p
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n
en
ts
[
2
1
]
.
A
u
n
it
w
it
h
P
O
Z
s
d
o
es
n
o
t
h
av
e
a
co
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ti
n
u
o
u
s
f
u
el
-
co
s
t
c
u
r
v
e
as
t
h
e
o
p
er
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n
s
h
o
u
ld
b
e
av
o
id
ed
in
th
ese
zo
n
e
s
.
T
h
is
t
y
p
e
o
f
f
u
n
ct
io
n
s
ca
n
b
e
m
ath
e
m
atica
ll
y
d
e
s
cr
ib
ed
as:
m
a
x
,
1
,
,
,
m
i
n
.
.
.
.
.
.
.
.
.
.
.
:
1
Gi
Gi
U
PZ
Gi
i
L
j
Gi
Gi
U
j
Gi
L
j
Gi
Gi
Gi
P
P
P
PZ
j
P
P
P
P
P
P
i
(
6
)
w
h
er
e
,
an
d
,
ar
e
lo
w
er
a
n
d
u
p
p
er
b
o
u
n
d
s
o
f
th
e
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-
t
h
P
OZ
o
f
u
n
it
i
a
n
d
PZ
i
is
t
h
e
n
u
m
b
er
o
f
P
OZ
s
o
f
g
en
er
atio
n
u
n
it
i
.
3.
CRO
W
SE
A
RCH
AL
G
O
R
I
T
H
M
C
r
o
w
s
ea
r
ch
a
lg
o
r
it
h
m
is
a
m
eta
-
h
eu
r
i
s
tic
o
p
ti
m
izatio
n
alg
o
r
ith
m
p
r
ese
n
ted
b
y
A
s
k
ar
za
d
eh
i
n
2
0
1
6
[
1
7
]
.
T
h
e
m
ai
n
id
ea
o
f
th
e
C
S
A
i
s
g
o
t
f
r
o
m
o
b
s
er
v
i
n
g
th
e
s
o
cial
b
eh
av
io
r
o
f
cr
o
w
s
,
w
h
ic
h
ch
ar
ac
ter
ized
by
t
h
eir
in
telli
g
en
ce
.
T
h
ese
b
ir
d
s
liv
e
in
t
h
e
f
o
r
m
o
f
f
lo
ck
s
.
T
h
ey
h
av
e
a
n
ex
ce
l
len
t
m
e
m
o
r
y
[
1
8
]
.
C
r
o
w
s
o
b
s
er
v
e
th
e
o
th
er
b
ir
d
s
,
in
clu
d
in
g
t
h
e
o
th
er
cr
o
w
m
e
m
b
er
s
i
n
th
e
f
lo
ck
an
d
w
atc
h
w
h
er
e
t
h
e
y
h
id
e
th
eir
f
o
o
d
.
T
h
en
,
th
e
y
s
to
le
th
at
f
o
o
d
o
n
ce
th
e
o
th
er
b
i
r
d
s
lef
t.
T
h
e
s
u
r
p
lu
s
f
o
o
d
is
h
id
d
en
in
a
h
id
eo
u
t
s
p
o
t
an
d
is
r
esto
r
ed
w
h
e
n
t
h
e
cr
o
w
n
ee
d
s
it
[
1
9
]
.
I
t
is
d
if
f
ic
u
lt
to
d
is
co
v
er
w
h
er
e
th
e
cr
o
w
s
to
r
ed
its
f
o
o
d
.
I
f
a
cr
o
w
o
b
s
er
v
es
a
n
o
th
er
o
n
e
g
o
es
af
ter
it,
it
w
i
ll
tr
y
to
tr
ic
k
t
h
at
cr
o
w
a
n
d
w
ill
g
o
to
a
n
o
t
h
er
p
o
s
itio
n
[
1
7
]
.
T
h
is
in
telli
g
e
n
t
b
eh
a
v
io
r
o
f
t
h
e
cr
o
w
s
i
s
s
i
m
i
lar
to
th
e
o
p
ti
m
iz
atio
n
p
r
o
ce
s
s
,
an
d
C
S
A
atte
m
p
ts
to
s
i
m
u
late
t
h
a
t
b
eh
av
io
r
to
f
i
n
d
th
e
o
p
ti
m
al
s
o
lu
tio
n
s
to
th
e
o
p
ti
m
izat
io
n
p
r
o
b
lem
s
[
1
7
]
.
I
f
w
e
h
a
v
e
a
s
o
lu
t
io
n
s
p
ac
e
w
i
th
d
i
m
en
s
io
n
d
t
h
at
h
as a
f
lo
ck
o
f
n
cr
o
w
s
,
t
h
en
t
h
e
p
o
s
itio
n
X
o
f
cr
o
w
i
at
iter
atio
n
t
ca
n
b
e
ex
p
r
ess
e
d
b
y
t
h
e
v
ec
to
r
:
,
=
[
1
,
,
2
,
,
…
…
,
,
]
(
7
)
w
h
er
e
i
=1
:
n
,
t
=1
:
t
max
an
d
t
max
is
th
e
m
ax
i
m
u
m
n
u
m
b
er
o
f
it
er
atio
n
s
.
E
ac
h
cr
o
w
h
as
a
m
e
m
o
r
y
,
in
w
h
ich
it
s
to
r
es
th
e
b
e
s
t
p
o
s
itio
n
o
f
its
s
to
r
in
g
f
o
o
d
s
o
u
r
ce
.
T
h
e
v
ec
to
r
X
h
as
th
e
r
a
n
d
o
m
in
itial
p
o
s
itio
n
s
o
f
th
e
cr
o
ws.
T
h
ese
p
o
s
itio
n
s
ar
e
u
p
d
ate
d
at
ea
ch
iter
atio
n
,
an
d
th
i
s
p
r
o
ce
s
s
i
s
r
ep
ea
ted
u
n
til
th
e
s
to
p
p
in
g
cr
iter
io
n
i
s
m
e
t.
T
h
er
e
ar
e
t
w
o
c
ases
f
o
r
th
e
p
o
s
itio
n
s
u
p
d
ate
o
f
th
e
cr
o
w
s
[
1
7
,
1
9
]
:
C
ase
1
:
C
r
o
w
j
d
o
es
n
o
t
o
b
s
e
r
v
e
t
h
at
cr
o
w
i
i
s
c
h
asi
n
g
it;
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ated
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s
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llo
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s
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,
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ase
2
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C
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o
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t
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r
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i
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e
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a
n
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m
m
ar
ized
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o
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w
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n
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ted
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n
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m
b
er
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t
h
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r
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g
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o
f
[
0
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1
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an
d
AP
is
th
e
a
w
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s
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ac
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.
Fig
u
r
e
1
s
h
o
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m
ain
s
tep
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o
f
th
e
C
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A
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r
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P
D
p
r
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b
lem
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
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:
2
0
8
8
-
8708
I
n
t J
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&
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p
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g
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10
,
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5
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Octo
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e
r
2
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0
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4
4
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4477
4472
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u
r
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1
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ai
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o
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alan
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ai
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atis
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y
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ated
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SA
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s
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lated
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lect
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2
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n
d
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:
2
0
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8
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(
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4473
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5.
SI
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M
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I
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N
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I
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Vo
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4477
4476
T
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.
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6.
CO
NCLU
SI
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I
n
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C
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A
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s
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A
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9
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B.
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Dr
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sli
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Ch
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ter
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e
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rc
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A
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m
(CS
A
)
,
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ti
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b
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-
In
sp
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Al
g
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ms
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Ju
l.
2
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trica
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En
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(
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v
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I.
N.
T
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d
i
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d
A
.
H.
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n
p
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y
a
,
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n
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m
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L
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a
d
Disp
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tch
P
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b
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w
it
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p
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lv
e
u
sin
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F
li
g
h
t
M
o
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lam
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ti
m
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r,
"
in
IEE
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2
0
1
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In
ter
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ti
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l
Co
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En
e
rg
y
Ef
fi
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t
T
e
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h
n
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l
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f
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r
S
u
st
a
in
a
b
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it
y
(
ICEE
T
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)
,
2
0
1
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.
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2
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A
.
Bh
a
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a
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h
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a
,
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y
b
rid
Diffe
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ti
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Ev
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w
it
h
Bio
g
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Disp
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IEE
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s
a
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ms
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v
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2
5
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n
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[2
3
]
P
.
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Ho
ta
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S
a
h
u
,
"
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n
-
Co
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v
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Eco
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m
ic
Disp
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t
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w
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ra
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lg
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h
m
,
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ter
n
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l
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o
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l
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f
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tri
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p
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En
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p
p
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1
2
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-
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2
4
4
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c
.
2
0
1
5
.
[2
4
]
A
.
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-
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,
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Disp
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tch
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b
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m
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m
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t
h
F
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l
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ti
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n
s
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Us
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n
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ti
c
A
lg
o
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h
m
,
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te
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a
ti
o
n
a
l
J
o
u
rn
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l
o
f
Co
mp
u
ter
a
n
d
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En
g
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g
(
IJ
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)
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v
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l.
3
,
n
o
.
5
,
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t.
2
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1
1
.
[2
5
]
F
.
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o
h
a
m
m
a
d
i,
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b
d
i,
"
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m
o
d
if
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c
ro
w
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a
rc
h
a
lg
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h
m
(M
CS
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)
f
o
r
so
lv
in
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lo
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isp
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tch
p
ro
b
lem
,
"
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p
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d
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ft
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mp
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g
,
v
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l.
7
1
,
p
p
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5
1
-
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5
,
2
0
1
8
.
[2
6
]
J.
Zh
a
o
,
e
t
a
l.
,
"
M
o
d
if
ied
c
u
c
k
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se
a
rc
h
a
lg
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rit
h
m
to
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lv
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e
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p
o
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isp
a
tch
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p
ti
m
iza
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p
r
o
b
lem
s
,
"
IEE
E/
CAA
J
o
u
rn
a
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f
A
u
to
m
a
ti
c
a
S
in
ica
,
v
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l
.
5
,
n
o
.
4
,
p
p
.
7
9
4
-
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l.
2
0
1
8
.
[2
7
]
N.
Çe
ti
n
k
a
y
a
,
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t
a
l.
,
"
A
Ne
w
A
l
g
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h
m
a
n
d
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m
p
u
tati
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n
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p
p
ro
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f
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r
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ic
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w
it
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P
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it
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d
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ra
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Zo
n
e
s in
P
o
w
e
r
S
y
ste
m
s
,
"
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e
rg
y
Exp
lo
ra
ti
o
n
&
Exp
lo
it
a
ti
o
n
,
v
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l.
2
3
,
n
o
.
4
,
p
p
.
2
6
7
–
2
7
6
,
2
0
0
5
.
[2
8
]
S
.
O.
Ore
ro
a
n
d
M
.
R
.
Irv
in
g
,
"
Eco
n
o
m
ic
Disp
a
tch
o
f
G
e
n
e
ra
to
rs
w
it
h
P
ro
h
ib
i
ted
Op
e
ra
ti
o
n
Zo
n
e
s:
A
G
e
n
e
ti
c
A
l
g
o
rit
h
m
A
p
p
ro
a
c
h
,
"
IEE
Pro
c
.
Ge
n
e
ra
ti
o
n
T
ra
n
sm
issio
n
Distrib
u
ti
o
n
,
v
o
l
.
1
4
3
,
n
o
.
6
,
p
p
.
5
2
9
–
5
3
4
,
1
9
9
6
.
[2
9
]
K.
M
in
,
e
t
a
l.
,
"
A
n
Eco
n
o
m
ic
Dis
p
a
tch
A
lg
o
rit
h
m
a
s
Co
m
b
in
a
to
rial
Op
ti
m
iza
ti
o
n
P
ro
b
lem
s,"
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
Co
n
tro
l,
A
u
to
m
a
ti
o
n
,
a
n
d
S
y
ste
ms
,
v
o
l.
6
,
n
o
.
4
,
p
p
.
4
6
8
–
4
7
6
,
2
0
0
8
.
[3
0
]
T
.
T
.
Ng
u
y
e
n
,
e
t
a
l.
,
"
M
o
d
if
ied
Cu
c
k
o
o
S
e
a
rc
h
A
lg
o
rit
h
m
:
A
No
v
e
l
M
e
th
o
d
t
o
M
i
n
im
ize
th
e
F
u
e
l
C
o
st,"
En
e
rg
ies
,
v
o
l.
1
1
,
n
o
.
6
,
2
0
1
8
.
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