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16 U
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ver
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s A
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I
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[
1
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.
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and
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5
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c
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7]
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Lagr
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[
8]
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d
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[
9]
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t
y
a
nd
non
l
i
n
ear
i
t
y
of
t
he s
e
ar
c
h d
om
ai
n,
t
o obt
ai
n t
he o
pt
i
m
al
s
ol
ut
i
o
n l
e
ad t
o s
u
b
-
opt
i
m
al
s
ol
ut
i
on d
ue
t
o t
h
e en
t
r
app
i
n
g i
n a
l
oc
a
l
opt
i
m
um
[
7]
.
K
en
ned
y
a
nd
E
ber
har
t
[
1
1
]
i
nt
r
o
duc
e
P
ar
t
i
c
l
e s
w
ar
m
opt
i
m
i
z
at
i
o
n (
P
S
O
)
as
a m
oder
n
heur
i
s
t
i
c
t
ec
hni
que
w
h
i
c
h
m
i
m
i
c
s
t
he
behav
i
or
of
bi
r
ds
f
l
oc
k
or
f
i
s
h
s
c
hool
.
T
he
P
S
O
al
gor
i
t
hm
c
an l
ea
d t
o a h
i
gh
er
qua
l
i
t
y
s
ol
ut
i
on
w
i
t
h t
i
m
e and s
ec
ur
e c
onv
er
genc
e
i
n c
om
par
i
s
on
w
i
t
h ot
h
er
s
t
oc
has
t
i
c
m
et
hods
.
D
E
D
i
s
s
ol
v
i
ng t
he ec
o
nom
i
c
d
i
s
pat
c
h i
n e
v
er
y
t
i
m
e i
nc
r
em
ent
pow
e
r
v
ar
i
at
i
on.
I
n t
h
e r
ec
ent
y
e
ar
s
,
ne
w
m
et
a
-
he
ur
i
s
t
i
c
o
pt
i
m
i
z
a
t
i
o
n a
ppr
oac
h
es
and
m
et
hods
ar
e be
i
ng
s
i
gni
f
i
c
an
t
l
y
ut
i
l
i
z
ed as
an
al
t
er
n
at
i
v
e t
o t
he t
r
a
di
t
i
on
a
l
m
et
hods
t
o addr
es
s
t
he
D
E
D
pr
ob
l
em
r
egar
di
ng
qua
l
i
t
y
,
s
p
ee
d,
and
ef
f
i
c
i
enc
y
,
d
ue t
o
t
hei
r
f
av
or
ab
l
e
s
ear
c
h
c
h
ar
ac
t
er
i
s
t
i
c
s
as
popu
l
at
i
o
n
-
bas
ed
.
P
S
O
t
e
c
hni
q
ue
w
as
a
dopt
ed
t
o
a
ddr
es
s
no
nl
i
ne
ar
i
t
y
a
nd
c
o
m
pl
ex
i
t
y
i
s
s
ues
of
t
he op
t
i
m
i
z
at
i
on
pr
ob
l
em
[
10
-
1
6
].
P
S
O
has
b
een c
har
ac
t
er
i
s
e
d w
i
t
h s
e
v
er
a
l
ad
v
a
nt
ag
es
of
c
r
uc
i
al
i
m
por
t
anc
e ov
e
r c
u
rre
n
t
opt
i
m
i
z
at
i
o
n
m
et
hods
on
t
hei
r
s
peed
of
c
onv
er
genc
e,
r
obus
t
nes
s
,
and
d
i
s
t
i
nc
t
i
v
e
s
i
m
pl
i
c
i
t
y
[
12
]
.
B
ec
aus
e
t
he
es
t
a
bl
i
s
hed
pr
oc
es
s
of
P
S
O
i
nv
ol
v
es
t
w
o
bas
i
c
up
dat
i
n
g r
ul
es
on
l
y
,
t
o i
m
pl
em
ent
i
n
c
o
m
put
er
s
i
m
ul
at
i
o
ns
us
i
ng
bas
i
c
l
o
gi
c
a
nd m
at
hem
at
i
c
a
l
op
er
at
i
ons
i
s
eas
y
.
F
ur
t
her
m
or
e,
P
S
O
c
an be c
om
pl
i
a
nt
w
h
en h
y
br
i
di
z
e
d
w
i
t
h o
t
her
o
pt
i
m
i
z
at
i
o
n t
ec
h
ni
q
ues
bec
aus
e i
t
has
a f
e
w
er
num
ber
of
oper
at
or
s
t
o c
o
n
f
or
m
t
o ot
her
t
ec
hn
i
q
ues
i
n
t
he
i
m
pl
em
ent
at
i
on
pr
oc
es
s
[
12
-
13
]
.
P
S
O
s
ho
w
s
t
hat
t
he
par
t
i
c
l
es
’
m
ot
i
on
i
s
r
e
gul
at
e
d
b
y
i
t
s
pr
ev
i
ous
v
e
lo
c
it
y
,
b
e
s
id
e
s
t
w
o
ot
her
e
l
em
ent
s
of
ac
c
el
er
a
t
i
on
,
nam
el
y
c
og
ni
t
i
v
e
c
om
pone
nt
a
nd s
oc
i
a
l
c
om
ponent
.
C
ogn
i
t
i
v
e
and s
oc
i
al
c
om
pone
nt
s
de
pend
on t
he
ac
c
el
er
at
i
o
n
c
oef
f
i
c
i
ent
s
and t
he
uni
f
or
m
l
y
d
i
s
t
r
i
bu
t
ed
r
andom
num
ber
s
as
s
oc
i
at
ed
w
i
t
h
P
S
O
v
ar
i
a
nt
s
.
T
he b
eha
v
i
or
of
t
h
e p
ar
t
i
c
l
es
i
s
hi
ghl
y
depe
nde
nt
on
t
he
r
e
l
at
i
v
e
v
a
l
ues
of
t
hes
e
c
om
ponent
s
.
I
n
c
as
e
t
h
e
c
o
gni
t
i
v
e
c
o
m
ponent
h
as
a
hi
g
her
v
a
l
ue c
om
par
ed t
o t
he s
oc
i
al
c
om
ponent
,
i
t
w
i
l
l
r
es
ul
t
i
n ai
m
l
es
s
l
y
unr
es
t
r
a
i
ne
d
m
ot
i
on of
a
p
a
r
t
ic
le
t
hr
o
ugh
s
e
ar
c
h
s
pac
e.
O
n
t
h
e
c
ont
r
ar
y
,
par
t
i
c
l
es
m
a
y
r
es
u
l
t
s
i
n
a
n
unt
i
m
el
y
a
dv
anc
e
t
o
w
ar
ds
l
oc
al
opt
i
m
a
and
as
s
u
m
e i
t
as
t
h
e r
eq
ui
r
e
d
s
ol
ut
i
on
w
he
n t
h
e s
oc
i
a
l
el
em
ent
has
a
r
el
at
i
v
el
y
h
i
g
h v
al
ue,
i
n
ot
h
er
w
or
ds
,
i
t
i
s
m
or
e s
us
c
ept
i
bl
e t
o
be ent
r
a
ppe
d
i
nt
o
l
o
c
al
op
t
i
m
a.
E
x
pl
or
i
ng s
e
ar
c
h s
pac
e a
nd ex
p
l
oi
t
i
n
g l
oc
al
d
om
ai
n hi
g
hl
y
r
el
y
o
n t
he
v
a
l
u
es
of
t
h
e
par
t
i
c
l
es
v
e
l
oc
i
t
y
w
her
e e
v
er
y
d
i
m
ens
i
on’
s
par
t
i
c
l
es
v
e
l
oc
i
t
y
i
s
e
ns
ur
ed t
o
ha
v
e a m
ax
i
m
u
m
v
e
lo
c
it
y
.
I
f
t
hi
s
m
ax
i
m
u
m
v
el
oc
i
t
y
as
s
um
es
hi
gh
v
a
l
ue
i
n
i
t
i
at
es
gl
o
ba
l
e
x
pl
or
at
i
on
,
c
onv
er
s
e
l
y
,
l
o
w
v
a
l
u
e
m
o
t
i
v
at
es
l
oc
al
ex
pl
o
i
t
a
t
i
o
n.
F
or
t
hi
s
r
eas
on
,
S
h
i
a
nd
E
ber
h
ar
t
[
17
]
pr
opos
e t
h
e i
n
er
t
i
a
w
e
i
g
ht
c
onc
ept
t
o ef
f
i
c
i
ent
l
y
m
ani
p
ul
a
t
e ex
pl
or
at
i
on a
nd e
x
pl
oi
t
at
i
on a
nd
at
t
a
i
ni
ng
enh
anc
ed
qu
al
i
t
y
of
t
he o
p
t
i
m
al
s
ol
u
t
i
o
n a
nd
m
i
ni
m
i
z
i
n
g c
on
v
er
g
enc
e t
i
m
e.
U
nl
i
k
e al
t
er
n
at
i
v
e
an
d s
i
m
i
l
ar
m
oder
n o
pt
i
m
i
z
at
i
o
n t
e
c
hni
q
ues
l
i
k
e gen
et
i
c
al
go
r
i
t
hm
s
w
hi
c
h
ha
v
e ex
or
bi
t
ant
ev
ol
ut
i
o
nal
op
er
at
i
ons
r
eg
ar
di
n
g c
om
put
at
i
o
na
l
r
es
our
c
es
s
uc
h as
m
ut
at
i
on and c
r
os
s
ov
er
,
P
S
O
f
ac
i
l
i
t
at
es
a bet
t
er
per
f
or
m
anc
e and ex
pedi
t
e c
on
v
er
ge
nc
e [
10]
.
T
he
m
ec
hani
s
m
o
f
P
S
O
m
a
k
e
s
i
t
a der
i
v
at
i
v
e
-
f
r
ee
al
g
or
i
t
hm
unl
i
k
e t
he c
l
as
s
i
c
al
opt
i
m
i
z
at
i
on
t
ec
hni
ques
and
t
h
i
s
f
eat
ur
e es
pec
i
al
l
y
m
ak
es
i
t
s
ui
t
a
bl
y
ef
f
ec
t
i
v
e
i
n
han
dl
i
ng
n
onl
i
ne
ar
i
t
y
a
nd
c
o
m
pl
ex
pr
obl
em
s
.
P
S
O
s
ho
w
s
m
or
e
r
obus
t
nes
s
t
o
deal
w
i
t
h
s
uc
h
pr
obl
em
s
bec
aus
e
i
t
i
s
l
es
s
s
us
c
ept
i
b
l
e
t
o
t
he
o
bj
ec
t
i
v
e
f
unc
t
i
on
n
at
ur
e
r
eg
ar
di
ng
c
ont
i
nui
t
y
a
nd
c
onv
ex
i
t
y
[
14]
t
o
t
h
e
opt
i
m
i
z
er
p
ar
am
et
er
s
[
9]
.
I
nher
e
nt
l
y
,
t
h
e
i
n
ner
w
or
k
i
ng
m
ec
hani
s
m
o
f
P
S
O
as
s
i
s
t
s
i
n
br
eak
i
ng
f
r
ee f
r
o
m
l
oc
al
opt
i
m
a.
I
n t
hi
s
p
aper
,
t
he par
t
i
c
l
e
s
w
ar
m
opt
i
m
i
z
at
i
on (
P
S
O
)
al
gor
i
t
hm
w
as
pr
op
os
ed t
o dea
l
w
i
t
h
t
he
D
E
D
pr
obl
em
c
ons
i
der
i
ng v
ar
i
ous
equ
al
i
t
y
a
nd i
ne
qua
l
i
t
y
c
ons
t
r
ai
nt
s
.
C
om
par
ed w
i
t
h
t
he D
a
nt
z
i
g
-
W
ol
f
e dec
o
m
p
os
i
t
i
on t
ec
h
ni
q
ue.
T
he
per
f
or
m
anc
e of
t
he pr
opos
ed
opt
i
m
i
z
at
i
o
n
m
et
hod w
as
t
es
t
e
d on
a r
e
al
d
at
a s
y
s
t
em
w
i
t
h 2
0 an
d
100
gen
er
at
i
on
uni
t
s
as
a t
es
t
s
y
s
t
em
.
2.
P
r
o
b
l
e
m
F
o
r
m
u
l
a
ti
o
n
T
he D
E
D
pr
ob
l
em
i
s
t
o as
s
i
gn eac
h c
om
m
i
t
t
ed gen
er
at
i
n
g un
i
t
w
i
t
h a
por
t
i
on
of
t
he
s
y
s
t
em
l
oad
dem
and
ov
er
t
he
pr
ogr
am
t
i
m
e
hor
i
z
on
a
c
hi
e
v
i
n
g
t
h
e
m
ai
n
obj
ec
t
i
v
e
of
m
i
ni
m
i
z
i
ng
t
he
oper
a
t
i
o
n c
os
t
w
h
i
l
e
t
a
k
i
ng ph
y
s
i
c
al
c
ons
t
r
a
i
nt
s
i
nt
o c
o
ns
i
d
er
at
i
on
t
hr
ou
gh
s
a
t
is
f
y
in
g
t
h
e
ir
l
i
m
i
t
s
i
n a
ddi
t
i
o
n t
o
ot
h
er
oper
a
t
i
o
na
l
m
at
t
er
s
i
n t
he f
or
m
of
s
pec
i
f
i
ed
r
equi
r
em
ent
s
.
Mat
h
em
at
i
c
al
l
y
,
t
hi
s
o
pt
i
m
i
z
at
i
on
pr
o
bl
em
c
an
be
f
or
m
ul
at
ed
as
a
non
l
i
ne
ar
pr
ogr
am
m
i
ng
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
:
1
6
9
3
-
6
930
T
E
L
KO
M
NI
K
A
V
o
l.
14
,
N
o
.
3,
S
ept
em
ber
2016
:
10
42
–
1
051
1044
pr
obl
em
.
T
he
obj
ec
t
i
v
e
f
un
c
t
i
on
t
o
b
e
o
pt
i
m
i
z
e
d
(
m
i
ni
m
i
z
ed
i
n
t
h
i
s
c
as
e)
i
s
t
h
e
T
ot
al
ge
ner
at
i
on
co
st
:
∑
(
)
=
1
(
1)
I
n pr
ac
t
i
c
e
,
us
ua
l
l
y
,
F
i
(
P
i
)
i
s
ex
pr
es
s
ed
i
n
f
or
m
of
a quadr
at
i
c
f
unc
t
i
on
as
f
ol
l
o
w
s
:
(
)
=
+
+
2
(
2)
W
h
er
e,
a
i
,
b
i
an
d c
i
r
epr
es
ent
t
h
e c
os
t
c
oef
f
i
c
i
ent
s
of
t
he gener
at
or
,
N
i
s
t
he n
um
ber
of
gener
at
or
s
,
P
i
i
s
t
he
p
o
w
er
pr
oduc
ed
b
y
t
h
e
i
t
h
ge
ner
at
or
(
M
W
)
,
F
i
(
P
i
)
i
s
t
he
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er
at
i
n
g
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os
t
of
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he g
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at
i
on u
ni
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i
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z
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ubj
e
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t
t
o t
h
e f
ol
l
o
w
i
ng c
ons
t
r
a
i
nt
s
.
2.
1
.
E
q
u
al
i
t
y C
o
n
s
tr
a
i
n
ts
T
he
pow
er
ba
l
anc
e
w
hi
c
h
i
s
def
i
ne
d
as
t
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al
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r
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i
nt
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,
w
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e
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t
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us
t
m
eet
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nc
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u
de t
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or
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ul
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as
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n t
h
e f
ol
l
o
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i
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eq
uat
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on:
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=
1
−
−
=
0
(
3)
2.
2
.
In
e
q
u
a
lit
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o
n
s
tr
a
i
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ts
T
ak
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m
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t
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on p
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ur
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t
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l
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of
po
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i
n a
ddi
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i
on t
o
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ar
ant
e
e s
y
s
t
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ur
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c
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at
es
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d
er
at
i
on
of
anot
her
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et
of
c
ons
t
r
ai
nt
s
r
ef
er
r
ed t
o
as
t
he i
neq
ua
l
i
t
y
c
ons
t
r
a
i
nt
s
,
w
hi
c
h ar
e r
epr
es
en
t
ed
b
y
t
he f
ol
l
o
w
i
n
g
f
or
m
ul
a:
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≤
=
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,
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…
.
.
=
∑
∑
+
∑
0
+
0
0
=
1
=
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=
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(
4)
R
am
p r
at
e l
i
m
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t
,
or
t
he l
oa
di
n
g and de
l
o
adi
ng r
at
e l
i
m
i
t
s
of
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at
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ar
e def
i
ned
bas
ed o
n pr
ac
t
i
c
a
l
as
pe
c
t
s
and oper
at
i
o
na
l
c
ons
i
der
at
i
o
ns
of
t
he gen
er
at
or
s
s
uc
h as
m
e
c
hani
c
a
l
s
t
r
es
s
es
an
d
l
oad,
F
i
g
ur
e
1
.
T
her
ef
or
e,
t
he
c
ap
ac
i
t
y
of
g
ener
a
t
i
ng
uni
t
s
r
e
qu
i
r
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a
f
i
ni
t
e t
i
m
e t
o c
han
ge t
he c
a
pac
i
t
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of
a s
pec
i
f
i
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her
m
a
l p
la
n
t
.
F
i
gur
e
1.
T
y
pi
c
a
l
l
oa
d pr
of
i
l
e un
i
t
v
ar
i
at
i
ons
w
i
t
h t
i
m
e
2.
3
.
A
d
d
it
io
n
a
l C
o
n
s
tr
a
i
n
ts
I
n add
i
t
i
on t
o e
qu
al
i
t
y
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nd i
nequ
al
i
t
y
c
o
ns
t
r
ai
n
t
s
,
d
y
n
a
m
i
c
ec
onom
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c
di
s
pat
c
h add
r
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i
n t
hi
s
pap
er
a
l
s
o c
ons
i
d
er
s
an
add
i
t
i
on
al
c
o
ns
t
r
ai
nt
w
h
i
c
h
i
s
s
pi
nn
i
ng
r
es
e
r
v
e
and
gr
ou
p
c
ons
t
r
ai
nt
s
.
S
pi
nni
ng
r
es
e
r
v
e
gen
er
at
es
t
h
e
ex
t
r
a
c
apac
i
t
y
t
o
ha
ndl
e
f
ai
l
ur
e
,
uns
c
hedu
l
ed
i
nt
er
r
u
pt
i
on,
an
d unex
p
ec
t
e
d l
oa
d v
ar
i
at
i
on.
S
pi
nn
i
ng r
es
er
v
e of
gener
at
or
s
i
s
pr
opor
t
i
o
na
l
t
o t
he
gener
at
i
on
l
e
v
el
be
l
o
w
a d
e
f
i
ned o
ut
pu
t
k
now
n as
t
h
e
S
pi
nn
i
ng
R
es
er
v
e L
ev
el
(
S
L)
and
equ
al
t
o
t
he s
par
e c
apac
i
t
y
a
bo
v
e S
L.
T
o
f
or
m
ul
at
e
t
hi
s
c
ons
t
r
a
i
nt
m
at
hem
at
i
c
al
l
y
,
w
e ha
v
e t
he f
ol
l
o
w
i
n
g
equa
t
i
o
n:
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NI
K
A
I
S
S
N
:
1
693
-
6
930
P
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z
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nc
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C
o
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ar
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s
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D
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(
M
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hd R
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n
A
b G
han
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)
1045
=
≤
≤
−
≤
≤
A
not
her
t
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p
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c
ons
t
r
ai
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t
,
r
ef
er
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t
he gr
oup c
ons
t
r
ai
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,
w
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e
i
n d
i
f
f
er
ent
gen
er
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s
c
o
m
bi
ned
o
ut
pu
t
i
s
l
i
m
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ed b
y
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er
t
a
i
n bo
und
ar
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s
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aus
es
m
a
y
i
nc
l
ude r
egu
l
at
or
y
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es
t
r
i
c
t
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l
i
m
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t
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n
t
r
ans
m
i
s
s
i
on l
i
ne c
o
nduc
t
i
ng c
apac
i
t
y
,
a
nd
ar
ea s
ec
ur
i
t
y
c
ons
i
der
a
t
i
o
ns
.
3.
P
a
r
ti
c
l
e
S
w
a
r
m
O
p
ti
m
i
z
a
ti
o
n
w
i
th
D
a
n
tz
i
g
-
W
o
l
fe
M
e
th
o
d
P
ar
t
i
c
l
e s
w
ar
m
opt
i
m
i
z
at
i
on (
P
S
O
)
i
s
a p
opu
l
at
i
o
n
-
bas
ed c
o
nt
i
nuo
us
opt
i
m
i
z
at
i
o
n
t
ec
hni
que
a
nd
one
of
t
h
e
gr
ad
ual
l
y
d
e
v
el
ope
d
m
oder
n
opt
i
m
i
z
at
i
on
m
et
hod
,
pr
op
os
ed
b
y
K
en
ned
y
an
d
E
ber
h
ar
t
(
19
95)
.
A
pop
ul
a
t
i
on
of
r
ando
m
s
ol
ut
i
ons
i
s
us
ed
t
o
i
n
i
t
i
a
l
i
z
e
t
he
s
y
s
t
em
f
or
i
t
er
at
i
v
e s
ear
c
hes
f
or
opt
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m
a
b
y
c
o
nt
i
nuo
us
l
y
upd
at
i
n
g t
he g
en
er
at
i
on l
ev
el
s
[
13]
.
P
S
O
i
s
C
har
ac
t
er
i
z
e
d b
y
a
dv
ant
a
geo
us
f
eat
ur
es
,
un
l
i
k
e ot
h
er
s
i
m
i
l
ar
ev
o
l
ut
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on
ar
y
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ec
hni
que
l
i
k
e t
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e
G
enet
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c
A
l
gor
i
t
hm
G
A
w
i
t
h
no c
os
t
l
y
e
v
o
l
ut
i
o
nar
y
op
er
at
or
s
l
i
k
e m
ut
ant
and
c
r
os
s
ov
er
w
hi
c
h
m
a
k
e
s
P
S
O
s
ui
t
ab
l
e f
or
pr
ov
i
di
ng bet
t
er
per
f
or
m
anc
e and ex
p
ed
i
t
i
ng c
on
v
er
ge
nc
e.
T
he
par
t
i
c
l
es
i
n t
h
e
P
S
O
r
epr
e
s
ent
t
he
po
t
ent
i
a
l
s
ol
u
t
i
o
n
s
;
t
hes
e par
t
i
c
l
es
c
hange
t
hei
r
pos
i
t
i
ons
t
hr
oug
h t
h
e s
ear
c
h s
pac
e
b
y
t
r
a
v
e
l
i
n
g t
o
w
ar
ds
t
h
e pr
es
ent
p
ar
t
i
c
l
es
.
F
i
gur
e
2.
P
ar
t
i
c
l
e
S
w
ar
m
O
pt
i
m
i
z
at
i
on
G
ener
i
c
F
l
o
w
c
h
ar
t
P
ar
t
i
c
l
e S
w
ar
m
O
pt
i
m
i
z
at
i
on c
an be ut
i
l
i
z
ed
t
o a
ddr
es
s
s
ev
er
al
pr
ob
l
em
s
as
s
oc
i
at
e
d
w
i
t
h
ot
her
s
i
m
i
l
ar
m
oder
n
al
g
or
i
t
hm
s
.
P
S
O
f
eat
ur
es
gr
oup
i
n
t
er
ac
t
i
on
w
h
i
c
h
pr
o
v
i
des
a
po
ol
of
s
har
ed
i
nf
or
m
at
i
on
w
h
i
c
h
ac
t
s
as
a m
e
m
or
y
t
hat
f
a
c
i
l
i
t
at
es
t
o pr
o
gr
es
s
t
o
w
ar
d t
he
opt
i
m
al
s
ol
ut
i
on.
W
i
t
hi
n t
he s
et
of
t
he p
op
ul
a
t
i
o
n,
e
ac
h p
ar
t
i
c
l
e k
eeps
t
r
ac
k
o
f
‘
m
e
m
or
i
z
i
ng
’
t
he b
es
t
s
ol
ut
i
on r
ef
er
r
ed t
o as
t
he
P
b
es
t
,
w
h
i
c
h i
s
as
s
oc
i
at
e
d
w
i
t
h i
t
s
c
oor
d
i
na
t
es
i
n t
h
e h
y
p
er
s
pac
e.
F
ol
l
o
w
i
ng t
h
i
s
t
r
end and t
r
a
c
k
i
ng anot
her
bes
t
v
a
l
u
e un
t
i
l
t
h
e ‘
G
l
o
ba
l
’
v
er
s
i
on of
t
he P
S
opt
i
m
i
z
er
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
:
1
6
9
3
-
6
930
T
E
L
KO
M
NI
K
A
V
o
l.
14
,
N
o
.
3,
S
ept
em
ber
2016
:
10
42
–
1
051
1046
i
s
r
eac
hed
t
hr
ou
gh
t
h
e
t
r
ac
k
i
ng
of
t
he
ov
er
al
l
b
es
t
v
a
l
ue,
w
hi
c
h
i
s
c
al
l
e
d
G
bes
t
.
T
he
c
onc
ept
of
P
S
O
i
n
vo
l
ve
s
va
r
y
i
n
g
t
he
v
e
l
oc
i
t
y
of
eac
h par
t
i
c
l
e t
o
w
ar
d i
t
s
P
b
es
t
an
d G
b
es
t
at
eac
h s
t
ep as
i
l
l
us
t
r
at
e
d i
n,
F
i
gur
e 2
.
A
c
c
el
er
at
i
on
t
o
w
ar
d P
b
es
t
an
d G
b
es
t
is
b
ei
n
g w
e
i
g
ht
ed ac
c
or
di
ng t
o a
r
andom
t
er
m
[
14,
15]
.
I
n
t
h
e
be
gi
nn
i
ng,
t
h
e
r
es
e
ar
c
h
i
s
ai
m
i
ng
a
t
m
odel
t
he
s
oc
i
al
beh
av
i
or
of
bi
r
d f
l
oc
k
s
,
f
i
s
h s
c
hool
s
,
a
nd a
ni
m
al
h
er
ds
gr
a
ph
i
c
al
l
y
.
N
e
v
er
t
hel
es
s
,
t
h
e or
i
gi
nal
v
er
s
i
on
i
s
c
apab
l
e
of
addr
es
s
i
ng
n
on
l
i
ne
ar
c
ont
i
nuo
us
opt
i
m
i
z
at
i
on
pr
ob
l
em
s
onl
y
.
F
ur
t
her
dev
el
opm
ent
s
i
n
t
hi
s
P
S
O
a
l
g
or
i
t
hm
ha
v
e
ena
bl
e
d
t
h
e
s
ear
c
h f
or
gl
o
ba
l
o
pt
i
m
al
s
ol
ut
i
on
s
of
c
o
m
pl
ex
eng
i
ne
er
i
n
g an
d s
c
i
enc
es
p
r
obl
em
s
.
C
om
par
i
ng par
t
i
c
l
e
s
w
ar
m
opt
i
m
i
z
at
i
on P
S
O
w
i
t
h D
ant
z
i
g
-
W
ol
f
e D
-
W
r
egar
di
ng
t
he
f
ol
l
o
w
i
ng po
i
nt
s
:
1.
I
m
pl
e
m
ent
at
i
o
n:
D
-
W
m
et
h
od i
s
di
f
f
i
c
ul
t
a
nd c
um
ber
s
om
e.
C
ons
t
r
uc
t
i
ng
t
he
bl
oc
k
di
agona
l
s
t
r
uc
t
ur
e f
or
dec
om
pos
i
t
i
o
n r
equ
i
r
es
a
n en
or
m
ous
m
anua
l
w
or
k
,
obs
er
v
at
i
on
a
nd d
ec
i
s
i
o
n.
O
n t
he ot
her
ha
nd,
t
he P
S
O
c
an be m
or
e eas
i
l
y
i
m
pl
e
m
ent
ed bot
h f
or
c
ons
t
r
ai
nt
s
a
nd
obj
ec
t
i
v
e f
unc
t
i
on t
o be
opt
i
m
i
z
ed.
2.
A
dd
i
t
i
on
or
r
em
ov
a
l
of
c
on
s
t
r
ai
nt
s
c
an
b
e
ac
h
i
e
v
e
d
e
as
i
l
y
w
i
t
h
P
S
O
,
w
hi
l
e
i
n
t
h
e
D
-
W
,
th
i
s
pr
oc
es
s
needs
t
o b
e an
al
y
z
ed f
r
om
t
he begi
nni
ng.
3.
T
he D
-
W
m
et
hod t
ak
es
l
es
s
t
i
m
e t
o f
i
nd t
he s
o
l
ut
i
on i
n c
om
par
i
s
on
w
i
t
h
P
S
O
m
et
hod.
H
o
w
e
v
er
,
t
hi
s
pr
ob
l
em
c
an be
gr
e
at
l
y
al
l
e
v
i
at
e
d b
y
ado
pt
i
ng
h
y
br
i
di
z
at
i
on
t
o
r
eac
h t
h
e
r
equi
r
e
d o
pt
i
m
al
s
ol
ut
i
on.
C
ode
deb
ugg
i
n
g of
un
i
nt
en
t
i
on
al
er
r
or
s
i
n t
he
i
m
pl
em
e
nt
ed
bl
oc
k
di
agon
al
s
t
r
uc
t
ur
e of
t
he D
-
W
m
et
hod i
s
t
i
r
es
om
e and s
us
c
ept
i
b
l
e
t
o f
u
r
t
her
m
i
s
t
ak
es
w
hi
l
e
P
S
O
c
o
de c
an
be de
bugg
ed
eas
i
l
y
.
4.
O
p
ti
m
i
z
a
ti
o
n
R
e
s
u
l
ts
a
n
d
D
i
s
c
u
s
s
i
o
n
s
T
he per
f
or
m
anc
e of
t
he dev
e
l
o
ped
al
g
or
i
t
hm
o
f
par
t
i
c
l
e s
w
ar
m
opt
i
m
i
z
at
i
on P
S
O
i
s
t
es
t
ed
us
i
ng
r
ea
l
da
t
a
of
p
o
w
er
s
y
s
t
em
i
n
t
w
o
c
as
e
s
t
udi
es
;
w
i
t
h
a
pr
i
m
ar
y
t
ar
ge
t
of
m
i
ni
m
i
z
i
ng
t
he c
os
t
f
unc
t
i
on f
or
bo
t
h c
as
e s
t
ud
i
es
.
T
he f
i
r
s
t
c
as
e
s
t
ud
y
i
n
v
o
l
v
es
t
w
e
nt
y
g
ene
r
at
i
on
un
i
t
s
w
i
t
h
t
w
ent
y
-
f
our
per
i
ods
,
f
or
t
h
i
s
pr
obl
em
,
t
he
eq
ual
i
t
y
c
o
ns
t
r
ai
nt
s
,
i
n
equ
al
i
t
y
c
ons
t
r
ai
n
t
s
,
r
am
p
r
at
e
l
i
m
i
t
s
,
s
pi
nn
i
ng r
es
er
v
e,
a
nd bo
und
gen
er
at
i
on l
i
m
i
t
s
hav
e
be
en def
i
n
ed
f
or
ea
c
h gener
a
t
i
o
n
uni
t
s
.
T
he
opt
i
m
i
z
er
has
t
o
f
i
nd an
op
t
i
m
u
m
s
ol
ut
i
o
n t
o
a pr
obl
em
w
i
t
h
4
80
v
ar
i
a
bl
es
w
hi
c
h
i
s
c
ons
i
der
e
d a
hi
gh d
i
m
ens
i
o
nal
i
t
y
pr
o
bl
em
.
T
he
s
ec
ond
c
a
s
e
s
t
ud
y
i
nv
ol
v
es
one
hun
dr
ed
g
ener
at
i
on
u
ni
t
s
w
i
t
h
f
i
v
e
per
i
ods
w
i
t
h
a
s
im
ila
r
t
y
pe of
c
ons
t
r
ai
nt
s
a
s
i
n t
he f
i
r
s
t
c
as
e s
t
ud
y
i
n a
ddi
t
i
o
n t
o t
he gr
o
up c
ons
t
r
a
i
ne
d w
hi
c
h
is
as
s
oc
i
at
ed
w
i
t
h t
hi
s
pr
ob
l
em
of
500 v
ar
i
a
bl
es
,
w
h
i
c
h m
eans
anot
her
hi
g
h
-
di
m
ens
i
ona
l
i
t
y
pr
obl
em
.
T
he
s
i
m
ul
at
i
on
r
es
u
l
t
s
c
ov
er
t
w
o
c
as
es
;
a
n
o
pt
i
m
al
c
as
e
w
h
i
c
h
i
nv
ol
v
es
m
i
ni
m
i
z
i
ng
t
h
e
c
os
t
f
unc
t
i
on
s
ubj
ec
t
t
o t
h
e c
ons
t
r
a
i
nt
s
of
t
ot
a
l
p
er
i
o
ds
t
ak
en i
nt
o
c
ons
i
der
at
i
o
n at
t
h
e s
am
e
t
i
m
e.
W
hi
l
e,
t
he
s
ub
-
opt
i
m
al
c
as
e i
n
v
o
l
v
es
f
i
ndi
ng
t
h
e s
ol
ut
i
on
per
i
od b
y
per
i
od
s
ubj
ec
t
t
o t
h
e
c
ons
t
r
ai
nt
s
,
t
h
us
r
eac
hi
n
g
a s
ub
-
opt
i
m
al
s
ol
ut
i
on,
but
i
n s
ub
-
o
pt
i
m
al
c
as
e t
he r
equ
i
r
ed
c
o
m
put
at
i
ona
l
r
es
our
c
es
ar
e
f
ar
l
es
s
t
han i
n t
he
opt
i
m
al
c
as
e.
T
he i
n
put
dat
a f
or
bot
h c
as
es
ar
e
gi
v
en
i
n t
he A
p
pen
di
x
A
.
4.
1
.
C
ase
S
t
u
d
y
1
T
he
f
i
r
s
t
ca
se
s
t
ud
y
ex
a
m
i
ned
t
he
per
f
or
m
anc
e
of
t
he
P
S
O
a
l
g
or
i
t
hm
f
or
t
he
20
gener
at
or
s
w
i
t
h
24
per
i
od
s
.
T
h
i
s
r
es
ul
t
i
s
a
n o
pt
i
m
i
z
at
i
on
pr
o
bl
em
w
i
t
h a
d
i
m
ens
i
o
n of
5
0
0
(
20
x
25,
i
nc
l
udi
ng
t
he
i
n
i
t
i
al
c
ondi
t
i
o
ns
)
v
ar
i
ab
l
es
t
o
be
ev
al
u
at
e
d
an
d
o
pt
i
m
i
z
e
d
ac
c
or
di
ng
l
y
.
In
add
i
t
i
on t
o t
he r
am
p r
at
e c
ons
t
r
ai
n
t
s
,
t
hi
s
pr
o
bl
em
had s
pi
n
ni
n
g r
es
er
v
e c
ons
t
r
a
i
nt
s
.
T
he 500
v
ar
i
ab
l
es
pr
o
bl
em
w
as
s
ol
v
ed us
i
ng
t
he
P
S
O
m
et
hod.
F
or
24
per
i
od
’
s
c
as
e,
t
he t
ot
al
c
os
t
us
i
n
g
P
S
O
m
et
hod
w
a
s
m
in
im
iz
e
d
t
o
9
883
6.
58
un
i
t
s
as
t
h
e opt
i
m
al
s
ol
ut
i
on
c
om
par
ed t
o 9
954
5.
54
uni
t
s
us
i
ng D
a
nt
z
i
g
-
W
ol
f
e
m
et
hod.
A
s
f
or
t
he s
ub
-
opt
i
m
al
s
ol
ut
i
o
n
w
her
e t
h
e pr
obl
em
w
as
s
ol
v
ed
per
i
od
b
y
per
i
od,
t
he t
ot
a
l
c
os
t
f
or
P
S
O
m
et
ho
d
w
as
f
ou
nd t
o b
e 9
8843
.
06
un
i
t
s
c
o
m
par
ed 99
595.
35 u
ni
t
s
us
i
ng
D
ant
zi
g
-
W
ol
f
e m
et
hod
.
T
he r
es
ul
t
s
w
er
e f
oun
d f
or
di
f
f
er
ent
per
i
o
ds
f
or
t
hi
s
pr
ob
l
em
,
t
h
e per
i
ods
w
er
e
6,
12,
18
,
a
nd 2
4
and
t
h
e c
os
t
s
ar
e
s
h
o
w
n
i
n
T
abl
e
1.
I
t
s
u
m
m
ar
i
z
es
t
he
f
i
nd
i
n
gs
f
or
t
hi
s
c
as
e
o
f
20
gener
at
or
and
di
f
f
er
ent
per
i
o
ds
an
d
t
he
r
es
ul
t
s
of
D
ant
z
i
g
-
W
ol
f
e S
ol
ut
i
on f
or
bot
h o
pt
i
m
al
an
d s
ub
-
opt
i
m
al
ar
e t
ak
en
f
r
o
m
A
b G
hani
(
1
989)
,
[
1
]
.
P
S
O
m
et
hod
g
i
v
es
bet
t
er
c
os
t
v
al
u
e f
or
eac
h
op
t
i
m
al
and s
ub
-
o
pt
i
m
al
c
as
e
w
i
t
h d
i
f
f
er
ent
per
i
o
ds
.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NI
K
A
I
S
S
N
:
1
693
-
6
930
P
ar
t
i
c
l
e
S
w
ar
m
O
pt
i
mi
z
at
i
o
n
P
er
f
or
ma
nc
e:
C
o
mp
ar
i
s
o
n of
D
y
n
am
i
c
…
(
M
o
hd R
ud
di
n
A
b G
han
i
)
1047
T
abl
e 1.
S
i
m
ul
at
i
on
r
es
ul
t
s
of
20
-
gen
er
at
or
w
i
t
h 24 per
i
ods
s
y
s
t
em
C
om
par
i
s
on bet
w
ee
n t
h
e D
ant
z
i
g
-
W
ol
f
e and P
S
O
m
et
hods
f
or
D
E
D
No
.
G
ener
at
or
s
/
per
i
ods
Ca
s
e
Co
s
t
(
Un
i
t
Co
s
t
)
PSO
D
-
W
1
20/
6
O
pt
i
m
al
27000.
78
27028.
43
2
S
ub
-
O
pt
i
m
al
27033.
60
27031.
22
3
20/
12
O
pt
i
m
al
52207.
89
52652.
89
4
S
ub
-
O
pt
i
m
al
52210.
53
52653.
22
5
20/
18
O
pt
i
m
al
76416.
21
76982.
39
6
S
ub
-
O
pt
i
m
al
76455.
49
77000.
74
7
20/
24
O
pt
i
m
al
98836.
58
99545.
54
8
S
ub
-
O
pt
i
m
al
98843.
06
99595.
35
D
-
W
:
D
ant
z
i
g
-
W
ol
f
e dec
om
pos
i
t
i
on m
et
hod
P
S
O
:
P
ar
t
i
c
l
e
S
w
ar
m
O
pt
i
m
i
z
at
i
on m
et
hod
O
pt
i
m
al
:
S
o
l
ut
i
o
n o
v
er
t
he
ent
i
r
e
per
i
ods
Su
b
-
O
p
t
im
a
l:
S
o
lu
t
io
n
p
e
r
io
d
-
by
-
pe
r
i
od
4.
2
.
C
ase
S
t
u
d
y
2
T
he s
ec
ond c
as
e
s
t
ud
y
ex
am
i
ned
t
h
e p
er
f
or
m
anc
e o
f
t
he P
S
O
al
g
or
i
t
hm
f
or
t
he 10
0
gener
at
or
s
w
i
t
h
f
i
ve
per
i
od
s
.
T
h
i
s
r
es
ul
t
i
s
an opt
i
m
i
z
at
i
on
pr
ob
l
em
w
i
t
h a
di
m
ens
i
o
n of
600
(
100
x
6,
i
nc
l
u
di
ng
t
he
i
n
i
t
i
al
c
ondi
t
i
o
ns
)
v
ar
i
ab
l
es
t
o
be
ev
al
u
at
e
d
an
d
o
pt
i
m
i
z
e
d
ac
c
or
di
ng
l
y
.
In
add
i
t
i
on
t
o
t
he
r
am
p
r
at
e
c
ons
t
r
ai
n
t
s
,
t
h
i
s
pr
o
bl
em
had
s
pi
nni
ng
r
es
er
v
e
c
ons
t
r
a
i
nt
s
an
d
gr
o
up
c
ons
t
r
ai
nt
s
.
T
he
60
0
v
ar
i
a
bl
es
pr
o
bl
em
w
as
s
ol
v
e
d
u
s
i
ng
t
h
e
P
S
O
m
et
hod.
T
he
t
ot
al
c
os
t
wa
s
m
in
i
m
iz
e
d
t
o
6
59
395.
10
uni
t
s
as
t
he
opt
i
m
al
s
ol
ut
i
on
c
om
par
ed t
o 66
301
7.
40 un
i
t
s
us
i
ng
D
ant
z
i
g
-
W
ol
f
e m
et
hod.
A
s
f
or
t
he s
u
b
-
opt
i
m
al
s
ol
ut
i
on
w
her
e t
he pr
o
bl
em
w
as
s
ol
v
ed
per
i
od
b
y
per
i
o
d,
t
he t
ot
al
c
os
t
w
as
f
o
und t
o be 6
594
30 un
i
t
s
c
om
par
ed 663099 un
i
t
s
us
i
n
g
D
ant
z
i
g
-
W
o
l
f
e
m
et
hod.
T
abl
e 2 s
um
m
ar
i
z
es
t
he f
i
n
di
n
gs
f
or
t
hi
s
c
as
e of
100
gener
at
or
s
wi
t
h
f
i
ve
p
er
i
o
ds
(
wi
t
h
22 gr
oup
i
m
por
t
-
ex
por
t
c
o
ns
t
r
ai
nt
s
)
a
nd
s
ho
w
s
t
he r
es
ul
t
s
of
D
ant
z
i
g
-
W
ol
f
e s
i
m
ul
at
i
on r
es
ul
t
s
f
or
bot
h o
pt
i
m
al
a
nd
s
ub
-
o
p
t
im
a
l [
1
-
2]
.
F
or
b
ot
h c
as
e
s
t
udi
es
,
t
h
e par
t
i
c
l
e
s
w
ar
m
opt
i
m
i
z
at
i
on
P
S
O
out
per
f
or
m
s
t
he D
a
nt
z
i
g
-
W
ol
f
e D
-
W
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F
001
67.
R
ef
er
en
ces
[1
]
A
b
G
hani
M
R
.
O
pt
i
m
i
s
ed
U
n
i
t
C
om
m
i
t
m
e
nt
a
nd
D
y
nam
i
c
E
c
ono
m
i
c
D
i
s
pat
c
h
f
or
Lar
g
e
S
c
al
e
P
ow
er
S
y
s
t
em
s
.
P
hD
.
T
hes
i
s
.
U
ni
t
ed
K
i
ng
d
om
:
T
he U
ni
v
er
s
i
t
y
o
f
M
anc
hes
t
er
I
ns
t
i
t
ut
e
of
S
c
i
enc
e
an
d
T
ec
hnol
o
g
y
(U
M
I
S
T
);
1989
.
[2
]
H
i
ndi
K
S,
A
b G
han
i
M
R.
M
ul
t
i
per
i
od S
e
c
ur
e E
c
onom
i
c
D
i
s
pat
c
h f
or
L
ar
ge S
c
al
e P
ow
e
r
S
y
s
t
em
.
G
ener
at
i
on,
T
r
ans
m
i
s
s
i
on
and
D
i
s
t
r
i
but
i
on,
I
E
E
P
r
oc
eed
i
ng
s
.
1989;
136
(
3)
:
13
0
-
1
36.
[3
]
O
ri
k
e
S,
C
o
r
ne
D
W.
A
M
em
et
i
c
A
l
g
or
i
t
hm
f
or
D
y
n
am
i
c
E
c
o
nom
i
c
L
oad D
i
s
pa
t
c
h O
pt
i
m
i
z
at
i
on
.
Pro
c
.
2013 I
E
E
E
S
y
m
po
s
i
u
m
S
er
i
es
on C
o
m
p.
I
nt
el
l
i
g
enc
e (
S
S
C
I
)
.
S
i
nga
por
e.
201
3
:
92
-
99.
[4
]
O
ri
k
e
S,
C
o
r
ne
DW
.
I
m
pr
o
v
e
d E
v
ol
ut
i
o
nar
y
A
l
g
or
i
t
hm
s
f
or
E
c
onom
i
c
Lo
ad D
i
s
pat
c
h O
pt
i
m
i
s
a
t
i
on
P
r
obl
em
s
.
I
n P
r
o
c
ee
di
ng
s
o
f
12t
h I
E
E
E
U
K
W
or
k
s
ho
p on C
o
m
pu
t
at
i
onal
I
n
t
el
l
i
g
enc
e (
U
K
C
I
)
.
E
di
nbur
gh.
201
2
:
1
-
8.
[5
]
A
bi
do
M
A
.
M
ul
t
i
obj
e
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t
i
v
e E
v
ol
ut
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.
I
EEE
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r
ans
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i
on
s
on
E
v
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ut
i
onar
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C
om
put
at
i
o
n
.
2
006;
10
(
3
):
3
15
-
329.
[6
]
H
e
m
m
a
lin
i
S
,
S
im
o
n
S
P
.
D
y
na
m
ic
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s
pa
t
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us
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g
a
r
t
i
f
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ia
l
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un
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y
s
t
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un
i
t
s
w
i
t
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v
a
l
v
e
-
poi
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e
ffe
c
t
.
E
l
e
c
t
r
i
c
a
l
P
ow
er
and E
n
er
gy
S
y
s
t
em
s
.
2
011
;
33
:
868
-
8
74.
[7
]
M
oham
m
adi
–
i
v
at
l
oo B
A
,
R
ab
i
ee A
,
E
hs
an
M
M
.
T
i
m
e v
ar
y
i
ng ac
c
el
er
at
i
o
n c
o
ef
f
i
c
i
e
nt
s
I
P
S
O
f
or
s
ol
v
i
n
g dy
na
m
i
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e
c
on
om
i
c
d
i
s
pat
c
h w
i
t
h
non
c
om
-
s
m
oot
h
c
os
t
f
un
c
t
i
on
.
E
ner
g
y
c
on
v
er
s
i
on
an
d
m
anagem
ent
.
201
2
;
56
:
1
75
-
1
83.
[8
]
H
i
ndi
K
S,
M
R
A
b G
hani
.
D
y
na
m
i
c
E
c
ono
m
i
c
D
i
s
pat
c
h f
or
La
r
ge S
c
al
e P
ow
er
S
y
s
t
em
s
:
a
Lagr
ang
i
a
n
R
el
ax
at
i
on A
p
pr
oa
c
h.
I
nt
er
nat
i
onal
J
o
ur
na
l
of
E
l
e
c
t
r
i
c
a
l
P
ow
er
an
d E
ner
gy
S
y
s
t
em
.
1
991;
13(
1)
:
51
-
56.
[9
]
S
om
ua
h
C
B,
K
hunai
z
i
N
.
A
ppl
i
c
at
i
on of
l
i
near
pr
ogr
a
m
m
i
ng r
e
-
di
s
pat
c
h t
e
c
hn
i
que t
o
dy
nam
i
c
gener
a
t
i
o
n al
l
oc
at
i
o
n.
I
EEE
T
r
a
n
s
Po
w
e
r Sy
s
t
.
1990
;
5:
20
-
2
6.
[1
0
]
J
uan
g
C
F
.
A
hy
br
i
d o
f
gen
et
i
c
al
gor
i
t
h
m
and p
a
r
t
i
c
l
e s
w
ar
m
o
pt
i
m
i
z
at
i
on
f
or
r
e
c
ur
r
en
t
net
w
or
k
de
s
i
gn
.
I
E
E
E
T
r
an
s
on S
y
s
t
em
s
,
M
an,
and C
y
ber
n
et
i
c
s
-
Pa
rt
B:
C
y
b
e
rn
e
t
i
c
s
.
20
04
;
34
(
2
):
997
-
100
6.
[1
1
]
K
ennedy
J
,
E
b
er
har
t
RC.
P
ar
t
i
c
l
e
S
w
ar
m
O
pt
i
m
i
z
at
i
on
.
P
r
oc
ee
di
ng
s
of
I
E
E
E
I
n
t
er
nat
i
ona
l
C
onf
er
en
c
e on
N
e
ur
al
N
e
tw
o
r
k
s
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Evaluation Warning : The document was created with Spire.PDF for Python.
T
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P
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d
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x
A
(
A
b G
h
ani
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M.
R
.,
[1
])
T
abl
e A
1.
I
n
put
par
am
et
er
s
f
or
t
he 20
gen
er
at
or
s
D
E
D
pr
obl
em
G
ener
at
or
N
o.
G
ener
at
i
on
l
i
m
i
t
(
M
W
)
Loadi
ng r
at
e (
M
W
/
hr
)
De
-
l
oadi
ng r
at
e (
M
W
/
hr
)
Co
s
t
(
uni
t
s
)
S
L
(
MW
)
ma
x
i
mu
m
m
i
n
i
m
um
1
430
360
300
600
1.
0000
0
2
410
360
300
600
1.
0063
0
3
82
50
180
600
1.
0111
77
4
82
50
180
600
1.
0124
77
5
82
50
180
600
1.
0137
77
6
82
50
180
600
1.
0150
77
7
430
250
300
900
1.
0629
411
8
430
300
300
900
1.
0636
411
9
430
140
300
900
1.
0643
411
10
102
70
240
360
1.
1304
92
11
483
130
180
600
1.
1318
463
12
483
130
180
600
1.
1325
463
13
483
130
180
600
1.
1332
463
14
483
130
180
600
1.
1339
463
15
102
70
240
360
1.
1464
92
16
102
70
240
360
1.
1512
92
17
56
30
120
600
1.
1548
51
18
56
30
120
600
1.
1565
51
19
57
30
300
360
1.
2327
52
20
28
15
120
120
1.
4457
26
T
abl
e A
2.
D
em
and a
nd
S
p
i
nni
ng R
es
er
v
e
D
at
a (
20
ge
ner
at
or
s
)
P
er
i
o
d
D
e
m
a
n
d
(
M
W
)
R
eq
u
i
r
ed
r
es
er
v
e
(
M
W
)
0
4
3
4
6
8
0
1
4
2
4
0
8
0
2
4
2
1
4
8
0
3
4
1
2
4
8
0
4
4
0
9
7
8
0
5
4
0
7
4
8
0
6
4
1
7
3
8
0
7
4
2
6
7
8
0
8
4
1
4
7
8
0
9
3
9
1
8
8
0
1
0
3
6
9
0
8
0
1
1
3
7
6
9
8
0
1
2
3
8
5
1
8
0
P
er
i
o
d
D
e
m
a
n
d
(
M
W
)
R
eq
u
i
r
ed
r
es
er
v
e
(
M
W
)
1
3
3
8
2
5
8
0
1
4
3
7
7
6
8
0
1
5
3
8
4
7
8
0
1
6
3
8
5
9
8
0
1
7
3
7
7
8
8
0
1
8
3
5
6
7
8
0
1
9
3
3
3
5
8
0
2
0
3
2
2
0
8
0
2
1
3
2
4
7
8
0
2
2
3
4
1
8
8
0
2
3
3
8
5
6
8
0
2
4
3
9
8
3
8
0
T
abl
e A
3.
I
n
put
par
am
et
er
s
f
or
t
he 10
0 ge
ner
at
or
s
D
E
D
pr
ob
l
em
G
ener
at
or
N
o.
G
ener
at
i
on
l
i
m
i
t
(
M
W
)
Loadi
ng r
at
e (
M
W
/
hr
)
De
-
l
oadi
ng r
at
e (
M
W
/
hr
)
Co
s
t
(
uni
t
s
)
S
L
(
MW
)
ma
x
i
mu
m
m
i
n
i
m
um
1
60
10
120
180
19
55
2
60
10
120
180
19
55
3
60
10
120
180
20
55
4
60
10
120
180
20
55
5
60
10
120
180
20
55
6
100
20
120
360
20
90
7
100
20
120
360
20
90
8
500
50
1000
1500
15
0
9
500
50
1000
1500
15
0
10
500
50
1000
1500
15
0
11
500
50
1000
1500
15
0
12
60
10
120
300
19
55
13
60
10
120
300
19
55
14
60
10
120
300
19
55
15
100
20
120
300
20
90
16
100
20
120
300
20
90
17
100
20
120
300
19
90
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
:
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3
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930
T
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3,
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ber
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42
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1050
18
100
20
120
300
19
90
19
100
50
120
300
20
94
20
100
20
120
300
20
90
21
100
20
120
300
20
90
22
100
20
120
300
20
90
23
60
10
30
180
21
55
24
50
20
30
180
22
48
25
40
10
30
180
22
38
26
60
30
30
180
21
56
27
50
10
60
180
20
46
28
50
10
60
180
20
46
29
60
10
120
300
19
55
30
60
10
120
300
19
55
31
60
10
120
300
19
55
32
100
20
120
300
20
90
33
100
20
120
300
20
90
34
100
20
120
300
20
90
35
100
20
120
300
20
90
36
100
20
120
300
19
90
37
50
10
60
180
19
46
38
50
10
60
180
19
46
39
50
10
60
180
20
46
40
50
10
60
180
20
46
41
50
10
60
180
20
46
42
50
20
60
180
19
46
43
50
10
60
180
19
46
44
50
10
60
180
19
46
45
50
20
60
180
21
48
46
50
20
60
180
22
48
47
60
10
60
180
19
55
48
60
10
60
180
19
55
49
60
10
60
180
19
55
50
60
10
60
180
19
55
51
30
5
30
180
22
28
52
30
5
30
180
22
28
53
30
5
30
180
22
28
54
30
5
30
180
22
28
55
30
5
30
180
22
28
56
60
10
60
180
20
55
57
60
10
60
180
20
55
58
60
10
60
180
20
55
59
50
20
60
180
21
48
60
50
20
60
180
21
48
61
50
20
60
180
21
48
62
50
30
60
180
21
48
63
50
20
60
180
21
48
64
50
10
60
180
21
48
65
50
20
60
300
21
48
66
100
20
60
300
18
46
67
100
20
60
180
18
48
68
60
20
60
180
20
90
69
60
10
60
180
20
90
70
60
10
60
180
20
55
71
60
10
60
180
20
55
72
60
10
60
180
20
55
73
50
10
60
180
19
46
74
50
10
60
180
21
46
75
50
10
60
180
21
46
76
50
10
60
180
21
46
77
50
10
60
180
21
46
78
60
20
60
180
20
55
79
60
20
60
180
19
55
80
50
10
60
180
15
46
81
500
50
1000
1500
16
0
82
400
40
1000
1500
15
0
83
500
50
1000
1500
20
0
84
50
10
60
180
19
46
85
50
10
60
180
19
46
86
50
10
60
180
19
46
87
50
10
60
180
19
46
88
50
10
120
180
19
46
89
40
10
120
180
19
38
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NI
K
A
I
S
S
N
:
1
693
-
6
930
P
ar
t
i
c
l
e
S
w
ar
m
O
pt
i
mi
z
at
i
o
n
P
er
f
or
ma
nc
e:
C
o
mp
ar
i
s
o
n of
D
y
n
am
i
c
…
(
M
o
hd R
ud
di
n
A
b G
han
i
)
1051
90
60
20
120
180
20
55
91
60
20
120
180
20
55
92
50
10
120
180
20
46
93
60
20
120
180
20
55
94
50
10
120
180
22
46
95
50
10
120
180
22
46
96
50
30
120
180
21
48
97
50
20
120
180
22
48
98
50
20
120
180
22
48
99
50
20
120
180
22
48
100
50
20
120
180
22
48
T
abl
e A
4.
D
em
and a
nd
S
p
i
nni
ng R
es
er
v
e
D
at
a (
10
0 g
ener
at
or
s
)
P
er
i
od
D
em
and (
M
W
)
R
equi
r
ed r
es
er
v
e
(
MW
)
0
6464
240
1
7000
240
2
7500
240
3
7250
240
4
7700
240
5
7100
240
T
abl
e A
5.
G
r
oup
C
o
ns
t
r
ai
nt
s
D
at
a
(
10
0
g
ener
a
t
or
s
)
G
r
oup l
i
m
i
t
s
G
ener
at
or
s
i
n
gr
oup
Low
e
r
U
pper
40
250
1
,2
,
3
,4
,5
40
200
6,
7
100
1500
8,
9,
10,
11
20
160
12,
13,
14
140
750
15,
16,
17,
18
,
19,
20,
21,
22
40
200
23,
24,
25,
26
20
2000
27,
28
10
450
32,
33,
34,
35
,
36
10
190
37,
38,
39,
40
10
150
45,
46
40
200
47,
48,
49,
50
10
160
51,
52,
53,
54
,
55
30
200
56,
57,
58
100
300
59,
60,
61,
62
,
63,
64,
65
40
150
66,
67
10
280
68,
69,
70,
71
,
72
50
200
73,
74,
75,
76
,
77
50
180
78,
79,
80
120
1200
81,
82,
83
60
6000
84,
85,
86,
87
,
88,
89
20
4000
90,
91,
92,
93
100
200
96,
97,
98,
99
,
100
Evaluation Warning : The document was created with Spire.PDF for Python.