I
nte
rna
t
io
na
l J
o
urna
l o
f
E
lect
rica
l a
nd
Co
m
pu
t
er
E
ng
ineering
(
I
J
E
CE
)
Vo
l.
1
6
,
No
.
1
,
Feb
r
u
ar
y
20
2
6
,
p
p
.
49
~
64
I
SS
N:
2088
-
8
7
0
8
,
DOI
: 1
0
.
1
1
5
9
1
/ijece.
v
1
6
i
1
.
pp
49
-
64
49
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ttp
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Stocha
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echnique
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nfo
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ticle
his
to
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y:
R
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ev
is
ed
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1
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2
0
2
5
Acc
ep
ted
No
v
2
3
,
2
0
2
5
Hy
d
ro
th
e
rm
a
l
o
p
e
ra
ti
o
n
p
lan
n
i
n
g
(HTOP)
is
a
c
o
m
p
le
x
,
lar
g
e
-
sc
a
le
o
p
ti
m
a
l
c
o
n
tro
l
p
r
o
b
lem
.
Trad
it
io
n
a
ll
y
,
m
a
th
e
m
a
ti
c
a
l
p
ro
g
ra
m
m
in
g
is
u
s
e
d
to
so
l
v
e
it
;
h
o
we
v
e
r,
m
e
tah
e
u
risti
c
tec
h
n
iq
u
e
s
h
a
v
e
e
m
e
rg
e
d
a
s
a
n
a
lt
e
rn
a
ti
v
e
a
p
p
ro
a
c
h
.
Ho
we
v
e
r,
e
v
e
n
in
th
e
c
o
n
tex
t
o
f
c
u
rre
n
t
tec
h
n
o
lo
g
ica
l
d
e
v
e
lo
p
m
e
n
ts,
th
e
m
o
d
e
ls
d
e
v
e
lo
p
e
d
to
d
a
te
g
e
n
e
ra
ll
y
re
q
u
ire
sim
p
li
fica
ti
o
n
s
i
n
t
h
e
fo
rm
u
lati
o
n
.
In
p
a
rti
c
u
lar,
in
m
e
d
i
u
m
-
term
p
lan
n
in
g
,
th
e
y
h
a
v
e
u
se
d
a
d
e
term
in
isti
c
m
o
d
e
l
o
r
sim
p
li
fied
tran
sm
issio
n
li
n
e
s
in
t
o
a
sin
g
le
b
u
s.
Ho
we
v
e
r,
th
is
a
p
p
r
o
a
c
h
lea
d
s
to
c
o
n
se
r
v
a
ti
v
e
a
n
d
u
n
re
a
li
stic
so
lu
ti
o
n
s
th
a
t
m
a
y
re
su
lt
i
n
e
it
h
e
r
o
v
e
rsiz
in
g
o
r
u
n
d
e
r
u
ti
li
z
a
ti
o
n
o
f
re
so
u
rc
e
s.
Th
e
re
fo
re
,
th
is
wo
r
k
p
r
o
p
o
se
s
a
m
e
th
o
d
o
lo
g
y
f
o
r
in
c
o
r
p
o
ra
ti
n
g
u
n
c
e
rtain
ti
e
s
in
to
th
e
HTOP
p
ro
b
lem
with
a
m
u
lt
i
-
b
u
s
t
o
p
o
lo
g
y
.
It
wa
s
tes
ted
in
a
th
re
e
-
b
u
s
sy
ste
m
,
wh
e
re
li
n
e
a
r
f
u
n
c
ti
o
n
s
a
re
a
p
p
li
e
d
t
o
sim
p
li
f
y
t
h
e
p
ro
d
u
c
ti
o
n
o
f
h
y
d
ro
e
lec
tri
c
p
lan
ts
a
n
d
t
h
e
c
o
st
o
f
th
e
rm
a
l
u
n
it
s
.
Th
e
m
e
th
o
d
o
l
o
g
y
in
c
o
rp
o
ra
ted
we
ll
-
e
sta
b
l
ish
e
d
tec
h
n
iq
u
e
s
in
a
n
imp
li
c
it
sto
c
h
a
stic
o
p
ti
m
iza
ti
o
n
(IS
O)
m
o
d
e
l,
u
si
n
g
a
tree
o
f
5
0
s
c
e
n
a
rio
s
to
m
o
d
e
l
t
h
e
h
y
d
ro
l
o
g
ica
l
se
ries
,
wh
ich
is
so
lv
e
d
with
li
n
e
a
r
p
r
o
g
ra
m
m
in
g
(
LP
).
Th
e
re
su
lt
s
we
re
v
a
li
d
a
ted
wit
h
t
h
e
c
o
sts
o
f
th
e
1
0
0
0
0
g
e
n
e
ra
ted
se
rie
s,
sh
o
wi
n
g
a
n
e
rro
r
o
f
5
.
0
7
%
.
Ad
d
it
i
o
n
a
ll
y
,
t
h
e
so
lu
t
io
n
s
we
re
c
o
m
p
a
re
d
with
a
n
a
d
a
p
ted
m
e
tah
e
u
risti
c
tec
h
n
iq
u
e
fo
r
th
is
p
ro
b
lem
to
e
x
p
l
o
r
e
m
o
d
e
ls
a
p
p
li
c
a
b
le t
o
m
o
re
c
o
m
p
lex
f
o
rm
u
latio
n
s.
K
ey
w
o
r
d
s
:
E
co
n
o
m
ical
d
is
p
atch
Hy
d
r
o
th
er
m
al
p
o
wer
g
en
e
r
atio
n
Op
tim
izatio
n
m
eth
o
d
s
Scen
ar
io
tr
ee
Sto
ch
asti
c
p
r
o
g
r
am
m
i
n
g
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Ma
r
th
a
Patr
icia
C
am
ar
g
o
-
Ma
r
tín
ez
Pro
g
r
am
a
d
e
I
n
g
en
ier
ía
E
léctr
ica,
Un
iv
er
s
id
ad
d
e
L
a
Salle
C
ar
r
er
a
2
#
1
0
-
7
0
B
o
g
o
tá,
D.
C
.
,
L
a
C
an
d
elar
ia,
1
1
1
7
1
1
,
C
o
l
o
m
b
ia
E
m
ail: m
p
ca
m
ar
g
o
@
u
n
is
alle.
ed
u
.
co
1.
I
NT
RO
D
UCT
I
O
N
An
ess
en
tial
r
eq
u
ir
em
en
t
f
o
r
t
h
e
o
p
er
atio
n
o
f
an
y
elec
tr
ic
p
o
wer
s
y
s
tem
is
th
e
en
er
g
y
s
u
p
p
ly
to
m
ee
t
th
e
d
em
an
d
ec
o
n
o
m
ically
,
i
.
e.
,
m
ax
im
izi
n
g
s
o
cial
b
en
e
f
it
o
r
,
u
n
d
er
ce
r
tain
ass
u
m
p
tio
n
s
,
m
in
im
izin
g
o
p
er
atin
g
co
s
ts
[
1
]
.
T
o
ac
h
iev
e
th
is
g
o
al,
s
y
s
tem
s
r
eq
u
ir
e
ca
r
ef
u
l
p
lan
n
in
g
th
at
m
ee
ts
s
ta
n
d
ar
d
s
f
o
r
q
u
ality
,
s
ec
u
r
ity
,
en
v
ir
o
n
m
en
tal
p
r
o
tec
tio
n
,
an
d
r
eliab
ilit
y
,
en
s
u
r
i
n
g
s
u
s
tain
ab
le
an
d
ef
f
icien
t p
o
wer
s
y
s
tem
o
p
er
atio
n
.
T
h
e
ty
p
e
o
f
p
r
im
a
r
y
r
eso
u
r
ce
u
s
ed
to
o
b
tain
elec
tr
ic
en
er
g
y
d
ec
is
iv
ely
d
eter
m
in
es
th
e
co
m
p
lex
ity
o
f
p
lan
n
in
g
.
Hy
d
r
o
p
o
wer
,
wh
ic
h
r
elies
o
n
wate
r
r
eser
v
o
ir
s
,
is
s
ig
n
if
ican
tly
af
f
ec
ted
b
y
s
ea
s
o
n
al
ch
an
g
es
an
d
clim
ate
p
h
en
o
m
e
n
a
s
u
ch
as
th
e
E
l
Niñ
o
-
So
u
th
er
n
Oscill
at
io
n
(
E
NSO)
.
On
t
h
e
o
th
e
r
h
a
n
d
,
th
er
m
al
p
o
wer
p
lan
ts
,
ty
p
ically
p
o
wer
ed
b
y
f
o
s
s
il
f
u
els,
o
f
f
er
a
s
tab
le
en
er
g
y
s
u
p
p
ly
b
u
t
r
esu
lt
in
en
v
ir
o
n
m
en
tal
h
ar
m
.
A
h
y
d
r
o
th
er
m
al
s
y
s
tem
,
th
er
ef
o
r
e,
b
alan
ce
s
b
o
th
r
eso
u
r
ce
s
b
y
co
n
s
id
er
in
g
th
at
th
e
wate
r
r
eso
u
r
ce
h
as
n
o
d
ir
ec
t
m
o
n
etar
y
c
o
s
t; th
u
s
,
th
e
o
p
er
a
tin
g
co
s
t is d
eter
m
in
ed
b
y
th
e
am
o
u
n
t o
f
th
er
m
al
g
e
n
er
atio
n
u
s
ed
.
Ho
wev
er
,
th
e
p
h
y
s
ical
ca
p
ac
ity
o
f
r
eser
v
o
ir
s
lim
its
th
e
s
to
r
a
g
e
o
f
wate
r
r
e
s
o
u
r
ce
s
.
C
o
m
b
in
e
d
with
th
e
u
n
p
r
ed
ictab
le
n
atu
r
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
1
,
Feb
r
u
ar
y
20
2
6
:
49
-
64
50
o
f
wate
r
in
f
lo
w,
th
is
cr
ea
tes
a
d
ilem
m
a
ab
o
u
t
wh
eth
er
to
u
s
e
th
e
r
eso
u
r
ce
im
m
ed
iately
o
r
co
n
s
er
v
e
it
f
o
r
f
u
tu
r
e
u
s
e,
r
esu
ltin
g
in
a
tem
p
o
r
ar
y
in
ter
d
ep
en
d
en
ce
b
etwe
en
th
ese
ch
o
ices.
T
h
u
s
,
h
y
d
r
o
th
er
m
al
o
p
er
atio
n
p
lan
n
in
g
(
HT
OP)
is
a
d
y
n
am
i
c
p
r
o
ce
s
s
th
at
ca
n
b
e
m
o
d
eled
as
an
o
p
tim
izatio
n
p
r
o
b
lem
,
wh
er
e
th
e
o
b
jectiv
e
is
to
ass
es
s
th
e
am
o
u
n
t o
f
wate
r
th
at
co
u
ld
r
ep
lace
th
e
r
m
al
e
n
er
g
y
with
in
a
tim
e
h
o
r
izo
n
[
2
]
.
I
n
ad
d
itio
n
t
o
th
ese
d
y
n
am
i
c
an
d
s
to
ch
asti
c
ch
ar
ac
ter
is
tics
,
HT
OP
is
r
eg
ar
d
ed
as
a
co
m
p
le
x
o
p
tim
izatio
n
p
r
o
b
lem
b
ec
au
s
e
o
f
i
)
its
n
o
n
-
lin
ea
r
,
n
o
n
-
s
ep
a
r
ab
le,
an
d
n
o
n
-
c
o
n
v
e
x
n
atu
r
e
[
3
]
;
ii
)
it
in
clu
d
es
s
ev
er
al
co
n
s
tr
ain
ts
,
s
u
ch
as
e
n
er
g
y
b
alan
ce
,
lim
its
o
f
wat
er
r
eser
v
e
v
o
lu
m
e
,
to
tal
o
u
tf
lo
ws,
h
y
d
r
o
elec
tr
ic
g
en
er
atio
n
f
u
n
ctio
n
s
,
an
d
w
ater
b
alan
ce
eq
u
atio
n
s
;
iii
)
i
t
in
v
o
lv
es
m
an
y
v
a
r
iab
les
with
d
if
f
er
en
t
tim
e
d
is
cr
etiza
tio
n
;
an
d
iv
)
it
is
h
a
r
d
to
co
n
s
id
er
a
lo
n
g
-
tim
e
h
o
r
izo
n
d
iv
id
ed
in
to
s
ev
er
al
s
h
o
r
t
in
ter
v
als.
Fo
r
all
th
ese
r
ea
s
o
n
s
,
it
is
n
ec
ess
ar
y
to
h
ier
ar
c
h
ically
d
is
ag
g
r
eg
ate
th
e
p
r
o
b
lem
in
to
lo
n
g
-
ter
m
,
m
ed
iu
m
-
ter
m
,
an
d
s
h
o
r
t
-
ter
m
h
o
r
izo
n
s
.
T
h
e
co
u
p
lin
g
b
etwe
en
h
o
r
izo
n
s
is
ca
r
r
ied
o
u
t
f
r
o
m
t
h
e
lar
g
est
t
o
th
e
s
m
allest,
b
ased
o
n
th
e
av
ailab
ilit
y
o
f
wate
r
r
eso
u
r
ce
s
o
r
o
th
er
p
ar
am
eter
s
r
esu
lt
in
g
f
r
o
m
p
r
e
v
io
u
s
p
lan
n
in
g
,
s
u
ch
as
th
e
v
alu
e
o
f
wate
r
[
4
]
.
C
o
n
v
en
tio
n
ally
,
HT
OP
p
r
o
b
l
em
s
ar
e
s
o
lv
ed
b
y
m
ath
em
a
tical
p
r
o
g
r
am
m
in
g
[
5
]
,
s
u
c
h
as
lin
ea
r
p
r
o
g
r
a
m
m
in
g
(
L
P),
d
y
n
am
ic
p
r
o
g
r
am
m
i
n
g
(
DP)
,
n
o
n
lin
e
ar
p
r
o
g
r
a
m
m
in
g
(
NL
P),
o
r
s
to
ch
asti
c
d
y
n
am
ic
p
r
o
g
r
a
m
m
in
g
(
SDP)
an
d
s
to
c
h
asti
c
d
u
al
d
y
n
am
ic
p
r
o
g
r
am
m
in
g
(
SDDP)
[
6
]
,
[
7
]
.
T
h
ese
p
r
o
ce
d
u
r
es
o
b
tain
th
e
g
lo
b
al
o
p
tim
al
s
o
lu
tio
n
if
th
e
n
ec
ess
ar
y
o
p
tim
ality
co
n
d
iti
o
n
s
ar
e
s
atis
f
ied
;
h
o
wev
er
,
in
co
m
p
lex
s
y
s
tem
s
,
th
ey
r
e
q
u
ir
e
b
ein
g
co
m
b
in
ed
with
d
ec
o
m
p
o
s
itio
n
[
8
]
,
[
9
]
lin
ea
r
a
p
p
r
o
x
im
atio
n
s
[
1
0
]
,
[
1
1
]
o
r
s
im
u
latio
n
tech
n
iq
u
es
(
e.
g
.
,
Mo
n
te
C
ar
lo
)
[
1
2
]
,
[
1
3
]
an
d
also
n
ee
d
to
co
n
s
id
er
s
ig
n
if
ican
t
s
im
p
lific
a
tio
n
s
,
ev
en
th
o
u
g
h
tech
n
o
lo
g
ical
a
d
v
an
ce
s
i
n
p
r
o
ce
s
s
o
r
s
an
d
s
o
f
twar
e
h
av
e
r
ed
u
ce
d
t
h
e
n
u
m
b
er
o
f
th
ese
r
ed
u
ctio
n
s
.
An
o
th
er
em
er
g
in
g
ap
p
r
o
ac
h
in
r
ec
e
n
t
d
ec
ad
es
to
s
o
lv
in
g
o
p
tim
izatio
n
p
r
o
b
lem
s
is
m
etah
eu
r
is
tic
tec
h
n
iq
u
es.
Alth
o
u
g
h
an
o
p
tim
al
g
lo
b
al
s
o
lu
tio
n
is
n
o
t
g
u
ar
an
tee
d
,
esp
ec
ially
f
o
r
co
m
p
le
x
a
n
d
h
ig
h
-
d
im
en
s
io
n
al
p
r
o
b
lem
s
,
t
h
ey
p
r
o
v
id
e
n
ea
r
-
o
p
tim
al
s
o
lu
tio
n
s
in
a
r
ea
s
o
n
ab
le
tim
e
[
1
4
]
.
Gi
v
en
th
eir
f
ea
tu
r
es
s
u
ch
as
s
im
p
licity
,
ad
ap
tab
ilit
y
,
an
d
r
o
b
u
s
tn
ess
,
m
etah
eu
r
is
tic
to
o
ls
h
av
e
b
ee
n
ap
p
lied
to
s
o
lv
e
HT
OP
p
r
o
b
lem
s
,
s
h
o
win
g
g
r
ea
t
p
o
ten
tial
to
ad
d
r
ess
th
eir
c
o
m
p
lex
f
o
r
m
u
l
atio
n
an
d
to
m
o
d
el
th
em
with
o
u
t
ex
ten
s
iv
e
s
im
p
lific
atio
n
s
[
1
5
]
,
[
1
6
]
.
I
n
[
1
7
]
,
a
co
m
p
r
eh
e
n
s
iv
e
an
d
u
p
-
to
-
d
at
e
o
v
er
v
iew
o
f
th
e
m
etah
eu
r
is
tic
to
o
ls
ap
p
lied
to
HT
OP
i
n
th
e
s
h
o
r
t
ter
m
is
p
r
o
v
id
e
d
.
R
eg
ar
d
i
n
g
th
e
d
ev
e
lo
p
m
en
t
o
f
to
o
ls
ap
p
lied
in
m
ed
iu
m
-
ter
m
p
lan
n
in
g
p
r
o
b
lem
s
,
th
e
wo
r
k
s
[
1
8
]
–
[
2
1
]
r
em
a
r
k
th
at
d
if
f
er
en
t
to
o
l
s
,
s
u
ch
as
g
en
etic
a
lg
o
r
ith
m
(
GA)
o
r
p
ar
ticle
s
war
m
(
PS
O)
,
ar
e
im
p
lem
en
ted
to
s
o
lv
e
d
eter
m
in
is
tic
an
d
s
in
g
le
-
b
u
s
p
r
o
b
lem
s
.
Ma
th
em
atica
l
an
d
m
etah
eu
r
is
tic
m
o
d
els
d
ev
elo
p
ed
s
o
f
ar
t
o
s
o
lv
e
th
e
HT
OP
p
r
o
b
lem
s
i
m
p
lify
th
e
n
atu
r
e
o
f
th
e
o
b
jectiv
e
f
u
n
cti
o
n
,
th
e
r
estrictio
n
s
,
o
r
th
e
v
ar
iab
les.
Fo
r
ex
am
p
le,
s
tu
d
ies
s
u
ch
as
[
1
1
]
ass
u
m
e
th
e
co
s
ts
o
f
th
er
m
al
p
o
wer
p
l
an
ts
as
lin
ea
r
f
u
n
cti
o
n
s
.
Alter
n
ativ
ely
,
w
o
r
k
s
lik
e
[
2
2
]
an
d
d
if
f
er
en
t
v
er
s
io
n
s
o
f
SDDP
r
ed
u
ce
th
e
o
b
jectiv
e
f
u
n
ctio
n
to
a
p
iece
wis
e
lin
ea
r
f
o
r
m
,
b
u
t
it
is
s
till
co
n
v
ex
.
R
eg
ar
d
in
g
s
to
ch
asti
c
m
o
d
elin
g
,
[
2
3
]
ass
u
m
es
u
n
ce
r
tain
ty
with
a
two
-
s
tag
e
m
o
d
el,
wh
ile
[
2
4
]
in
clu
d
es
a
s
to
c
h
asti
c
en
v
ir
o
n
m
en
t
o
n
ly
in
th
e
f
in
al
s
tag
es.
I
n
ad
d
itio
n
,
s
o
m
e
m
o
d
els
co
n
d
e
n
s
e
th
e
s
y
s
tem
in
to
a
s
in
g
le
b
u
s
[
2
5
]
,
an
d
o
t
h
er
s
s
im
p
lify
th
e
r
eser
v
o
ir
s
u
s
in
g
ag
g
r
e
g
atio
n
m
eth
o
d
o
lo
g
y
[
2
6
]
.
On
th
e
m
etah
eu
r
is
tics
s
id
e,
wo
r
k
s
s
u
ch
as
[
2
7
]
–
[
2
9
]
co
n
s
id
er
n
o
n
-
co
n
v
e
x
co
s
t
f
u
n
ctio
n
s
s
to
ch
asti
ca
ll
y
an
d
n
o
n
-
lin
ea
r
wate
r
p
r
o
d
u
ctio
n
f
u
n
ctio
n
s
,
b
u
t
em
p
lo
y
a
s
in
g
le
-
b
u
s
m
o
d
el.
I
n
s
tead
,
[
3
0
]
–
[
3
2
]
tak
e
o
n
th
e
tr
an
s
m
is
s
io
n
n
etwo
r
k
b
u
t
ass
u
m
e
a
d
eter
m
in
is
tic
o
p
tim
izatio
n
p
r
o
b
lem
.
Dep
en
d
in
g
o
n
th
e
tim
e
h
o
r
iz
o
n
s
tu
d
ied
,
ea
ch
s
im
p
lific
atio
n
co
u
l
d
af
f
ec
t
th
e
r
esu
lts
an
d
d
ec
is
io
n
-
m
ak
in
g
.
Fo
r
i
n
s
tan
ce
,
in
th
e
m
ed
iu
m
-
ter
m
h
o
r
izo
n
,
elec
tr
ic
al
tr
an
s
m
is
s
io
n
co
n
s
tr
ain
ts
ar
e
s
ig
n
if
ican
t
in
lar
g
e
,
lo
o
s
ely
m
esh
ed
s
y
s
tem
s
s
u
ch
as
th
o
s
e
in
So
u
th
Am
er
ica,
b
ec
au
s
e
th
e
lin
es
ar
e
m
o
r
e
v
u
ln
e
r
ab
le
to
ex
ce
ed
in
g
th
eir
o
p
er
atin
g
lim
its
.
Fu
r
th
er
m
o
r
e,
it
is
im
p
o
r
tan
t
to
s
to
c
h
a
s
tically
m
o
d
el
s
p
ec
if
ic
in
p
u
t
p
ar
am
eter
s
,
s
u
ch
as
r
en
ewa
b
le
p
r
im
ar
y
r
eso
u
r
ce
s
an
d
elec
tr
icity
d
em
an
d
,
s
in
ce
u
n
ce
r
tain
ty
p
r
o
p
ag
ates
o
v
er
lo
n
g
er
p
lan
n
in
g
h
o
r
izo
n
s
[
3
3
]
.
T
a
k
in
g
in
t
o
ac
c
o
u
n
t
th
e
ab
o
v
e
-
m
en
tio
n
e
d
asp
ec
ts
,
an
d
co
n
s
id
er
in
g
th
at
im
p
lem
en
tin
g
r
ea
lis
tic
ec
o
n
o
m
ic
d
is
p
atch
m
o
d
els
t
h
at
r
ef
lect
th
e
p
h
y
s
ical
r
estrictio
n
s
an
d
u
n
p
r
ed
ictab
ilit
y
o
f
th
e
g
en
e
r
atio
n
is
ess
en
tial
to
av
o
id
eith
er
ass
i
g
n
m
en
t
o
f
lo
a
d
th
at
ca
n
n
o
t
b
e
p
r
o
d
u
ce
d
o
r
o
v
er
s
izin
g
o
r
u
n
d
er
u
tili
za
tio
n
o
f
r
eso
u
r
ce
s
,
th
e
co
r
e
r
esear
c
h
q
u
esti
o
n
ad
d
r
ess
ed
in
th
is
wo
r
k
is
h
o
w
to
m
o
d
el
th
e
in
h
er
en
t
u
n
ce
r
tain
t
y
o
f
v
ar
iab
les ass
o
ciate
d
with
r
en
ewa
b
le
g
en
er
atio
n
r
eso
u
r
ce
s
wi
th
in
a
m
ed
iu
m
-
ter
m
HT
OP,
w
h
ile
s
im
u
ltan
eo
u
s
ly
ac
co
u
n
tin
g
f
o
r
th
e
tr
an
s
m
is
s
io
n
n
etwo
r
k
an
d
en
s
u
r
i
n
g
th
e
r
esu
ltin
g
m
eth
o
d
o
lo
g
y
ca
n
s
o
lv
e
th
e
p
r
o
b
lem
d
esp
ite
co
m
p
lex
f
o
r
m
u
latio
n
s
.
I
n
th
is
r
eg
a
r
d
,
th
is
wo
r
k
p
r
o
p
o
s
es
a
n
o
v
el
o
p
tim
izatio
n
m
et
h
o
d
o
lo
g
y
th
at
ca
n
b
e
ap
p
lied
to
m
ed
iu
m
-
ter
m
p
r
o
b
lem
s
,
wh
er
e
th
e
n
etwo
r
k
a
n
d
th
e
s
to
ch
asti
city
o
f
wate
r
i
n
p
u
ts
ar
e
in
clu
d
ed
.
An
im
p
licit
s
to
ch
asti
c
o
p
tim
i
za
tio
n
(
I
SO)
s
tr
ateg
y
was
ap
p
lied
to
ad
d
r
ess
u
n
ce
r
tain
ty
in
h
y
d
r
o
u
n
it
in
f
lo
ws,
u
s
in
g
a
s
ce
n
a
r
io
tr
ee
with
th
e
p
r
o
g
r
ess
iv
e
clu
s
ter
in
g
m
eth
o
d
(
PC
M)
[
3
4
]
,
wh
ich
was
r
ed
u
ce
d
t
h
r
o
u
g
h
an
alg
o
r
ith
m
b
ased
o
n
p
ar
ticle
s
war
m
o
p
tim
izatio
n
[
3
5
]
.
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
o
lo
g
y
was
test
ed
in
a
ca
s
e
s
tu
d
y
in
wh
ich
th
e
lo
ca
tio
n
s
o
f
th
e
h
y
d
r
o
a
n
d
th
er
m
al
p
o
wer
g
en
er
ato
r
s
,
as
well
as
th
e
lo
ad
d
em
an
d
,
wer
e
co
n
s
id
er
ed
at
d
i
f
f
er
en
t
s
y
s
tem
b
u
s
es,
a
n
d
th
e
in
f
lo
ws
o
f
th
e
h
y
d
r
o
p
lan
t
wer
e
m
o
d
el
ed
u
s
in
g
a
r
ed
u
ce
d
s
ce
n
ar
io
tr
ee
with
5
0
s
ce
n
ar
io
s
.
L
in
ea
r
f
u
n
ctio
n
s
wer
e
u
s
ed
to
r
ep
r
esen
t
h
y
d
r
o
p
la
n
t
p
r
o
d
u
ctio
n
an
d
th
er
m
al
u
n
it
co
s
ts
,
an
d
a
lin
ea
r
p
r
o
g
r
am
m
in
g
(
L
P)
t
o
o
l
was
im
p
le
m
en
ted
t
o
s
o
lv
e
th
e
o
p
tim
iza
tio
n
;
h
o
we
v
er
,
th
e
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
-
8
7
0
8
S
to
ch
a
s
tic
p
la
n
n
in
g
o
f m
u
lti
-
b
u
s
h
yd
r
o
th
erma
l sys
tems u
s
i
n
g
…
(
Ma
r
th
a
P
a
tr
icia
C
a
ma
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g
o
-
Ma
r
tín
ez
)
51
m
eth
o
d
o
l
o
g
y
in
co
r
p
o
r
ated
a
m
eta
-
h
eu
r
is
tic
tech
n
iq
u
e
to
v
a
lid
ate
th
e
ca
s
e
an
d
to
p
r
o
v
i
d
e
a
to
o
l
th
at
ca
n
tr
ea
t
non
-
lin
ea
r
an
d
n
o
n
-
co
n
v
ex
p
r
o
b
lem
s
.
I
n
s
u
m
m
ar
y
,
th
is
r
esear
ch
estab
lis
h
ed
s
o
m
e
th
eo
r
etica
l
id
ea
s
in
p
o
wer
s
y
s
tem
o
p
tim
izatio
n
,
s
to
ch
asti
c
m
o
d
elin
g
,
m
etah
e
u
r
is
tic
tech
n
iq
u
es,
an
d
s
u
s
tain
ab
le
en
e
r
g
y
p
lan
n
in
g
to
c
o
m
p
u
te
an
o
p
tim
al
s
o
lu
tio
n
p
r
esen
ted
th
r
o
u
g
h
a
n
o
v
el
m
eth
o
d
o
l
o
g
y
to
ad
d
r
ess
th
e
HT
OP
p
r
o
b
lem
,
o
f
f
er
in
g
a
p
r
ac
tical
to
o
l
f
o
r
m
ed
iu
m
-
ter
m
p
la
n
n
in
g
in
h
y
d
r
o
lo
g
ically
v
ar
iab
le
r
eg
i
o
n
s
,
in
wh
ich
,
m
o
r
eo
v
er
,
an
im
p
r
o
v
em
e
n
t
o
v
er
class
ical
ap
p
r
o
ac
h
es
th
at
co
n
s
id
er
s
in
g
le
-
b
u
s
s
im
p
lific
atio
n
s
is
in
clu
d
ed
,
lead
in
g
to
a
p
ar
ticu
lar
an
aly
s
is
o
f
m
esh
ed
g
r
id
s
with
h
ig
h
h
y
d
r
o
p
o
wer
p
o
ten
tial.
T
h
e
d
e
v
elo
p
m
en
t
o
f
th
is
ef
f
icien
t
s
ce
n
ar
io
r
ed
u
cti
o
n
tech
n
iq
u
e,
wh
ic
h
en
ab
les
th
e
s
o
lu
tio
n
o
f
a
co
m
p
lex
s
to
ch
as
tic
o
p
tim
izatio
n
p
r
o
b
lem
cr
itical
to
elec
tr
ical
g
r
id
r
eliab
ilit
y
,
d
ir
ec
tly
alig
n
s
wit
h
I
J
E
C
E
’
s
s
co
p
e
b
y
p
r
esen
tin
g
a
s
ig
n
if
ican
t
c
o
m
p
u
te
r
en
g
i
n
ee
r
in
g
s
o
lu
tio
n
to
th
e
f
ield
o
f
elec
tr
ical
p
o
wer
s
y
s
tem
s
en
g
in
ee
r
in
g
.
T
h
e
s
tr
u
ctu
r
e
o
f
th
is
p
ap
er
is
s
h
o
wn
as
f
o
llo
ws:
I
n
itially
,
s
ec
tio
n
2
ex
p
lai
n
s
th
e
th
eo
r
etica
l
d
escr
ip
tio
n
o
f
th
e
s
to
ch
asti
c
m
o
d
el,
o
u
tlin
in
g
h
o
w
u
n
ce
r
tain
ties
in
h
y
d
r
o
th
er
m
al
o
p
er
atio
n
p
lan
n
in
g
ar
e
ad
d
r
ess
ed
th
r
o
u
g
h
s
ce
n
ar
io
-
b
ased
ap
p
r
o
ac
h
es
u
s
in
g
a
n
I
SO
m
o
d
el.
Su
b
s
eq
u
en
tly
,
th
e
I
SO
f
o
r
m
u
latio
n
f
o
r
HT
OP
is
in
tr
o
d
u
ce
d
as
a
m
i
n
im
izatio
n
p
r
o
b
lem
to
o
p
tim
ize
to
tal
o
p
er
atin
g
co
s
ts
wh
ile
ac
c
o
u
n
tin
g
f
o
r
s
y
s
tem
co
n
s
tr
ain
ts
an
d
in
cl
u
d
in
g
th
e
p
o
wer
f
lo
w
f
o
r
lin
es
an
d
s
to
ch
asti
c
v
ar
iab
les.
T
h
en
,
th
e
m
o
s
t
r
ele
v
an
t
ch
ar
ac
ter
is
tics
o
f
th
e
m
etah
eu
r
is
tic
tech
n
iq
u
e
u
s
ed
to
v
alid
ate
th
e
r
esu
lts
ar
e
d
escr
ib
ed
.
Sectio
n
3
d
escr
ib
es
th
e
ap
p
licatio
n
o
f
th
e
p
r
o
p
o
s
ed
m
eth
o
d
o
lo
g
y
to
th
e
ca
s
e
s
tu
d
y
.
Sectio
n
4
p
r
esen
ts
th
e
r
es
u
lts
,
co
m
p
ar
in
g
th
e
p
r
o
p
o
s
ed
s
ce
n
ar
io
tr
ee
m
o
d
el
ag
ain
s
t
a
b
aselin
e
ap
p
r
o
ac
h
a
n
d
h
i
g
h
lig
h
tin
g
its
ef
f
ec
tiv
e
n
e
s
s
in
ter
m
s
o
f
c
o
s
t
an
d
r
eliab
ilit
y
.
Fin
ally
,
s
ec
t
io
n
5
p
r
esen
ts
th
e
co
n
clu
s
i
o
n
s
,
s
h
o
win
g
th
e
b
en
ef
its
f
o
r
p
o
wer
s
y
s
tem
m
an
ag
em
en
t a
n
d
s
u
g
g
esti
n
g
d
ir
ec
tio
n
s
f
o
r
f
u
tu
r
e
w
o
r
k
.
2.
T
H
E
CO
M
P
RE
H
E
NS
I
VE
T
H
E
O
RE
T
I
CA
L
B
ASI
S
2
.
1
.
Sto
cha
s
t
ic
pro
g
ra
mm
ing
Op
tim
izatio
n
m
o
d
el
s
o
lu
tio
n
s
th
at
in
clu
d
e
ex
p
licit
u
n
ce
r
tain
ties
in
p
ar
am
eter
s
o
r
v
ar
iab
les
ar
e
d
ev
elo
p
e
d
th
r
o
u
g
h
s
to
ch
asti
c
p
r
o
g
r
am
m
in
g
(
SP
)
,
w
h
er
e
th
e
u
n
ce
r
tain
t
y
o
f
a
r
a
n
d
o
m
v
a
r
iab
le
is
d
escr
ib
e
d
u
s
in
g
a
co
n
tin
u
o
u
s
p
r
o
b
ab
ilit
y
d
en
s
ity
f
u
n
ctio
n
,
wh
ich
im
p
lies
th
e
p
r
esen
ce
o
f
ex
p
ec
ted
v
alu
es
with
in
th
e
f
o
r
m
u
latio
n
.
T
h
is
ap
p
r
o
ac
h
g
e
n
er
ally
h
as
a
co
m
p
lex
ev
alu
ati
o
n
,
b
u
t
o
n
e
way
to
o
v
er
c
o
m
e
th
is
d
if
f
icu
lty
is
to
ap
p
r
o
x
im
ate
th
e
co
n
tin
u
o
u
s
f
u
n
ctio
n
to
a
d
is
cr
ete
d
is
tr
ib
u
tio
n
f
u
n
ctio
n
.
T
h
e
r
ef
o
r
e,
if
a
r
an
d
o
m
v
a
r
iab
le
is
o
b
s
er
v
ab
le
o
v
e
r
tim
e,
s
tan
d
ar
d
an
aly
s
is
u
s
ed
to
ev
alu
ate
it
s
b
eh
av
io
r
is
p
er
f
o
r
m
ed
b
y
d
ef
in
in
g
s
ce
n
ar
io
s
o
r
s
tep
s
.
T
wo
m
eth
o
d
s
ar
e
em
p
lo
y
ed
t
o
p
er
f
o
r
m
th
is
o
p
tim
izatio
n
.
I
n
th
e
f
ir
s
t
ap
p
r
o
ac
h
,
ex
p
licit
s
to
ch
asti
c
o
p
tim
izatio
n
(
E
SO)
is
an
ap
p
r
o
ac
h
wh
er
e
t
h
e
u
n
ce
r
tain
ty
is
co
n
s
id
er
ed
with
in
th
e
f
o
r
m
u
la
tio
n
o
f
th
e
p
r
o
b
lem
.
T
h
is
o
p
tim
izatio
n
is
b
ased
o
n
th
e
two
-
s
tag
e
m
o
d
el
[
3
4
]
.
I
n
th
e
f
i
r
s
t
s
tag
e,
a
d
ec
is
io
n
is
tak
en
,
ass
u
m
in
g
a
p
r
io
r
i
in
f
o
r
m
atio
n
(
i.e
.
,
a
v
alu
e
f
o
r
th
e
r
an
d
o
m
v
ar
iab
le
is
e
s
tab
lis
h
ed
)
.
Du
e
to
th
e
u
n
ce
r
t
ain
ty
,
th
e
ass
u
m
ed
v
alu
e
n
ee
d
s
co
r
r
ec
tiv
e
ac
tio
n
s
(
r
eso
u
r
ce
s
)
i
n
th
e
s
ec
o
n
d
s
ta
g
e.
T
h
is
m
o
d
el
ca
n
b
e
e
x
p
an
d
ed
to
in
cl
u
d
e
m
o
r
e
r
eso
u
r
ce
s
–
a
m
u
ltis
tag
e
p
r
o
b
lem
–
wh
ich
wo
u
ld
c
o
r
r
esp
o
n
d
t
o
th
e
e
v
o
lu
tio
n
o
f
th
e
u
n
ce
r
ta
in
ty
o
v
e
r
tim
e.
T
h
e
d
ec
is
io
n
s
f
o
r
ea
ch
s
tag
e
d
e
p
e
n
d
o
n
l
y
o
n
th
is
o
b
s
er
v
ab
le
d
at
a,
an
d
th
e
d
ec
is
io
n
s
at
an
y
s
tag
e
ar
e
in
d
e
p
en
d
e
n
t
o
f
th
e
n
ex
t
o
n
e.
T
h
is
ch
ar
ac
t
er
is
tic
is
n
am
ed
n
o
n
-
a
n
ticip
at
iv
e
o
f
th
e
d
ec
is
io
n
s
[
3
6
]
.
T
h
e
s
ec
o
n
d
ap
p
r
o
ac
h
in
v
o
lv
es
u
s
in
g
im
p
licit
s
to
ch
asti
c
o
p
tim
izatio
n
(
I
SO)
[
3
7
]
,
wh
ich
in
clu
d
es
in
d
ir
ec
t
u
n
ce
r
tain
ty
.
I
n
th
is
ca
s
e,
d
if
f
er
en
t
s
ce
n
ar
io
s
m
o
d
el
t
h
e
v
ar
iab
le,
an
d
ea
ch
o
n
e
is
r
u
n
in
d
e
p
en
d
e
n
tly
.
T
h
en
,
a
m
u
l
tiv
ar
iate
an
aly
s
is
is
r
eq
u
ir
ed
to
o
b
tain
th
e
o
p
tim
a
l
s
o
lu
tio
n
.
T
h
ese
m
o
d
els
ar
e
k
n
o
wn
as
Mo
n
te
C
ar
lo
o
r
Sto
ch
asti
c
Simu
latio
n
(
SS
)
.
W
h
ile
th
ey
d
o
n
o
t
co
n
s
id
er
th
e
n
o
n
-
an
ticip
ativ
e
p
r
in
ci
p
le,
its
im
p
lem
en
tatio
n
im
p
lies
a
r
ed
u
ctio
n
in
th
e
v
ar
iab
les o
f
th
e
p
r
o
b
lem
an
d
,
t
h
er
ef
o
r
e
,
less
co
m
p
u
tatio
n
tim
e.
2.
1
.
1.
Scena
rio
t
re
e
I
n
a
m
u
ltis
tag
e
p
r
o
b
lem
,
th
e
u
n
ce
r
tain
ty
in
ea
c
h
s
tag
e
t
o
f
th
e
r
an
d
o
m
v
ar
ia
b
le
ca
n
b
e
s
am
p
led
,
g
en
er
atin
g
r
ea
lizatio
n
s
th
at
ca
n
b
e
o
r
g
an
ized
u
s
in
g
a
s
ce
n
ar
io
tr
ee
.
Fo
r
its
co
n
s
tr
u
ctio
n
,
it
is
as
s
u
m
ed
th
at
d
is
cr
ete
v
alu
es m
ay
r
e
p
r
esen
t
th
e
p
r
o
b
ab
ilit
y
d
is
tr
ib
u
tio
n
o
f
th
e
v
ar
iab
le
at
ea
c
h
s
tag
e.
I
n
th
e
tr
ee
,
a
s
ce
n
ar
io
is
d
ef
in
ed
as
an
y
p
ath
f
r
o
m
th
e
v
al
u
e
o
f
th
e
v
a
r
iab
le
in
th
e
f
ir
s
t
s
tag
e
1
(
r
o
o
t)
,
tak
in
g
d
is
cr
ete
v
alu
es
(
n
o
d
es
)
in
ea
ch
s
tag
e
1
,
2
,
3
,
.
.
.
,
.
I
t
m
ea
n
s
th
at
ea
ch
s
ce
n
ar
io
,
,
h
as
n
o
d
es.
T
h
e
s
tr
u
ctu
r
e
o
f
th
e
s
ce
n
ar
io
is
ex
em
p
lar
y
in
Fig
u
r
e
1
.
I
n
th
is
ca
s
e,
th
e
r
an
d
o
m
v
ar
iab
le
is
r
ep
r
esen
ted
b
y
a
tr
ee
o
f
=
3
s
tag
es,
with
4
s
ce
n
ar
io
s
an
d
7
n
o
d
e
s
.
Fo
r
ex
am
p
le,
it c
an
b
e
o
b
s
er
v
ed
th
at
1
is
d
escr
ib
ed
b
y
n
o
d
es
1
,
2
y
4
,
wh
e
r
e
ea
ch
o
n
e
b
elo
n
g
s
t
o
a
s
tag
e
1
,
2
,
an
d
3
,
r
esp
ec
tiv
ely
.
E
a
ch
n
o
d
e
b
r
an
ch
es
in
to
a
s
et
o
f
s
u
cc
ess
iv
e
n
o
d
es
+
,
wh
er
e
th
e
p
ath
b
etwe
en
th
em
h
as
a
tr
an
s
iti
o
n
p
r
o
b
ab
ilit
y
+
/
>
0
(
r
ep
r
esen
ted
in
t
h
e
f
ig
u
r
e
b
y
th
e
b
lu
e
b
o
x
es).
I
t
r
e
p
r
esen
ts
th
e
p
r
o
b
ab
ilit
y
th
at
s
u
cc
ess
o
r
n
o
d
e
b
ec
o
m
es
+
.
T
h
e
p
r
o
b
ab
ilit
y
+
o
f
n
o
d
e
+
is
ca
lcu
lated
b
y
(
1
)
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
1
,
Feb
r
u
ar
y
20
2
6
:
49
-
64
52
1
=
1
f
o
r
+
=
1
(
1
)
+
=
+
/
∙
f
o
r
+
≠
1
wh
er
e
n
o
d
es
in
th
e
last
s
tag
e
h
av
e
a
p
r
o
b
ab
ilit
y
o
f
ea
ch
s
ce
n
ar
io
;
e.
g
.
,
in
Fig
u
r
e
1
,
5
co
r
r
e
s
p
o
n
d
s
to
t
h
e
p
r
o
b
a
b
ilit
y
o
f
5
,
an
d
also
d
ef
in
e
s
th
e
p
r
o
b
a
b
ilit
y
2
o
f
2
.
Fig
u
r
e
1
.
E
x
am
p
le
o
f
a
s
ce
n
ar
i
o
tr
ee
I
t
is
wo
r
th
o
b
s
er
v
in
g
t
h
at
in
a
tr
ee
,
th
e
s
ce
n
ar
i
o
s
s
h
ar
e
n
o
d
es
in
th
e
ea
r
ly
s
tag
es
an
d
b
r
a
n
ch
o
u
t
to
r
ef
lect
th
e
g
r
o
wth
o
f
u
n
ce
r
tain
ty
o
v
e
r
tim
e.
T
h
is
b
e
h
av
io
r
o
c
cu
r
s
b
ec
au
s
e
a
r
a
n
d
o
m
v
ar
ia
b
l
e
ca
n
ass
u
m
e
b
o
th
r
ed
u
ce
d
a
n
d
p
r
ed
ictab
le
v
alu
e
s
in
th
e
p
r
esen
t.
I
n
co
n
tr
ast,
th
e
s
et
o
f
p
o
s
s
ib
le
v
alu
es in
th
e
later
s
tag
es,
i.e
.
,
th
e
n
u
m
b
er
o
f
n
o
d
es
in
th
e
f
u
tu
r
e,
is
g
r
ea
ter
.
On
th
e
o
th
er
h
a
n
d
,
th
is
b
r
an
ch
i
n
g
s
tr
u
ctu
r
e
g
u
ar
an
tees
th
at
th
e
non
-
a
n
ticip
ativ
e
ch
a
r
ac
ter
is
tic
is
ex
p
licitly
a
n
d
n
atu
r
ally
r
e
p
r
esen
ted
,
b
ec
a
u
s
e
a
n
o
d
e
m
u
s
t
b
e
th
e
s
am
e
ac
r
o
s
s
all
s
ce
n
ar
io
s
th
at
s
h
ar
e
th
at
h
is
to
r
y
[
3
6
]
.
2.
1
.
2.
B
uil
din
g
a
s
ce
na
rio
t
re
e
Gen
er
atin
g
a
s
ce
n
ar
io
tr
ee
r
e
q
u
ir
es
d
ata
to
r
ep
r
esen
t
th
e
o
cc
u
r
r
en
ce
o
f
a
r
an
d
o
m
p
r
o
ce
s
s
,
wh
ich
is
d
escr
ib
ed
b
y
a
r
an
d
o
m
v
ar
i
ab
le
f
am
ily
an
d
its
tem
p
o
r
al
ev
o
lu
tio
n
.
T
h
e
r
e
ar
e
d
if
f
er
e
n
t
m
eth
o
d
s
in
th
e
liter
atu
r
e
f
o
r
b
u
ild
in
g
a
tr
ee
[
3
4
]
,
wh
er
e
its
s
tr
u
ctu
r
e
is
g
en
er
ally
p
r
o
p
o
s
ed
as
an
in
p
u
t
p
a
r
am
eter
;
th
at
is
,
th
e
n
u
m
b
er
o
f
n
o
d
es
p
er
s
tag
e
is
estab
lis
h
ed
a
p
r
io
r
i,
an
d
th
er
e
f
o
r
e,
th
e
t
o
tal
n
u
m
b
er
o
f
s
ce
n
ar
io
s
o
f
th
e
tr
ee
.
PC
M
[
3
8
]
was u
s
ed
in
th
is
wo
r
k
,
as d
escr
ib
ed
b
elo
w.
a.
Pro
g
r
ess
iv
e
clu
s
ter
in
g
m
eth
o
d
(
PC
M)
T
h
e
r
an
d
o
m
p
r
o
ce
s
s
r
ea
lizatio
n
s
ar
e
d
en
o
ted
as
{
}
an
d
ar
e
co
n
s
id
er
ed
b
r
o
k
e
n
in
to
s
tag
es
{
}
,
as
it
is
s
h
o
wn
in
Fig
u
r
e
2
.
T
h
e
s
ce
n
ar
io
tr
ee
is
d
ef
i
n
ed
b
y
{
}
s
ce
n
ar
io
s
,
wh
er
e
{
}
∈
{
}
,
ea
ch
o
n
e
h
a
s
a
p
r
o
b
a
b
ilit
y
f
o
r
=
1
,
2
,
.
.
.
,
,
an
d
{
}
n
o
d
es f
o
r
=
1
,
2
,
.
.
.
,
,
as
p
r
ev
io
u
s
ly
s
tated
.
T
h
is
m
eth
o
d
s
tar
ts
b
y
d
ef
in
in
g
a
r
o
o
t n
o
d
e
1
to
r
e
p
r
esen
t
th
e
f
ir
s
t
co
m
p
o
n
en
t
1
,
e.
g
.
,
u
s
in
g
th
e
m
ea
n
v
alu
e
o
f
th
e
w
h
o
le
s
er
ies
s
et
{
1
}
f
o
r
=
1
,
2
,
.
.
.
,
.
T
h
e
p
r
o
ce
s
s
co
n
tin
u
es
b
y
co
n
d
itio
n
al
clu
s
ter
in
g
o
f
th
e
s
ec
o
n
d
co
m
p
o
n
en
t
2
in
to
as
m
an
y
clu
s
ter
s
as
th
e
n
u
m
b
er
o
f
n
o
d
es
in
th
e
tr
ee
at
s
tag
e
2
.
T
h
e
ce
n
tr
o
id
s
r
esu
ltin
g
f
r
o
m
th
e
cl
u
s
ter
in
g
p
r
o
ce
s
s
ar
e
u
s
ed
to
estab
lis
h
th
e
v
alu
es o
f
t
h
e
n
o
d
es.
I
n
s
tag
e
3
,
t
h
e
s
er
ies
{
3
}
ar
e
n
o
w
g
r
o
u
p
e
d
ac
co
r
d
in
g
to
th
eir
co
n
n
ec
tio
n
with
t
h
e
n
o
d
es
o
f
th
e
s
ec
o
n
d
s
tag
e.
T
h
en
,
ea
ch
g
r
o
u
p
is
clu
s
ter
ed
with
r
esp
ec
t
to
th
e
b
r
an
ch
es
d
ef
in
e
d
f
o
r
ea
ch
n
o
d
e
in
th
e
th
ir
d
s
tag
e.
Ag
ain
,
t
h
e
n
o
d
e
v
alu
es
a
r
e
b
ased
o
n
th
e
ce
n
tr
o
id
s
f
o
u
n
d
d
u
r
in
g
clu
s
ter
in
g
.
T
h
e
p
r
o
ce
s
s
co
n
tin
u
es in
th
e
s
am
e
way
u
n
til r
ea
ch
in
g
th
e
last
s
tag
e.
b.
Scen
ar
io
tr
ee
r
ed
u
ctio
n
Gen
er
ally
,
s
ce
n
ar
io
r
ed
u
ctio
n
tech
n
iq
u
es m
in
im
ize
th
e
d
is
tan
ce
b
etwe
en
th
e
o
r
ig
in
al
an
d
th
e
r
ed
u
ce
d
tr
ee
.
T
h
e
estab
lis
h
ed
d
is
tan
ce
f
u
n
ctio
n
d
ef
in
es
th
e
o
b
jectiv
e
f
u
n
ctio
n
,
wh
ich
s
elec
ts
th
e
b
est
-
r
ed
u
ce
d
t
r
ee
co
m
p
o
s
ed
o
f
th
e
m
o
s
t
r
ep
r
esen
tativ
e
s
ce
n
ar
io
s
am
o
n
g
th
e
en
tire
s
et.
T
h
is
h
ig
h
-
lev
el
o
p
tim
izatio
n
p
r
o
b
lem
h
as
a
co
m
b
in
ato
r
ial
n
atu
r
e,
an
d
it
is
ess
en
tially
a
s
et
co
v
e
r
p
r
o
b
lem
[
7
]
.
Giv
en
th
e
b
en
ef
i
ts
o
f
m
etah
e
u
r
is
tics
an
d
th
e
ea
s
e
o
f
ex
p
r
ess
in
g
th
e
p
r
o
b
lem
in
ter
m
s
o
f
a
f
itn
e
s
s
f
u
n
ctio
n
,
th
e
m
o
d
el
cited
i
n
[
3
5
]
p
r
o
p
o
s
es
a
s
ce
n
ar
io
tr
ee
r
ed
u
ctio
n
u
s
in
g
t
h
e
PS
O
tech
n
iq
u
e.
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
-
8
7
0
8
S
to
ch
a
s
tic
p
la
n
n
in
g
o
f m
u
lti
-
b
u
s
h
yd
r
o
th
erma
l sys
tems u
s
i
n
g
…
(
Ma
r
th
a
P
a
tr
icia
C
a
ma
r
g
o
-
Ma
r
tín
ez
)
53
Fig
u
r
e
2
.
E
x
am
p
le
o
f
a
r
a
n
d
o
m
p
r
o
ce
s
s
r
ea
lizatio
n
I
n
th
is
p
r
o
b
lem
,
th
e
s
ea
r
ch
s
p
ac
e
co
n
s
is
ts
o
f
th
e
s
et
o
f
all
s
ce
n
ar
io
s
o
f
th
e
o
r
i
g
in
al
tr
ee
,
wh
er
e
ℑ
s
ce
n
ar
io
s
o
f
t
h
e
r
e
d
u
ce
d
tr
ee
ar
e
estab
lis
h
ed
a
p
r
i
o
r
i
as
i
n
p
u
t
d
ata.
T
h
e
o
b
jectiv
e
o
f
t
h
e
s
war
m
is
to
d
eter
m
in
e
ℑ
∈
s
ce
n
ar
io
s
th
at
ar
e
th
e
f
u
r
th
est
f
r
o
m
ea
c
h
o
th
er
,
i.e
.
,
th
o
s
e
th
at
m
ax
im
ize
th
e
d
is
tan
ce
to
th
eir
n
eig
h
b
o
r
s
.
E
ac
h
-
th
p
ar
ticle
o
f
th
e
s
war
m
is
m
ea
s
u
r
ed
in
te
r
m
s
o
f
its
ad
ap
tab
ilit
y
o
r
f
itn
e
s
s
f
u
n
ctio
n
u
s
in
g
th
e
m
in
im
u
m
m
u
ltiv
ar
iate
n
o
r
m
alize
d
E
u
clid
ea
n
d
is
tan
ce
ℶ
o
f
th
e
s
war
m
,
m
u
ltip
lied
b
y
its
p
r
o
b
ab
ilit
y
,
as
d
escr
ib
ed
in
(
2
)
.
=
ℶ
∈
ℑ
{
1
∑
√
∑
(
,
−
,
ℶ
)
2
=
1
=
1
}
(
2
)
wh
er
e
ℑ
is
n
u
m
b
e
r
o
f
s
ce
n
ar
i
o
s
in
th
e
r
ed
u
ce
d
tr
ee
(
i.e
,
n
u
m
b
er
o
f
p
ar
ticles
o
f
th
e
s
war
m
)
,
is
i
n
d
ex
f
o
r
th
e
p
ar
ticle
o
r
s
ce
n
ar
io
f
o
r
t
h
e
r
ed
u
ce
d
tr
ee
,
ℶ
is
in
d
ex
f
o
r
(
ℑ
−
1
)
d
if
f
er
en
t
s
ce
n
ar
io
s
to
s
ce
n
ar
io
,
is
p
r
o
b
a
b
ilit
y
o
f
s
ce
n
ar
io
in
t
h
e
r
ed
u
ce
d
t
r
ee
,
is
n
u
m
b
er
o
f
r
an
d
o
m
v
ar
ia
b
les
,
is
T
o
tal
n
u
m
b
er
o
f
s
tag
es
,
,
is
v
alu
e
o
f
r
an
d
o
m
v
a
r
iab
le
co
r
r
esp
o
n
d
in
g
to
p
ar
ticle
at
s
tag
e
,
,
ℶ
is
v
alu
e
o
f
r
an
d
o
m
v
ar
iab
le
co
r
r
esp
o
n
d
in
g
t
o
p
ar
ticle
ℶ
at
s
tag
e
t
,
an
d
an
d
n
o
r
m
alize
d
f
a
cto
r
f
o
r
r
an
d
o
m
v
ar
iab
le
.
T
h
e
ap
p
lied
al
g
o
r
ith
m
is
s
u
m
m
ar
ized
in
th
e
n
ex
t step
s
:
−
Def
in
e
p
ar
am
eter
s
f
o
r
PS
O:
s
ea
r
ch
s
p
ac
e,
n
u
m
b
er
o
f
p
ar
ticles,
an
d
in
itializatio
n
o
f
s
war
m
.
−
C
alcu
late
th
e
p
r
o
b
ab
ilit
y
o
f
e
ac
h
s
ce
n
ar
io
-
p
ar
ticle
κ
o
f
th
e
s
war
m
:
T
h
is
is
o
b
tain
ed
b
y
co
m
p
ar
in
g
ea
ch
p
ar
ticle
with
th
e
o
r
ig
i
n
al
tr
ee
;
th
u
s
,
th
e
p
r
o
b
ab
ilit
y
o
f
th
e
-
th
s
ce
n
ar
io
co
r
r
esp
o
n
d
s
to
th
e
p
r
o
b
ab
ilit
ies
o
f
th
e
s
ce
n
ar
io
s
in
t
h
e
o
r
ig
in
al
t
r
ee
th
at
wer
e
clo
s
est
to
th
at
s
ce
n
ar
io
.
Sin
ce
th
e
s
war
m
is
u
p
d
ated
in
ea
ch
iter
atio
n
,
th
e
p
r
o
b
a
b
ilit
y
v
alu
e
s
v
ar
y
,
s
o
p
a
r
ticles h
av
e
a
d
y
n
am
ic
p
r
o
b
a
b
ilit
y
.
−
Ass
ig
n
to
ea
ch
p
ar
ticle
a
f
itn
ess
f
u
n
ctio
n
v
alu
e,
(
2
)
.
T
h
e
o
b
jectiv
e
f
u
n
ctio
n
is
th
e
m
ax
im
izatio
n
o
f
th
e
d
is
tan
ce
b
etwe
en
th
e
p
a
r
ticles in
th
e
s
war
m
,
i.e
.
,
Ob
j
e
c
tive
(
pa
r
tic
l
e
)
=
ma
x
(
fit
n
e
s
s
)
−
Sav
e
th
e
b
est p
o
s
itio
n
o
f
ea
ch
p
ar
ticle
κ
an
d
th
at
o
f
its
n
eig
h
b
o
r
h
o
o
d
,
u
s
in
g
(
3
)
:
+
1
=
+
1
1
(
−
)
−
1
2
(
−
)
(
3
)
wh
e
r
e
+
1
e
x
p
r
ess
es
t
h
at
th
e
n
ew
v
el
o
cit
y
o
f
p
a
r
t
icl
e
a
n
d
ite
r
a
tio
n
+
1
,
i.
e.
;
+
1
is
i
n
f
lu
e
n
ce
d
b
y
its
p
r
e
v
i
o
u
s
v
el
o
ci
ty
,
th
e
c
o
n
s
t
an
t in
e
r
tia
we
ig
h
t
,
th
e
d
is
t
an
ce
f
r
o
m
i
ts
p
r
ev
io
u
s
b
est
p
e
r
f
o
r
m
a
n
c
e
th
e
d
is
ta
n
ce
f
r
o
m
i
ts
n
ea
r
est
n
ei
g
h
b
o
r
,
i
ts
a
ct
u
al
p
o
s
i
ti
o
n
,
an
d
th
e
a
cc
ele
r
ati
o
n
c
o
e
f
f
ic
ie
n
ts
1
an
d
2
,
an
d
f
i
n
all
y
,
1
an
d
2
ar
e
i
n
d
e
p
e
n
d
e
n
t
r
a
n
d
o
m
v
a
r
ia
b
l
es
s
am
p
l
e
d
f
r
o
m
a
u
n
if
o
r
m
d
is
tr
i
b
u
ti
o
n
(
0
,
1
)
.
W
it
h
t
h
e
n
ew
v
el
o
c
it
y
,
t
h
e
p
o
s
iti
o
n
is
u
p
d
a
te
d
in
e
ac
h
it
er
ati
o
n
,
as
is
s
h
o
w
n
i
n
(
4
)
:
+
1
=
+
+
1
(
4
)
T
h
e
p
r
o
ce
s
s
is
ca
r
r
ied
o
u
t u
n
til th
e
s
to
p
p
in
g
c
r
iter
io
n
d
ef
in
e
d
b
y
th
e
u
s
er
is
ac
h
iev
ed
[
3
9
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
1
,
Feb
r
u
ar
y
20
2
6
:
49
-
64
54
2
.
2
.
I
m
pli
cit
s
t
o
cha
s
t
ic
o
pti
m
iza
t
io
n f
o
rm
ula
t
io
n f
o
r
t
he
hy
dro
-
t
herm
a
l
o
pera
t
io
n pla
nn
ing
I
n
g
en
er
al,
HT
OP
is
wr
itten
as
a
m
in
im
izatio
n
f
u
n
ctio
n
wh
o
s
e
aim
is
t
o
d
eter
m
in
e
t
h
e
o
p
tim
al
co
m
b
in
atio
n
o
f
a
v
ailab
le
g
e
n
er
atio
n
r
eso
u
r
ce
s
to
p
r
o
v
id
e
th
e
d
em
an
d
to
m
i
n
im
ize
th
e
s
u
m
o
f
p
r
o
d
u
ctio
n
co
s
ts
ass
o
ciate
d
with
th
er
m
al
u
n
its
an
d
p
e
n
alty
co
s
ts
d
u
e
to
n
o
n
-
s
u
p
p
lied
en
e
r
g
y
f
o
r
a
g
iv
e
n
h
o
r
iz
o
n
,
wh
ic
h
is
u
s
u
ally
s
u
b
d
iv
id
e
d
in
to
s
ev
er
al
in
ter
v
als
[
3
]
.
T
h
e
a
n
n
u
al
h
o
r
izo
n
is
d
iv
id
e
d
in
to
s
u
cc
ess
iv
e
wee
k
ly
in
ter
v
als
to
r
ed
u
ce
co
m
p
u
tatio
n
al
ef
f
o
r
t.
T
o
co
n
s
id
er
th
e
s
to
ch
asti
c
n
atu
r
e
o
f
wate
r
in
f
lo
ws
with
in
th
e
o
p
tim
izatio
n
p
r
o
b
lem
,
t
h
is
wo
r
k
em
p
lo
y
ed
th
e
I
SO
s
tr
ateg
y
.
I
n
th
is
way
,
th
e
f
o
r
m
u
latio
n
f
o
r
t
h
e
HOT
P
p
r
o
b
lem
is
wr
itten
in
ter
m
s
o
f
an
o
b
jectiv
e
f
u
n
c
tio
n
f
o
r
ea
ch
s
ce
n
a
r
io
(
)
,
d
e
f
in
ed
b
y
n
o
d
es,
as
s
h
o
wn
in
(
5
)
,
an
d
its
ass
o
ciate
d
r
estrictio
n
s
,
d
escr
ib
ed
b
y
(
5
)
:
=
min
∑
[
∑
(
,
)
=
1
+
∑
̃
(
̃
,
)
=
1
]
=
1
(
5
)
s
u
b
ject
to
:
∑
,
=
1
+
∑
,
=
1
+
∑
̃
,
=
1
=
∑
,
=
1
,
(
6
a)
,
=
∑
,
∈
,
(
6
b
)
,
=
⋅
(
,
,
,
)
,
(
6
c)
,
+
1
=
,
+
[
,
−
∑
,
,
∈
−
,
+
∑
(
,
,
+
,
,
)
∈
]
⋅
,
(
6
d
)
,
=
ℒ
×
ℬ
⋅
(
,
+
,
+
̃
,
−
,
)
,
(
6
e)
≤
,
≤
,
(
6
f
)
≤
,
≤
,
(
6
g
)
≤
,
,
≤
,
(
6
h
)
≤
,
≤
,
(
6
i)
≤
,
≤
,
(
6
j)
wh
er
e:
: Sce
n
ar
io
s
in
d
ex
(
: to
tal
n
u
m
b
er
o
f
s
ce
n
a
r
io
s
o
f
th
e
tr
ee
to
b
e
o
p
tim
ized
)
: Stag
es in
d
ex
(
: to
tal
n
u
m
b
er
o
f
s
tag
es)
: T
h
er
m
al
u
n
its
in
d
ex
(
: to
tal
n
u
m
b
er
o
f
t
h
er
m
al
p
lan
ts
)
: Res
er
v
o
ir
s
in
d
ex
(
: to
tal
n
u
m
b
er
o
f
r
eser
v
o
i
r
s
)
: H
y
d
r
o
p
lan
ts
in
d
ex
(
: to
tal
n
u
m
b
er
o
f
h
y
d
r
o
p
lan
ts
)
: T
r
an
s
m
is
s
io
n
lin
es in
d
ex
(
: to
tal
n
u
m
b
e
r
o
f
lin
es)
: I
n
d
ex
to
th
e
s
et
o
f
p
lan
ts
d
ir
ec
tly
u
p
s
tr
ea
m
o
f
r
eser
v
o
ir
: I
n
d
ex
o
f
s
y
s
tem
b
u
s
es (
: to
tal
n
u
m
b
er
o
f
b
u
s
es)
: T
im
e
d
u
r
atio
n
o
f
ea
ch
s
tag
e
[
h
]
,
:
T
h
er
m
al
g
e
n
er
atio
n
o
f
u
n
it
n
at
s
tag
e
o
f
s
ce
n
ar
io
in
[
MW]
̃
,
:
Po
wer
n
o
t su
p
p
lied
in
b
u
s
at
s
tag
e
o
f
s
ce
n
ar
io
in
[
MW]
(
,
)
:
C
o
s
t f
u
n
ctio
n
o
f
u
n
it
at
s
tag
e
o
f
s
ce
n
ar
io
in
[
$
]
̃
(
̃
,
)
:
C
o
s
t o
f
n
o
t ser
v
ed
en
er
g
y
in
[
$
]
ass
o
ciate
d
to
b
u
s
at
s
tag
e
o
f
s
ce
n
ar
io
,
:
Po
wer
o
u
tp
u
t in
[
MW]
o
f
th
er
m
al
u
n
its
co
n
n
ec
ted
to
b
u
s
at
s
tag
e
o
f
s
ce
n
ar
io
,
:
Po
wer
o
u
tp
u
t in
[
MW]
o
f
h
y
d
r
o
p
la
n
ts
co
n
n
ec
ted
to
b
u
s
at
s
tag
e
o
f
s
ce
n
ar
io
,
:
L
o
ad
d
e
m
an
d
i
n
[
MW]
o
f
b
u
s
at
s
tag
e
o
f
s
ce
n
ar
io
,
:
Po
wer
o
u
tp
u
t in
[
MW]
o
f
h
y
d
r
o
p
la
n
t
ass
o
ciate
d
to
r
eser
v
o
ir
at
s
tag
e
o
f
s
ce
n
ar
io
,
:
Po
wer
o
u
tp
u
t in
[
MW]
o
f
h
y
d
r
o
p
la
n
ts
ass
o
ciate
d
to
r
eser
v
o
ir
at
s
tag
e
o
f
s
ce
n
ar
io
,
:
Vo
lu
m
e
in
[
h
m
3
]
o
f
wate
r
s
t
o
r
ed
in
r
eser
v
o
ir
at
s
tag
e
o
f
s
ce
n
ar
io
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
-
8
7
0
8
S
to
ch
a
s
tic
p
la
n
n
in
g
o
f m
u
lti
-
b
u
s
h
yd
r
o
th
erma
l sys
tems u
s
i
n
g
…
(
Ma
r
th
a
P
a
tr
icia
C
a
ma
r
g
o
-
Ma
r
tín
ez
)
55
,
: Water
in
f
lo
w
in
[
h
m
3
/
h
]
ar
r
i
v
in
g
at
r
eser
v
o
ir
at
s
tag
e
o
f
s
ce
n
ar
io
,
:
T
u
r
b
in
e
d
o
u
tf
lo
w
in
[
h
m
3
/h
]
o
f
a
h
y
d
r
o
p
lan
t a
s
s
o
ciate
d
to
r
eser
v
o
ir
at
s
tag
e
o
f
s
ce
n
ar
io
,
:
Sp
illag
e
in
[
h
m
3
/h
]
o
f
r
eser
v
o
ir
at
s
tag
e
in
s
ce
n
ar
io
:
Pro
d
u
ctiv
ity
f
ac
to
r
o
f
h
y
d
r
o
p
lan
t m
in
[
MWh
/m
3
]
,
:
Po
wer
f
lo
w
f
o
r
lin
e
l
at
s
tag
e
o
f
s
ce
n
ar
io
in
[
MW]
ℒ
×
ℬ
:
B
r
an
ch
-
to
-
b
u
s
in
cid
en
ce
m
a
tr
ix
Kee
p
in
m
in
d
th
at
in
th
e
I
SO m
o
d
el,
ea
ch
s
ce
n
ar
io
is
o
p
tim
i
ze
d
in
d
ep
e
n
d
en
tly
.
T
h
en
,
th
ey
ar
e
weig
h
ted
b
y
th
eir
p
r
o
b
ab
ilit
y
o
f
o
b
tain
i
n
g
t
h
e
ex
p
ec
ted
v
alu
e
(
E
V)
d
escr
i
b
ed
b
y
(
7
)
.
=
∑
=
1
⋅
π
(
7
)
2
.
3
.
M
et
a
heuris
t
ics
t
ec
hn
iq
ues
Mo
s
t
m
etah
eu
r
is
tic
alg
o
r
ith
m
s
ar
e
b
ased
o
n
e
v
o
lu
tio
n
alg
o
r
ith
m
s
s
u
ch
as
GA,
PS
O,
d
if
f
er
en
tial
ev
o
lu
tio
n
a
n
d
ev
o
lu
tio
n
a
r
y
s
tr
ateg
ies
(
E
S)
[
1
7
]
.
Oth
er
ev
o
lu
tio
n
alg
o
r
ith
m
s
wer
e
r
ec
en
t
ly
d
ev
elo
p
e
d
,
e.
g
.
,
m
ed
ian
-
v
a
r
ian
ce
m
ap
p
i
n
g
o
p
t
im
izatio
n
(
MV
MO
)
[
4
0
]
.
Pre
v
io
u
s
wo
r
k
s
s
h
o
wed
a
f
av
o
r
a
b
le
ad
ap
tatio
n
o
f
th
e
alg
o
r
ith
m
i
n
co
m
p
ar
is
o
n
to
s
i
m
ilar
tech
n
iq
u
es
wh
en
ap
p
lie
d
to
t
h
e
HT
OP
p
r
o
b
lem
[
4
1
]
.
MV
MO
h
as
s
o
m
e
f
u
n
d
am
e
n
tal
co
n
ce
p
t
u
al
s
im
ilar
ities
to
o
th
er
h
eu
r
is
tic
ap
p
r
o
ac
h
es.
Ho
wev
er
,
it
ex
p
lo
its
th
e
s
tatis
tical
attr
ib
u
te
o
f
s
ea
r
ch
d
y
n
a
m
ics
b
y
u
s
in
g
a
u
n
iq
u
e
m
ap
p
i
n
g
f
u
n
ctio
n
f
o
r
m
u
tatio
n
o
p
er
atio
n
s
b
ase
d
o
n
th
e
m
ea
n
an
d
v
ar
ian
ce
o
f
th
e
-
b
est
s
o
lu
tio
n
s
ac
h
iev
ed
s
o
f
ar
an
d
s
av
ed
in
a
co
n
tin
u
o
u
s
ly
u
p
d
ated
ar
ch
i
v
e.
I
n
ad
d
itio
n
,
th
e
b
asic
im
p
lem
en
tatio
n
o
f
MV
MO
is
ch
ar
ac
ter
ized
b
y
a
s
in
g
le
-
p
ar
ticle
ap
p
r
o
ac
h
wh
o
s
e
tr
ad
e
-
o
f
f
b
etwe
en
s
ea
r
ch
d
iv
er
s
if
icatio
n
an
d
in
t
en
s
if
icatio
n
tr
an
s
lates
in
to
f
a
s
t
p
r
o
g
r
ess
r
ates
with
r
ed
u
ce
d
r
is
k
o
f
p
r
em
atu
r
e
co
n
v
er
g
en
ce
.
T
h
e
r
ec
en
t
v
ar
ian
t
o
f
th
e
m
ea
n
-
v
ar
ian
ce
m
ap
p
i
n
g
o
p
tim
izat
io
n
(
MV
MO
-
SH)
alg
o
r
ith
m
e
n
h
an
ce
s
its
ef
f
icien
cy
b
y
i
n
co
r
p
o
r
atin
g
a
m
u
lti
-
p
ar
en
t
cr
o
s
s
o
v
er
s
tr
ateg
y
,
in
cr
ea
s
in
g
p
o
p
u
latio
n
d
iv
er
s
ity
,
an
d
im
p
r
o
v
in
g
s
o
lu
tio
n
q
u
ality
.
As
d
escr
ib
e
d
in
[
4
2
]
,
th
e
al
g
o
r
ith
m
b
eg
i
n
s
b
y
in
itializin
g
its
p
ar
am
et
er
s
an
d
g
en
e
r
atin
g
a
n
o
r
m
alize
d
in
itial
p
o
p
u
latio
n
o
f
p
ar
ticles.
I
t
th
en
ev
alu
ates
th
e
p
o
p
u
latio
n
f
itn
ess
an
d
ap
p
lies
lo
ca
l
s
ea
r
ch
tech
n
iq
u
es
wh
en
n
ec
ess
ar
y
t
o
im
p
r
o
v
e
s
o
lu
tio
n
s
wh
ile
m
ain
tain
in
g
a
co
u
n
ter
to
tr
a
ck
th
e
n
u
m
b
er
o
f
iter
atio
n
s
.
B
y
u
p
d
atin
g
a
n
in
d
i
v
id
u
al
ar
ch
i
v
e,
th
e
alg
o
r
ith
m
m
ain
tain
s
a
s
et
o
f
g
o
o
d
an
d
b
a
d
p
ar
ticles,
th
er
eb
y
g
u
id
in
g
f
u
tu
r
e
s
ea
r
ch
s
tep
s
.
Du
r
in
g
th
e
o
f
f
s
p
r
in
g
g
en
er
at
io
n
p
h
ase,
th
e
alg
o
r
ith
m
ap
p
lies
s
in
g
le
-
p
ar
en
t
cr
o
s
s
o
v
er
to
b
ad
p
ar
ticles
b
as
ed
o
n
th
e
l
o
ca
l
b
est
s
o
lu
tio
n
s
to
ex
p
lo
it
n
ea
r
b
y
p
r
o
m
is
in
g
r
e
g
io
n
s
.
On
th
e
o
t
h
er
h
an
d
,
th
e
m
u
tatio
n
is
ap
p
lied
b
y
m
ap
p
i
n
g
s
elec
ted
d
im
en
s
io
n
s
u
s
in
g
th
e
lo
ca
l
m
ea
n
an
d
v
ar
ian
ce
,
en
s
u
r
in
g
v
ar
iab
ilit
y
in
th
e
g
en
er
ate
d
o
f
f
s
p
r
in
g
.
T
h
e
alg
o
r
ith
m
e
v
alu
ates
if
th
e
s
to
p
p
in
g
co
n
d
itio
n
s
ar
e
m
et,
s
u
ch
as
co
m
p
letin
g
t
h
e
m
ax
im
u
m
n
u
m
b
er
o
f
iter
atio
n
s
o
r
ac
h
iev
in
g
a
s
o
lu
ti
o
n
o
f
th
e
r
eq
u
i
r
ed
q
u
ality
.
I
f
th
e
co
n
v
er
g
en
ce
c
r
iter
ia
ar
e
n
o
t
ac
co
m
p
lis
h
ed
,
t
h
e
p
r
o
ce
s
s
r
e
p
ea
ts
f
r
o
m
th
e
f
itn
ess
ev
alu
a
tio
n
s
tep
u
n
til
th
e
alg
o
r
ith
m
s
to
p
s
an
d
o
u
t
p
u
ts
th
e
b
est s
o
lu
tio
n
f
o
u
n
d
.
3.
M
E
T
H
O
D
T
h
e
p
r
im
ar
y
o
b
jectiv
e
o
f
t
h
is
s
ec
tio
n
is
to
em
p
ir
ically
v
alid
ate
th
e
co
n
ce
p
ts
,
ass
er
tio
n
s
,
an
d
th
eo
r
etica
l
id
ea
s
d
escr
ib
ed
ab
o
v
e,
ex
h
i
b
itin
g
th
e
co
m
p
lex
ch
ar
ac
ter
is
tics
o
f
th
e
HT
OP
p
r
o
b
lem
th
at
wer
e
in
clu
d
ed
in
th
e
p
r
o
p
o
s
ed
m
eth
o
d
o
lo
g
y
.
T
h
e
p
o
wer
s
y
s
tem
an
d
ex
p
er
im
en
tal
p
r
o
ce
s
s
ar
e
d
etailed
b
elo
w.
3
.
1
.
Sy
s
t
e
m
W
e
p
r
o
p
o
s
e
a
s
im
u
lated
th
r
ee
-
b
u
s
p
o
wer
s
y
s
tem
w
h
ich
c
o
n
s
id
er
s
th
r
ee
tr
a
n
s
m
is
s
io
n
lin
es,
as
s
h
o
wn
Fig
u
r
e
3
.
T
h
e
tr
an
s
m
is
s
io
n
s
y
s
tem
is
ass
u
m
ed
to
b
e
lo
s
s
less
.
B
u
s
B
1
is
s
u
p
p
lied
b
y
two
th
e
r
m
al
g
en
e
r
ato
r
s
:
GT
1
an
d
GT
2
;
b
u
s
B
2
b
y
a
h
y
d
r
au
lic
g
e
n
er
ato
r
GH
1
;
an
d
b
u
s
B
3
b
y
a
h
y
d
r
au
lic
g
en
er
ato
r
GH
2
.
I
n
ea
ch
b
u
s
,
f
ictitio
u
s
g
en
er
ato
r
s
GF
1
,
GF
2
,
an
d
GF
3
a
r
e
in
co
r
p
o
r
ated
t
o
co
n
s
id
er
ca
s
es
wh
er
e
th
e
s
y
s
tem
ca
n
n
o
t
s
u
p
p
ly
en
er
g
y
.
T
h
er
m
al
p
o
wer
p
lan
ts
ar
e
m
o
d
eled
b
y
a
lin
ea
r
co
s
t f
u
n
ctio
n
,
g
iv
en
i
n
(
8
)
.
(
,
)
=
⋅
,
(
8
)
T
h
eir
co
s
ts
an
d
m
ain
tech
n
i
ca
l
p
ar
am
eter
s
ar
e
p
r
esen
te
d
in
T
ab
le
1
.
Similar
ly
,
a
li
n
ea
r
co
s
t
f
u
n
ctio
n
1500
̃
,
[
$
]
was a
s
s
u
m
ed
f
o
r
p
o
wer
n
o
t su
p
p
lied
b
y
g
en
er
at
o
r
s
.
On
th
e
o
th
e
r
h
a
n
d
,
h
y
d
r
o
elec
t
r
ic
p
lan
ts
ar
e
m
o
d
eled
with
t
h
e
co
n
s
tan
t
p
r
o
d
u
ctio
n
f
u
n
ctio
n
d
escr
ib
ed
in
(
9
)
.
I
n
th
is
ca
s
e,
ea
ch
r
eser
v
o
ir
o
n
ly
h
as
o
n
e
h
y
d
r
o
-
p
lan
t
ass
o
ciate
d
with
it,
s
o
was
u
s
e
d
as
a
s
u
b
s
cr
ip
t
in
th
e
ex
p
r
ess
io
n
s
.
(
m
,
)
=
⋅
,
(
9
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
1
,
Feb
r
u
ar
y
20
2
6
:
49
-
64
56
All
p
ar
am
eter
s
f
o
r
h
y
d
r
o
-
p
la
n
ts
ar
e
d
escr
ib
ed
in
T
a
b
le
2
.
T
h
e
p
ar
am
ete
r
s
o
f
th
e
tr
an
s
m
is
s
io
n
n
etwo
r
k
ar
e
s
h
o
wn
in
T
ab
le
3
.
Fig
u
r
e
3
.
Sin
g
le
-
p
h
ase
d
iag
r
a
m
o
f
th
e
p
o
wer
s
y
s
tem
T
ab
le
1
.
Par
am
eter
s
of
the
r
m
a
l
ge
n
e
r
a
tor
s
Th
e
r
m
a
l
P
l
a
n
t
(
)
B
u
s
(
)
í
[
M
W
]
[
M
W
]
[
$
/
M
W
h
]
GT
1
1
0
1
0
0
9
0
.
2
2
GT
2
1
0
50
1
3
5
.
3
2
GF
1
,
GF
2
,
GF
3
1
,
2
,
3
0
1
0
0
0
1
5
0
0
0
T
ab
le
2
.
Par
am
eter
s
o
f
h
y
d
r
au
lic
g
en
er
ato
r
s
H
y
d
r
o
P
l
a
n
t
(
)
B
u
s
(
)
í
[
h
m
3
]
[
hm
3
]
0
[
h
m
3
]
[
h
m
3
]
[
M
W
/
m
3
/
s]
á
[m
3
/
s]
á
[
M
W
]
GN
1
2
3
0
0
1
2
0
0
5
0
0
5
0
0
0
.
7
2
3
0
0
2
1
6
GN
2
3
3
0
0
8
0
0
4
0
0
4
0
0
0
.
7
2
1
5
0
1
0
8
T
ab
le
3
.
Par
am
eter
s
o
f
tr
an
s
m
is
s
io
n
n
etwo
r
k
Li
n
e
(
)
B
u
s
c
o
n
n
e
c
t
i
o
n
S
u
sce
p
t
a
n
c
e
[
p
.
u
]
[
MW
]
1
1
-
2
0
.
0
4
7
60
2
1
-
3
0
.
0
2
3
60
3
3
-
2
0
.
0
6
4
60
W
ith
r
esp
ec
t
to
lo
ad
d
em
an
d
,
it
is
m
o
d
eled
b
y
D
1
,
D
2
,
an
d
D
3
u
s
in
g
a
l
o
ad
d
u
r
atio
n
cu
r
v
e
(
L
DC
)
with
f
o
u
r
(
4
)
lo
ad
lev
els
f
o
r
e
ac
h
o
n
e
,
as
illu
s
tr
ated
in
Fig
u
r
e
4
.
T
h
e
L
DC
g
r
ap
h
d
ep
icts
th
e
p
o
wer
s
u
p
p
lied
o
v
er
tim
e,
with
d
is
tin
ct
m
o
n
th
ly
lo
ad
s
eg
m
en
ts
(
b
lo
ck
s
)
co
r
r
esp
o
n
d
in
g
to
d
if
f
er
e
n
t
p
o
wer
l
ev
els,
all
with
th
e
s
am
e
d
u
r
atio
n
s
o
f
4
0
,
3
0
0
,
2
7
0
,
an
d
1
2
0
h
o
u
r
s
p
er
m
o
n
th
.
No
te
th
at
th
e
tim
e
h
o
r
izo
n
f
o
r
th
e
o
p
tim
izatio
n
is
d
ef
in
ed
as o
n
e
y
ea
r
,
d
iv
id
e
d
in
to
twelv
e
m
o
n
th
l
y
in
ter
v
als.
Fig
u
r
e
4
.
L
DC
with
f
o
u
r
lo
a
d
lev
els
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
-
8
7
0
8
S
to
ch
a
s
tic
p
la
n
n
in
g
o
f m
u
lti
-
b
u
s
h
yd
r
o
th
erma
l sys
tems u
s
i
n
g
…
(
Ma
r
th
a
P
a
tr
icia
C
a
ma
r
g
o
-
Ma
r
tín
ez
)
57
3
.
2
.
M
et
ho
do
lo
g
y
T
h
is
s
ec
tio
n
p
r
o
v
i
d
es
a
clea
r
an
d
s
tr
u
ctu
r
ed
e
x
p
o
s
itio
n
o
f
th
e
m
eth
o
d
s
ap
p
lied
.
T
h
i
s
ap
p
r
o
ac
h
in
teg
r
ates
g
en
er
atio
n
tim
e
s
er
ies,
s
ce
n
ar
io
tr
ee
co
n
s
tr
u
ctio
n
an
d
r
ed
u
ctio
n
,
an
d
o
p
tim
iz
atio
n
tech
n
iq
u
es
to
ad
d
r
ess
th
e
co
m
p
le
x
ities
o
f
HT
OP u
n
d
er
u
n
ce
r
tain
ty
.
3
.
2
.
1
.
T
im
e
s
er
ies
g
ener
a
t
io
n
A
to
tal
of
1
0
0
0
0
tim
e
s
er
ies
o
f
wate
r
in
f
l
o
ws
f
o
r
th
e
2
r
eser
v
o
ir
s
wer
e
g
en
er
ate
d
d
u
r
i
n
g
th
e
1
2
s
tag
es,
u
s
in
g
an
au
to
-
r
eg
r
ess
iv
e
m
o
d
el
[
4
3
]
,
as sh
o
wn
in
(
1
0
).
,
=
,
+
,
,
(
10
)
wh
er
e
is
in
d
ex
r
esp
ec
t to
s
to
r
ag
e
,
,
is
wate
r
in
f
lo
w
o
f
r
eser
v
o
ir
at
s
tag
e
,
,
is
p
er
io
d
ic
m
ea
n
o
f
wate
r
in
f
lo
w
o
f
r
eser
v
o
ir
at
s
tag
e
,
,
is
p
er
io
d
ic
s
tan
d
ar
d
d
ev
iatio
n
o
f
wate
r
in
f
lo
w
o
f
r
eser
v
o
ir
at
s
tag
e
;
,
is
r
an
d
o
m
v
ar
iab
le
.
I
n
th
is
ca
s
e,
,
r
ep
r
esen
ts
th
e
in
f
lo
ws
in
r
eser
v
o
i
r
at
s
tag
e
.
E
ac
h
o
n
e
ca
n
b
e
m
o
d
eled
w
ith
a
f
ir
s
t o
r
d
er
a
u
to
-
r
e
g
r
ess
iv
e
m
o
d
el
d
escr
ib
ed
b
y
(
1
1
)
:
,
=
1
,
(
−
1
)
+
√
1
−
1
2
(
11)
B
y
r
ep
lacin
g
(
1
1
)
i
n
(
1
0
)
,
it is
o
b
tain
ed
:
,
=
,
+
,
(
1
,
(
−
1
)
−
,
(
−
1
)
,
(
−
1
)
+
√
1
−
1
2
)
wh
er
e
1
is
th
e
au
to
c
o
r
r
elatio
n
co
ef
f
icien
t
in
=
1
o
f
th
e
r
an
d
o
m
v
ar
iab
le
an
d
is
th
e
i
n
d
e
p
en
d
en
t
r
an
d
o
m
r
esid
u
e
.
,
an
d
,
ar
e
esti
m
ated
f
r
o
m
h
is
to
r
ical
wate
r
in
f
lo
w.
I
t
was
ass
u
m
ed
t
h
at
1
was
eq
u
al
t
o
0
.
5
.
is
a
r
an
d
o
m
n
u
m
b
er
tak
en
f
r
o
m
a
n
o
r
m
al
d
is
tr
ib
u
tio
n
(
0
,
1
)
.
T
h
e
o
r
ig
in
al
d
ata
an
d
th
e
o
b
tain
ed
s
er
ies ar
e
s
h
o
wn
in
Fig
u
r
e
5
.
Fig
u
r
e
5
.
Or
ig
i
n
al
d
ata
an
d
th
e
o
b
tain
ed
s
er
ies f
o
r
th
e
r
eser
v
o
ir
s
o
f
1
an
d
2
3
.
2
.
2
.
Scena
rio
s
t
re
e
T
h
e
PC
M
d
escr
ib
ed
in
s
ec
tio
n
2
.
1
.
2
.
was
ap
p
lied
to
g
en
er
ate
a
s
ce
n
ar
io
t
r
ee
.
T
h
e
p
r
o
p
o
s
ed
s
tr
u
ctu
r
e
is
as
f
o
llo
ws:
th
e
f
ir
s
t
s
tag
e
h
as
o
n
e
b
r
an
ch
;
f
r
o
m
th
e
2
nd
t
o
th
e
1
2
th
s
tag
e,
e
ac
h
n
o
d
e
b
r
an
ch
es
in
to
two
to
o
b
tain
a
tr
ee
(
with
two
d
im
en
s
io
n
s
,
o
n
e
f
o
r
ea
c
h
r
eser
v
o
i
r
)
w
ith
2
11
s
ce
n
ar
io
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
1
,
Feb
r
u
ar
y
20
2
6
:
49
-
64
58
3
.
2
.
3
.
Scena
rio
re
du
ct
io
n
T
h
e
s
ce
n
ar
io
r
ed
u
ctio
n
PS
O
m
en
tio
n
ed
ab
o
v
e
was
ap
p
lied
,
wh
er
e
t
h
e
s
ea
r
ch
s
p
ac
e
co
m
p
r
is
es
th
e
co
m
p
lete
s
et
o
f
s
ce
n
ar
io
s
f
r
o
m
th
e
o
r
ig
in
al
tr
ee
.
Fifty
p
a
r
ticles
wer
e
s
elec
ted
as
in
p
u
t
p
ar
am
eter
s
f
o
r
th
e
s
war
m
.
I
n
th
is
way
,
(
2
11
)
2
s
ce
n
ar
i
o
s
f
r
o
m
t
h
e
o
r
i
g
in
al
tr
ee
we
r
e
r
ed
u
ce
d
o
n
ly
to
5
0
s
ce
n
a
r
io
s
f
o
r
ea
ch
r
eser
v
o
ir
,
as is
d
ep
icted
i
n
Fig
u
r
e
6
.
Fig
u
r
e
6
.
Or
ig
i
n
al
an
d
r
ed
u
ce
d
tr
ee
f
o
r
th
e
r
eser
v
o
ir
s
o
f
1
an
d
2
3
.
2
.
4
.
O
ptim
iza
t
io
n
m
o
del f
o
r
ea
ch
s
ce
na
rio
E
ac
h
s
ce
n
ar
io
was so
lv
ed
b
y
m
ea
n
s
o
f
two
tech
n
iq
u
es:
a.
L
P:
Usi
n
g
th
e
f
u
n
ctio
n
o
f
M
AT
L
AB
,
th
e
f
o
r
m
u
latio
n
was
wr
itten
in
m
atr
ix
ter
m
s
.
Du
e
to
th
e
m
ath
em
atica
l f
u
n
d
am
en
tals
o
f
th
is
k
in
d
o
f
o
p
tim
izatio
n
,
th
e
g
lo
b
al
s
o
lu
tio
n
is
o
b
tain
ed
.
b.
MV
MO
:
T
h
e
ad
ap
tab
ilit
y
o
f
m
etah
eu
r
is
tic
tech
n
iq
u
es
f
ac
il
itates
th
e
d
iv
is
io
n
o
f
HOT
P
in
to
h
y
d
r
o
a
n
d
th
er
m
al
s
u
b
-
p
r
o
b
lem
s
.
T
h
is
r
e
s
u
lt
was
u
s
ed
a
s
v
alid
atio
n
an
d
in
tr
o
d
u
ce
d
a
to
o
l
th
at
co
u
ld
b
e
u
s
ed
in
n
o
n
-
lin
ea
r
o
r
n
o
n
-
c
o
n
v
e
x
p
r
o
b
lem
s
.
T
h
is
p
r
o
ce
d
u
r
e
is
d
escr
ib
ed
b
elo
w.
−
T
h
e
s
to
r
ag
e
v
ar
ia
b
les
,
ar
e
d
e
f
in
ed
as
o
p
tim
izatio
n
v
a
r
iab
l
es
o
r
in
d
iv
id
u
als.
I
n
th
is
way
,
ev
er
y
in
d
iv
id
u
al
h
as
a
le
n
g
th
o
f
·
=
12
·
2
=
24
.
A
L
P
alg
o
r
ith
m
is
u
s
ed
t
o
h
a
n
d
l
e
wate
r
b
alan
ce
co
n
s
tr
ain
ts
in
s
tead
o
f
u
s
in
g
a
p
en
alty
s
ch
em
e.
Giv
en
th
at
in
f
lo
ws
,
ar
e
p
r
ed
eter
m
in
ed
in
ea
ch
s
ce
n
ar
io
an
d
th
at
th
e
o
p
tim
izatio
n
alg
o
r
ith
m
s
p
r
o
p
o
s
e
th
e
,
v
alu
es
with
in
t
h
e
s
ea
r
c
h
b
o
u
n
d
a
r
ies,
th
e
p
u
r
p
o
s
e
o
f
u
s
in
g
a
L
P
is
to
d
eter
m
in
e
t
h
e
v
alu
es
o
f
,
an
d
,
s
u
ch
th
at
(
6
d
)
is
s
atis
f
ied
.
Nev
er
th
eless
,
th
e
f
u
lf
illme
n
t
o
f
th
e
m
ax
im
u
m
b
o
u
n
d
s
o
f
,
an
d
,
is
n
o
t
g
u
ar
a
n
teed
wh
en
u
s
in
g
L
P.
T
o
o
v
er
c
o
m
e
th
is
p
r
o
b
lem
,
a
h
eu
r
is
tic
r
u
le
is
ap
p
lied
af
ter
p
er
f
o
r
m
i
n
g
L
P
to
en
s
u
r
e
th
at
,
≤
.
C
o
n
s
i
d
er
in
g
th
at
,
≥
0
is
th
e
o
n
ly
co
n
d
itio
n
f
o
r
,
,
th
e
r
u
le
is
d
ef
in
ed
as f
o
llo
ws:
,
=
{
0
,
0
<
,
≤
,
−
,
,
>
with
,
an
d
,
in
[
h
m
3
/h
]
f
r
o
m
h
y
d
r
o
elec
tr
ic
g
en
er
ati
o
n
6
d
a
n
d
th
e
p
r
o
d
u
ctio
n
f
ac
to
r
f
r
o
m
T
a
b
le
2
,
t
h
e
to
tal
h
y
d
r
au
lic
en
er
g
y
in
ea
ch
s
tag
e
ca
n
b
e
ca
lcu
lated
.
−
Fro
m
th
e
v
alu
es,
th
er
m
al
g
en
er
atio
n
s
,
an
d
h
y
d
r
o
elec
tr
ic
g
en
er
atio
n
s
,
in
ea
ch
lo
ad
d
em
an
d
b
o
x
ar
e
o
b
tain
ed
t
h
r
o
u
g
h
a
D
C
lo
ad
f
lo
w
u
s
in
g
L
P.
Valu
es
o
f
,
ar
e
r
ep
lace
d
in
th
e
c
o
s
t
f
u
n
ctio
n
f
r
o
m
(8
)
,
wh
er
e
th
e
o
u
tco
m
es
ar
e
c
o
n
s
id
er
ed
as
th
e
f
itn
ess
f
u
n
ctio
n
o
f
th
e
in
d
iv
id
u
al
.
T
h
e
MV
MO
alg
o
r
ith
m
r
u
n
s
u
n
til th
e
c
o
n
v
e
r
g
en
ce
c
r
iter
io
n
is
ac
co
m
p
lis
h
ed
.
Evaluation Warning : The document was created with Spire.PDF for Python.