T
E
L
KO
M
NIK
A
, V
ol
.
17
,
No.
5,
O
c
tob
er
20
1
9,
p
p.
2
53
5
~
2546
IS
S
N: 1
69
3
-
6
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accr
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F
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K
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r
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No: 2
1/E/
K
P
T
/20
18
DOI:
10.12928/TE
LK
OM
N
IK
A
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1
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12539
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strac
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i
s
p
a
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t
s
a
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a
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i
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p
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ta
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ti
c
,
c
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d
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s
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c
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a
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c
fra
c
ta
l
s
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a
rc
h
b
a
s
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d
m
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th
o
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(SFS)
fo
r
c
o
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g
wit
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m
p
l
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c
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o
a
d
d
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D)
p
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o
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e
m
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SF
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d
s
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c
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d
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m
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n
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f
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n
d
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m
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s
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s
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n
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c
h
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a
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s
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a
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ra
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k
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s
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d
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a
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s
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g
h
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SFS
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y
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e
p
e
r
fo
rm
a
n
c
e
o
f
t
h
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two
a
p
p
l
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d
m
e
th
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d
s
i
s
i
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v
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g
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te
d
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o
m
p
a
ri
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g
r
e
s
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l
t
s
o
b
ta
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d
fro
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c
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t
s
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c
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d
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d
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s
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i
s
e
l
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d
a
te
s
th
a
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th
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EL
D p
r
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b
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m
.
Key
w
ords
:
e
c
o
n
o
m
i
c
l
o
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d
d
i
s
p
a
tc
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p
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o
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,
s
t
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ta
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s
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v
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p
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Copy
righ
t
©
2
0
1
9
Uni
v
e
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t
a
s
Ahm
a
d
D
a
hl
a
n.
All
rig
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s
r
e
s
e
rve
d
.
No
men
cla
t
u
r
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m
i
, n
i
,
o
i
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f
f
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of
th
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th
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p
i
, q
i
v
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l
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ef
f
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c
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c
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ts
of
th
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i
th
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m
il
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o
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f
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l
c
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f
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or f
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or f
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t
C
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N
tot
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r
of
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ne
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at
ors
P
SL
D
tot
a
l
s
y
s
t
em
l
oa
d
d
em
an
d
1.
Int
r
o
d
u
ctio
n
E
c
on
om
i
c
l
o
ad
di
s
p
atc
h
(
E
LD)
prob
l
em
i
s
be
c
om
i
ng
m
ore
i
m
po
r
tan
t
i
n
po
wer
s
y
s
t
em
op
erat
i
o
n
a
nd
c
o
ntrol
.
T
he
prim
e
ob
j
ec
ti
v
e
of
th
e
E
LD
probl
em
i
s
to
m
i
ni
m
i
z
e
th
e
tot
a
l
f
ue
l
c
os
t
b
y
ec
o
no
m
i
c
al
l
y
d
i
s
tr
i
b
uti
ng
po
w
er
of
ge
ne
r
at
i
n
g
un
i
ts
t
o
el
ec
tr
i
c
l
o
ad
.
I
n
a
dd
i
ti
o
n,
l
oa
d
d
em
an
d,
al
l
ph
y
s
i
c
al
an
d
op
era
ti
o
na
l
c
o
ns
tr
ai
nts
ar
e
r
eq
u
i
r
ed
to
b
e
w
i
thi
n
pre
de
ter
m
i
ne
d
bo
un
ds
.
In
tr
ad
i
ti
on
a
l
E
LD
prob
l
e
m
,
a
f
ue
l
c
os
t
f
un
c
ti
on
of
ge
n
erators
i
s
c
on
s
i
de
r
e
d
as
the
s
i
ng
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e
qu
ad
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ati
c
c
os
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f
un
c
ti
o
n
w
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t
h
l
i
ne
ar
c
o
ns
tr
ai
n
t
[1]
.
In
p
r
ac
ti
c
al
,
r
e
al
i
s
ti
c
E
LD
pro
bl
em
m
u
s
t
tak
e
c
o
m
pl
ex
a
nd
no
n
l
i
ne
ar
c
ha
r
ac
teri
s
ti
c
wi
th
m
an
y
e
qu
al
i
t
y
an
d
i
ne
q
ua
l
i
t
y
c
on
s
tr
ai
nt
s
i
nt
o
ac
c
ou
nt
to
pro
v
i
de
t
he
c
om
pl
ete
ne
s
s
f
or the
E
LD
prob
l
em
f
or
mu
l
at
i
o
n.
Evaluation Warning : The document was created with Spire.PDF for Python.
◼
IS
S
N: 16
93
-
6
93
0
T
E
L
KO
M
NIK
A
V
ol
.
17
,
No
.
5,
O
c
tob
er 20
19
:
25
3
5
-
25
46
2536
T
hu
s
,
f
ue
l
c
os
t
c
ur
v
e
of
th
erm
al
un
i
ts
s
ho
u
l
d
be
pr
es
en
t
e
d
as
no
n
-
s
m
oo
th
pres
en
te
d
f
or
m
,
a
pi
ec
e
wi
s
e
f
un
c
ti
o
n
when
the
r
m
al
un
i
ts
are
s
up
pl
i
ed
b
y
m
ul
ti
-
f
ue
l
s
o
u
r
c
es
l
i
k
e
c
oa
l
,
na
tura
l
ga
s
,
an
d
oi
l
[2]
.
A
l
s
o,
t
o
ge
t
m
ore
prec
i
s
e
c
os
t
m
od
el
,
th
e
v
al
v
e
-
p
o
i
nt
ef
f
ec
ts
an
d
the
pro
hi
bi
t
ed
z
o
ne
s
m
us
t
al
s
o
be
t
ak
en
c
on
s
i
de
r
ati
on
[3
,
4].
T
he
c
om
pl
ex
i
t
y
of
the
pro
bl
em
dram
ati
c
al
l
y
i
nc
r
ea
s
es
on
c
e
bo
th
m
ul
ti
-
f
ue
l
op
t
i
o
n
an
d
v
a
l
v
e
-
po
i
nt
ef
f
ec
ts
are
c
on
s
i
d
ered
s
i
m
ul
tan
eo
us
l
y
.
G
en
eral
l
y
,
the
E
L
D
pro
bl
em
on
l
at
e
r
i
s
m
ore
an
d
m
ore
di
f
f
i
c
ul
t
w
h
en
tak
i
ng
m
an
y
po
wer
s
y
s
tem
s
an
d
ge
ne
r
a
tor
c
on
s
tr
ai
nts
i
nt
o
ac
c
ou
nt.
O
v
er
the
p
as
t
d
ec
ad
es
,
th
ere
wer
e
m
an
y
ap
pl
i
ed
m
eth
od
s
w
i
t
h
t
he
tas
k
of
s
ol
v
i
n
g
E
L
D
prob
l
em
s
uc
h
as
L
a
m
bd
a
Ite
r
ati
on
m
eth
od
[5]
,
D
y
n
am
i
c
P
r
og
r
am
m
i
ng
(
DP
)
[
6],
G
r
a
di
en
t
Me
t
ho
d
[
7],
La
grang
i
an
Rel
ax
ati
on
al
g
orit
hm
[8]
,
an
d
Ho
p
f
i
el
d
ne
ura
l
n
et
w
ork
ba
s
ed
n
um
eric
al
m
eth
od
(
HNNN
M)
[
9].
F
or
the
c
l
as
s
i
c
al
m
eth
od
s
ab
o
v
e,
pa
r
am
ete
r
s
of
the
s
e
al
go
r
i
t
hm
s
are
s
urv
e
y
e
d
an
d
s
e
l
ec
te
d
af
ter
m
an
y
tr
i
a
l
r
un
ti
m
es
,
w
h
i
c
h
he
l
ps
to
f
i
nd
a
g
l
ob
a
l
s
o
l
ut
i
on
i
n
a
s
h
ort
t
i
m
e.
Howev
er,
the
proc
es
s
of
s
ett
i
n
g
pa
r
a
m
ete
r
s
ta
k
es
m
uc
h
ti
m
e.
A
s
c
o
m
pl
ex
E
LD
prob
l
em
ha
s
no
n
-
c
o
nv
ex
f
ea
tures
an
d
v
ari
ou
s
no
nl
i
ne
ar
c
on
s
tr
a
i
nts
,
th
e
m
en
ti
on
ed
c
l
as
s
i
c
al
m
eth
od
s
c
a
nn
ot
af
f
ord
to
ha
nd
l
e
an
d
r
es
ul
t
i
n
l
o
w
c
o
nv
erg
en
c
e.
A
s
er
i
es
of
no
v
el
m
eth
od
o
l
o
gi
es
ha
v
e
be
e
n
bo
r
n
c
al
l
ed
m
eta
-
he
uris
ti
c
m
eth
od
to
d
ea
l
wi
th
the
s
e
di
s
ad
v
a
nta
g
es
s
uc
h
as
G
en
et
i
c
al
g
orit
hm
(
G
A
)
[10
],
F
i
r
ef
l
y
al
go
r
i
thm
[11
],
P
ar
ti
c
l
e
S
w
arm
O
pti
m
i
z
ati
on
(
P
S
O
)
[12
],
D
i
f
f
erenti
al
E
v
o
l
ut
i
on
(
D
E
)
al
g
orit
hm
[13
],
A
nti
-
pr
ed
at
or
y
pa
r
ti
c
l
e
s
w
arm
op
ti
m
i
z
ati
o
n
(
A
P
P
S
O
)
[
1
4],
B
i
o
ge
og
r
ap
h
y
-
B
as
ed
O
pti
m
i
z
ati
on
(
B
B
O
)
[1
5],
an
d
A
nt
Li
on
a
l
g
orit
hm
(
A
LO
)
[16
].
B
ec
au
s
e
of
the
i
r
ou
ts
tan
d
i
n
g
c
ha
r
ac
teri
s
ti
c
s
,
s
uc
h
m
eta
-
he
uris
ti
c
m
eth
od
s
prov
e
d
t
he
i
r
ef
f
i
c
i
en
c
y
f
or
s
ol
v
i
ng
the
af
orem
en
ti
on
e
d
di
f
f
i
c
ul
ti
es
.
Co
ns
eq
ue
nt
l
y
,
m
eta
-
he
uris
t
i
c
m
eth
od
s
h
a
v
e
b
ee
n
r
ec
ei
v
e
d
m
u
c
h
m
ore
c
urio
s
i
t
y
b
y
r
es
ea
r
c
he
r
s
.
B
es
i
d
es
,
a
l
arge
nu
m
be
r
of
s
c
i
en
ti
s
ts
i
n
m
an
y
en
gi
n
ee
r
i
ng
f
i
el
ds
ha
v
e
be
en
c
on
s
ta
ntl
y
s
tr
i
v
ed
a
nd
s
el
ec
ted
th
e
s
tr
on
g
po
i
nts
of
m
eth
od
s
to
m
od
i
f
y
/i
m
prov
e
the
m
i
nto
t
he
prom
i
s
i
ng
m
eth
od
s
s
uc
h
as
Co
l
on
i
al
Com
pe
ti
ti
v
e
Di
f
f
erenti
a
l
E
v
ol
uti
on
(
CCDE)
[1
7],
E
f
f
i
c
i
en
t
Re
al
-
Co
de
d
G
e
ne
t
i
c
al
go
r
i
th
m
(
E
RCG
A
)
[18
]
,
Im
prov
e
d
Rea
l
-
Cod
ed
G
en
et
i
c
a
l
go
r
i
thm
(
IRCG
A
)
[19
]
,
an
d
M
od
i
f
i
ed
Cuc
k
oo
S
ea
r
c
h
a
l
go
r
i
thm
(
MCS
A
)
[2
0].
A
s
k
no
w
n,
ob
t
ai
n
ed
r
es
ul
ts
of
t
he
m
eta
-
heu
r
i
s
t
i
c
f
am
i
l
y
ar
e b
et
ter t
ha
n
th
a
t o
f
th
e
s
ta
nd
ard m
eth
od
s
al
th
ou
g
h
t
he
y
m
a
y
s
ti
l
l
e
x
i
s
t
s
om
e
w
e
ak
ne
s
s
es
.
Henc
e,
i
m
prov
i
n
g
m
eta
-
he
u
r
i
s
ti
c
on
es
i
s
the
ex
pe
c
tat
i
o
n
of
r
es
ea
r
c
h
ers
w
i
t
h
t
he
go
al
of
f
i
nd
i
ng
the
be
s
t
s
ol
u
ti
o
n
qu
a
l
i
t
y
i
n
ex
pl
or
i
ng
an
d
ex
pl
o
i
ti
ng
s
e
arc
h s
pa
c
e e
f
f
ec
ti
v
el
y
.
In
a
dd
i
ti
on
,
th
e
c
om
bi
na
ti
o
n
b
et
w
e
en
t
w
o
or
m
ore
m
eth
o
ds
i
s
a
l
s
o
k
no
w
n
as
a
un
i
qu
e
wa
y
to
c
r
ea
te
po
wer
f
ul
h
y
b
r
i
d
a
l
g
orit
hm
s
s
uc
h
as
G
en
et
i
c
A
l
go
r
i
t
hm
w
i
t
h
an
an
t
c
o
l
o
n
y
ap
pro
ac
h
(
G
A
A
P
I)
[21
],
P
a
r
ti
c
l
e
S
war
m
O
pti
m
i
z
ati
on
b
as
ed
Di
ffe
r
en
ti
a
l
E
v
o
l
ut
i
on
(
P
S
O
D
E
)
[22
],
Di
s
tr
i
bu
ted
S
o
bo
l
P
art
i
c
l
e
S
w
arm
O
pti
m
i
z
at
i
on
an
d
T
ab
u
S
ea
r
c
h
a
l
go
r
i
thm
(
DS
P
S
O
-
T
S
A
)
[23
]
,
Di
f
f
erenti
al
E
v
o
l
ut
i
on
-
P
ar
ti
c
l
e
S
war
m
O
pti
m
i
z
at
i
on
-
Di
f
f
erenti
a
l
E
v
ol
uti
on
(
DP
D)
[
24
],
B
i
o
ge
og
r
ap
h
y
-
B
as
ed
O
p
ti
m
i
z
at
i
on
,
an
d
m
od
i
f
i
ed
Di
f
f
erenti
al
E
v
ol
uti
on
(
aB
B
O
m
DE
)
[25
].
In
r
ec
en
t
y
e
ars
,
v
ar
i
ou
s
o
pti
m
i
z
at
i
on
m
eth
od
s
ha
v
e
be
en
s
uc
c
es
s
f
ul
l
y
a
pp
l
i
e
d
to
de
a
l
w
i
th
the
r
ea
l
i
s
t
i
c
E
LD
prob
l
em
i
n
l
arge
-
s
c
al
e
po
wer
s
y
s
tem
i
nc
l
ud
i
n
g
Cr
i
s
s
c
r
os
s
O
pti
m
i
z
ati
on
(
CS
O
)
[26
],
Di
m
en
s
i
on
al
S
t
ee
pe
s
t
De
c
l
i
ne
m
eth
od
(
DS
D)
[2
7],
a
n
Im
prov
ed
O
r
th
og
on
al
Des
i
g
n
P
arti
c
l
e
S
w
arm
O
pti
m
i
z
a
ti
on
(
A
IO
D
P
S
O
)
al
go
r
i
t
hm
[28
],
Dou
bl
e
W
ei
gh
ted
P
arti
c
l
e
S
war
m
O
pti
m
i
z
ati
on
(
D
W
P
S
O
)
[2
9],
an
d
Mo
di
f
i
e
d Cro
w
S
e
arc
h a
l
go
r
i
t
hm
(
MCS
A
)
[3
0].
In
thi
s
p
ap
er,
a
n
atu
r
e
-
i
ns
p
i
r
ed
S
toc
ha
s
t
i
c
F
r
ac
tal
S
ea
r
c
h
(
S
F
S
)
al
g
orit
hm
i
s
ap
pl
i
ed
t
o
de
term
i
ne
th
e
m
i
ni
m
u
m
c
o
s
t
of
the
E
LD
prob
l
em
.
S
F
S
w
as
f
i
r
s
t
r
ec
om
m
en
de
d
b
y
S
a
l
i
m
i
[31
]
an
d
a
pp
l
i
e
d
to
op
ti
m
i
z
e
t
went
y
-
t
hree
b
en
c
hm
ar
k
f
un
c
ti
on
s
wi
th
a
q
ui
t
e
go
od
s
o
l
ut
i
on
q
ua
l
i
t
y
.
In
the
pa
p
er,
ou
r
p
urpos
e
i
s
to
i
n
v
es
ti
ga
te
the
ef
f
i
c
ac
y
an
d
r
ob
us
t
ne
s
s
of
the
S
F
S
m
eth
od
on
v
ari
ou
s
s
tan
da
r
d
I
E
E
E
s
y
s
t
em
s
throug
h
us
i
n
g
t
w
o
di
f
f
erent
r
an
d
om
w
al
k
ge
n
erator
s
f
or
di
ff
us
i
on
proc
es
s
.
F
i
r
s
tl
y
,
S
F
S
wi
t
h
G
au
s
s
i
an
r
a
nd
om
w
a
l
k
i
s
c
al
l
ed
S
F
S
-
G
au
s
s
an
d
s
ec
o
nd
l
y
,
S
F
S
wi
th
Le
v
y
F
l
i
g
ht
r
an
d
om
w
al
k
i
s
c
al
l
e
d
S
F
S
-
Le
v
y
.
In
a
dd
i
ti
on
,
th
e
ac
hi
ev
em
en
t
of
S
F
S
m
eth
od
ha
s
al
s
o c
om
pe
ted
ag
a
i
ns
t o
the
r
on
es
a
v
a
i
l
ab
l
e i
n t
h
e l
i
ter
a
ture.
2.
P
r
o
b
lem
Fo
r
mu
latio
n
2.1.
F
o
r
mu
latio
n
o
f
t
h
e
S
mo
o
t
h
E
L
D
P
r
o
b
lem
T
he
tr
ad
i
t
i
o
na
l
f
ue
l
c
os
t
f
u
nc
ti
on
i
s
of
ten
r
ep
r
es
en
t
ed
as
a
s
i
n
gl
e
q
ua
dr
ati
c
po
l
y
no
m
i
al
f
un
c
ti
on
p
ol
y
n
om
i
al
f
un
c
ti
o
n i
n
(
1
)
:
2
()
i
F
P
o
P
n
P
m
i
i
i
i
i
i
=
+
+
(
1)
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NIK
A
IS
S
N: 1
69
3
-
6
93
0
◼
S
toc
ha
s
t
i
c
frac
ta
l
s
ea
r
c
h b
as
ed
m
eth
o
d f
or ec
on
o
mi
c
l
oa
d d
i
s
pa
tc
h
..
. (T
ha
n
g Tr
u
ng
Ng
uy
en
)
2537
t
he
(
1)
c
an
i
nd
i
c
a
te
tha
t
t
he
f
ue
l
c
os
t
f
or
ea
c
h
M
W
h
i
s
di
f
f
erent
f
or
d
i
f
f
erent
po
w
er
ou
t
pu
t
of
the
r
m
al
ge
ne
r
ati
ng
u
ni
t
.
T
hu
s
,
the
m
aj
or
target
of
the
E
LD
pr
ob
l
em
i
s
to
r
ed
uc
e
the
t
ota
l
f
ue
l
c
os
t
of
al
l
the
r
m
al
ge
ne
r
at
i
ng
un
i
ts
an
d i
t
c
an
be
de
s
c
r
i
be
d a
s
t
he
f
ol
l
o
w
i
n
g m
od
el
:
1
()
N
i
i
M
i
n
F
F
P
i
=
=
(
2)
2.2.
F
o
r
mu
latio
n
o
f
t
h
e Non
-
s
mo
o
t
h
E
L
D P
r
o
b
lem
2.2
.1
.
E
L
D
P
r
o
b
lem
Co
n
side
r
in
g
V
alv
e
-
p
o
int
E
f
f
ec
t
s
In
th
e
prac
t
i
c
al
po
wer
s
y
s
t
em
,
the
r
m
al
un
i
ts
of
ten
us
e
m
an
y
v
al
v
e
f
or
a
dj
us
ti
ng
the
i
r
po
w
er o
utp
ut.
T
hi
s
m
a
k
es
th
e f
ue
l
c
os
t f
un
c
t
i
on
be
c
om
e d
i
s
c
on
ti
n
uo
us
f
orm
as
s
h
o
w
n
i
n
(
3
).
(
)
2
m
i
n
(
P
)
s
i
n
pq
F
o
P
n
P
m
P
P
i
i
i
i
i
i
i
i
i
i
=
+
+
+
−
(
3)
2.2.
2
.
E
L
D
P
r
o
b
lem Co
n
s
i
d
er
ing
M
u
lt
i
-
f
u
el
O
p
t
ion
s
S
i
nc
e
the
ge
ne
r
at
ors
are
s
up
pl
i
ed
b
y
v
ario
us
f
ue
l
s
ou
r
c
es
s
uc
h
as
c
oa
l
,
na
tur
al
g
as
,
oi
l
et
c
.,
th
e t
ota
l
f
ue
l
c
os
t
f
un
c
ti
on
of
e
ac
h
un
i
t c
an
b
e r
ep
r
es
en
t
ed
b
y
a
p
i
ec
e
wi
s
e
qu
ad
r
ati
c
c
os
t
f
un
c
ti
on
as
f
ol
l
o
w
s
:
2
m
in
m
a
x
,f
or
f
ue
l
1
,
P
,
1
1
1
1
2
m
in
m
a
x
,f
or
f
ue
l
2,
2
2
2
22
(
2
m
in
m
a
x
,f
or
f
ue
l
,
)
i
o
P
n
P
m
P
P
i
i
i
i
i
ii
i
o
P
n
P
m
P
P
P
i
i
i
i
i
i
ii
i
o
P
n
P
m
M
i
P
P
P
iM
i
iM
i
i
iM
i
i
ii
iM
i
F
P
+
+
+
+
+
+
=
K
(
4)
2.2.
3
.
E
L
D
P
r
o
b
lem Co
n
s
i
d
er
ing
Bo
t
h
V
alv
e
-
p
o
int
E
f
f
ec
t
s
and
M
u
lt
iple Fu
el
O
p
t
ion
s
T
he
E
LD
prob
l
em
w
i
l
l
be
prac
ti
c
al
an
d
m
ore
ac
c
urate
i
f
bo
th
v
a
l
v
e
-
po
i
nt
ef
f
ec
ts
an
d
m
ul
ti
pl
e f
ue
l
o
pti
on
s
are c
o
ns
i
de
r
e
d a
s
t
he
f
ol
l
o
wi
ng
[2
2]
.
2
m
in
m
in
m
a
x
s
in
(
q
(
)
)
,
f
o
r
f
u
e
l
1
,
P
1
1
1
1
1
11
2
m
in
m
in
m
a
x
s
in
(
q
(
)
)
,
f
o
r
f
u
e
l
2,
2
2
2
2
2
2
2
2
(
2
m
in
s
in
(
q
(
)
)
,
f
o
r
f
u
e
l
,
,
)
i
o
P
n
P
m
p
P
P
P
P
i
i
i
i
i
i
i
i
ii
ii
o
P
n
P
m
p
P
P
P
P
P
i
i
i
i
i
i
i
i
i
i
i
i
i
o
P
n
P
m
p
P
P
M
i
iM
i
iM
i
i
iM
i
iM
i
iM
i
i
i
iM
i
F
P
+
+
+
−
+
+
+
−
+
+
+
−
=
K
m
in
m
a
x
P
P
P
i
i
iM
i
(
5)
2.3.
Co
n
strai
n
s
2.3
.1
.
G
ener
atin
g
C
apacit
y Limi
t
A
r
ea
l
po
wer
ou
tpu
t
of
un
i
t
s
i
s
ge
ne
r
a
ted
t
ha
t
m
us
t
be
l
i
ed
i
n
t
he
r
an
ge
of
th
ei
r
l
o
w
er
an
d t
he
i
r
up
pe
r
l
i
m
i
t a
s
:
m
i
n
m
ax
i
i
i
P
P
P
(
6)
2.3
.2
.
P
o
w
er
Ba
lanc
e Con
strai
n
t
T
he
f
or
m
ul
a
of
the
ge
n
erator
p
o
w
er
ba
l
an
c
e
c
on
s
t
r
ai
nt
wi
t
h
c
on
s
i
de
r
i
ng
the
tot
a
l
tr
an
s
m
i
s
s
i
on
po
w
er
l
os
s
es
are pres
en
ted
b
y
:
1
0
N
i
S
L
D
T
T
L
i
P
P
P
=
−
−
=
(
7)
where
P
L
i
s
c
al
c
ul
ate
d b
y
th
e K
r
o
n’
s
l
os
s
f
or
m
ul
a e
x
pre
s
s
ed
as
:
Evaluation Warning : The document was created with Spire.PDF for Python.
◼
IS
S
N: 16
93
-
6
93
0
T
E
L
KO
M
NIK
A
V
ol
.
17
,
No
.
5,
O
c
tob
er 20
19
:
25
3
5
-
25
46
2538
0
0
0
1
1
1
N
N
N
i
i
j
j
i
i
i
j
i
L
P
P
C
P
C
P
B
C
=
=
=
=
+
+
(
8)
3.
S
t
o
ch
as
t
ic
F
r
ac
t
a
l S
ea
r
ch
T
he
S
F
S
a
l
go
r
i
thm
tha
t
w
a
s
f
or
m
ul
ate
d
b
y
S
al
i
m
i
i
n
2
01
4,
i
s
a
v
ar
i
an
t
of
F
r
ac
ta
l
S
ea
r
c
h
b
y
a
dd
i
ng
t
wo
up
da
t
e
proc
es
s
es
.
S
o,
th
e
s
tr
uc
ture
of
S
F
S
c
om
pris
es
of
three
up
da
t
e
ph
as
es
s
uc
h
as
di
f
f
us
i
on
ph
as
e
,
th
e
f
i
r
s
t
up
da
te
ph
as
e
an
d
th
e
s
ec
on
d
u
pd
a
te
p
ha
s
e.
A
s
r
es
ul
ts
,
three
ne
w
s
ol
uti
on
g
en
era
ti
o
ns
are
c
r
ea
ted
b
y
S
F
S
i
n
ea
c
h
i
terat
i
on
.
In
S
F
S
,
th
e
t
as
k
o
f
di
ff
us
i
on
ph
as
e
i
s
to
f
i
nd
s
o
l
ut
i
o
ns
i
n
s
m
al
l
s
ea
r
c
h
s
pa
c
e
whi
l
s
t
the
t
as
k
of
tw
o
up
da
te
ph
as
es
i
s
t
o
s
ea
r
c
h
s
ol
ut
i
o
ns
i
n
l
arge
s
ea
r
c
h
s
pa
c
e.
B
as
i
c
a
l
l
y
,
S
F
S
ha
s
a
po
pu
l
at
i
on
c
o
r
r
es
po
nd
i
ng
to
the
n
um
be
r
of
po
i
nts
wher
e
ea
c
h
p
oi
nt
Y
d
i
s
r
ep
r
es
e
nte
d
as
an
o
pti
m
al
s
ol
u
ti
o
n
d
(
d=
1,
Np
)
.
A
t
th
e
be
gi
n
ni
ng
,
a
l
l
the
po
i
nts
are
r
a
nd
om
l
y
c
r
ea
te
d
an
d
t
he
i
r
f
i
tn
es
s
f
un
c
ti
on
ar
e
c
al
c
ul
ate
d
to
f
i
nd
the
be
s
t
s
o
l
ut
i
on
Y
best
a
m
on
g
al
l
s
ol
ut
i
o
ns
i
n
th
e
po
pu
l
ati
on
.
T
he
n,
S
F
S
c
on
t
i
n
ue
s
to
pe
r
f
or
m
the
i
terat
i
v
e
s
e
arc
h
proc
es
s
wi
th
thre
e
p
ha
s
es
ab
o
v
e.
T
he
de
t
ai
l
of
thr
ee
p
ha
s
e
i
s
de
s
c
r
i
be
d
as
f
ol
l
o
w
s
:
3.1
. D
if
f
u
sion
P
h
a
se
B
as
ed
o
n
the
pre
v
i
ou
s
po
i
nts
,
the
f
i
r
s
t
ne
w
s
ol
ut
i
on
s
are
produc
e
d
b
y
us
i
ng
o
ne
of
tw
o
r
an
do
m
wal
k
s
as
Le
v
y
f
l
i
gh
t
an
d
G
a
us
s
i
an
.
In
th
i
s
ph
as
e,
ea
c
h
s
ol
uti
on
(
po
i
nt)
Y
d
d
i
f
f
us
es
aroun
d
i
ts
po
s
i
t
i
o
n
i
nt
o
a
n
um
be
r
of
ne
w
d
i
f
f
us
i
on
s
ol
uti
o
ns
Y
di
w
h
ere
di
=
1,
..
,N
df
.
T
he
di
ff
us
i
on
c
an
be
m
ath
em
ati
c
al
l
y
f
orm
ul
at
ed
as
f
ol
l
o
w
s
:
3.1
.1
.
Dif
f
u
sion
P
h
as
e
w
it
h
L
ev
y
F
ligh
t
T
he
eq
ua
ti
on
of
the
di
f
f
us
i
on
ph
as
e
us
i
ng
Le
v
y
f
l
i
g
ht
r
an
d
om
w
a
l
k
i
s
pe
r
f
or
m
ed
i
n
(
9
)
:
L
e
v
y
L
e
v
y
d
i
d
d
Y
Y
Y
=
+
(
9)
where
α
>
0
i
s
s
c
al
e
f
ac
tor;
ε
i
s
a
n
orm
al
l
y
di
s
tr
i
bu
ted
r
an
d
om
nu
m
be
r
s
r
es
tr
i
c
ted
to
(
0,1
)
;
Y
d
d
en
ot
ed
t
he
d
th
s
o
l
ut
i
on
i
n t
he
c
urr
en
t p
op
u
l
at
i
o
n a
n
d
∆
i
s
de
s
c
r
i
be
d
b
y
[2
0]:
(
)
(
)
(
)
x
Le
v
y
d
d
be
st
y
Y
v
Y
Y
=
−
(
10
)
1/
x
y
r
a
n
d
v
r
a
n
d
=
(
11
)
where
r
a
nd
x
and
r
a
nd
y
are t
wo n
orm
al
l
y
d
i
s
tr
i
bu
ted
s
t
o
c
ha
s
ti
c
v
aria
bl
es
.
3.1
.2
.
Dif
f
u
sion
P
h
as
e
w
it
h
G
aussia
n
W
a
lk
T
he
proc
es
s
of
c
r
ea
ti
ng
s
o
l
uti
o
n f
ol
l
o
w
i
ng
G
a
us
s
i
an
r
a
nd
om
w
a
l
k
i
s
pe
r
f
or
m
ed
b
y
:
12
(
1
)
G
a
u
d
i
d
d
d
d
Y
b
G
W
b
G
W
=
+
−
(
12
)
where
b
d
i
s
a
bi
na
r
y
n
um
be
r
(
0
or
1)
d
ep
e
nd
e
nt
on
c
om
pa
r
i
s
on
of
a
r
an
do
m
nu
m
be
r
r
an
d
d
a
nd
wal
k
f
ac
tor
w
(
0≤
w≤
1
)
as
f
ol
l
o
w
s
:
1
0
d
d
if
ra
n
d
w
b
o
the
rwise
=
(
13
)
an
d
on
e
ou
t
of
1
and
2
i
s
us
e
d t
o c
r
ea
t
e s
ol
uti
on
s
,
de
s
c
r
i
be
d
(
1
4)
:
(
)
1
(
Y
,
)
d
b
e
s
t
d
b
e
s
t
d
G
W
n
o
rm
rn
d
Y
Y
=
+
−
(
14
)
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NIK
A
IS
S
N: 1
69
3
-
6
93
0
◼
S
toc
ha
s
t
i
c
frac
ta
l
s
ea
r
c
h b
as
ed
m
eth
o
d f
or ec
on
o
mi
c
l
oa
d d
i
s
pa
tc
h
..
. (T
ha
n
g Tr
u
ng
Ng
uy
en
)
2539
(
)
2
,
d
d
d
G
W
no
rm
rnd
Y
=
(
15
)
where
i
s
un
i
f
orm
l
y
d
i
s
tr
i
b
ut
ed
r
an
do
m
nu
m
be
r
s
;
i
s
th
e
s
tan
da
r
d
de
v
i
at
i
on
.
A
t
the
e
nd
of
c
r
ea
t
i
ng
th
e
ne
w
s
ol
u
ti
o
ns
,
al
l
ne
w
s
ol
u
ti
on
s
are
ap
prai
s
e
d
b
y
c
om
pu
ti
ng
the
f
i
tn
es
s
f
un
c
ti
on
an
d
t
he
n
th
e
e
v
a
l
ua
ti
o
n
be
t
ween
e
ac
h
o
l
d
s
o
l
ut
i
o
n
a
nd
N
df
n
e
w
s
ol
u
ti
o
ns
at
ea
c
h p
oi
n
t i
s
d
on
e
i
n o
r
de
r
to
r
eta
i
n
a b
e
tte
r
s
o
l
ut
i
on
wi
th
th
e b
es
t f
i
t
ne
s
s
, n
am
ed
Y
d
.
3.2.
T
h
e Fir
st Up
d
ate P
h
a
se
F
i
r
s
t
of
al
l
,
a
l
l
c
urr
en
t
po
i
nts
ar
e
as
s
i
g
ne
d
to
a
v
a
l
ue
of
prob
ab
i
l
i
t
y
Pa
d
,
wh
i
c
h
i
s
de
term
i
ne
d b
y
:
d
d
p
R
a
n
k
Pa
N
=
(
16
)
a
c
c
ordi
ng
to
(
1
6),
th
e
po
i
nt
wi
th
the
be
s
t
f
i
tn
es
s
ha
s
th
e
hi
gh
es
t
prob
ab
i
l
i
t
y
an
d
r
a
nk
s
at
the
l
as
t
po
s
i
t
i
on
oth
erw
i
s
e
s
ta
nd
s
a
t
the
f
i
r
s
t
po
s
i
ti
o
n.
A
f
ter
r
an
k
i
ng
f
or
al
l
p
oi
n
ts
,
ea
c
h
po
i
nt
Y
d
i
n
group
i
s
up
da
te
d
b
y
th
e
c
om
pa
r
i
s
on
of
th
e
proba
bi
l
i
t
y
Pa
d
a
nd
a
r
a
nd
om
nu
m
be
r
α
1
(
0<
α
1
<
1).
If
Pa
d
<
α
1
,
the
d
th
po
i
nt
i
s
u
pd
at
ed
l
i
k
e
(
17
)
, o
t
he
r
w
i
s
e
i
t d
oe
s
n
’
t rem
ai
n c
ha
ng
ed
.
1
12
()
d
n
e
w
d
Y
Y
ra
n
d
Y
Y
=
−
−
(
17
)
w
he
r
e
1
the
ne
w
m
od
i
f
i
ed
po
s
i
ti
o
n
of
Y
d
;
Y
1
an
d
Y
2
i
s
s
y
m
bo
l
i
z
e
r
an
d
om
l
y
s
el
ec
ted
po
i
nts
i
n
the
gr
ou
p.
T
hrough
t
he
f
i
r
s
t
up
d
ate
ph
as
e,
i
t
i
s
e
as
i
l
y
s
ee
n
t
ha
t
al
l
of
po
i
nts
wi
t
h
a
b
ad
qu
a
l
i
t
y
are
of
ten
up
d
ate
d
whi
l
e
th
e
po
i
nts
w
i
th
a
be
tte
r
qu
al
i
t
y
ha
v
e
l
o
w
po
s
s
i
b
i
l
i
t
y
t
o
be
n
e
w
l
y
up
d
ate
d.
A
f
ter
pe
r
f
or
m
i
ng
the
s
ec
on
d
g
en
er
ati
on
,
o
nc
e
ag
ai
n,
m
ec
ha
ni
s
m
of
the
c
o
m
pa
r
i
s
on
i
s
re
-
pe
r
f
or
m
ed
to
s
e
l
ec
t
the
be
tte
r
s
ol
uti
on
be
t
wee
n
o
l
d
s
ol
u
ti
o
n
an
d
n
e
w
s
o
l
ut
i
o
n
at
e
ac
h
po
i
nt,
na
m
ed
Y
d
.
3.3.
T
h
e S
e
con
d
Up
d
ate
P
h
as
e
S
i
m
i
l
ar
to
th
e
f
i
r
s
t
up
da
t
e
s
tag
e,
th
e
f
i
r
s
t
s
tep
i
n
th
e
s
ec
on
d
up
d
ate
s
ta
ge
i
s
a
l
s
o
to
de
term
i
ne
r
an
k
d
and
Pa
d
f
or
ea
c
h
s
ol
ut
i
on
d
an
d
th
e
n
Pa
d
i
s
c
om
pa
r
ed
to
a
r
an
do
m
nu
m
be
r
wi
th
i
n
0
an
d 1
f
or de
term
i
ni
ng
i
f
th
e
s
ol
uti
on
i
s
ne
wl
y
u
pd
at
ed
.
In
c
as
e t
ha
t
c
o
ns
i
d
ered s
o
l
ut
i
o
n
d
i
s
ac
c
ep
te
d t
o
be
ne
wl
y
up
da
te
d,
th
ere are
t
w
o m
od
el
s
to
be
us
ed
as
f
ol
l
o
w
s
:
(
)
23
'
0
.
5
n
e
w
d
d
b
e
s
t
d
Y
Y
Y
Y
i
f
r
a
n
d
=
−
−
(
18
)
(
)
2
3
4
'
>
0
.
5
n
e
w
d
d
d
Y
Y
Y
Y
if
r
a
n
d
=
+
−
(
19
)
where
r
an
do
m
s
el
ec
ted
po
i
nts
Y
3
,
Y
4
a
nd
the
be
s
t
po
i
n
t
Y
best
are
ob
tai
ne
d
f
r
o
m
the
f
i
r
s
t
ph
as
e;
ε’
i
s
r
an
do
m
nu
m
be
r
i
n t
h
e ra
ng
e (0,
1).
4.
Imp
lement
atio
n
o
f
S
F
S
f
o
r
S
o
lv
ing
E
L
D
P
r
o
b
l
em
4.1.
Co
n
strai
n
t
V
iolat
ion
H
and
ling
T
ec
h
n
iqu
e
A
p
un
i
s
hm
en
t f
un
c
ti
on
tec
h
ni
q
ue
i
s
em
pl
o
y
ed
i
n
th
e
E
LD p
r
o
bl
em
to
de
a
l
wi
th
c
o
ns
tr
ai
nt
v
i
ol
a
ti
o
ns
b
y
us
i
n
g
t
w
o
v
aria
b
l
e
t
y
p
es
s
uc
h
as
de
pe
nd
en
t
v
ar
i
ab
l
e
a
nd
c
o
ntrol
v
ari
ab
l
e.
F
r
o
m
(
7
)
,
P
1d
c
orr
es
po
n
di
n
g
to
po
wer
ou
tp
ut
of
the
1
st
un
i
t
of
the
d
th
s
ol
u
ti
o
n
i
s
s
el
ec
te
d
t
o
b
e
a
de
pe
nd
e
nt
v
aria
bl
e.
O
the
r
v
ari
ab
l
es
f
r
o
m
P
d2
to
P
dN
a
r
e
c
on
tr
ol
v
ari
ab
l
es
an
d
i
nc
l
ud
ed
i
n
ea
c
h
s
ol
ut
i
on
d
.
T
hu
s
,
the
s
e
c
o
ntrol
v
aria
bl
es
are
s
up
p
os
ed
t
o
b
e
gi
v
e
n
a
nd
the
n
t
he
de
p
en
d
en
t
v
ari
ab
l
e
ne
e
ds
to
be
d
ete
r
m
i
ne
d.
T
he
v
al
u
e
of
P
1d
ob
tai
n
ed
ha
s
no
as
s
uranc
e
t
ha
t
s
at
i
s
f
i
es
i
ts
l
i
m
i
t
po
wer
as
(
6
)
.
T
he
r
ef
o
r
e,
the
v
i
o
l
at
i
on
of
the
de
p
en
de
nt
v
ari
ab
l
e
m
us
t
be
p
en
a
l
i
z
ed
i
f
on
e
oc
c
urs
an
d i
s
c
a
l
c
ul
ate
d
b
y
:
Evaluation Warning : The document was created with Spire.PDF for Python.
◼
IS
S
N: 16
93
-
6
93
0
T
E
L
KO
M
NIK
A
V
ol
.
17
,
No
.
5,
O
c
tob
er 20
19
:
25
3
5
-
25
46
2540
1
d
1
m
a
x
1
d
1
m
a
x
1
m
i
n
1
d
1
d
1
,
m
i
n
1
m
i
n
1
d
1
m
a
x
0
d
P
P
i
f
P
P
P
U
N
P
P
i
f
P
P
i
f
P
P
P
−
=
−
(
20
)
where
P
UN
d
i
s
th
e v
i
o
l
at
i
on
of
s
ol
uti
on
d
T
hu
s
,
i
n
ord
er
to
op
t
i
m
i
z
e
the
E
LD
pr
ob
l
em
r
el
at
ed
to
th
e
c
os
t
f
un
c
ti
o
n
(
1)
-
(
5),
pu
n
i
s
hm
en
t
f
un
c
ti
on
P
UN
d
m
us
t
be
c
on
s
i
de
r
ed
i
n
f
i
tne
s
s
f
un
c
ti
on
i
n
the
c
as
e
of
oc
c
urr
i
ng
v
i
ol
a
ti
o
n
of
v
a
l
u
e
of
P
1d
.
A
c
c
ordi
n
gl
y
,
the
f
i
tne
s
s
f
u
nc
ti
o
n
i
s
de
term
i
ne
d
as
the
f
ol
l
o
wi
ng
(
21
)
:
2
1
(
)
(
)
N
d
d
i
d
i
F
F
P
K
P
U
N
=
=
+
(
21
)
w
he
r
e
K
i
s
f
ac
tor f
or han
dl
i
ng
c
on
s
tr
a
i
nt
v
i
ol
ati
on
.
4.2.
T
h
e De
t
ail
o
f
S
F
S
’s
P
r
o
ce
d
u
r
e
f
t
h
e E
L
D
P
r
o
b
le
m
S
tep
1:
S
et
p
aram
ete
r
s
i
nc
l
ud
i
ng
the
nu
m
be
r
of
po
pu
l
ati
o
n
N
p
,
t
he
n
um
be
r
of
di
ffu
s
i
on
po
pu
l
at
i
o
n
N
df
an
d
th
e
m
ax
i
m
u
m
nu
m
be
r
of
i
terat
i
on
s
MI
.
S
tep
2:
In
i
ti
al
i
z
i
ng
po
pu
l
at
i
on
Y
d
(
d
=
1,
..
,
N
p
)
.
T
he
m
a
x
i
m
u
m
an
d
m
i
ni
m
u
m
of
ea
c
h
po
i
nt
are
Y
mi
n
=
[
P
imi
n
]
a
nd
Y
m
a
x
=
[
P
ima
x
]
w
h
ere
i
=
2,
…,
N
.
T
hu
s
,
e
ac
h
p
oi
nt
Y
d
i
s
r
a
nd
om
l
y
i
n
i
ti
a
l
i
z
ed
b
as
ed
on
th
e c
on
s
tr
a
i
nt:
Y
mi
n
≤
Y
d
≤
Y
m
a
x
S
tep
3:
C
al
c
u
l
at
e f
i
tne
s
s
f
un
c
ti
on
F
d
f
ol
l
o
w
i
ng
(
21
)
an
d
f
i
nd
th
e b
es
t
po
i
nt
Y
best
i
n
g
r
ou
p.
-
S
et
=
1
.
S
tep
4:
-
T
he
di
f
f
us
i
on
ph
as
e
i
s
ex
e
c
ute
d b
y
us
i
ng
ei
the
r
Le
v
y
F
l
i
g
ht
or G
a
us
s
i
an
wal
k
.
-
Chec
k
bo
un
ds
f
or ne
w
s
o
l
uti
o
ns
an
d c
orr
ec
t th
em
i
f
v
i
ol
at
ed
;
-
Cal
c
ul
ate
f
i
tne
s
s
f
un
c
ti
on
.
-
Com
pa
r
e o
l
d s
o
l
ut
i
on
an
d
ne
w
s
o
l
ut
i
on
s
at
e
ac
h p
oi
n
t to
k
ee
p t
h
e b
es
t o
n
e,
c
al
l
e
d
Y
d
S
tep
5:
-
T
he
ne
w
s
ol
uti
on
s
are
pro
du
c
ed
b
y
us
i
n
g t
h
e f
i
r
s
t u
pd
ate
p
ha
s
e.
-
Chec
k
bo
un
ds
f
or ne
w
s
o
l
uti
o
ns
an
d c
orr
ec
t th
em
i
f
v
i
ol
at
ed
.
-
Cal
c
ul
ate
f
i
tne
s
s
f
un
c
ti
on
.
-
Com
pa
r
e o
l
d s
o
l
ut
i
on
an
d
ne
w
s
o
l
ut
i
on
s
at
e
ac
h p
oi
n
t to
k
ee
p b
ett
er o
ne
, c
a
l
l
ed
Y
d
-
S
el
ec
t th
e c
urr
en
t
be
s
t s
ol
uti
o
n i
n g
r
o
up
.
S
tep
6:
-
T
he
ne
w
s
ol
uti
on
s
are
pro
du
c
ed
b
y
us
i
n
g t
h
e s
ec
on
d
up
da
te
p
ha
s
e.
-
Chec
k
bo
un
ds
f
or ne
w
s
o
l
uti
o
ns
an
d c
orr
ec
t th
em
i
f
v
i
ol
at
ed
.
-
Cal
c
ul
ate
f
i
tne
s
s
f
un
c
ti
on
.
-
Com
pa
r
e o
l
d s
o
l
ut
i
on
an
d
ne
w
s
o
l
ut
i
on
s
at
e
ac
h p
oi
n
t to
k
ee
p b
ett
er o
ne
.
S
tep
7:
S
a
v
e
the
be
s
t p
oi
nt
Y
best
f
or th
e c
urr
en
t
i
tera
ti
o
n.
S
tep
8:
C
he
c
k
s
top
pi
n
g c
on
di
t
i
on
.
If
<
,
=
+
1
an
d b
ac
k
to
s
tep
4.
O
t
h
erw
i
s
e,
s
to
p t
h
e p
r
oc
e
du
r
e.
5.
Nu
mb
e
r
ica
l Re
sult
s
In
thi
s
s
ec
ti
on
,
we
pr
es
e
nt
t
w
o
i
s
s
ue
s
as
f
ol
l
o
w
s
:
1)
A
na
l
y
s
i
s
of
the
ef
f
i
c
i
en
c
y
of
the
S
F
S
m
eth
od
ba
s
ed
o
n
th
e
s
i
m
ul
at
i
on
r
es
ul
ts
a
pp
l
y
i
ng
Le
v
y
F
l
i
g
ht
or
G
a
us
s
wal
k
f
or
the
d
i
f
f
us
i
on
ph
as
e
;
2)
C
o
m
pa
r
i
ng
r
es
ul
ts
f
r
o
m
three
v
ari
ou
s
s
tan
d
ard
IE
E
E
tes
t
s
y
s
t
em
s
w
i
th
6
un
i
ts
,
1
0
un
i
ts
a
nd
20
u
ni
ts
to
e
v
a
l
ua
t
e
p
erf
or
m
an
c
e
of
S
F
S
m
eth
od
s
.
T
hree
tes
t
s
y
s
t
em
s
are
s
ol
v
ed
b
y
r
un
n
i
n
g
S
F
S
on
M
atl
ab
20
16
a
a
nd
a
c
om
pu
ter
w
i
th
2.4
G
H
z
proc
es
s
or
an
d
4
GB
of
RA
M
.
5.1.
A
p
p
ling
L
ev
y Fligh
t
o
r
G
auss
ian Rand
o
m W
a
lk
f
o
r
t
h
e Diff
u
sion
P
h
as
e
In
[3
1],
a
uth
or
de
s
c
r
i
b
ed
tha
t
t
he
di
f
f
us
i
on
p
ha
s
e
o
f
S
F
S
c
ou
l
d
us
e
Le
v
y
F
l
i
gh
t
or
G
au
s
s
i
an
r
an
do
m
w
al
k
.
Ho
w
e
v
er,
al
l
ap
pl
i
c
at
i
on
s
f
or
s
ol
v
i
ng
b
en
c
hm
ar
k
f
un
c
ti
on
s
,
G
au
s
s
i
an
r
an
do
m
w
a
l
k
w
as
o
nl
y
s
el
ec
te
d.
I
n
ord
er
to
f
ul
l
y
i
n
v
es
ti
ga
t
e
th
e
c
ha
r
ac
ter
i
s
ti
c
s
of
S
F
S
,
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NIK
A
IS
S
N: 1
69
3
-
6
93
0
◼
S
toc
ha
s
t
i
c
frac
ta
l
s
ea
r
c
h b
as
ed
m
eth
o
d f
or ec
on
o
mi
c
l
oa
d d
i
s
pa
tc
h
..
. (T
ha
n
g Tr
u
ng
Ng
uy
en
)
2541
we
ex
am
i
ne
i
ts
c
ha
r
ac
t
eris
t
i
c
s
v
i
a
ap
p
l
y
i
n
g
L
ev
y
F
l
i
g
ht
or
G
au
s
s
w
a
l
k
i
n
the
di
f
f
us
i
on
p
ha
s
e
v
i
a
three
t
es
t
s
y
s
tem
s
.
T
he
y
c
o
m
pris
e
of
6
-
un
i
t
t
es
t
s
y
s
tem
c
on
s
i
de
r
i
ng
wi
th
an
d
w
i
t
ho
ut
l
i
ne
tr
an
s
m
i
s
s
i
on
l
os
s
es
,
1
0
-
un
i
t
tes
t
s
y
s
t
em
w
i
t
h
b
oth
m
ul
ti
f
ue
l
s
an
d
v
al
v
e
po
i
nt
ef
f
ec
t,
an
d
2
0
un
i
t
tes
t
s
y
s
t
em
w
i
th
tr
an
s
m
i
s
s
i
on
l
os
s
es
.
S
uc
h
i
nv
es
ti
g
at
i
on
proc
es
s
of
us
i
ng
L
ev
y
F
l
i
g
ht
or
G
au
s
s
wal
k
ha
s
a
v
er
y
i
m
po
r
tan
t
r
ol
e
be
c
a
us
e
i
t
h
el
ps
r
es
ea
r
c
he
r
s
ea
s
i
l
y
to
k
no
w
t
he
ef
f
ec
ti
v
en
es
s
o
f
S
F
S
to
ap
p
l
i
c
at
i
o
n
f
or
di
f
f
e
r
en
t
s
y
s
tem
s
.
T
hi
s
i
nv
es
ti
g
ati
o
n
wi
l
l
b
e
i
m
pl
em
en
ted
ba
s
ed
on
t
wo
c
as
es
i
nc
l
u
di
ng
t
he
i
nf
l
ue
nc
e
of
wal
k
f
ac
tor
ꞷ
on
th
e
o
bta
i
ne
d
r
es
ul
ts
of
S
F
S
_G
a
us
s
an
d
i
m
pa
c
t
of
the
nu
m
be
r
of
po
pu
l
ati
on
an
d
th
e
nu
m
be
r
of
i
terati
o
ns
on
th
e
r
es
ul
ts
of
S
F
S
_G
au
s
s
an
d
S
F
S
_L
ev
y
.
5.1
.1
.
S
u
r
v
e
y
1:
t
h
e
Inf
lue
n
ce
o
f
t
h
e
W
alk
F
ac
t
o
r
F
or
the
f
i
r
s
t
c
as
e,
w
a
l
k
f
ac
tor
of
S
F
S
_G
au
s
s
i
s
s
et
f
r
om
0
to
1
w
i
t
h
a
s
tep
of
0
.25
to
an
a
l
y
z
e
i
ts
i
m
pa
c
t
on
t
he
t
es
ted
r
es
ul
ts
f
r
om
c
on
v
ex
or
n
on
-
c
on
v
ex
tes
t
s
y
s
t
em
s
.
If
i
s
s
e
l
ec
t
to
0,
(
15
)
i
s
us
ed
to
c
r
ea
te
t
he
ne
w
s
ol
u
ti
o
ns
i
n
the
d
i
f
f
us
i
on
ph
as
e.
If
i
s
s
el
ec
t
t
o
1,
(
14
)
i
s
em
pl
o
y
e
d
to
prod
uc
e
t
he
ne
w
s
ol
u
ti
on
s
.
O
th
er
w
i
s
e,
bo
t
h.
(
14
-
15
)
are
uti
l
i
z
e
d
f
or
the
s
o
l
ut
i
o
n
c
r
ea
t
i
n
g
pro
c
es
s
.
T
o
s
ee
th
e
c
h
an
ge
s
c
l
ea
r
l
y
,
s
om
e
pa
r
am
ete
r
s
l
i
k
e
the
n
u
m
be
r
of
po
pu
l
ati
on
s
an
d
nu
m
be
r
of
i
terati
on
s
ne
ed
to
be
es
ta
bl
i
s
he
d
s
u
i
ta
bl
y
f
or
di
f
f
erent
tes
t
s
y
s
t
em
s
.
P
arti
c
ul
arl
y
,
the
n
um
be
r
of
po
pu
l
a
ti
o
ns
an
d
nu
m
be
r
of
i
terati
on
s
are
r
e
s
pe
c
ti
v
el
y
s
et
to
5
an
d
30
f
or
6
-
un
i
t
s
y
s
te
m
,
10
an
d
50
f
or
20
-
un
i
t
s
y
s
tem
,
an
d
20
an
d
50
0
f
or
1
0
-
un
i
t
s
y
s
tem
.
T
he
ob
tai
ne
d res
ul
ts
f
r
om
t
he
s
e s
y
s
tem
s
are s
um
m
ariz
ed
i
n
T
ab
l
es
1,
2 a
nd
3.
A
s
s
ho
w
n
i
n
th
es
e
tab
l
es
,
when
t
he
v
al
ue
of
i
s
v
arie
d
f
r
om
0
to
1
w
i
t
h
th
e
s
tep
s
i
z
e
of
0.
25
,
th
e
m
i
ni
m
u
m
c
os
ts
of
v
ari
ou
s
t
hree
tes
t
s
y
s
t
em
s
de
c
r
ea
s
ed
f
r
om
a
hi
g
h
v
a
l
ue
to
a
l
o
w
v
al
ue
.
S
pe
c
i
f
i
c
a
l
l
y
,
f
or
6
-
un
i
t
s
y
s
tem
w
i
t
ho
u
t
tr
an
s
m
i
s
s
i
on
l
os
s
es
,
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m
i
ni
m
u
m
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os
t
s
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r
es
pe
c
ti
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el
y
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14
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6.8
9
81
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0
03
.
53
9
6
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an
d
4
0
67
9.
04
6
6
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f
or
c
as
es
1.1
,
1.2
,
an
d
1
.3
c
orr
es
po
nd
i
ng
to
ω
=
0.
T
he
s
e
c
o
s
ts
c
ou
l
d
be
m
i
ni
m
i
z
ed
a
nd
eq
ua
l
t
o
31
44
5.
62
3
3
$/h
,
36
00
3.1
27
8
$/
h,
an
d
40
6
7
5.9
8
24
$/h
as
s
ett
i
ng
=1
.
S
i
m
i
l
arl
y
,
when
th
e
v
a
l
u
e
of
i
s
0,
c
os
ts
of
10
-
un
i
t
s
y
s
tem
an
d
2
0
-
un
i
t
s
y
s
t
em
are
31
44
6
.89
81
$/
h
an
d
62
46
0.
87
$/h
,
r
es
p
e
c
ti
v
e
l
y
.
W
he
n
the
v
al
u
e
of
i
s
1,
tho
s
e
of
10
-
un
i
t
an
d
20
-
un
i
t
tes
t
s
y
s
tem
s
are
33
14
4
5.6
2
33
$/
h
an
d
62
45
6.9
1
$/h
,
r
es
p
ec
ti
v
e
l
y
.
F
r
om
s
uc
h
an
al
y
s
i
s
,
i
t
p
oi
n
ts
ou
t
tha
t
(
14
)
ha
s
be
tt
er
pe
r
f
orm
an
c
e
tha
n
(
15
)
on
r
es
ul
t
ob
tai
ne
d
f
r
om
the
m
eth
o
d.
F
urtherm
ore,
i
f
on
l
y
(
14
)
i
s
ap
p
l
i
e
d,
th
e
ob
t
ai
n
ed
r
es
ul
t
s
are
the
m
os
t e
ff
ec
ti
v
e.
T
ab
l
e 1
.
T
he
O
bt
ai
ne
d
Res
ul
ts
f
r
om
6
-
Uni
t S
y
s
t
em
w
i
th
ou
t T
r
an
s
m
i
s
s
i
on
Lo
s
s
es
w
i
th
Di
f
f
erent
ω
ω
C
a
s
e
1
.
1
:
P
D
=6
0
0
W
C
a
s
e
1
.
2
:
P
D
=7
0
0
W
C
a
s
e
1
.
3
:
P
D
=8
0
0
W
M
in.
c
o
s
t
(
$
/
h
)
0
3
1
4
4
6
.
8
9
8
1
3
6
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0
3
.
5
3
9
6
4
0
6
7
9
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0
4
6
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2
5
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4
5
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ab
l
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. T
he
O
bt
ai
ne
d
Res
ul
ts
f
r
om
10
-
Uni
t S
y
s
tem
wi
th
Mu
l
ti
F
ue
l
s
an
d
V
al
v
e
P
oi
nt
E
f
f
ec
t
w
i
t
h
Di
f
f
erent
ω
ω
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in.
c
o
s
t
(
$
/
h
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v
e
r
.
c
o
s
t
(
$
/
h
)
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a
x
.
c
o
s
t
(
$
/
h
)
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6
2
3
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8
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1
1
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5
T
ab
l
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. T
he
O
bt
ai
ne
d
Res
ul
ts
f
r
om
20
-
Uni
t S
y
s
tem
w
i
th
T
r
an
s
m
i
s
s
i
on
Lo
s
s
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w
i
th
Di
f
f
erent
ω
ω
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in.
c
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s
t
(
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v
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7
Evaluation Warning : The document was created with Spire.PDF for Python.
◼
IS
S
N: 16
93
-
6
93
0
T
E
L
KO
M
NIK
A
V
ol
.
17
,
No
.
5,
O
c
tob
er 20
19
:
25
3
5
-
25
46
2542
5.1
.2
.
S
u
r
v
e
y
2:
t
h
e
Imp
ac
t
o
f
t
h
e
Nu
mb
er
o
f
P
o
p
u
latio
n
and
Nu
mb
er
o
f
It
er
atio
n
s
o
n
O
b
t
ained Re
sult
s
F
or
the
s
ec
on
d
s
urv
e
y
,
we
s
c
r
uti
n
i
z
e
t
he
i
m
pa
c
t
of
N
p
an
d
MI
o
n
th
e
r
es
ul
ts
of
S
F
S
_G
au
s
s
a
nd
S
F
S
_L
e
v
y
f
or
1
0
-
un
i
t
an
d
2
0
-
un
i
t
tes
t
s
y
s
tem
.
N
p
i
s
f
i
x
e
d
a
nd
c
ho
s
en
to
be
20
f
or
10
-
u
ni
t
s
y
s
tem
an
d
10
f
or
20
-
un
i
t
s
y
s
t
em
whi
l
e
MI
i
s
a
l
tere
d
f
r
om
10
0
to
5
50
f
or
the
c
o
m
er,
an
d
f
r
om
50
to
25
0
f
or
the
l
att
er.
M
oreo
v
er,
ac
c
ordi
ng
to
the
s
urv
e
y
1,
S
F
S
_G
au
s
s
h
ad
goo
d
s
ol
u
ti
o
ns
i
f
on
l
y
(
14
)
i
s
us
ed
f
or
pro
du
c
i
ng
ne
w
s
o
l
ut
i
on
s
.
S
o
,
w
e
on
l
y
us
e
(
14
)
c
orr
es
po
nd
i
ng
t
o
ω
=
1.
A
nd
s
tat
i
s
ti
c
al
r
es
ul
ts
f
r
om
10
-
un
i
t
s
y
s
tem
an
d
2
0
-
u
ni
t
s
y
s
t
em
ar
e
s
ho
w
n
i
n T
ab
l
es
4
a
nd
5
.
In
ac
c
orda
nc
e
wi
th
T
ab
l
es
4
a
nd
5,
t
he
m
i
ni
m
u
m
c
os
t
of
S
F
S
_G
au
s
s
an
d
S
F
S
_L
e
v
y
are
m
ore
an
d
m
ore
c
ha
ng
ef
ul
when
MI
i
s
c
ha
ng
e
d.
F
or
the
c
as
e
w
i
t
h
no
n
-
s
m
oo
th
o
bj
ec
ti
v
e
f
un
c
ti
on
,
the
b
es
t
c
os
t
of
S
F
S
-
G
au
s
s
a
nd
S
F
S
-
F
l
e
v
y
are
6
23
.
82
5
2
$/h
an
d
62
3.8
2
35
$/
h,
r
es
p
ec
ti
v
el
y
.
F
or
the
c
as
e
wi
th
s
m
oo
th
ob
j
ec
ti
v
e
f
un
c
ti
on
,
t
ho
s
e
of
S
F
S
-
G
au
s
s
an
d
S
F
S
-
F
l
e
v
y
are
62
4
56
.6
33
1
$/h
a
nd
6
24
56
.63
38
(
$/h
)
,
r
es
pe
c
t
i
v
el
y
.
It
i
s
c
l
ea
r
l
y
r
ec
og
ni
z
e
d
tha
t
th
e
be
s
t
c
os
t
of
S
F
S
-
G
au
s
s
i
s
al
wa
y
s
b
ett
er
th
an
th
at
of
S
F
S
-
F
l
ev
y
at
t
he
s
am
e
nu
m
b
er
of
i
terati
o
ns
f
o
r
20
-
un
i
t
s
y
s
t
em
.
In
c
on
tr
as
t
to
th
e
c
as
e
ab
ov
e,
t
he
be
s
t
c
os
t
of
S
F
S
-
F
l
e
v
y
o
utp
erf
o
r
m
s
tha
n
th
at
of
S
F
S
-
G
au
s
s
w
i
t
h t
h
e s
am
e m
an
ne
r
f
or 10
-
un
i
t
s
y
s
te
m
.
T
hi
s
i
m
pl
i
es
th
at
S
F
S
_L
e
v
y
i
s
s
ui
t
ab
l
e
f
or
s
o
l
v
i
n
g
n
o
n
-
c
on
v
ex
ec
on
om
i
c
l
oa
d
d
i
s
pa
tc
h
probl
em
w
i
th
m
an
y
l
oc
al
op
ti
m
um
s
ol
uti
on
s
b
ec
au
s
e
i
ts
s
tr
on
g
c
ha
r
ac
teri
s
t
i
c
i
s
to
s
ea
r
c
h
s
ol
ut
i
on
s
i
n
l
ar
ge
s
pa
c
e,
whi
l
e
S
F
S
_G
a
us
s
i
s
ap
propr
i
ate
f
or
di
s
e
nta
ng
l
i
n
g
c
on
v
ex
on
e
as
i
t
i
s
po
w
erf
ul
l
y
c
a
p
ab
l
e f
or f
i
nd
i
ng
s
ol
uti
on
s
i
n s
m
al
l
s
pa
c
e.
T
ab
l
e 4
.
S
ta
ti
s
ti
c
a
l
R
es
ul
ts
of
S
urv
e
y
2 f
or 10
-
Un
i
t
S
y
s
t
em
S
FS
_
Ga
u
s
s
S
FS
_
L
e
v
y
N
p
MI
S
FS
_
Ga
u
s
s
S
FS
_
L
e
v
y
N
p
MI
M
in.
c
o
s
t
(
$
/
h
)
Mi
n
.
c
o
s
t
(
$
/
h
)
6
2
3
.
9
0
7
2
6
2
3
.
9
3
4
8
20
100
6
2
3
.
8
3
6
0
6
2
3
.
8
2
6
4
20
350
6
2
3
.
8
4
7
4
6
2
3
.
8
8
8
8
20
150
6
2
3
.
8
3
4
0
6
2
3
.
8
2
7
2
20
400
6
2
3
.
8
3
4
0
6
2
3
.
8
4
4
2
20
200
6
2
3
.
8
2
7
0
6
2
3
.
8
2
8
5
20
450
6
2
3
.
8
3
1
8
6
2
3
.
8
3
1
6
20
250
6
2
3
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8
2
5
2
6
2
3
.
8
2
4
0
20
500
6
2
3
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8
2
6
8
6
2
3
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8
2
7
9
20
300
6
2
3
.
8
2
9
3
6
2
3
.
8
2
3
5
20
550
T
ab
l
e 5
.
S
ta
ti
s
ti
c
a
l
R
es
ul
t
s
of
S
urv
e
y
2 f
or
20
-
Un
i
t
S
y
s
t
em
S
FS
_
Ga
u
s
s
S
FS
_
L
e
v
y
N
p
MI
M
in.
c
o
s
t
(
$
/
h
)
6
2
4
5
6
.
7
7
1
7
6
2
4
5
8
.
3
0
3
8
10
50
6
2
4
5
6
.
6
3
4
3
6
2
4
5
6
.
6
8
4
1
10
100
6
2
4
5
6
.
6
3
3
1
6
2
4
5
6
.
6
3
3
8
10
150
6
2
4
5
6
.
6
3
3
1
6
2
4
5
6
.
6
3
3
1
10
200
6
2
4
5
6
.
6
3
3
1
6
2
4
5
6
.
6
3
3
1
10
250
5.2.
Co
mp
ar
i
son
a
n
d
Di
sc
u
ss
ion
In
s
ec
ti
on
,
th
e
S
F
S
m
eth
od
pe
r
f
orm
an
c
e
i
s
e
v
al
ua
t
ed
b
y
c
om
pa
r
i
ng
t
he
m
i
ni
m
u
m
c
os
ts
wi
th
oth
er
a
v
a
i
l
ab
l
e
m
eth
o
ds
.
F
or
f
ai
r
c
om
pa
r
i
s
on
,
s
o
m
e
pa
r
a
m
ete
r
s
s
uc
h
as
N
p
an
d
MI
a
l
on
g
wi
th
the
nu
m
be
r
of
f
un
c
ti
on
ev
al
u
ati
on
s
F
es
are
al
s
o repo
r
te
d i
n
t
a
bl
es
.
5.2
.1
.
Ca
se
S
t
u
d
y
1: 6
-
Un
i
t
T
es
t
S
ys
t
em
T
hi
s
s
tud
y
s
ol
v
es
6
-
ge
n
era
ti
ng
un
i
t
t
ak
i
ng
w
i
t
h
or
wi
th
ou
t
l
i
n
e
tr
an
s
m
i
s
s
i
on
l
os
s
es
i
nto
ac
c
ou
nt.
L
oa
d
de
m
an
d
l
ev
el
of
60
0,
70
0,
a
nd
8
00
M
V
A
i
n
t
urn
f
or
bo
th
t
es
t
c
i
r
c
um
s
tan
c
es
are
s
c
r
uti
ni
z
ed
.
P
r
ob
l
em
da
ta
f
or
v
ario
us
l
oa
d
d
em
an
d
l
e
v
el
s
of
t
he
f
i
r
s
t
t
es
t
s
y
s
t
em
c
an
be
r
ea
c
he
d
i
n
Mo
us
taf
a
et
a
l
.
[11
]
.
In
s
uc
h
s
tud
y
,
we
s
et
N
p
t
o
1
0
an
d
MI
t
o
5
0
f
or
tes
ti
ng
al
l
the
c
as
es
wi
th
or
w
i
t
ho
u
t
tr
a
ns
m
i
s
s
i
on
l
os
s
es
.
T
ab
l
es
6
an
d
7
r
ep
ort
the
nu
m
eric
al
r
e
s
ul
ts
ac
h
i
e
v
ed
b
y
FF
A
[1
1],
MF
A
[
11
],
V
S
S
F
A
[
11
],
MFF
A
[1
1
], S
F
S
_
G
au
s
s
an
d
S
F
S
_L
e
v
y
.
F
r
o
m
T
ab
l
e
6,
i
t
c
an
be
s
e
en
t
ha
t
m
i
ni
m
u
m
f
ue
l
an
d
s
tan
da
r
d
c
os
t
v
al
ue
s
att
a
i
n
ed
b
y
S
F
S
_G
au
s
s
an
d
S
F
S
_L
e
v
y
are
m
uc
h
l
o
w
er
th
an
tho
s
e
of
oth
er
m
eth
od
s
.
In
ad
di
t
i
o
n,
S
F
S
_G
au
s
s
,
an
d
S
F
S
_L
e
v
y
o
nl
y
us
e
N
p
=
1
0,
MI
=
50
an
d
F
e
s
=
1
50
0
w
h
i
l
e
ot
he
r
on
es
ne
e
d
t
o
em
pl
o
y
N
p
=
5
0
MI
=
1
50
an
d
F
e
s
=
37
5
0.
It
ea
s
i
l
y
c
on
f
i
r
m
s
tha
t
S
F
S
_G
au
s
s
a
nd
S
F
S
_
Le
v
y
are
f
as
ter
tha
n
th
os
e
of
v
aria
nts
of
F
A
.
E
v
e
n
as
wi
th
the
c
as
e
i
nc
l
ud
i
ng
tr
a
ns
m
i
s
s
i
on
l
os
s
es
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NIK
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IS
S
N: 1
69
3
-
6
93
0
◼
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toc
ha
s
t
i
c
frac
ta
l
s
ea
r
c
h b
as
ed
m
eth
o
d f
or ec
on
o
mi
c
l
oa
d d
i
s
pa
tc
h
..
. (T
ha
n
g Tr
u
ng
Ng
uy
en
)
2543
ex
hi
b
i
te
d
i
n
T
ab
l
e
7,
S
F
S
_
G
au
s
s
an
d
S
F
S
_
Le
v
y
s
ti
l
l
di
s
pl
a
y
i
ts
s
up
r
em
ac
y
a
bo
u
t
the
b
es
t
c
os
t
wi
th
th
e
s
ho
r
t
es
t
ex
ec
u
ti
o
n
ti
m
e.
Cons
eq
u
en
t
l
y
,
i
t
c
a
n
c
l
i
nc
h
tha
t
S
F
S
_G
au
s
s
an
d
S
F
S
_L
ev
y
are the
be
s
t m
eth
od
s
f
or th
es
e c
as
es
.
T
ab
l
e 6
. N
um
eric
al
A
n
al
y
s
i
s
f
or the
6
-
Uni
t T
es
t S
y
s
te
m
w
i
tho
u
t
T
r
an
s
m
i
s
s
i
on
Lo
s
s
es
M
e
t
h
o
d
s
C
a
s
e
1
.
1
:
P
D
=6
0
0
W
C
a
s
e
1
.
2
:
P
D
=7
0
0
W
C
a
s
e
1
.
3
:
P
D
=8
0
0
W
Np
MI
F
e
s
M
in.
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o
s
t
(
$
/
h
)
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t
d
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o
s
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(
$
/
h
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in.
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s
t
(
$
/
h
)
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t
d
.
c
o
s
t
(
$
/
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in.
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o
s
t
(
$
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t
d
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c
o
s
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(
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FFA
[
1
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31489
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FA
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FFA
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7
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8
10
50
1500
T
ab
l
e 7
. N
um
eric
al
A
n
al
y
s
i
s
f
or the
6
-
Uni
t T
es
t S
y
s
te
m
w
i
th
T
r
an
s
m
i
s
s
i
on
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s
s
e
s
M
e
t
h
o
d
s
C
a
s
e
1
.
4
:
P
D
=6
0
0
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C
a
s
e
1
.
5
:
P
D
=7
0
0
W
C
a
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6
:
P
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=8
0
0
W
Np
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in.
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(
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(
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in.
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(
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in.
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(
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)
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t
d
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c
o
s
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(
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[
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[
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[
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6
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5.2
.2
.
Ca
se
S
t
u
d
y
2:
10
-
u
n
it
T
es
t
S
ys
t
em
T
hi
s
po
r
ti
on
ap
p
l
i
ed
1
0
-
un
i
t
s
y
s
t
em
w
i
th
v
a
l
v
e
-
po
i
nt
l
oa
d
i
ng
,
m
ul
ti
pl
e
f
ue
l
op
ti
o
ns
an
d
wi
th
ou
t
tr
a
ns
m
i
s
s
i
on
to
s
i
z
e
u
p
th
e
r
ea
l
pe
r
f
orm
an
c
e
of
the
S
F
S
on
no
n
-
c
o
nv
ex
pr
ob
l
em
.
T
he
da
ta
s
uc
h
as
up
p
er
an
d
l
o
wer
po
wer
s
of
the
u
ni
ts
an
d
f
ue
l
c
os
t
c
oe
f
f
i
c
i
en
ts
are
c
om
e
fr
o
m
the
pre
v
i
ou
s
s
tu
d
y
as
i
n [
1
7
, 2
3].
In
s
uc
h s
tu
d
y
, th
e l
oa
d o
f
al
l
th
erm
al
un
i
ts
i
s
27
0
0 M
W
.
T
ab
l
e
8
d
es
c
r
i
be
t
he
c
o
m
pa
r
i
s
on
of
r
es
ul
ts
pe
r
f
orm
ed
b
y
S
F
S
m
eth
od
an
d
oth
er
thi
r
te
en
o
ne
s
i
n
term
s
o
f
m
i
ni
m
um
c
os
t,
po
pu
l
ati
on
,
t
h
e
m
ax
i
m
u
m
i
terati
o
ns
,
an
d
the
nu
m
be
r
o
f
f
un
c
ti
on
e
v
a
l
u
ati
on
s
.
A
s
s
e
en
f
r
o
m
the
tab
l
e,
the
be
s
t
f
ue
l
c
os
t
of
D
W
P
S
O
[29
]
i
s
62
2.
74
$/h
an
d
i
s
be
tt
er
th
an
tho
s
e
of
oth
er
m
eth
od
s
.
A
f
ter
r
ec
he
c
k
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◼
IS
S
N: 16
93
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6
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17
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3
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46
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t
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th
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d
MCS
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20
].
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de
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d
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i
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2
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e 1
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n t
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as
t
on
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bu
t
S
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S
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ev
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j
u
s
t reduc
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r
a
du
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l
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.
Evaluation Warning : The document was created with Spire.PDF for Python.