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[
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[
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en
co
m
p
ar
ed
to
th
e
P
V
p
an
el,
th
e
b
atter
y
in
s
tallat
io
n
co
s
ts
ar
e
lo
w
er
.
Ho
w
e
v
er
,
o
w
in
g
to
its
s
h
o
r
t
s
er
v
ice
l
if
e,
th
e
b
atter
y
h
as
a
h
i
g
h
er
li
f
eti
m
e
co
s
t
th
a
n
a
P
V
s
y
s
te
m
.
L
o
n
g
er
p
er
io
d
s
o
f
lo
w
P
V
e
n
er
g
y
a
v
ai
lab
ilit
y
o
r
i
n
co
r
r
ec
t c
h
ar
g
i
n
g
a
n
d
d
is
ch
ar
g
i
n
g
s
h
o
r
ten
b
atter
y
lif
e.
T
h
e
c
h
ar
g
i
n
g
p
r
o
ce
s
s
n
ee
d
s
to
b
e
co
n
tr
o
lled
in
o
r
d
e
r
to
g
et
a
h
ig
h
s
tate
o
f
ch
ar
g
e
(
SOC
)
an
d
in
cr
ea
s
e
b
atter
y
li
f
e.
T
o
ex
ten
d
t
h
e
lif
e
o
f
b
atter
ies
,
th
e
y
m
u
s
t
b
e
p
r
o
p
er
ly
ch
ar
g
ed
.
I
n
a
f
r
ee
s
tan
d
i
n
g
P
V
s
y
s
te
m
,
th
e
b
atter
y
ch
ar
g
i
n
g
co
n
tr
o
ller
is
p
r
in
cip
ally
i
n
ch
a
r
g
e
o
f
h
alti
n
g
r
ev
er
s
e
cu
r
r
en
t
f
lo
w
,
p
r
ev
en
ti
n
g
d
ee
p
d
is
ch
ar
g
e
w
h
e
n
th
e
s
y
s
te
m
is
u
n
d
er
lo
ad
,
an
d
f
u
ll
y
ch
ar
g
in
g
th
e
b
atter
y
w
i
th
o
u
t
g
o
in
g
o
v
er
b
o
ar
d
.
T
h
e
b
atter
y
m
o
d
el,
P
V
m
o
d
el,
an
d
b
atter
y
c
h
ar
g
in
g
s
y
s
te
m
w
it
h
b
u
ck
co
n
v
er
ter
ar
e
all
in
c
lu
d
ed
in
th
i
s
p
r
o
p
o
s
ed
s
y
s
te
m
.
A
b
u
ck
co
n
v
er
ter
,
w
h
ic
h
i
s
also
u
s
ed
f
o
r
b
atter
y
ch
ar
g
i
n
g
,
co
n
tr
o
ls
th
e
f
lo
w
o
f
elec
tr
icit
y
f
r
o
m
t
h
e
P
V
p
an
e
l
to
th
e
b
atter
y
a
n
d
lo
ad
.
T
h
e
P
V
p
an
el'
s
p
o
w
er
m
u
s
t
b
e
m
ea
s
u
r
ed
u
s
in
g
a
n
MP
PT
c
o
n
tr
o
l
alg
o
r
ith
m
.
T
h
e
T
y
r
an
n
o
s
a
u
r
u
s
o
p
tim
izatio
n
al
g
o
r
ith
m
(
T
R
OA
)
is
u
s
ed
i
n
MP
P
tr
ac
k
in
g
.
T
h
e
co
m
p
lete
s
y
s
te
m
i
s
m
o
d
eled
u
s
i
n
g
M
A
T
L
A
B
/S
i
m
u
li
n
k
,
an
d
th
e
o
u
tco
m
es
ar
e
d
is
p
l
a
y
ed
.
T
h
e
b
atter
y
c
h
ar
g
i
n
g
cu
r
r
en
t
m
o
n
it
o
r
in
g
tec
h
n
iq
u
e
u
s
ed
in
th
is
wo
r
k
is
d
ep
icted
in
Fig
u
r
e
1.
T
o
in
cr
ea
s
e
th
e
s
o
lar
p
an
el's
m
ax
i
m
u
m
p
o
w
er
p
r
o
d
u
ctio
n
,
MP
PT
s
y
s
te
m
s
a
r
e
u
ti
lized
.
Desp
ite
c
h
a
n
g
e
s
in
lo
ad
f
ac
to
r
s
,
te
m
p
er
atu
r
e,
an
d
ir
r
ad
ian
ce
,
th
e
s
o
lar
P
V
p
an
el's
o
u
tp
u
t
r
e
m
ain
s
co
n
s
tan
t.
I
n
o
r
d
er
f
o
r
s
o
lar
p
an
els
to
g
en
er
ate
e
lectr
icit
y
m
o
r
e
e
f
f
ec
tiv
el
y
,
b
u
c
k
co
n
v
er
ter
s
ar
e
u
s
ed
to
co
n
v
er
t
D
C
to
D
C
elec
tr
icit
y
[
8
]
.
I
n
s
tan
d
alo
n
e
P
V
s
y
s
te
m
s
,
b
u
c
k
co
n
v
er
ter
s
ar
e
u
ti
lized
f
o
r
D
C
-
D
C
s
tep
-
d
o
w
n
a
n
d
b
atter
y
s
t
o
r
ag
e
[
9
]
.
Dio
d
es,
th
y
r
i
s
to
r
s
,
p
o
w
er
m
eta
l
–
o
x
id
e
–
s
e
m
ico
n
d
u
cto
r
f
ie
ld
-
e
f
f
ec
t
tr
an
s
i
s
to
r
s
(
MO
S
FET
s
)
,
an
d
o
th
er
co
m
p
o
n
e
n
ts
ar
e
f
r
eq
u
en
tl
y
u
s
ed
in
e
x
ch
a
n
g
e
a
p
p
licatio
n
s
.
B
y
o
p
er
atin
g
th
e
DC
-
DC
co
n
v
er
ter
i
n
a
clo
s
ed
l
o
o
p
an
d
alter
in
g
t
h
e
MO
SF
E
T
s
'
g
ate
s
i
g
n
a
l,
th
e
o
u
tp
u
t
v
o
lta
g
e
i
s
li
m
ited
[
1
0
]
.
Fo
r
m
o
n
i
to
r
in
g
s
o
lar
o
u
tp
u
t
f
r
o
m
P
V
p
an
el
s
,
a
v
ar
iet
y
o
f
MP
PT
alg
o
r
ith
m
s
ar
e
av
ailab
le,
Fo
r
b
atter
y
ch
a
r
g
in
g
ap
p
licatio
n
s
,
s
tep
-
d
o
w
n
co
n
v
er
ter
s
p
r
o
v
id
e
g
r
ea
ter
ef
f
icie
n
c
y
.
T
R
O
A
is
a
f
lex
ib
le
a
n
d
ef
f
icie
n
t
m
e
th
o
d
f
o
r
s
o
lv
in
g
te
m
p
er
atu
r
e
a
n
d
is
o
latio
n
i
s
s
u
es
.
I
n
s
o
latio
n
,
s
h
o
r
t
f
o
r
in
cid
en
t
o
r
in
co
m
in
g
s
o
lar
r
ad
iatio
n
,
is
a
m
et
h
o
d
th
at
m
ea
s
u
r
es
th
e
to
tal
q
u
an
tit
y
o
f
s
o
lar
r
ad
iatio
n
en
er
g
y
r
ec
eiv
ed
b
y
a
r
eg
io
n
o
v
er
a
g
i
v
e
n
ti
m
e
p
er
i
o
d
.
T
h
e
m
ea
s
u
r
e
m
e
n
t
o
f
r
ad
iatio
n
is
i
n
w
att
s
p
er
s
q
u
ar
e
m
eter
o
r
W
/
m
2
.
T
h
e
am
o
u
n
t
o
f
r
ad
iatio
n
th
a
t
is
r
ef
lecte
d
o
r
a
b
s
o
r
b
ed
in
P
V
s
y
s
te
m
s
d
ep
en
d
s
o
n
an
o
b
j
ec
t'
s
r
ef
lecti
v
it
y
.
T
h
e
a
m
o
u
n
t
o
f
i
n
s
o
latio
n
t
h
at
en
ter
s
a
s
u
r
f
ac
e
is
lar
g
es
t
w
h
e
n
it
f
ac
es
t
h
e
S
u
n
d
ir
ec
tl
y
.
A
s
t
h
e
an
g
le
b
et
w
ee
n
th
e
d
ir
ec
tio
n
o
f
th
e
s
u
n
's
b
ea
m
s
at
a
r
ig
h
t
an
g
le
to
th
e
s
u
r
f
ac
e
a
n
d
th
at
d
ir
ec
tio
n
r
is
es,
th
e
i
n
s
o
latio
n
f
alls
ac
co
r
d
in
g
to
th
e
co
s
in
e
o
f
t
h
e
a
n
g
le
[
9
]
.
T
h
e
b
u
ck
co
n
v
er
ter
u
s
e
s
b
u
c
k
o
p
er
atio
n
,
w
h
ich
s
tep
s
d
o
w
n
t
h
e
v
o
lta
g
e
an
d
is
u
s
ef
u
l
f
o
r
ch
ar
g
i
n
g
b
atter
ies
an
d
lo
w
-
p
o
w
er
ap
p
licatio
n
s
.
T
h
e
p
u
r
p
o
s
e
o
f
th
is
s
t
u
d
y
w
a
s
to
e
m
p
lo
y
t
h
e
MP
P
T
a
n
d
T
R
OA
to
i
m
p
r
o
v
e
th
e
e
f
f
icie
n
c
y
o
f
b
atter
y
c
h
ar
g
i
n
g
w
it
h
s
o
lar
en
er
g
y
.
Si
m
u
li
n
k
w
as
u
tili
ze
d
to
ass
e
s
s
th
e
i
n
q
u
ir
y
's e
f
f
icac
y
.
T
h
e
s
y
s
te
m
d
escr
ip
tio
n
th
at
t
h
e
MP
PT
b
lo
ck
is
m
o
s
tl
y
co
n
ce
r
n
ed
w
i
th
i
s
s
h
o
w
n
in
F
ig
u
r
e
1
o
f
th
e
cu
r
r
en
t
w
o
r
k
.
Usi
n
g
a
r
ec
en
t
l
y
d
ev
elo
p
ed
o
p
tim
izatio
n
tech
n
iq
u
e
ca
lled
T
R
OA
,
th
e
p
r
o
p
o
r
ti
o
n
al
in
te
g
r
al
d
er
iv
ativ
e
(
P
I
D
)
co
n
tr
o
ller
'
s
g
ain
s
ett
in
g
s
ar
e
ad
j
u
s
ted
to
o
p
ti
m
ize
t
h
e
p
o
w
er
o
u
tp
u
t
f
r
o
m
th
e
m
o
d
el
P
V.
T
h
e
p
u
ls
e
w
id
t
h
m
o
d
u
la
tio
n
(
P
W
M
)
tech
n
iq
u
e
is
u
tili
ze
d
to
s
u
p
p
ly
t
h
e
c
h
o
p
p
er
'
s
g
ate
w
ith
t
h
e
p
r
o
p
e
r
p
u
ls
es.
Fig
u
r
e
1
.
T
h
e
p
lan
n
ed
P
V
p
o
w
er
s
y
s
te
m
's
b
lo
ck
d
iag
r
a
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4864
I
n
t J
R
ec
o
n
f
i
g
u
r
ab
le
&
E
m
b
ed
d
ed
Sy
s
t
,
Vo
l.
15
,
No
.
1
,
Ma
r
c
h
202
6
:
1
7
0
-
182
172
2.
RE
S
E
ARCH
M
E
T
H
O
D
2
.
1
.
B
uck
co
nv
er
t
er
DC
-
DC
A
co
n
v
er
s
io
n
o
f
b
u
c
k
s
i
n
es
s
en
ce
,
DC
-
D
C
co
n
s
is
t
s
o
f
p
o
w
er
s
w
itc
h
es
t
h
at
co
n
tr
o
l
p
u
ls
e
s
,
lik
e
b
ip
o
lar
j
u
n
ctio
n
tr
an
s
i
s
to
r
s
(
B
J
T
s
)
o
r
MO
SF
E
T
s
.
Fig
u
r
e
2
s
h
o
w
s
t
h
e
cir
cu
it
co
n
f
ig
u
r
atio
n
,
b
y
lo
w
er
in
g
th
e
h
ig
h
-
le
v
el
DC
v
o
lta
g
e
to
th
e
lo
w
-
lev
e
l
DC
v
o
lta
g
e,
th
e
MO
SF
E
T
ac
ts
as
a
p
o
w
er
s
w
itc
h
.
T
h
e
o
u
tp
u
t
v
o
ltag
e
o
f
th
i
s
cir
cu
it
n
e
v
er
r
is
es
ab
o
v
e
th
e
i
n
p
u
t
v
o
lta
g
e
[
1
1
]
.
T
h
is
cir
cu
it
's
o
b
j
ec
tiv
e
is
to
p
r
o
d
u
ce
a
co
m
p
lete
DC
o
u
tp
u
t.
T
h
e
DC
o
u
tp
u
t
v
o
lta
g
e
in
t
h
e
b
asic
cir
cu
i
t
w
as
p
r
o
d
u
ce
d
u
s
in
g
an
L
C
lo
w
-
p
a
s
s
f
ilter
.
T
h
e
d
io
d
e
r
ev
er
s
es
b
iases
a
n
d
b
eg
in
s
s
u
p
p
ly
i
n
g
en
er
g
y
to
th
e
lo
ad
an
d
in
d
u
cto
r
o
n
ce
th
e
s
w
itc
h
is
ac
tiv
ated
.
On
ce
th
e
s
w
itc
h
is
d
ea
ctiv
ated
,
th
e
d
io
d
e
w
ill
co
n
d
u
ct
i
n
d
u
cto
r
cu
r
r
en
t
an
d
b
ec
o
m
e
f
o
r
w
ar
d
-
b
iased
.
T
o
p
o
w
er
th
e
lo
ad
,
s
o
m
e
o
f
it
s
e
n
er
g
y
r
eser
v
e
s
w
i
ll b
e
u
s
ed
.
T
h
is
cir
cu
it d
esi
g
n
ca
n
b
e
ap
p
lied
as a
h
i
g
h
-
le
v
el
v
o
ltag
e
co
n
n
ec
tio
n
to
a
lo
w
lo
ad
an
d
as
a
h
i
g
h
-
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
R
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f
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g
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ab
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&
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Sy
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I
SS
N:
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-
4864
Desig
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u
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u
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3
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[
1
6
]
,
[
1
7
]
.
T
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4864
I
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t J
R
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o
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f
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g
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r
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le
&
E
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b
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1
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202
6
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182
174
MP
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r
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e
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h
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m
u
s
t
th
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b
e
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an
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o
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ller
.
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h
e
MPPT
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m
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v
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t
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f
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e
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V
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atin
g
v
o
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e.
T
h
e
v
o
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g
e
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s
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it
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h
e
m
o
d
u
le
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u
tp
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t.
T
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is
o
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h
e
m
o
d
u
l
e
f
r
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m
th
e
b
atter
y
,
th
e
MP
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o
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ith
m
m
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d
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th
e
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W
M
to
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e
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C
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ter
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e
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t
y
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cle.
T
h
e
PV
m
o
d
u
le
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s
o
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atio
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al
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ar
a
m
ete
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l
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p
ti
m
ized
i
n
th
e
c
u
r
r
en
t r
esear
ch
e
m
p
lo
y
i
n
g
th
e
T
R
OA
.
2
.
4
.
O
ptim
iza
t
io
n a
lg
o
rit
h
m
I
t
is
p
o
s
s
ib
le
to
d
ef
in
e
m
an
y
r
ea
l
-
w
o
r
ld
is
s
u
es
as
o
p
ti
m
izat
i
o
n
p
r
o
b
lem
s
w
it
h
s
e
v
er
al
p
ar
a
m
eter
s
t
h
at
n
ee
d
to
b
e
ad
d
r
ess
ed
.
Fin
d
in
g
a
s
o
lu
tio
n
o
r
s
o
lu
t
io
n
s
to
r
ed
u
ce
o
r
m
a
x
i
m
ize
t
h
e
v
al
u
es
o
f
o
n
e
o
r
m
o
r
e
o
b
j
ec
tiv
es
is
t
h
e
m
a
th
e
m
atica
l
d
ef
in
itio
n
o
f
o
p
ti
m
iz
a
tio
n
.
M
o
r
eo
v
er
,
an
o
p
tim
izatio
n
p
r
o
b
le
m
is
r
ef
er
r
ed
to
as
r
estricte
d
w
h
en
i
t c
alls
f
o
r
ce
r
tain
p
ar
a
m
eter
s
to
s
ati
s
f
y
o
n
e
o
r
m
o
r
e
r
estrictio
n
s
.
2
.
4
.
1
.
T
y
ra
nn
o
s
a
urus
o
pti
m
i
za
t
io
n a
lg
o
ri
t
h
m
a.
I
ns
pira
t
io
n
T
h
ese
d
in
o
s
au
r
s
,
a
n
d
p
ar
ticu
l
ar
l
y
th
e
T
y
r
a
n
n
o
s
a
u
r
u
s
R
e
x
,
w
er
e
p
r
esen
t
i
n
w
e
s
ter
n
No
r
t
h
Am
er
ica
ar
o
u
n
d
6
6
m
il
lio
n
y
ea
r
s
ag
o
.
T
h
e
T
y
r
an
n
o
s
a
u
r
u
s
r
ei
g
n
s
s
u
p
r
e
m
e
a
m
o
n
g
t
h
e
d
in
o
s
a
u
r
s
p
ec
ies.
I
n
p
o
p
u
lar
cu
lt
u
r
e,
th
e
T
y
r
an
n
o
s
a
u
r
u
s
R
e
x
is
r
ef
er
r
ed
to
as
T
.
r
ex
o
r
T
-
R
e
x
,
is
o
n
e
o
f
th
e
m
o
s
t
w
ell
-
k
n
o
w
n
d
i
n
o
s
au
r
s
.
R
ex
m
ea
n
s
"
k
in
g
"
in
L
at
in
.
M
e
m
b
er
s
o
f
a
g
e
n
u
s
,
th
e
s
e
m
a
s
s
iv
e
th
er
o
p
o
d
d
in
o
s
au
r
s
w
er
e
3
.
6
6
to
3
.
9
6
m
eter
s
tall,
1
2
.
3
to
1
2
.
4
m
eter
s
lo
n
g
,
i
t t
y
p
icall
y
w
eig
h
ed
b
et
w
ee
n
8
.
4
an
d
1
4
m
etr
ic
to
n
s
.
P
eo
p
le
ass
u
m
e
t
h
at
t
y
r
an
n
o
s
a
u
r
u
s
r
ex
,
li
k
e
lio
n
s
,
w
o
l
v
e
s
,
an
d
o
th
er
an
i
m
a
ls
,
ar
e
ap
ex
p
r
ed
ato
r
s
s
in
ce
th
e
y
ar
e
a
m
o
n
g
th
e
lar
g
est
ca
r
n
iv
o
r
es
o
n
E
ar
th
.
T
h
e
T
-
R
ex
w
as
a
s
ca
v
e
n
g
er
,
ac
co
r
d
in
g
to
o
th
er
r
esear
ch
er
s
[
1
0
]
.
Ma
n
y
s
cie
n
tis
ts
n
o
w
co
n
cu
r
th
at
th
e
T
.
R
ex
w
as
b
o
th
a
n
ac
tiv
e
h
u
n
ter
an
d
a
s
ca
v
e
n
g
er
,
d
esp
ite
th
e
f
ac
t
th
at
it
w
as
o
n
ce
u
n
ce
r
tai
n
if
it
w
a
s
an
ap
ex
p
r
ed
ato
r
o
r
a
s
ca
v
en
g
er
[
1
8
]
.
Am
o
n
g
o
th
er
d
in
o
s
au
r
s
o
f
its
k
i
n
d
,
it
is
r
en
o
w
n
ed
f
o
r
its
h
u
n
tin
g
b
e
h
av
io
r
d
u
e
to
its
p
o
w
er
f
u
l b
iti
n
g
f
o
r
ce
Fig
u
r
e
5
.
Fig
u
r
e
5
.
T
y
r
an
n
o
s
au
r
u
s
[
1
9
]
b.
S
ug
g
este
d a
lg
o
rit
h
m
T
h
is
s
ec
tio
n
s
tar
ts
b
y
d
escr
ib
in
g
t
h
e
in
s
p
ir
atio
n
b
eh
i
n
d
th
e
r
ec
o
m
m
e
n
d
ed
s
tr
ateg
y
.
Nex
t,
an
alg
o
r
ith
m
a
n
d
f
lo
w
c
h
ar
t
ar
e
p
r
esen
ted
w
i
th
th
e
m
ath
e
m
at
ica
l
m
o
d
el.
T
h
e
T
R
OA
s
i
m
u
late
s
T
y
r
an
n
o
s
au
r
u
s
r
ex
h
u
n
ti
n
g
to
u
p
d
ate
p
o
p
u
latio
n
p
o
s
itio
n
s
.
P
r
ey
s
elec
tio
n
,
w
h
ich
f
i
n
all
y
s
elec
ts
t
h
e
b
est
o
p
tio
n
,
h
u
n
tin
g
an
d
p
u
r
s
u
i
t,
an
d
p
o
p
u
latio
n
in
itiat
io
n
ar
e
th
e
th
r
ee
p
r
i
m
ar
y
s
te
p
s
o
f
t
h
e
p
r
o
ce
s
s
[
1
9
]
-
[2
2
]
.
Fig
u
r
e
6
d
is
p
la
y
s
a
d
iag
r
a
m
t
h
at
ill
u
s
tr
ates
t
h
e
T
R
OA
al
g
o
r
ith
m
,
a
n
d
th
e
a
lg
o
r
ith
m
d
escr
ib
es
t
h
e
s
p
ec
i
f
ic
p
h
a
s
es
o
f
t
h
i
s
m
ec
h
a
n
i
s
m
's p
r
o
ce
d
u
r
e
.
−
I
n
itializatio
n
−
Hu
n
ti
n
g
−
Selectio
n
L
et
u
s
s
ee
t
h
e
s
tep
s
i
n
d
etail
:
i)
I
nitia
liza
t
io
n
T
R
OA
b
eg
i
n
s
b
y
e
m
p
lo
y
i
n
g
r
an
d
o
m
n
es
s
t
o
g
en
er
ate
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itial
p
o
p
u
latio
n
,
w
h
er
e
e
ac
h
p
r
ey
's
lo
ca
tio
n
co
r
r
elate
s
to
an
o
p
tim
izatio
n
p
r
o
b
lem
s
o
lu
t
io
n
,
m
u
c
h
lik
e
an
y
o
t
h
er
h
eu
r
i
s
tic
tech
n
iq
u
e
.
T
h
e
(
1
0
)
ca
n
b
e
u
s
ed
to
ex
p
r
ess
th
e
s
to
ch
a
s
t
ic
to
talit
y
.
=
(
,
)
∗
(
−
)
+
(
1
0
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J
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&
E
m
b
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Sy
s
t
I
SS
N:
2089
-
4864
Desig
n
o
f a
s
o
la
r
s
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w
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a
P
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co
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175
W
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in
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t
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tio
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o
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i
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p
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1
,
2
,
.
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.
.
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,
]
w
it
h
in
t
h
e
u
p
p
er
an
d
lo
w
er
b
o
u
n
d
ar
ies,
is
cr
ea
ted
at
r
an
d
o
m
,
w
it
h
b
ein
g
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e
d
i
m
en
s
io
n
,
w
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er
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t
h
e
p
o
p
u
latio
n
s
ize
is
d
e
n
o
ted
b
y
n
p
,
t
h
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u
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d
lo
w
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b
o
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ies
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ch
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ac
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d
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ea
r
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'
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.
ii)
H
un
t
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a
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pu
rsu
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As
w
it
h
w
o
lv
e
s
,
lio
n
s
,
a
n
d
o
th
er
ap
ex
p
r
ed
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r
s
,
a
T
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R
ex
p
u
r
s
u
es
it
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m
.
Up
o
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p
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it
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est
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th
e
T
-
R
ex
attem
p
ts
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h
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n
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P
r
ey
m
a
y
atte
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p
t
to
f
lee
o
r
p
r
o
tect
its
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f
r
o
m
p
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ed
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r
s
o
n
o
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n
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h
en
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ex
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r
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=
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(
1
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T
h
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o
r
e,
as
(
1
1
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illu
s
tr
ates,
w
h
e
n
t
h
e
T
-
R
ex
s
tar
ts
h
u
n
ti
n
g
,
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h
e
p
r
e
y
s
tar
ts
to
d
i
s
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teg
r
ate,
an
d
t
h
e
T
-
R
ex
tr
ac
k
s
it b
y
u
p
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atin
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ca
ti
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.
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h
er
e
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th
e
e
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ated
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ce
o
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ch
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n
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th
e
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atter
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p
r
ey
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=
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tp
o
s
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−
∗
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(
1
2
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W
h
en
t
h
e
h
u
n
ti
n
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at
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f
alls
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et
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ee
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[
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1
,
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h
u
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n
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u
n
s
u
cc
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f
u
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s
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is
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o
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o
ciate
d
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u
s
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ch
a
n
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t
h
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T
y
r
an
n
o
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a
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r
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s
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c
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o
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av
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k
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n
as t
h
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g
et.
iii)
Select
io
n
T
h
e
p
o
s
itio
n
o
f
th
e
p
r
e
y
—
t
h
at
is
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e
p
r
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t
a
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lo
ca
tio
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s
o
f
t
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e
i
n
ten
d
ed
p
r
e
y
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i
s
th
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b
asis
f
o
r
th
e
s
elec
tio
n
p
r
o
ce
s
s
.
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f
th
e
p
r
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a
w
a
y
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r
p
r
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f
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r
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ce
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d
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p
la
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in
(
1
3
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[
1
9
]
,
[
2
1
]
.
+
1
=
{
ℎ
(
)
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(
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ℎ
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A
r
ep
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ated
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in
it
ial
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o
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itio
n
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m
e
s
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h
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s
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ted
o
p
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ized
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ed
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r
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g
o
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ith
m
1
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h
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m
et
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ical
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o
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n
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a
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r
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s
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ti
m
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o
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ith
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OA
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h
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r
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d
u
r
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s
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w
it
h
t
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d
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m
i
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itializat
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d
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a
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t o
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ased
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th
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s
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i
f
ied
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o
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alg
o
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ith
m
t
h
e
n
d
eter
m
i
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es
t
h
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itio
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is
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o
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ir
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-
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n
ti
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t
h
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s
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m
atica
l
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ates.
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h
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c
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ak
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s
s
u
r
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t
h
at
t
h
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p
r
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y
'
s
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o
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s
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f
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m
p
ar
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itn
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ll
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es
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tio
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l
g
o
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ith
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R
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izatio
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ate
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f
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r
ey
c
ap
tu
r
e
I
n
p
u
t: P
o
p
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latio
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ize,
m
a
x
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m
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m
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ter
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tiv
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ctio
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O
ut
put
:
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he op
t
i
m
al
po
si
t
i
o
n of
t
he
t
ar
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et
.
1
-
B
eg
in
2
-
Usi
n
g
E
q
u
a
tio
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(
1
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,
r
an
d
o
m
l
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i
tialize
t
h
e
p
r
e
y
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s
p
o
s
iti
o
n
.
3
-
Use E
q
u
atio
n
(
1
0
)
to
c
o
m
p
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te
f
itn
e
s
s
.
4
-
Dete
r
m
i
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e
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p
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ca
tio
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d
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et
t
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-
R
ex
to
p
u
r
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u
e
it
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5
-
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q
u
atio
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s
(
1
1
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an
d
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1
2
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to
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eg
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th
e
T
-
R
ex
h
u
n
ti
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p
r
o
ce
d
u
r
e.
6
-
A
s
s
es
s
th
e
s
u
itab
il
it
y
o
f
th
e
p
r
ey
's n
e
w
h
ab
itat
.
7
-
Up
d
ate
th
e
p
r
ey
's p
o
s
itio
n
i
f
th
e
(
)
<
(
)
.
8
-
T
h
e
g
o
al
eq
u
als ze
r
o
if
th
e
co
n
d
itio
n
f
a
ils
.
9
-
s
to
p
P
s
eu
d
o
co
d
e
1
s
u
m
m
ar
izes
th
e
p
r
o
ce
d
u
r
al
lo
g
ic
o
f
t
h
e
T
OA
to
m
a
k
e
it
s
co
m
p
u
tatio
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a
l
i
m
p
le
m
en
ta
tio
n
m
o
r
e
u
n
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er
s
t
an
d
ab
le.
In
(
1
0
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is
u
s
ed
to
d
eter
m
i
n
e
th
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p
r
e
y
's
s
tar
ti
n
g
p
o
s
itio
n
.
I
ts
f
it
n
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s
is
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en
a
s
s
es
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ed
to
ch
o
o
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e
th
e
m
a
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tar
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et.
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h
e
m
o
v
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m
e
n
t
o
f
t
h
e
T
-
R
ex
i
s
co
n
tr
o
lled
b
y
a
s
t
o
ch
asti
c
p
ar
a
m
eter
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
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4864
I
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Sy
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15
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No
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1
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Ma
r
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202
6
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7
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-
182
176
in
s
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ate
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at
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ied
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ter
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u
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g
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1
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,
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e
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te
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.
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alu
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is
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d
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ter
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i
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ir
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1.
T
-
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g
o
r
ith
m
First, use Equation (10) to determine the prey's position.
Determine the prey's minimum position and compute its fitness.
Look at the intended prey
The start of the while loop
Ma
ke the T
-
Rex move at random.
(
)
<
Use equation (11) to update the prey's position.
else
Randomly update the prey's location.
End the if
Use Equation (12) to determine the new fitness
If
(
)
<
(
)
.
Update the target's and prey's
locations.
else
The objective is zero.
Close the if
Search for the best value.
=
+
1
Complete while
Go back
Fig
u
r
e
6
.
Diag
r
a
m
r
ep
r
esen
tin
g
th
e
T
R
O
A
al
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o
r
ith
m
Star
t
Set th
e
p
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ey
'
s
lo
ca
tio
n
to
s
tar
t D
eter
m
in
e
th
e
Pre
y
'
s
Fit
n
ess
(
F1
)
Det
er
m
ine t
he
f
it
nes
s
o
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t
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prey
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F
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)
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f
ra
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r
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andom
l
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p
dat
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he p
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Det
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it
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2
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ind t
he
T
-
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e
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nim
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l posi
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on whe
n it
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omes to pre
y.
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t
i
l
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t
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on
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2
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, upd
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t
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t
he p
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s
l
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t
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on.
if
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1
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F2
Tar
ge
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s z
e
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pdat
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ss
v
al
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e, t
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r
get
,
and T
-
R
ex pos
i
t
i
on.
S
top
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J
R
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o
n
f
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g
u
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ab
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&
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m
b
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Sy
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t
I
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N:
2089
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4864
Desig
n
o
f a
s
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la
r
s
ystem
w
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a
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co
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ller
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a
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(
K
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S
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b
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h
R
a
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)
177
2
.
5
.
T
he
T
y
ra
nn
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s
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urus
o
pt
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m
iza
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m
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P
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m
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h v
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ize
As
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h
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iz
e
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e
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o
r
ith
m
s
p
er
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r
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ad
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ir
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r
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elay
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o
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ar
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n
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P
p
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ac
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e
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i
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w
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y
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a
m
ic
s
o
s
cillat
io
n
s
ca
n
b
e
atten
u
a
ted
b
y
u
s
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g
a
s
m
al
ler
s
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ize.
Ma
n
y
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n
tr
i
b
u
tio
n
s
t
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to
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k
ad
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an
ta
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e
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ar
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ize
h
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v
e
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ad
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ig
n
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ica
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t p
r
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es
s
in
s
o
l
v
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n
g
t
h
ese
p
r
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le
m
s
.
W
ith
t
h
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m
et
h
o
d
,
th
e
s
y
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te
m
u
s
es
th
e
attr
ib
u
tes
o
f
th
e
P
V
ar
r
a
y
to
au
to
m
atica
ll
y
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eter
m
in
e
th
e
s
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s
ize.
Dep
en
d
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g
o
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ea
ch
o
p
er
atin
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itu
a
t
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,
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e
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ize
m
u
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t
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k
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alan
ce
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et
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n
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a
n
d
d
y
n
a
m
is
m
.
A
n
o
v
el
v
ar
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le
s
t
ep
s
ize
MP
PT
alg
o
r
ith
m
w
it
h
les
s
o
s
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tio
n
s
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q
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ick
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io
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s
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ted
in
t
h
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s
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t
u
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[
2
3
]
-
[
26]
.
Fig
u
r
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7
d
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ar
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le
s
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MP
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at
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m
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ated
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Fig
u
r
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.
I
m
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m
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tatio
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ar
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le
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