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a
n
d
R
id
ao
[
3
]
co
m
p
ar
ed
an
d
cl
ass
if
ied
v
ar
io
u
s
p
at
h
p
lan
n
i
n
g
tec
h
n
iq
u
es
i
n
clu
d
i
n
g
A
r
tif
ic
ial
P
o
ten
tial
Field
A
P
F
,
s
ea
r
ch
-
b
ased
m
eth
o
d
s
,
s
a
m
p
l
in
g
-
b
ased
m
et
h
o
d
s
an
d
o
p
ti
m
izatio
n
m
eth
o
d
s
.
T
h
e
A
P
F
m
eth
o
d
[
4
]
is
f
ast
a
n
d
ef
f
ic
ien
t,
b
u
t
v
er
y
s
u
s
ce
p
tib
le
to
lo
ca
l
m
i
n
i
m
a.
Sear
ch
h
eu
r
i
s
tic
-
b
ase
d
p
lan
n
er
s
s
u
ch
as F
ield
D
*
[
5
]
an
d
Fas
t M
ar
ch
i
n
g
*
(
FM
*
)
[
6
]
ar
e
ca
p
ab
le
o
f
g
e
n
er
atin
g
o
p
tim
a
l
an
d
r
o
b
u
s
t
p
ath
s
,
b
u
t
th
eir
co
m
p
u
tatio
n
al
e
f
f
ic
i
en
cies
ar
e
li
m
ited
to
less
co
m
p
le
x
an
d
lo
w
er
d
i
m
en
s
io
n
al
p
r
o
b
le
m
s
.
Sa
m
p
l
in
g
-
b
ased
m
eth
o
d
s
s
u
c
h
as
R
ap
id
ly
-
e
x
p
lo
r
i
n
g
R
an
d
o
m
T
r
ee
s
R
R
T
[
7
]
an
d
its
v
ar
ian
t
s
R
R
T
*
[
8
]
ar
e
e
f
f
ec
t
iv
e
f
o
r
h
ig
h
-
d
i
m
e
n
s
io
n
al
an
d
h
i
g
h
l
y
ti
m
e
-
co
n
s
tr
ain
t
s
ce
n
a
r
io
s
at
t
h
e
co
s
t
o
f
th
e
p
ath
o
p
ti
m
alit
y
,
a
n
d
th
e
r
esu
lta
n
t
p
at
h
s
o
f
ten
r
eq
u
ir
e
f
u
r
t
h
er
r
ef
i
n
e
m
e
n
t.
Me
ta
-
h
e
u
r
is
tic
o
p
ti
m
iza
tio
n
m
et
h
o
d
s
s
u
c
h
as
t
h
e
e
v
o
lu
ti
o
n
ar
y
al
g
o
r
ith
m
s
[
9
,
1
0
]
s
h
o
w
e
x
ce
lle
n
t
p
er
f
o
r
m
a
n
ce
i
n
ter
m
s
o
f
s
o
lu
tio
n
o
p
tim
a
lit
y
.
E
v
o
l
u
tio
n
ar
y
al
g
o
r
ith
m
s
ar
e
e
f
f
ec
ti
v
e
f
o
r
h
i
g
h
-
d
i
m
e
n
s
io
n
al
co
m
p
lex
p
r
o
b
le
m
s
b
u
t
t
h
e
y
m
a
y
co
n
v
er
g
e
to
lo
ca
l
m
i
n
i
m
a
w
it
h
in
f
i
n
ite
ti
m
e.
Am
o
n
g
th
e
e
x
is
ti
n
g
e
v
o
lu
tio
n
ar
y
a
lg
o
r
it
h
m
s
,
Z
en
g
,
Sa
m
m
u
t
[
2
]
f
u
r
t
h
er
p
o
in
ted
o
u
t
t
h
at
t
h
e
p
ar
ticle
s
w
ar
m
o
p
ti
m
iza
tio
n
(
P
SO)
-
b
ased
al
g
o
r
ith
m
s
ar
e
r
em
ar
k
ab
l
y
r
o
b
u
s
t
a
n
d
ef
f
icien
t f
o
r
s
o
lv
in
g
h
ig
h
-
d
i
m
en
s
io
n
al
p
ath
p
lan
n
i
n
g
p
r
o
b
le
m
s
.
P
SO
alg
o
r
ith
m
a
n
d
its
m
o
s
t
s
ig
n
if
ican
t
v
ar
ian
t,
th
e
q
u
a
n
t
u
m
-
b
e
h
a
v
ed
P
SO
(
Q
P
SO)
ar
e
ex
ten
s
i
v
el
y
u
s
ed
in
v
ar
io
u
s
o
p
ti
m
izatio
n
p
r
o
b
lem
s
e
v
er
s
i
n
ce
th
eir
e
m
er
g
en
ce
i
n
1
9
9
5
an
d
2
0
0
4
r
esp
ec
tiv
el
y
d
u
e
to
th
eir
f
i
n
e
s
ea
r
ch
ab
il
ities
a
n
d
ea
s
y
i
m
p
le
m
en
ta
tio
n
s
[
1
1
]
.
So
m
e
p
io
n
ee
r
in
g
e
x
a
m
p
les
o
f
th
e
ir
ap
p
licatio
n
s
i
n
p
ath
p
lan
n
i
n
g
ca
n
b
e
f
o
u
n
d
in
[
1
2
-
14]
.
P
SO
-
b
ased
p
ath
p
lan
n
er
s
ar
e
s
u
itab
le
f
o
r
d
y
n
a
m
ic
e
n
v
ir
o
n
m
en
ts
w
h
er
e
o
n
lin
e
p
ath
p
lan
n
i
n
g
is
r
eq
u
ir
ed
b
ec
au
s
e
th
e
y
m
a
in
ta
in
a
la
r
g
e
p
o
o
l
o
f
s
o
lu
tio
n
s
,
w
h
ic
h
i
s
av
ailab
le
at
an
y
ti
m
e
d
u
r
in
g
th
e
m
is
s
io
n
.
T
h
ese
s
o
l
u
tio
n
s
ca
n
s
er
v
e
as
t
h
e
i
n
itia
l
s
o
l
u
tio
n
s
w
h
e
n
e
v
er
p
ath
r
ep
la
n
n
i
n
g
i
s
r
eq
u
ir
ed
,
th
u
s
s
ig
n
i
f
ica
n
tl
y
i
m
p
r
o
v
i
n
g
th
e
co
m
p
u
tatio
n
a
l
ef
f
icie
n
c
y
.
So
m
e
s
u
cc
e
s
s
f
u
l
ap
p
licatio
n
s
o
f
P
SO
-
b
ased
alg
o
r
ith
m
i
n
o
n
l
i
n
e
p
ath
p
lan
n
i
n
g
o
f
A
UV
ca
n
b
e
f
o
u
n
d
in
[
1
5
,
1
6
]
.
No
n
e
th
eles
s
,
P
SO
-
b
ased
alg
o
r
ith
m
s
ar
e
s
u
s
ce
p
tib
le
to
co
n
v
er
g
e
n
ce
at
lo
ca
l
m
i
n
i
m
u
m
s
o
lu
tio
n
s
i
f
th
e
ti
m
e
allo
w
ed
f
o
r
p
ath
p
lan
n
in
g
i
s
li
m
ited
,
w
h
ich
i
s
o
f
te
n
t
h
e
ca
s
e
in
r
ea
l A
UV
o
p
er
atio
n
s
.
I
n
r
ec
en
t
y
ea
r
s
,
m
a
n
y
s
tr
ate
g
i
es
t
h
at
m
o
d
if
ied
t
h
e
P
SO
a
n
d
QP
SO
alg
o
r
it
h
m
s
h
a
v
e
b
ee
n
p
r
o
p
o
s
ed
in
o
r
d
er
to
im
p
r
o
v
e
th
eir
p
er
f
o
r
m
an
ce
s
i
n
p
ath
p
la
n
n
i
n
g
o
f
v
a
r
io
u
s
au
to
n
o
m
o
u
s
s
y
s
te
m
s
.
E
a
ch
o
f
t
h
ese
v
ar
ian
ts
o
f
th
e
al
g
o
r
ith
m
s
clai
m
ed
to
h
av
e
d
i
f
f
er
en
t
i
m
p
r
o
v
e
m
en
t
s
o
v
er
th
e
o
r
ig
i
n
al
P
SO
an
d
Q
P
SO
alg
o
r
ith
m
s
.
T
o
b
en
ch
m
ar
k
th
e
P
SO
a
n
d
QP
S
O
v
ar
ia
n
ts
in
th
e
ap
p
licatio
n
o
f
A
UV
p
at
h
p
la
n
n
i
n
g
,
a
r
ec
e
n
t
co
m
p
ar
is
o
n
s
tu
d
y
[
1
7
]
class
if
ied
an
d
e
v
al
u
ated
th
e
al
g
o
r
it
h
m
s
b
ased
o
n
t
h
eir
s
o
lu
tio
n
q
u
alit
ies,
s
tab
ilit
ie
s
an
d
co
m
p
u
tatio
n
a
l
ef
f
icien
c
y
.
I
t
w
as
co
n
cl
u
d
ed
f
r
o
m
th
e
r
es
u
lts
o
f
[
1
7
]
th
at
t
h
e
h
y
b
r
i
d
izatio
n
o
f
d
i
f
f
er
e
n
tial
ev
o
l
u
tio
n
(
DE
)
i
n
P
SO
an
d
QP
SO,
w
h
ich
w
er
e
p
r
o
p
o
s
ed
b
y
[
1
8
]
,
ar
e
ab
le
to
p
r
o
d
u
ce
p
ath
p
lan
n
in
g
s
o
l
u
tio
n
w
it
h
th
e
h
i
g
h
e
s
t
q
u
alit
y
d
u
e
to
t
h
eir
s
tr
o
n
g
er
r
e
s
is
ta
n
ce
to
lo
ca
l
m
i
n
i
m
a,
b
u
t
at
th
e
co
s
t
o
f
h
i
g
h
er
co
m
p
u
ta
t
io
n
al
r
eq
u
ir
e
m
en
t
s
.
Mo
r
eo
v
er
,
th
e
f
in
d
i
n
g
s
o
f
[
1
7
]
s
u
g
g
ested
t
h
at
h
a
v
in
g
an
ad
ap
tiv
e
m
ec
h
an
is
m
in
t
h
e
ev
o
l
u
tio
n
o
f
p
ar
ticles
i
n
th
e
P
SO
alg
o
r
it
h
m
ca
n
p
r
o
d
u
ce
s
o
lu
tio
n
q
u
a
lit
y
th
at
i
s
s
ec
o
n
d
o
n
l
y
to
DE
-
h
y
b
r
id
ized
al
g
o
r
ith
m
s
,
b
u
t
w
i
th
a
r
elativ
el
y
lo
w
co
m
p
u
ta
tio
n
al
r
eq
u
ir
e
m
e
n
t;
t
h
e
ad
ap
ti
v
e
P
S
O
(
A
P
SO)
p
r
o
p
o
s
ed
b
y
[
1
9
]
w
a
s
ab
le
to
g
en
er
ate
a
p
ath
p
lan
n
i
n
g
s
o
l
u
tio
n
t
h
at
a
ch
iev
e
s
a
b
alan
ce
b
et
w
ee
n
s
o
l
u
tio
n
q
u
a
lit
y
a
n
d
co
m
p
u
tatio
n
al
r
eq
u
ir
e
m
en
ts
.
I
n
s
p
ir
ed
b
y
th
e
DE
h
y
b
r
id
izati
o
n
,
a
n
u
m
b
er
o
f
alg
o
r
it
h
m
s
,
n
a
m
el
y
SDEP
SO
(
P
SO
w
ith
s
e
l
ec
tiv
e
DE
h
y
b
r
id
izatio
n
)
,
SDE
A
P
SO
(
P
SO
w
i
th
ad
ap
ti
v
e
f
ac
to
r
an
d
s
elec
ti
v
e
DE
h
y
b
r
id
izatio
n
)
,
an
d
S
DE
QP
SO
(
QP
SO
w
ith
s
e
lecti
v
e
DE
h
y
b
r
id
izatio
n
)
,
ar
e
p
r
o
p
o
s
ed
in
t
h
is
p
ap
er
.
T
h
ese
al
g
o
r
ith
m
s
e
x
p
lo
r
e
th
e
s
tr
en
g
t
h
s
o
f
DE
-
h
y
b
r
id
ized
alg
o
r
it
h
m
s
,
an
d
m
in
i
m
ize
t
h
eir
w
ea
k
n
es
s
e
s
i
n
o
r
d
er
to
i
m
p
r
o
v
e
t
h
e
a
lg
o
r
ith
m
p
er
f
o
r
m
a
n
ce
.
T
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
w
er
e
i
m
p
le
m
en
ted
in
a
n
o
f
f
l
in
e
A
U
V
p
ath
p
la
n
n
er
a
n
d
t
h
eir
p
er
f
o
r
m
a
n
ce
w
er
e
b
en
ch
m
ar
k
ed
ag
a
in
s
t
o
th
er
m
eta
-
h
eu
r
i
s
tic
al
g
o
r
ith
m
s
b
ec
au
s
e
if
t
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
ca
n
p
r
o
v
id
e
b
etter
co
m
p
u
tatio
n
al
e
f
f
icie
n
c
y
to
d
em
o
n
s
tr
ate
t
h
e
m
i
n
i
m
u
m
ca
p
ab
ilit
y
o
f
a
p
ath
p
lan
n
er
,
t
h
en
th
e
y
w
i
ll
o
u
tp
er
f
o
r
m
th
e
test
ed
al
g
o
r
ith
m
s
in
a
r
ea
l
is
tic
o
n
li
n
e
p
ath
p
la
n
n
er
.
T
h
e
o
b
j
ec
tiv
e
o
f
th
e
AUV
p
ath
p
l
an
n
er
i
s
d
ef
i
n
ed
as
f
i
n
d
in
g
a
n
ea
r
-
o
p
ti
m
al
p
at
h
t
h
at
s
af
el
y
g
u
id
es
th
e
A
UV
f
r
o
m
a
s
tar
tin
g
p
o
s
itio
n
to
a
d
esti
n
a
tio
n
b
ased
o
n
a
m
in
i
m
u
m
ti
m
e
cr
iter
io
n
.
T
h
e
p
ath
p
lan
n
i
n
g
s
ce
n
ar
io
w
it
h
a
p
r
io
r
i
k
n
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Sect
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QP
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n
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DE
P
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2.
RE
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ased
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ith
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1
.
P
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ce
d
b
y
Eb
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n
d
Ken
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ed
y
[
2
0
]
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P
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tic
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o
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u
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ased
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ac
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in
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s
.
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o
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ith
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o
f
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at
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m
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c
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h
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e
p
ar
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‟
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o
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.
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h
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e
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ativ
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p
d
ated
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o
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ce
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e
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e
(
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ated
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ased
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2
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f
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(
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as
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p
r
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es
[
2
3
,
2
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.
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)
()
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m
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o
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les
[
2
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2
5
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.
2
.
2
.
Q
P
SO
a
lg
o
rit
h
m
I
n
s
p
ir
ed
b
y
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h
e
m
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a
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m
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is
o
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th
e
P
SO
al
g
o
r
ith
m
,
S
u
n
,
Fen
g
[
2
6
]
p
r
o
p
o
s
ed
th
e
QP
S
O
a
lg
o
r
ith
m
.
I
n
QP
SO,
t
h
e
p
o
s
itio
n
o
f
t
h
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i
th
p
ar
ticle
ca
n
b
e
u
p
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ated
u
s
i
n
g
th
e
f
o
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w
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s
to
ch
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s
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eq
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:
{
(
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|
|
(
⁄
)
(
)
|
|
(
⁄
)
(
7
)
∑
⁄
(
8
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2089
-
4856
P
a
r
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Hu
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w
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ti
cles
in
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is
k
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x
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s
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(
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co
ef
f
icien
t,
w
h
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is
t
h
e
m
o
s
t
cr
itical
p
ar
am
eter
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o
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tu
n
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n
g
t
h
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n
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e
n
ce
b
eh
av
io
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r
o
f
QP
SO
.
A
s
s
u
g
g
e
s
ted
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y
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e
e
m
p
ir
ical
s
tu
d
y
o
f
p
ar
am
eter
s
elec
tio
n
in
[
1
1
]
,
a
lin
ea
r
l
y
d
ec
r
ea
s
in
g
f
r
o
m
a
m
ax
i
m
u
m
v
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e
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o
f
1
.
0
to
a
m
i
n
i
m
u
m
v
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lu
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m
in
o
f
0
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5
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co
r
d
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g
to
(
9
)
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s
u
itab
le
f
o
r
m
o
s
t a
p
p
licatio
n
s
.
(
)
(
9
)
2
.
3
.
DE
P
SO
a
nd
D
E
Q
P
SO
a
lg
o
rit
h
m
s
On
e
o
f
th
e
m
o
s
t
e
f
f
ec
ti
v
e
m
et
h
o
d
u
s
ed
f
o
r
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m
p
r
o
v
i
n
g
th
e
P
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-
b
ased
al
g
o
r
ith
m
i
s
b
y
h
y
b
r
id
izatio
n
,
in
w
h
ic
h
th
e
b
en
e
f
icia
l
f
ea
t
u
r
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o
f
o
th
er
o
p
tim
iza
tio
n
tech
n
iq
u
es
is
co
m
b
i
n
ed
w
i
t
h
P
SO
o
r
QP
SO
alg
o
r
ith
m
.
I
n
[
2
7
]
,
th
e
b
asic P
SO
w
as c
o
m
b
in
ed
w
it
h
Di
f
f
er
en
tia
l E
v
o
l
u
tio
n
(
DE
)
,
r
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l
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g
i
n
a
h
y
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r
id
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o
r
ith
m
k
n
o
wn
as
DE
P
SO.
B
ased
o
n
t
h
e
in
s
p
ir
atio
n
f
r
o
m
DE
P
SO,
[
1
8
]
a
p
p
lied
a
s
i
m
ilar
h
y
b
r
id
izatio
n
co
n
ce
p
t
in
QP
S
O
to
p
r
o
p
o
s
e
DE
QP
SO.
I
n
b
o
th
DE
P
SO
an
d
DE
QP
SO,
t
h
e
p
ar
ticles
u
n
d
er
g
o
t
h
e
u
s
u
al
p
o
s
itio
n
u
p
d
ate
o
p
er
atio
n
s
,
f
o
llo
w
ed
b
y
a
s
u
c
ce
s
s
i
v
e
t
h
r
ee
-
s
tep
DE
o
p
er
atio
n
,
w
h
ic
h
is
th
e
m
u
tatio
n
,
cr
o
s
s
o
v
er
a
n
d
s
elec
tio
n
as d
escr
ib
ed
b
elo
w
.
-
Mu
tatio
n
:
A
m
u
tated
d
o
n
o
r
v
e
cto
r
U
is
f
ir
s
t
g
en
er
ated
u
s
i
n
g
(
1
0
)
:
(
)
(
)
(
10
)
w
h
er
e
r
1
,
r
2
,
r
3
an
d
r
4
ar
e
r
an
d
o
m
l
y
s
elec
ted
p
ar
ticle
i
n
d
ices
th
at
ar
e
m
u
t
u
all
y
d
i
f
f
er
en
t,
a
n
d
d
if
f
er
e
n
t
f
r
o
m
th
e
cu
r
r
en
t
in
d
e
x
i a
n
d
th
e
p
ar
t
icle
in
d
ex
o
f
g
lo
b
al
b
est p
o
s
iti
o
n
,
i.e
.
r
1
r
2
r
3
r
4
i
g
b
est
.
-
C
r
o
s
s
o
v
er
:
A
tr
ial
v
ec
to
r
T
is
g
en
er
ated
to
in
cr
ea
s
e
t
h
e
d
iv
er
s
it
y
,
b
y
co
n
d
u
ct
in
g
cr
o
s
s
o
v
er
b
et
w
ee
n
th
e
d
o
n
o
r
v
ec
to
r
an
d
p
er
s
o
n
al
b
est p
o
s
itio
n
as s
h
o
w
n
i
n
(
1
1
)
.
[
]
{
(
11
)
w
h
er
e
CR
is
t
h
e
cr
o
s
s
o
v
er
p
r
o
b
ab
ilit
y
w
h
ic
h
is
s
u
g
g
ested
t
o
b
e
0
.
8
5
,
r
j
i
s
a
u
n
if
o
r
m
d
i
s
t
r
ib
u
ted
r
an
d
o
m
n
u
m
b
er
r
an
g
i
n
g
f
r
o
m
0
to
1
.
0
,
an
d
r
is
a
r
a
n
d
o
m
p
o
s
iti
v
e
i
n
t
eg
er
r
an
g
i
n
g
f
r
o
m
1
to
t
h
e
n
u
m
b
er
o
f
p
ar
ticl
e
d
i
m
en
s
io
n
s
D
.
-
Selectio
n
:
A
g
r
ee
d
y
s
elec
tio
n
is
u
s
ed
to
d
ec
id
e
w
h
e
th
er
th
e
tr
ial
v
ec
to
r
T
s
h
o
u
ld
r
ep
l
ac
e
th
e
c
u
r
r
en
t
pos
itio
n
X
i
n
t
h
e
(
t
+1
)
th
iter
ati
o
n
.
T
h
e
f
it
n
es
s
o
f
T
w
ill
b
e
ev
alu
ated
an
d
co
m
p
ar
ed
w
it
h
X
.
X
w
ill
o
n
l
y
b
e
r
ep
lace
d
if
T
h
a
s
b
etter
f
it
n
ess
v
al
u
e;
o
th
er
w
i
s
e
X
w
i
ll b
e
r
etain
ed
.
T
h
is
m
ea
n
s
t
h
e
h
y
b
r
id
izatio
n
o
f
t
h
e
D
E
o
p
er
atio
n
w
ill
n
ev
er
d
eter
io
r
ate
th
e
s
o
lu
t
io
n
,
b
u
t o
n
l
y
m
a
k
e
i
t b
etter
o
r
r
em
ain
u
n
c
h
a
n
g
ed
.
DE
P
SO
an
d
DE
QP
SO
alg
o
r
ith
m
s
w
er
e
ap
p
lied
to
s
o
lv
e
th
e
p
ath
p
lan
n
i
n
g
p
r
o
b
lem
o
f
Un
m
an
n
ed
A
er
ial
Ve
h
icle
(
U
AV)
in
[
1
8
]
,
an
d
h
as
p
r
o
v
en
to
b
e
ca
p
ab
le
o
f
g
en
er
ati
n
g
s
i
g
n
i
f
ica
n
tl
y
h
i
g
h
er
s
o
lu
tio
n
q
u
alit
y
t
h
a
n
b
a
s
ic
P
SO a
n
d
Q
P
SO a
lg
o
r
ith
m
s
.
2
.
4
.
AP
SO
a
lg
o
rit
h
m
I
n
b
asic P
SO,
th
e
ac
ce
ler
atio
n
co
ef
f
icie
n
t
s
C
1
an
d
C
2
,
an
d
i
n
e
r
tia
w
ei
g
h
t
w
i
n
t
h
e
u
p
d
ate
eq
u
atio
n
ar
e
i
m
p
o
r
tan
t
f
o
r
m
ai
n
tai
n
i
n
g
th
e
b
alan
ce
b
et
w
ee
n
t
h
e
g
lo
b
al
ex
p
lo
r
atio
n
an
d
lo
ca
l
e
x
p
lo
itati
o
n
o
f
t
h
e
p
ar
ticle
s
.
Z
h
an
,
Z
h
an
g
[
1
9
]
p
r
o
p
o
s
ed
an
ad
ap
tiv
e
P
SO
(
A
P
SO)
,
in
w
h
ich
a
n
ev
o
l
u
tio
n
ar
y
f
ac
to
r
is
u
s
ed
as
a
n
i
n
d
icato
r
r
ep
r
esen
tin
g
th
e
e
v
o
lu
tio
n
ar
y
s
tate
o
f
t
h
e
p
ar
ticles
to
co
n
tr
o
l
th
e
eq
u
atio
n
co
e
f
f
ic
ie
n
ts
ad
ap
tiv
el
y
.
T
o
d
eter
m
in
e
t
h
e
e
v
o
lu
t
io
n
ar
y
f
a
cto
r
,
th
e
m
ea
n
p
ar
ticle
d
is
ta
n
c
e
d
i
o
f
th
e
i
th
p
ar
ticle
to
o
th
er
p
ar
ticles
h
a
s
to
b
e
ca
lcu
lated
u
s
i
n
g
(
1
2
)
.
T
h
e
ev
o
lu
tio
n
ar
y
f
ac
to
r
f
is
th
e
n
co
m
p
u
ted
ac
co
r
d
in
g
to
(
1
3
)
.
∑
√
∑
(
)
(
12
)
(
)
(
)
⁄
,
-
(
13
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
I
n
t
J
R
o
b
&
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u
to
m
,
Vo
l.
9
,
No
.
2
,
J
u
n
e
2
0
2
0
:
94
–
1
1
2
98
w
h
er
e
d
g
is
th
e
m
ea
n
p
ar
ticl
e
d
is
tan
ce
o
f
th
e
g
lo
b
al
b
est
p
ar
ticle,
d
m
in
an
d
d
m
ax
ar
e
th
e
m
i
n
i
m
u
m
a
n
d
m
ax
i
m
u
m
o
f
t
h
e
m
ea
n
p
ar
t
icle
d
is
ta
n
ce
s
r
esp
ec
ti
v
el
y
.
T
h
e
in
er
tia
w
ei
g
h
t
w
ca
n
b
e
ca
lcu
lated
f
r
o
m
ev
o
lu
tio
n
ar
y
f
ac
to
r
f
u
s
i
n
g
(
1
4
)
.
T
h
e
ad
ap
tatio
n
o
f
th
e
a
cc
eler
atio
n
co
ef
f
icie
n
t
s
C
1
an
d
C
2
ca
n
also
b
e
ac
h
iev
ed
u
s
i
n
g
th
e
e
v
o
lu
t
io
n
ar
y
f
ac
to
r
as s
h
o
w
n
in
(
1
5
)
.
(
)
,
-
⁄
(
14
)
|
|
|
|
,
w
h
er
e
(
15
)
3.
M
E
T
H
O
DO
L
O
G
Y:
SE
L
E
C
T
I
V
E
DE
H
YB
RI
DI
Z
AT
I
O
N
A
lt
h
o
u
g
h
DE
P
SO
a
n
d
DE
Q
P
SO
alg
o
r
ith
m
s
ar
e
ab
le
to
g
en
er
ate
e
x
ce
lle
n
t
s
o
lu
tio
n
q
u
alitie
s
f
o
r
A
U
V
p
ath
p
la
n
n
in
g
,
t
h
e
h
y
b
r
id
izatio
n
o
f
DE
s
ig
n
i
f
ica
n
t
l
y
i
n
cr
ea
s
es
th
e
co
m
p
u
ta
tio
n
al
r
eq
u
ir
e
m
e
n
ts
o
f
th
e
al
g
o
r
ith
m
d
u
e
to
t
h
e
g
r
e
ed
y
s
elec
tio
n
o
p
er
ato
r
u
s
ed
i
n
th
e
DE
o
p
er
atio
n
[
1
7
]
.
T
h
e
g
r
ee
d
y
s
elec
tio
n
o
p
er
ato
r
r
eq
u
ir
es
th
e
f
itn
e
s
s
o
f
th
e
p
ar
ticles
to
b
e
e
v
alu
ated
t
w
ice
f
o
r
co
m
p
ar
is
o
n
p
u
r
p
o
s
es,
m
ea
n
i
n
g
an
ad
d
itio
n
al
f
it
n
es
s
ev
al
u
ati
o
n
f
o
r
ev
er
y
p
ar
ticle
in
ev
e
r
y
iter
atio
n
.
As
th
e
f
i
tn
e
s
s
ev
alu
a
tio
n
p
r
o
ce
s
s
u
s
u
all
y
co
n
tr
ib
u
te
s
to
th
e
m
aj
o
r
ity
o
f
t
h
e
co
m
p
u
tatio
n
al
ti
m
e
[
1
1
]
,
th
e
g
r
ee
d
y
o
p
er
ato
r
d
r
asti
ca
ll
y
i
n
cr
ea
s
e
s
th
e
co
m
p
u
ta
tio
n
al
r
eq
u
ir
e
m
e
n
ts
o
f
t
h
e
alg
o
r
it
h
m
s
.
T
h
e
in
cr
ea
s
e
in
co
m
p
u
tatio
n
a
l
r
eq
u
ir
e
m
e
n
ts
d
u
e
to
th
e
ad
d
itio
n
o
f
g
r
ee
d
y
s
ele
ctio
n
o
p
er
ato
r
w
ill
b
e
e
v
en
m
o
r
e
o
b
v
io
u
s
w
h
e
n
t
h
e
c
o
m
p
le
x
it
y
a
n
d
th
e
d
i
m
en
s
io
n
al
it
y
o
f
t
h
e
p
r
o
b
lem
in
cr
ea
s
e
[
1
7
]
.
I
n
o
r
d
e
r
to
m
i
n
i
m
ize
t
h
e
d
o
w
n
s
id
e
o
f
DE
o
p
e
r
ato
r
in
P
SO
-
b
ased
alg
o
r
ith
m
,
a
s
elec
ti
v
e
h
y
b
r
id
iz
atio
n
s
c
h
e
m
e
i
s
p
r
o
p
o
s
ed
in
th
is
p
ap
er
to
p
r
esen
t th
e
f
o
llo
w
i
n
g
al
g
o
r
ith
m
s
:
-
SDEP
SO (
P
SO
w
it
h
s
elec
t
iv
e
DE
h
y
b
r
id
izatio
n
)
-
SDE
A
P
SO (
P
SO
w
it
h
ad
ap
tiv
e
f
ac
to
r
an
d
s
elec
ti
v
e
DE
h
y
b
r
id
izatio
n
)
-
SDEQ
P
SO (
QP
SO
w
it
h
s
e
lect
iv
e
DE
h
y
b
r
id
izatio
n
)
Usi
n
g
th
e
s
elec
t
iv
e
s
c
h
e
m
e,
t
h
ese
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
ap
p
ly
t
h
e
DE
o
p
er
atio
n
to
a
s
elec
t
ed
n
u
m
b
er
o
f
p
ar
ticles
o
n
l
y
,
in
s
tead
o
f
th
e
en
tire
s
w
ar
m
.
T
h
e
n
u
m
b
er
o
f
p
ar
ticles
s
elec
ted
f
o
r
D
E
o
p
e
r
atio
n
,
N
S
,
is
co
n
tr
o
lled
b
y
a
s
elec
t
iv
e
f
ac
to
r
S
as sh
o
w
n
i
n
(
1
6
)
.
,
-
(
16
)
T
h
e
DE
o
p
er
atio
n
in
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
w
a
s
m
o
d
i
f
ied
b
y
r
ep
lacin
g
t
h
e
g
r
ee
d
y
s
elec
tio
n
o
p
er
ato
r
w
it
h
a
n
at
u
r
al
s
elec
ti
o
n
o
p
er
ato
r
.
T
h
e
DE
o
p
er
atio
n
p
r
o
p
o
s
ed
in
t
h
is
p
ap
er
i
n
itiat
es
b
y
s
o
r
tin
g
all
th
e
p
ar
ticles
in
t
h
e
e
n
tire
s
w
ar
m
ac
co
r
d
in
g
to
t
h
eir
p
er
s
o
n
a
l
b
e
s
t
p
o
s
itio
n
s
.
Ne
x
t,
a
n
u
m
b
er
o
f
s
elec
ted
p
ar
ticles
w
it
h
t
h
e
b
est
f
it
n
es
s
u
n
d
er
g
o
t
h
e
m
u
tat
io
n
a
n
d
cr
o
s
s
o
v
er
o
p
er
ato
r
s
,
s
i
m
ilar
to
t
h
o
s
e
i
n
DE
P
SO
an
d
DE
QP
SO,
to
g
en
er
ate
t
h
e
s
a
m
e
n
u
m
b
er
o
f
tr
ial
v
ec
to
r
s
.
T
h
e
tr
ial
v
ec
to
r
s
ar
e
th
en
s
u
b
j
ec
ted
to
a
n
atu
r
al
s
elec
tio
n
o
p
er
ato
r
,
in
w
h
ic
h
th
e
s
a
m
e
n
u
m
b
er
o
f
p
ar
ticles
w
i
th
t
h
e
w
o
r
s
t f
it
n
es
s
is
r
ep
lace
d
b
y
t
h
e
tr
i
al
v
ec
to
r
s
.
As
o
n
l
y
th
e
w
o
r
s
t
p
ar
ticles
a
r
e
r
ep
lace
d
in
th
is
p
r
o
ce
s
s
,
all
p
o
ten
tiall
y
b
es
t
s
o
lu
tio
n
s
w
il
l
n
e
v
er
d
eter
io
r
ate.
Fu
r
th
er
m
o
r
e,
th
e
co
m
p
u
tatio
n
al
r
eq
u
ir
e
m
e
n
ts
o
f
th
e
alg
o
r
it
h
m
s
w
ill
n
o
t
b
e
s
i
g
n
i
f
ica
n
tl
y
af
f
ec
ted
b
ec
au
s
e
th
e
n
a
tu
r
al
s
elec
tio
n
o
p
er
ato
r
d
o
es
n
o
t
in
v
o
lv
e
f
itn
es
s
co
m
p
ar
is
o
n
b
et
w
ee
n
th
e
p
ar
ticles,
w
h
ic
h
r
eq
u
ir
es
ad
d
itio
n
al
p
ar
ticle
f
i
tn
es
s
ev
al
u
a
tio
n
in
e
v
er
y
iter
atio
n
.
T
h
e
DE
o
p
er
atio
n
w
it
h
n
at
u
r
al
s
elec
t
io
n
in
cr
ea
s
es
t
h
e
d
iv
er
s
it
y
an
d
t
h
e
ev
o
lu
tio
n
ar
y
r
ate
o
f
th
e
en
tire
s
w
ar
m
b
y
eli
m
i
n
ati
n
g
th
e
least
d
esira
b
le
s
o
lu
tio
n
s
,
h
e
n
ce
lead
in
g
to
a
f
aster
an
d
b
etter
g
lo
b
al
co
n
v
er
g
en
ce
t
h
eo
r
etica
ll
y
.
T
h
e
s
elec
tiv
e
DE
h
y
b
r
id
izatio
n
w
as
ap
p
lied
to
P
SO
an
d
QPSO
alg
o
r
it
h
m
s
to
d
ev
elo
p
th
e
SDEP
SO
an
d
SDEQ
P
SO
al
g
o
r
ith
m
s
in
th
is
p
ap
er
.
I
n
ad
d
itio
n
,
a
n
o
t
h
e
r
alg
o
r
ith
m
,
n
a
m
el
y
SDE
A
P
S
O,
w
as
d
e
v
elo
p
ed
b
y
ad
d
i
n
g
a
n
ad
ap
tiv
e
m
ec
h
an
is
m
to
t
h
e
co
n
tr
o
l
o
f
i
n
er
t
ia
w
ei
g
h
t
a
n
d
ac
ce
ler
atio
n
c
o
ef
f
icie
n
t
s
i
n
P
SO
alg
o
r
ith
m
,
s
i
m
ilar
l
y
to
th
e
AP
SO
alg
o
r
ith
m
.
T
h
e
i
m
p
le
m
e
n
tatio
n
o
f
SDEP
SO,
SDE
A
P
SO
an
d
SDEQ
P
S
O
alg
o
r
ith
m
s
i
n
A
U
V
p
ath
p
lan
n
in
g
ca
n
b
e
co
n
d
u
cted
as d
escr
i
b
ed
in
th
e
f
o
llo
w
i
n
g
p
s
eu
d
o
co
d
e
.
Step 1.
Input
the algorithm parameters and
environmental information of the ocean field.
Step 2.
Initialize
particles
with
random
positions
in
(1)
to
represent
an
initial
g
roup
of
candidate paths. Set
pbest
to be the current particle positions.
Step 3.
While
the stop criteria is not met,
Step 3.1
For
t
= 1, 2, …,
t
max
,
SD
EPSO
SDEAPSO
SDEQPSO
Evaluate the cost
function
f (X
i
t
)
.
Update
pbest
and
gbest
according to (4) and
(5) respectively.
Update
w
according to
(6).
Evaluate the cost
function
f (X
i
t
)
.
Update
pbest
and
gbest
according to (4) and
(5) respectively.
Update
w
,
C
1
and
C
2
according to (14) and
(15) respectively.
Compute
mbest
according
to (8).
Evaluate the cost function
f (X
i
t
)
.
Update
pbest
and
gbest
according to (4) and (5)
respectively.
Update
according to (9)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2089
-
4856
P
a
r
ticle
s
w
a
r
m
o
p
timiz
a
tio
n
a
lg
o
r
ith
ms w
ith
s
elec
t
ive
d
iffer
en
tia
l e
vo
lu
tio
n
.
.
.
(
Hu
i S
h
en
g
Lim
)
99
Step 3.2
For
each particle
i
= 1, 2, …,
N
,
SDEPSO
SD
EAPSO
SDEQPSO
Update particle velocity and
position according to (2)
and (3) respectively.
Update particle velocity
and position according to
(2) and (3) respectively.
Update particle
position according
to
(7).
End
Step 3.3
Sort all particles according to the fit
ness of their personal best positions.
Step 3.4
For
k
= 1, 2,…,
N
S
th
best performing particle,
Mutation
: Generate mutated vector
U
k
t
according to (10).
Crossover
: Generate trial vector
T
k
t
according to (11).
Natural
selection
:
Re
pl
ac
e
k
th
wo
rs
t
pe
rf
or
mi
ng
pa
r
ti
cl
e
wi
th
tr
ia
l
ve
ct
or
T
k
t
.
End
End
Step 4.
Output
gb
es
t
th
at
ho
ld
s
t
he
op
ti
ma
l
pa
th
wh
en
th
e
st
op
cr
it
er
ia
is
me
t
or
w
he
n
t
max
is reached.
3
.
1
.
Co
m
plex
it
y
Ana
ly
s
is
T
h
e
ti
m
e
co
m
p
le
x
it
y
o
f
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
ca
n
b
e
m
ea
s
u
r
ed
b
y
co
u
n
ti
n
g
t
h
e
n
u
m
b
er
o
f
p
r
im
iti
v
e
o
p
er
atio
n
s
in
th
e
alg
o
r
ith
m
.
B
y
r
ef
er
r
in
g
to
th
e
p
s
eu
d
o
co
d
e
o
f
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
,
th
e
n
u
m
b
er
o
f
o
p
er
atio
n
s
ca
n
b
e
co
u
n
ted
a
s
f
o
llo
w
s
:
-
I
n
Step
2
,
in
itializatio
n
co
n
tr
ib
u
tes o
n
e
o
p
er
atio
n
f
o
r
N
ti
m
e
s
.
-
I
n
Step
3
.
1
,
co
s
t
f
u
n
ctio
n
ev
alu
a
tio
n
co
n
tr
ib
u
tes
o
n
e
o
p
er
at
io
n
f
o
r
N
ti
m
es;
f
in
d
i
n
g
p
b
est
r
e
q
u
ir
es
N
⋅
lo
g
(
N
)
o
p
er
atio
n
s
;
f
i
n
d
in
g
g
b
est
r
eq
u
ir
e
s
lo
g
(
N
)
o
p
er
atio
n
s
;
u
p
d
ati
n
g
co
ef
f
icie
n
ts
co
n
tr
ib
u
tes
o
n
e
o
p
er
atio
n
; SDE
QP
SO r
eq
u
ir
es
N
ad
d
itio
n
al
o
p
er
atio
n
s
to
ca
lcu
late
mb
est
.
-
I
n
Step
3
.
2
,
SDEP
SO
an
d
SDEA
P
SO
p
er
f
o
r
m
N
lo
o
p
s
w
i
t
h
1
4
o
p
er
atio
n
s
;
SDEQ
P
SO
p
er
f
o
r
m
N
lo
o
p
s
w
it
h
1
2
o
p
er
atio
n
s
.
-
Step
3
.
3
co
n
tr
ib
u
tes lo
g
(
N
)
o
p
er
atio
n
s
.
-
Step
3
.
4
p
e
r
f
o
r
m
s
N
S
lo
o
p
s
w
i
th
8
o
p
er
atio
n
s
.
Step
s
1
–
3
.
2
ar
e
th
e
s
ta
n
d
ar
d
o
p
er
atio
n
s
in
b
asic
P
SO,
A
P
SO
an
d
QP
SO,
w
h
er
ea
s
Step
3
.
3
an
d
3
.
4
ar
e
th
e
ad
d
itio
n
al
o
p
er
atio
n
s
in
tr
o
d
u
ce
d
b
y
t
h
e
s
elec
t
iv
e
DE
o
p
er
ato
r
.
O
-
n
o
tatio
n
is
u
s
ed
in
t
h
is
w
o
r
k
to
d
en
o
te
th
e
a
s
y
m
p
to
tic
u
p
p
er
b
o
u
n
d
o
f
ti
m
e
co
m
p
le
x
it
y
,
w
h
ic
h
i
n
d
icate
s
t
h
e
co
m
p
u
ta
tio
n
al
ti
m
e
o
f
t
h
e
alg
o
r
ith
m
i
n
th
e
w
o
r
s
t c
ase
s
c
en
ar
io
.
W
h
en
co
m
p
u
tin
g
th
e
O
-
n
o
tatio
n
,
t
h
e
lo
w
er
o
r
d
er
ter
m
s
in
t
h
e
n
u
m
b
er
o
f
o
p
er
atio
n
s
is
n
e
g
li
g
ib
le
b
ec
au
s
e
th
eir
i
m
p
ac
t
o
n
co
m
p
u
tatio
n
al
ti
m
e
ar
e
r
elativ
el
y
i
n
s
i
g
n
i
f
ican
t
f
o
r
lar
g
e
in
p
u
t
[
2
8
]
.
T
h
e
h
i
g
h
e
s
t
o
r
d
er
ter
m
in
t
h
e
o
p
er
atio
n
is
N
⋅
lo
g
(
N
)
in
Step
3
.
1
,
an
d
it
p
er
f
o
r
m
s
t
m
ax
ti
m
es
to
c
h
ec
k
th
e
ter
m
in
at
io
n
co
n
d
i
tio
n
.
T
h
e
o
p
er
atio
n
s
ad
d
ed
b
y
t
h
e
s
elec
tiv
e
DE
o
p
er
ato
r
(
Step
3
.
3
an
d
3
.
4
)
ar
e
o
f
lo
w
er
o
r
d
er
an
d
d
o
n
o
t
h
av
e
s
i
g
n
if
ican
t
i
m
p
ac
t
o
n
t
h
e
ti
m
e
co
m
p
lex
i
t
y
.
T
h
u
s
,
t
h
e
co
m
p
lex
i
t
y
o
f
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
i
n
li
n
ea
r
f
o
r
m
is
O
(
N
⋅
lo
g
(
N
)
⋅
t
m
ax
)
,
s
i
m
ilar
to
th
e
s
t
an
d
ar
d
P
SO
alg
o
r
ith
m
.
P
SO
-
b
ased
alg
o
r
it
h
m
s
h
av
e
t
w
o
i
n
n
er
lo
o
p
s
w
h
e
n
g
o
in
g
t
h
r
o
u
g
h
t
h
e
p
o
p
u
latio
n
o
f
N
p
ar
ticles,
an
d
o
n
e
o
u
ter
lo
o
p
f
o
r
t
m
ax
iter
atio
n
s
;
th
is
r
en
d
er
s
th
e
ti
m
e
co
m
p
l
ex
it
y
to
b
e
O
(
N
2
⋅
t
m
ax
)
in
th
e
ex
tr
e
m
e
ca
s
e.
T
h
e
s
p
atial
co
m
p
le
x
it
y
o
f
th
e
alg
o
r
it
h
m
s
i
s
O
(
N
2
)
,
w
h
ic
h
d
ep
en
d
s
o
n
th
e
p
o
p
u
latio
n
s
i
ze
.
3
.
2
.
B
ench
m
a
r
k F
un
ct
io
ns
Me
tah
e
u
r
is
tic
a
lg
o
r
it
h
m
s
s
u
c
h
as
th
e
P
SO
-
b
ased
a
lg
o
r
it
h
m
s
ca
n
b
e
e
v
al
u
ated
e
m
p
i
r
icall
y
b
y
co
m
p
ar
i
n
g
th
e
ir
p
er
f
o
r
m
a
n
ce
in
s
o
lv
i
n
g
a
s
et
o
f
o
b
j
ec
ti
v
e
f
u
n
ctio
n
p
r
o
b
le
m
s
.
I
n
ad
d
itio
n
to
t
h
e
A
U
V
p
ath
p
lan
n
i
n
g
p
r
o
b
lem
,
a
n
u
m
b
er
o
f
n
o
n
-
li
n
ea
r
co
n
ti
n
u
o
u
s
f
u
n
c
tio
n
p
r
o
b
le
m
s
w
er
e
u
s
ed
to
s
tu
d
y
an
d
b
en
ch
m
ar
k
t
h
e
c
h
ar
ac
ter
is
tic
s
o
f
t
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
.
A
cc
o
r
d
in
g
to
t
h
e
“n
o
f
r
ee
l
u
n
c
h
”
(
NF
L
)
th
eo
r
e
m
[
2
9
]
,
th
e
d
ev
elo
p
m
e
n
t
a
n
d
ev
al
u
ati
o
n
o
f
an
a
lg
o
r
ith
m
f
o
r
a
s
p
ec
if
ic
p
r
o
b
le
m
s
h
o
u
ld
b
e
b
ased
o
n
th
e
b
en
c
h
m
ar
k
f
u
n
ctio
n
p
r
o
b
le
m
s
o
f
s
i
m
ilar
class
a
n
d
p
r
o
p
e
r
ties
,
b
ec
au
s
e
th
e
al
g
o
r
ith
m
p
er
f
o
r
m
an
ce
w
i
ll
n
o
t
b
e
co
n
s
is
te
n
t
f
o
r
ev
er
y
k
i
n
d
o
f
p
r
o
b
lem
.
T
h
u
s
,
t
h
ese
b
e
n
ch
m
ar
k
f
u
n
ctio
n
s
w
er
e
s
ele
cted
b
ased
o
n
th
eir
r
ese
m
b
lan
ce
s
to
th
e
p
r
o
p
er
ties
o
f
p
ath
p
lan
n
i
n
g
p
r
o
b
le
m
.
T
h
e
s
elec
ted
b
en
ch
m
ar
k
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ch
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f
f
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izatio
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u
n
ct
io
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,
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it
p
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T
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est
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ate
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er
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o
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m
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th
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a
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o
t
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o
r
ith
m
s
f
o
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ev
er
y
p
r
o
b
lem
.
I
n
f
ac
t,
th
e
i
m
p
r
o
v
ed
alg
o
r
ith
m
p
er
f
o
r
m
a
n
ce
in
o
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e
cla
s
s
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lem
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n
o
t
n
ec
e
s
s
ar
il
y
co
n
s
i
s
te
n
t
in
all
k
in
d
s
o
f
p
r
o
b
lem
s
;
i
n
s
tead
,
it
is
ex
ac
tl
y
tr
ad
e
d
w
ith
p
er
f
o
r
m
an
ce
in
a
n
o
th
er
cla
s
s
o
f
p
r
o
b
le
m
[
2
9
]
.
A
lth
o
u
g
h
al
l
t
h
e
f
u
n
ctio
n
p
r
o
b
le
m
s
s
elec
ted
f
o
r
b
en
c
h
m
ar
k
i
n
g
p
u
r
p
o
s
es
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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-
4856
P
a
r
ticle
s
w
a
r
m
o
p
timiz
a
tio
n
a
lg
o
r
ith
ms w
ith
s
elec
t
ive
d
iffer
en
tia
l e
vo
lu
tio
n
.
.
.
(
Hu
i S
h
en
g
Lim
)
101
h
av
e
s
i
m
ilar
p
r
o
p
er
ties
(
th
e
y
ar
e
all
m
u
lti
m
o
d
al
a
n
d
m
u
lt
i
-
d
i
m
en
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io
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t
h
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m
etr
y
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p
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s
ar
e
d
if
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er
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n
t.
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o
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e,
t
h
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s
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ld
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e
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ased
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test
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p
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lem
s
i
s
in
t
h
e
r
an
g
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o
f
0
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1
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3
.
M
o
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s
p
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th
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p
ath
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0
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3
w
a
s
f
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n
d
to
b
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ap
p
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p
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iate
a
n
d
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f
ec
ti
v
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3
.
4
.
B
ench
m
a
r
k St
ud
y
T
h
e
b
en
ch
m
ar
k
f
u
n
ctio
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s
w
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ased
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A
t
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t
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n
itial
p
ar
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p
o
s
itio
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s
f
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all
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m
s
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th
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b
o
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n
d
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i
n
t
er
v
als
g
i
v
en
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n
T
ab
le
3
.
As
t
h
e
d
ata
w
as
n
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m
all
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d
is
tr
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d
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to
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S
h
ap
ir
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-
W
ilk
test
,
t
h
e
Kr
u
s
k
al
-
W
allis
test
[
3
4
]
,
w
h
ic
h
i
s
a
n
o
n
-
p
ar
a
m
etr
i
c
A
NO
V
A
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an
al
y
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i
s
o
f
v
ar
ia
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ce
)
,
w
as
u
s
ed
w
ith
a
s
ig
n
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f
ica
n
ce
lev
el
o
f
0
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0
5
to
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an
k
t
h
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al
g
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ith
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m
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ce
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ased
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n
th
e
s
o
lu
tio
n
q
u
a
liti
es
(
f
it
n
ess
o
b
tain
ed
)
.
T
h
e
r
an
k
i
n
g
p
r
o
ce
d
u
r
e
u
s
ed
t
h
e
Ho
l
m
–
B
o
n
f
er
r
o
n
i
„
s
t
ep
d
o
w
n
‟
ap
p
r
o
ac
h
[
3
5
]
,
w
h
ic
h
i
s
b
est
s
u
ited
f
o
r
all
p
air
w
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s
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s
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th
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id
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ter
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als
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o
t
n
ee
d
ed
an
d
s
a
m
p
le
s
ize
s
ar
e
eq
u
al
[
1
1
]
.
T
h
e
alg
o
r
ith
m
s
ar
e
g
iv
e
n
th
e
s
a
m
e
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k
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h
e
y
ar
e
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o
t
s
tati
s
ti
ca
ll
y
d
i
f
f
er
en
t
f
r
o
m
o
n
e
an
o
th
er
.
T
h
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m
ed
ia
n
s
(
Med
.
)
o
f
f
itn
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s
s
o
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tain
ed
,
th
e
A
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V
A
r
an
k
s
(
#R
)
an
d
th
e
m
ed
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n
s
o
f
co
m
p
u
ta
ti
o
n
al
ti
m
e
r
eq
u
ir
ed
w
er
e
tab
u
lated
in
T
ab
le
3
.
T
h
e
m
ed
ian
s
o
f
th
e
to
p
t
w
o
b
est
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p
er
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o
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m
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s
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ts
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ld
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o
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all
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m
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ce
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ith
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g
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v
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n
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tal
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a
n
k
s
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w
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h
ar
e
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lcu
lated
f
r
o
m
th
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m
m
a
ti
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th
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k
s
o
f
th
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o
r
it
h
m
f
o
r
all
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r
o
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lem
s
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ased
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h
e
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lts
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it
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a
n
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e
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t
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s
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o
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n
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le
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th
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lt
s
f
o
r
all
p
r
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le
m
s
;
t
h
i
s
o
b
s
er
v
a
tio
n
ag
r
ee
s
w
it
h
t
h
e
N
F
L
t
h
e
o
r
y
.
Fo
r
t
h
e
Gr
ie
w
a
n
k
f
u
n
cti
o
n
(
F
1
)
,
DE
QP
SO
p
r
o
d
u
ce
d
th
e
b
est
r
esu
lt.
I
n
f
ac
t,
A
P
SO,
SDE
A
P
SO,
QP
SO,
DE
QP
SO,
an
d
SDEQ
P
S
O
alg
o
r
ith
m
s
w
er
e
f
o
u
n
d
to
b
e
p
r
o
d
u
cin
g
s
atis
f
ac
to
r
y
r
esu
lts
,
in
d
icati
n
g
t
h
at
th
e
ad
ap
tiv
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m
ec
h
a
n
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s
m
a
n
d
q
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an
tu
m
b
e
h
a
v
io
u
r
o
f
th
e
p
ar
ticles
ar
e
b
en
e
f
icial
f
o
r
s
o
lv
i
n
g
t
h
is
p
r
o
b
lem
.
DE
P
SO
an
d
SDEP
SO
al
g
o
r
it
h
m
s
p
r
o
d
u
ce
d
eq
u
all
y
g
o
o
d
p
er
f
o
r
m
a
n
ce
f
o
r
th
e
R
as
tr
i
g
i
n
f
u
n
ctio
n
(
F
2
)
.
Fo
r
th
e
A
c
k
le
y
f
u
n
c
tio
n
(
F
3
)
,
th
e
QP
SO
-
b
ased
alg
o
r
it
h
m
s
,
i.e
.
QP
SO,
DE
QP
SO
an
d
SDEQ
P
SO
p
r
o
d
u
ce
d
th
e
b
est
p
er
f
o
r
m
an
ce
,
f
o
llo
w
ed
b
y
th
e
a
d
ap
tiv
e
P
SO
-
b
ased
alg
o
r
ith
m
s
,
i.e
.
A
P
SO
a
n
d
S
DE
A
P
SO.
As
f
ar
as
th
e
Sc
h
w
e
f
el
f
u
n
c
tio
n
(
F
4
)
i
s
co
n
ce
r
n
e
d
,
o
n
l
y
DE
P
SO,
SDEP
SO
an
d
SDE
A
P
SO
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e
ab
le
to
g
e
n
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ate
s
atis
f
ac
to
r
y
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lt
s
,
w
h
ile
all
th
e
o
th
er
a
lg
o
r
ith
m
s
s
ee
m
to
h
a
v
e
in
f
er
io
r
p
er
f
o
r
m
a
n
ce
s
.
T
h
e
to
tal
r
an
k
i
n
g
o
f
t
h
e
al
g
o
r
ith
m
s
r
ev
ea
l
t
h
at
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QP
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a
ch
iev
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etter
o
v
er
all
p
er
f
o
r
m
an
ce
t
h
an
o
th
er
alg
o
r
it
h
m
s
.
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h
e
s
ec
o
n
d
-
b
est
p
er
f
o
r
m
i
n
g
alg
o
r
it
h
m
s
ar
e
f
o
u
n
d
to
b
e
DE
P
SO
a
n
d
SDE
A
P
SO.
Mo
s
t
i
m
p
o
r
tan
tl
y
,
t
h
e
r
es
u
lt
s
f
o
r
a
ll
p
r
o
b
lem
s
s
h
o
w
th
a
t
t
h
e
f
u
ll
y
DE
-
h
y
b
r
id
ized
al
g
o
r
ith
m
s
,
i.e
.
DE
P
SO
an
d
DE
QP
SO
r
eq
u
ir
ed
s
ig
n
if
ica
n
tl
y
h
ig
h
er
co
m
p
u
ta
tio
n
al
ti
m
e
to
o
b
tain
th
e
s
o
lu
tio
n
s
,
wh
ile
t
h
e
s
elec
ti
v
el
y
DE
-
h
y
b
r
id
ized
alg
o
r
ith
m
s
ar
e
ab
le
to
m
ain
ta
in
a
r
ea
s
o
n
ab
l
y
s
i
m
ilar
co
m
p
u
ta
tio
n
al
r
eq
u
i
r
e
m
en
t
as
t
h
e
P
SO,
QP
SO a
n
d
A
P
SO a
l
g
o
r
ith
m
s
.
T
ab
le
3
.
B
en
ch
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2
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s
s
i
n
d
icate
s
a
b
etter
s
o
lu
tio
n
.
T
h
e
m
a
in
cr
iter
ia
f
o
r
ev
alu
a
tin
g
t
h
e
A
UV
p
ath
ar
e:
-
Min
i
m
u
m
le
n
g
t
h
o
r
tr
av
el
ti
m
e
r
eq
u
ir
ed
to
r
ea
ch
th
e
tar
g
et
-
Min
i
m
u
m
e
x
p
o
s
u
r
e
to
th
e
t
h
r
e
ats
-
C
o
m
p
lia
n
ce
w
it
h
p
h
y
s
ical
m
o
t
io
n
li
m
itatio
n
s
o
f
A
UV
As t
h
e
o
p
ti
m
u
m
o
f
al
l c
r
iter
ia
d
o
es n
o
t n
ec
e
s
s
ar
il
y
co
in
cid
e,
a
tr
ad
e
-
o
f
f
b
et
w
ee
n
th
e
s
e
cr
ite
r
ia
ca
n
b
e
estab
lis
h
ed
u
s
i
n
g
a
w
e
ig
h
ti
n
g
s
ch
e
m
e
w
it
h
m
u
ltip
le
e
v
alu
a
tio
n
f
u
n
ctio
n
s
,
w
h
ic
h
in
c
lu
d
e
a
m
a
in
e
v
alu
a
tio
n
f
u
n
ctio
n
to
m
ea
s
u
r
e
th
e
p
ath
len
g
t
h
/ti
m
e
co
s
t,
a
f
u
n
ctio
n
to
m
ea
s
u
r
e
th
e
t
h
r
ea
t
co
s
t
a
lo
n
g
t
h
e
p
ath
,
an
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2089
-
4856
P
a
r
ticle
s
w
a
r
m
o
p
timiz
a
tio
n
a
lg
o
r
ith
ms w
ith
s
elec
t
ive
d
iffer
en
tia
l e
vo
lu
tio
n
.
.
.
(
Hu
i S
h
en
g
Lim
)
103
f
u
n
ctio
n
s
to
m
ea
s
u
r
e
th
e
co
m
p
lian
ce
o
f
t
h
e
p
ath
w
ith
r
e
s
p
ec
t to
th
e
A
UV
m
o
tio
n
li
m
itatio
n
s
.
T
h
u
s
,
th
e
f
it
n
es
s
o
f
a
p
ar
ticle/p
ath
X
i
ca
n
b
e
g
i
v
en
b
y
a
co
m
b
i
n
atio
n
o
f
s
ev
e
r
al
ev
al
u
atio
n
f
u
n
c
tio
n
s
F
k
f
o
r
d
if
f
er
e
n
t
cr
iter
ia,
w
it
h
ea
c
h
cr
iter
io
n
w
ei
g
h
ted
b
y
a
co
s
t f
ac
to
r
f
k
.
(
)
∑
(
)
*
+
(
22
)
w
h
e
r
e
k
r
ef
er
s
to
d
if
f
er
en
t e
v
a
lu
atio
n
f
u
n
c
tio
n
s
a
n
d
K
is
t
h
e
t
o
tal
n
u
m
b
er
o
f
f
u
n
ctio
n
s
f
o
r
t
h
e
p
r
o
b
lem
.
4
.
3
.
P
a
t
h T
ra
v
el
T
i
m
e
Co
s
t
T
h
e
m
ai
n
e
v
alu
a
tio
n
f
u
n
c
tio
n
f
o
r
p
ath
p
lan
n
i
n
g
p
r
o
b
lem
is
to
m
ea
s
u
r
e
th
e
p
ath
co
s
t
b
as
ed
o
n
it
s
len
g
th
o
r
ti
m
e
to
tr
av
el
o
n
th
e
p
at
h
.
T
h
is
s
t
u
d
y
f
o
cu
s
es
o
n
f
i
n
d
in
g
an
o
p
ti
m
al
p
ath
th
at
is
ca
p
ab
le
o
f
tak
i
n
g
ad
v
an
ta
g
e
o
f
f
a
v
o
u
r
ab
le
c
u
r
r
en
t
to
ass
is
t
th
e
A
UV
m
o
tio
n
,
w
h
ile
av
o
id
i
n
g
t
h
e
le
s
s
f
a
v
o
u
r
ab
le
c
u
r
r
en
t
to
ac
h
iev
e
a
s
h
o
r
ter
tr
a
v
el
t
i
m
e
.
Fo
r
th
i
s
p
u
r
p
o
s
e,
a
tr
av
el
-
t
i
m
e
-
b
ased
e
v
alu
a
ti
o
n
f
u
n
c
tio
n
i
s
d
ev
e
lo
p
ed
i
n
th
is
s
t
u
d
y
.
B
ased
o
n
p
r
ev
io
u
s
f
o
r
m
u
la
ti
o
n
,
a
g
i
v
e
n
p
ath
X
i
ca
n
b
e
r
ep
r
esen
ted
as
a
s
er
ies
o
f
p
at
h
n
o
d
es
o
r
alter
n
ati
v
el
y
in
t
h
e
f
o
r
m
o
f
d
is
cr
etis
ed
w
a
y
p
o
in
t
s
P
=
[
p
i
,1
,
p
i
,2
,
…
,
p
i
,
m
]
,
w
h
er
e
P
is
th
e
o
u
tp
u
t
f
r
o
m
B
-
s
p
li
n
e
f
u
n
ctio
n
a
n
d
m
i
s
t
h
e
to
tal
n
u
m
b
er
o
f
d
is
cr
eti
s
ed
w
a
y
p
o
i
n
ts
.
T
h
e
tr
av
el
ti
m
e
co
s
t
F
1
al
o
n
g
a
p
ath
ca
n
b
e
d
eter
m
in
ed
b
y
f
in
d
i
n
g
t
h
e
s
u
m
o
f
d
is
cr
eti
s
ed
ti
m
e
r
eq
u
ir
ed
to
tr
av
el
o
n
ea
ch
s
m
all
p
at
h
s
e
g
m
e
n
t
th
a
t c
o
n
n
ec
ts
th
e
co
n
s
ec
u
ti
v
e
d
is
cr
eti
s
ed
w
a
y
p
o
i
n
ts
i
n
P
.
(
)
∑
‖
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
‖
|
|
*
+
(
23
)
w
h
er
e
V
g
is
th
e
g
r
o
u
n
d
r
e
f
er
en
ce
v
elo
cit
y
o
f
t
h
e
A
U
V,
w
h
i
ch
i
s
t
h
e
r
e
s
u
lta
n
t
A
UV
v
e
lo
cit
y
u
n
d
er
th
e
e
f
f
ec
t
o
f
s
u
r
r
o
u
n
d
in
g
o
ce
an
c
u
r
r
en
t.
T
h
e
co
n
tr
ib
u
tio
n
o
f
c
u
r
r
en
t
o
n
t
h
e
A
UV
ca
n
b
e
o
b
tain
ed
b
y
p
r
o
j
ec
tin
g
th
e
cu
r
r
en
t
v
elo
cit
y
V
c
in
t
h
e
d
ir
ec
tio
n
o
f
th
e
A
UV
w
ater
r
ef
er
en
ce
v
elo
cit
y
V
a
,
w
h
ic
h
is
ess
e
n
tiall
y
th
e
d
ir
ec
tio
n
o
f
th
e
p
ath
v
ec
to
r
.
T
h
u
s
,
V
g
is
g
iv
e
n
b
y
t
h
e
s
u
m
o
f
V
a
an
d
th
e
co
n
tr
ib
u
tio
n
o
f
V
c
a
s
s
h
o
w
n
i
n
(
2
4
)
.
⋅
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
‖
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
‖
(
24
)
4
.
4
.
T
hrea
t
Co
s
t
T
h
e
o
b
s
tacle
s
a
v
o
id
an
ce
ab
ili
t
y
o
f
t
h
e
p
at
h
p
la
n
n
er
r
elies
o
n
t
h
e
t
h
r
ea
t
co
s
t
e
v
al
u
atio
n
f
u
n
ctio
n
,
i
n
w
h
ic
h
t
h
e
ex
p
o
s
u
r
e
o
f
th
e
p
at
h
to
t
h
r
ea
ts
/o
b
s
tacle
s
is
m
ea
s
u
r
ed
.
A
ll t
h
r
ea
ts
in
t
h
e
p
r
o
b
le
m
s
p
ac
e
ar
e
m
o
d
elled
as
ellip
s
es
(
o
r
cir
cles
i
f
th
e
m
aj
o
r
ax
is
an
d
m
in
o
r
ax
i
s
ar
e
eq
u
al)
u
n
d
er
2
D
co
n
d
itio
n
,
an
d
as
ellip
s
o
id
s
(
o
r
s
p
h
er
es
i
f
all
th
e
p
r
in
c
ip
al
ax
es
ar
e
eq
u
al)
u
n
d
er
3
D
co
n
d
itio
n
w
ith
t
h
eir
p
r
in
cip
al
ax
es
a
lig
n
ed
w
it
h
th
e
co
o
r
d
in
ate
ax
es.
A
t
h
r
ea
t
co
s
t
ev
alu
a
tio
n
m
et
h
o
d
b
ased
o
n
th
e
in
ter
s
ec
tio
n
b
et
w
ee
n
th
e
p
at
h
an
d
t
h
e
t
h
r
ea
ts
is
e
m
p
lo
y
ed
in
t
h
i
s
s
t
u
d
y
.
Ass
u
m
in
g
a
th
r
ea
t
h
in
3
D
p
r
o
b
lem
s
p
ac
e
w
it
h
ce
n
tr
e
O
c,
h
=
(
O
cx
,
O
cy
,
O
cz
)
an
d
s
em
i
p
r
in
cip
al
ax
e
s
O
r,
h
=
(
O
rx
,
O
ry
,
O
rz
)
,
its
p
ar
a
m
etr
ic
eq
u
atio
n
ca
n
b
e
ex
p
r
ess
ed
in
(
2
5
)
.
T
h
e
p
ar
am
etr
ic
eq
u
atio
n
o
f
a
p
ath
s
eg
m
e
n
t
t
h
at
co
n
n
ec
ts
t
w
o
co
n
s
ec
u
ti
v
e
w
a
y
p
o
in
t
s
p
i,
j
=
(
x
1
,
y
1
,
z
1
)
a
n
d
p
i,
j+
1
=
(
x
2
,
y
2
,
z
2
)
ca
n
b
e
w
r
i
tten
as
(
2
6
)
.
T
h
e
co
s
t
ev
al
u
atio
n
i
n
2
D
tak
e
s
a
s
i
m
ilar
ap
p
r
o
ac
h
,
e
x
ce
p
t
t
h
at
t
h
e
d
i
m
e
n
s
io
n
r
ed
u
ctio
n
i
n
2
D
r
ed
u
ce
s
th
e
n
u
m
b
er
o
f
v
ar
iab
les a
n
d
h
en
ce
s
i
m
p
li
f
ies t
h
e
co
m
p
u
tatio
n
.
(
)
(
)
(
)
(
25
)
(
)
(
)
(
)
(
26
)
Su
b
s
ti
tu
t
in
g
(
2
6
)
in
to
(
2
5
)
y
ield
s
th
e
f
o
llo
w
i
n
g
eq
u
at
io
n
s
,
wh
ic
h
ar
e
ex
p
r
ess
ed
in
ter
m
s
o
f
s
.
T
h
e
in
ter
s
ec
tio
n
o
f
th
e
p
ath
w
i
th
t
h
e
t
h
r
ea
t c
an
b
e
ev
alu
ated
b
y
o
b
tain
i
n
g
th
e
d
is
cr
i
m
i
n
an
t
ξ
o
f
(
2
7
)
ac
co
r
d
i
n
g
to
(
3
1
)
.
(
27
)
Evaluation Warning : The document was created with Spire.PDF for Python.