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I
J
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Vo
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16
,
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.
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Octo
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20
26
,
p
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2
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CC B
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C
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p
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A
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r
:
T
u
n
g
Kh
ac
T
r
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o
n
g
Facu
lty
o
f
Data
Scien
ce
,
Un
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s
ity
o
f
Fin
an
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–
Ma
r
k
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g
7
7
8
Ng
u
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Kiem
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Du
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Vi
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m
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@
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u
.
v
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1.
I
NT
RO
D
UCT
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O
N
T
h
e
k
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ap
s
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p
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b
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to
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Pra
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ar
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[
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ca
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R
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[
2
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a
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[
3
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in
tr
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m
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Fir
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
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N:
2088
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in
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r
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kn
a
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2681
an
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p
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alg
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ith
m
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with
p
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[
4
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it
h
m
f
o
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n
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r
in
g
th
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[
5
]
.
B
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s
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ex
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s
s
ca
le
p
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ly
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[
6
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Mo
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tter
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[
7
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am
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[
8
]
.
W
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[
9
]
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y
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r
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g
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ased
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1
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W
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ased
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[
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ith
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(
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[
1
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o
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ies a
u
s
ef
u
l p
o
s
itio
n
in
th
is
lan
d
s
ca
p
e.
I
t
m
o
d
el
s
a
co
lo
n
y
th
at
lo
ca
tes
p
r
ey
b
y
ec
h
o
lo
ca
t
io
n
[
1
4
]
:
a
b
at
em
its
a
s
h
o
r
t,
l
o
u
d
p
u
ls
e,
waits
f
o
r
th
e
ec
h
o
t
o
r
etu
r
n
,
a
n
d
in
f
er
s
th
e
d
is
tan
ce
to
th
e
tar
g
et
f
r
o
m
th
e
d
elay
[
1
5
]
.
T
h
e
s
am
e
m
ec
h
an
is
m
lets
th
e
an
im
al
s
ep
ar
ate
an
o
b
s
tacle
f
r
o
m
p
r
ey
a
n
d
h
u
n
t
i
n
co
m
p
lete
d
a
r
k
n
ess
[
1
6
]
.
T
r
a
n
s
lated
in
to
a
n
o
p
tim
izatio
n
r
u
le,
th
is
b
eh
a
v
io
r
r
e
q
u
ir
es
o
n
ly
a
p
o
p
u
latio
n
s
ize,
a
lo
u
d
n
ess
an
d
a
p
u
ls
e
-
em
is
s
io
n
r
ate,
s
o
th
e
tu
n
in
g
b
u
r
d
e
n
is
f
ar
lig
h
ter
th
an
th
at
o
f
alg
o
r
ith
m
s
ca
r
r
y
in
g
f
iv
e
o
r
m
o
r
e
co
n
tr
o
l
p
ar
am
eter
s
.
B
A
h
as
s
in
ce
b
ee
n
ex
te
n
d
ed
to
m
u
lti
-
o
b
jectiv
e
d
esig
n
[
1
7
]
an
d
ch
a
o
tic
s
ea
r
ch
[
1
8
]
,
an
d
a
p
p
lied
t
o
p
r
o
b
lem
s
s
u
ch
as
n
etwo
r
k
p
r
o
t
o
co
l
t
u
n
in
g
[
1
9
]
.
A
b
in
ar
y
v
ar
ian
t
was
f
o
r
m
alize
d
b
y
Mir
jalili
et
a
l.
[
2
0
]
,
an
d
R
izk
-
Allah
a
n
d
H
ass
an
ien
[
2
1
]
co
m
b
in
ed
a
b
in
a
r
y
b
at
with
a
lo
ca
l
s
ea
r
ch
s
ch
em
e
f
o
r
th
e
class
ical
0
-
1
k
n
ap
s
ac
k
p
r
o
b
lem
.
On
e
ea
r
lier
s
tu
d
y
h
as a
p
p
lied
a
b
at
m
etah
eu
r
is
tic
to
th
e
D0
-
1
KP: W
u
et
a
l.
[
2
2
]
m
u
tated
th
e
s
tan
d
ar
d
b
at
o
p
e
r
ato
r
s
to
wo
r
k
o
n
t
h
e
q
u
ater
n
ar
y
r
e
p
r
esen
tatio
n
o
f
th
e
p
r
o
b
lem
.
T
h
e
ap
p
r
o
ac
h
tak
en
h
er
e
d
i
f
f
er
s
in
two
r
esp
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ts
.
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th
e
s
ea
r
ch
o
p
e
r
ates
d
ir
ec
tly
o
n
a
b
in
a
r
y
v
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t
o
r
o
f
len
g
th
3
n
an
d
r
ea
ch
es
f
ea
s
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ilit
y
th
r
o
u
g
h
a
tr
an
s
f
er
f
u
n
ctio
n
co
m
b
in
ed
w
ith
a
r
ep
air
o
p
e
r
ato
r
,
r
ath
er
t
h
an
th
r
o
u
g
h
a
q
u
ater
n
ar
y
en
c
o
d
in
g
.
Seco
n
d
,
th
is
s
tu
d
y
r
ep
o
r
ts
th
e
f
u
ll
d
is
tr
ib
u
ti
o
n
o
f
3
0
r
u
n
s
p
e
r
in
s
tan
ce
a
n
d
an
aly
s
es
th
e
two
b
en
ch
m
ar
k
f
am
ilies
s
ep
ar
ately
,
wh
ich
ex
p
o
s
es
a
s
tab
ilit
y
p
a
tter
n
th
at
a
g
g
r
eg
ate
co
m
p
ar
is
o
n
s
o
b
s
cu
r
e
.
T
h
e
co
n
tr
ib
u
tio
n
o
f
th
is
p
ap
e
r
is
th
er
ef
o
r
e
t
h
r
ee
f
o
l
d
:
a
b
in
ar
y
b
at
f
o
r
m
u
latio
n
o
f
th
e
D0
-
1
KP
b
u
ilt
o
n
a
s
ig
m
o
id
tr
a
n
s
f
er
f
u
n
ctio
n
;
th
e
in
teg
r
atio
n
o
f
a
g
r
ee
d
y
r
ep
air
-
an
d
-
o
p
tim
izatio
n
o
p
e
r
ato
r
th
at
b
o
th
r
esto
r
es f
ea
s
ib
ilit
y
an
d
i
m
p
r
o
v
es p
r
o
f
it; an
d
an
ev
alu
atio
n
o
n
1
4
in
s
tan
ce
s
th
at
r
ep
o
r
ts
wh
er
e
th
e
m
eth
o
d
is
co
m
p
etitiv
e
an
d
,
e
q
u
ally
,
w
h
er
e
it is
n
o
t.
T
h
is
p
ap
er
is
s
tr
u
ctu
r
ed
as
f
o
l
lo
ws.
T
h
e
p
r
o
b
lem
d
ef
in
itio
n
an
d
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
ar
e
g
iv
en
in
s
ec
tio
n
2
.
C
o
m
p
u
tatio
n
al
r
esu
lts
ar
e
p
r
esen
ted
an
d
an
aly
ze
d
in
s
ec
tio
n
3
.
C
o
n
clu
s
io
n
s
an
d
p
o
s
s
ib
le
ex
ten
s
io
n
s
o
f
th
e
wo
r
k
ap
p
ea
r
in
s
ec
tio
n
4.
2.
M
E
T
H
O
D
2
.
1
.
P
r
o
blem
f
o
rm
ula
t
io
n
L
et
th
er
e
b
e
n
g
r
o
u
p
s
,
ea
ch
c
o
n
tain
in
g
th
r
ee
item
s
,
g
iv
in
g
3
n
item
s
in
to
tal.
I
tem
j
ca
r
r
ies
an
weig
h
t
wⱼ
an
d
an
p
r
o
f
it
pⱼ
,
a
n
d
th
e
k
n
ap
s
ac
k
ca
p
ac
ity
is
C
.
A
ca
n
d
id
ate
s
o
lu
tio
n
is
a
b
i
n
ar
y
v
e
cto
r
X
=
(
x₀
,
x₁
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₋₁
)
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,
1
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ⁿ
in
w
h
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m
ea
n
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th
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ad
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a
n
d
xⱼ
=
0
m
ea
n
s
t
h
at
it
is
n
o
t.
T
h
e
D0
-
1
KP
is
th
en
s
tated
as (
1
)
to
(
4
)
.
(
)
=
∑
(
3
ᵢ
3
ᵢ
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3
ᵢ
+
1
3
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1
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3
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+
2
3
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2
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−
1
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0
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1
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s
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3
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1
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3
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2
≤
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,
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0
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1
,
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−
1
(
2
)
∑
(
3
ᵢ
3
ᵢ
+
3
ᵢ
+
1
3
ᵢ
+
1
+
3
ᵢ
+
2
3
ᵢ
+
2
)
−
1
=
0
≤
(
3
)
3
,
3
+
1
,
3
+
2
∈
{
0
,
1
}
,
=
0
,
1
,
…
,
−
1
(
4
)
Her
e
(
)
is
th
e
to
tal
p
r
o
f
it
to
b
e
m
ax
im
ized
.
C
o
n
s
tr
ain
t
(
2
)
is
t
h
e
ex
clu
s
iv
ity
co
n
d
itio
n
th
at
f
o
r
b
id
s
lo
ad
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g
m
o
r
e
th
an
o
n
e
item
f
r
o
m
a
n
y
g
r
o
u
p
,
an
d
(
3
)
is
th
e
ca
p
ac
ity
co
n
d
itio
n
.
A
v
ec
t
o
r
s
ati
s
f
y
in
g
b
o
th
(
2
)
an
d
(
3
)
is
a
f
ea
s
ib
le
s
o
lu
tio
n
;
a
v
e
cto
r
v
i
o
latin
g
eith
e
r
is
in
f
e
asib
le
an
d
m
u
s
t
b
e
r
ep
ai
r
ed
b
ef
o
r
e
its
p
r
o
f
it
ca
n
b
e
in
ter
p
r
eted
.
2
.
2
.
T
he
ba
t
a
lg
o
rit
hm
B
A
m
ain
tain
s
a
p
o
p
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latio
n
o
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m
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tific
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b
ats.
B
at
i
is
d
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b
y
a
p
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xᵢ
in
th
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ch
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p
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a
v
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vᵢ
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a
p
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en
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ᵢ
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lo
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d
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Aᵢ
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d
a
p
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ls
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em
is
s
io
n
r
ate
rᵢ
.
At
ea
ch
iter
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n
th
e
f
r
eq
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e
n
cy
is
d
r
awn
f
r
o
m
a
f
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ed
in
ter
v
al
a
n
d
u
s
ed
t
o
ac
ce
ler
ate
th
e
b
at
t
o
war
d
th
e
b
est
p
o
s
itio
n
f
o
u
n
d
s
o
f
ar
,
as
in
(
5
)
to
(
7
)
.
=
+
(
−
)
(
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
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8
8
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8
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I
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&
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p
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g
,
Vo
l.
16
,
No
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5
,
Octo
b
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r
20
26
:
2
6
8
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2
6
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2682
(
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(
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̂
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−
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(
6
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−
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7
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I
n
(
5
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to
(
7
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β
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an
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n
u
m
b
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d
r
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th
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in
cu
m
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en
t
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(
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wh
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9
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d
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1
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wh
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h
if
ts
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e
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lo
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(
+
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(
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[
1
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−
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o
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ch
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2
.
3
.
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ra
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a
ry
po
s
it
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a
t
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E
q
u
atio
n
s
(
5
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to
(
7
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ar
e
d
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i
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ed
o
v
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tin
u
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u
s
d
o
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n
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wh
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s
a
s
o
lu
tio
n
o
f
th
e
D0
-
1
KP
is
a
b
in
ar
y
v
ec
to
r
.
B
r
id
g
in
g
th
e
tw
o
r
eq
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ir
es
a
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an
s
f
er
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n
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th
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d
f
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o
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izatio
n
b
y
Ken
n
ed
y
an
d
E
b
er
h
a
r
t
[
2
3
]
an
d
ca
r
r
ied
o
v
er
to
th
e
b
at
m
etah
eu
r
is
tic
b
y
Mir
jalili
et
a
l.
[
2
0
]
.
T
r
an
s
f
er
f
u
n
ctio
n
s
a
r
e
co
m
m
o
n
l
y
g
r
o
u
p
ed
in
to
S
-
s
h
ap
ed
an
d
V
-
s
h
a
p
ed
f
am
ilies
,
an
d
t
h
eir
r
elativ
e
m
er
its
o
n
th
is
p
r
o
b
lem
h
av
e
b
ee
n
ex
am
in
e
d
in
[
2
4
]
.
T
h
is
wo
r
k
ad
o
p
ts
th
e
S
-
s
h
ap
e
d
s
ig
m
o
id
in
(
1
1
)
.
(
)
=
1
/
(
1
+
−
2
ᵛ
)
(
1
1
)
T
h
e
p
o
s
itio
n
o
f
b
at
i
i
n
d
im
e
n
s
io
n
j
is
th
en
s
et
b
y
co
m
p
ar
in
g
a
u
n
if
o
r
m
r
an
d
o
m
d
r
aw
ag
ai
n
s
t
th
is
p
r
o
b
ab
ilit
y
,
as in
(
1
2
)
.
(
+
1
)
=
1
if
r
an
d
(
)
<
(
(
+
1
)
)
,
ℎ
0
(
1
2
)
A
v
elo
city
o
f
lar
g
e
m
ag
n
itu
d
e
th
er
ef
o
r
e
d
r
iv
es th
e
co
r
r
esp
o
n
d
in
g
b
it to
war
d
a
d
ec
is
iv
e
v
alu
e,
wh
ile
a
v
elo
city
n
ea
r
ze
r
o
leav
es
th
e
b
it
clo
s
e
to
a
c
o
in
f
lip
,
wh
ic
h
p
r
eser
v
e
s
d
iv
er
s
ity
in
d
im
en
s
io
n
s
th
e
co
lo
n
y
h
as
n
o
t
y
et
r
eso
lv
ed
.
2
.
4
.
Repa
ir
a
nd
o
pti
m
iza
t
io
n o
pera
t
o
r
A
v
ec
to
r
p
r
o
d
u
ce
d
b
y
(
1
2
)
will
in
g
en
er
al
v
io
late
(
2
)
,
(
3
)
o
r
b
o
t
h
.
Dis
ca
r
d
in
g
s
u
ch
v
ec
to
r
s
wastes
ev
alu
atio
n
s
,
an
d
p
en
alizin
g
th
em
d
is
to
r
ts
th
e
o
b
jectiv
e
lan
d
s
ca
p
e;
th
e
alter
n
ativ
e
ad
o
p
ted
h
er
e,
f
o
llo
win
g
th
e
s
tr
ateg
y
v
alid
ated
f
o
r
th
is
b
en
ch
m
ar
k
b
y
He
et
a
l.
[
3
]
,
is
to
r
ep
air
ev
er
y
ca
n
d
id
ate.
T
h
e
o
p
er
ato
r
r
u
n
s
in
two
s
tag
es.
T
h
e
f
ir
s
t
s
tag
e
r
esto
r
es
f
ea
s
ib
i
lity
.
Gr
o
u
p
s
v
io
latin
g
(
2
)
a
r
e
r
ed
u
ce
d
to
a
s
in
g
le
lo
ad
ed
item
,
th
e
o
n
e
with
th
e
h
ig
h
est
p
r
o
f
it
-
to
-
weig
h
t
r
atio
,
an
d
th
e
r
e
m
ain
in
g
b
its
o
f
th
at
g
r
o
u
p
ar
e
clea
r
ed
.
I
f
th
e
ca
p
ac
ity
co
n
d
itio
n
(
3
)
is
s
till
v
io
lated
,
l
o
ad
ed
item
s
ar
e
v
is
ited
in
ascen
d
in
g
o
r
d
e
r
o
f
p
r
o
f
it
d
en
s
ity
a
n
d
r
em
o
v
ed
o
n
e
a
t
a
tim
e
u
n
til th
e
to
tal
weig
h
t
f
a
lls
with
in
C
.
T
h
e
s
ec
o
n
d
s
tag
e
im
p
r
o
v
es
th
e
r
ep
air
ed
s
o
lu
tio
n
.
Gr
o
u
p
s
th
at
h
o
ld
n
o
item
a
r
e
ex
a
m
in
ed
in
d
escen
d
in
g
o
r
d
e
r
o
f
p
r
o
f
it
d
e
n
s
ity
,
an
d
th
e
b
est
-
r
an
k
e
d
ite
m
th
at
f
its
in
th
e
r
esid
u
al
ca
p
ac
ity
is
lo
ad
ed
.
T
h
e
p
ass
r
ep
ea
ts
u
n
til
n
o
f
u
r
th
er
item
ca
n
b
e
ad
d
ed
.
B
ec
au
s
e
th
e
o
p
er
at
o
r
n
ev
er
r
etu
r
n
s
an
in
f
e
asib
le
v
ec
to
r
,
e
v
er
y
f
itn
ess
ev
alu
atio
n
ca
r
r
ies
in
f
o
r
m
atio
n
,
an
d
b
ec
a
u
s
e
th
e
s
ec
o
n
d
s
tag
e
is
m
o
n
o
to
n
e
in
p
r
o
f
it,
th
e
r
ep
air
ed
s
o
lu
tio
n
is
n
ev
er
wo
r
s
e
th
an
th
e
f
ea
s
ib
le
co
r
e
it st
ar
ted
f
r
o
m
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
B
in
a
r
y
b
a
t
a
lg
o
r
ith
m
w
ith
g
r
ee
d
y
r
ep
a
ir
fo
r
th
e
d
is
co
u
n
te
d
0
-
1
kn
a
p
s
a
ck
p
r
o
b
lem
(
Tu
n
g
K
h
a
c
Tr
u
o
n
g
)
2683
2
.
5
.
Alg
o
rit
hm
a
nd
co
m
plex
it
y
T
h
e
co
m
p
lete
p
r
o
ce
d
u
r
e
is
s
h
o
wn
in
Alg
o
r
ith
m
1
.
T
h
e
p
o
p
u
latio
n
is
in
itialized
at
r
an
d
o
m
an
d
r
ep
air
ed
,
a
f
ter
wh
ich
th
e
m
a
in
lo
o
p
a
p
p
lies
(
5
)
to
(
1
2
)
to
ev
er
y
b
at,
r
ep
air
s
th
e
o
u
t
co
m
e,
u
p
d
ates
th
e
in
cu
m
b
en
t
b
est,
an
d
ad
ju
s
ts
lo
u
d
n
ess
an
d
p
u
ls
e
r
ate
t
h
r
o
u
g
h
(
9
)
an
d
(
1
0
)
.
E
ac
h
iter
atio
n
u
p
d
ates
3
n
b
its
f
o
r
ea
ch
o
f
th
e
m
b
ats,
an
d
th
e
r
e
p
air
o
p
er
ato
r
s
o
r
ts
at
m
o
s
t
3
n
item
s
,
s
o
th
e
co
s
t
o
f
o
n
e
iter
at
io
n
is
O
(
m
n
lo
g
n
)
an
d
th
e
to
tal
c
o
s
t is
O
(
T
m
n
lo
g
n
)
.
Me
m
o
r
y
is
d
o
m
in
ate
d
b
y
th
e
p
o
p
u
latio
n
its
elf
,
at
O
(
m
n
).
Alg
o
r
ith
m
1
.
B
B
AT
f
o
r
th
e
D
0
-
1
KP
Input
: instance data (
p
,
w
,
C
,
n
), population size
m
, loudness
A
, pulse rate
r
, iteration
limit
T
Output
: best feasible solution
x̂
and its profit
f
(
x̂
)
1: initialize position
xᵢ
, velocity
vᵢ
and frequency
f
ᵢ for every bat
i = 1,.., m
2: repair every
xᵢ
and evaluate
f
(
xᵢ
); set
x̂
to the best solution found
3: for
t
= 1 to
T
do
4: for each bat
i
do
5: update
fᵢ
,
vᵢ
by (5) and (6); update
xᵢ
by (11) and (12)
6: if rand() >
rᵢ
then generate a local solution around
x̂
by (8)
7: repair
xᵢ
and evaluate
f
(
xᵢ
)
8: if rand() <
Aᵢ
and
f
(
xᵢ
) >
f
(
x̂
) then accept
xᵢ
; reduce
Aᵢ
and increase
rᵢ
by
(9) and (10)
9: end for
10: update the incumbent best
x̂
11: end for
12: return
x̂
and
f
(
x̂
)
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
3
.
1
.
E
x
perim
ent
a
l set
up
B
B
AT
was
ev
alu
ated
o
n
1
4
i
n
s
tan
ce
s
f
r
o
m
th
e
b
en
c
h
m
ar
k
s
et
o
f
He
et
a
l.
[
3
]
,
co
m
p
r
is
in
g
s
ev
en
in
v
er
s
e
s
tr
o
n
g
ly
co
r
r
elate
d
in
s
tan
ce
s
(
I
DKP1
to
I
DKP7
)
an
d
s
ev
en
s
tr
o
n
g
ly
c
o
r
r
elate
d
in
s
tan
ce
s
(
SDKP1
to
SDKP7
)
.
T
h
ese
two
f
am
ilies
ar
e
th
e
h
ar
d
est
o
f
th
e
f
o
u
r
p
u
b
lis
h
ed
g
r
o
u
p
s
,
b
ec
au
s
e
p
r
o
f
it
an
d
weig
h
t
a
r
e
tig
h
tly
lin
k
ed
an
d
p
r
o
f
it
d
en
s
i
ty
ca
r
r
ies
litt
le
d
is
cr
im
in
atin
g
in
f
o
r
m
atio
n
,
wh
ich
is
p
r
ec
is
ely
th
e
s
itu
atio
n
in
wh
ich
a
g
r
ee
d
y
r
ep
air
o
p
er
at
o
r
is
least
ab
le
to
g
u
id
e
th
e
s
ea
r
ch
.
R
esu
lts
f
o
r
FirE
GA
an
d
SecE
GA
ar
e
tak
en
f
r
o
m
[
5
]
,
wh
ic
h
r
ep
o
r
ts
th
em
u
n
d
er
t
h
e
s
am
e
ex
p
e
r
im
en
tal
p
r
o
to
co
l.
All
ex
p
er
im
en
ts
wer
e
ca
r
r
ied
o
u
t
in
MA
T
L
AB
R
2
0
1
8
a
o
n
a
lap
to
p
eq
u
ip
p
e
d
with
an
I
n
t
el
C
o
r
e
i5
-
8
2
5
0
U
p
r
o
ce
s
s
o
r
(
1
.
6
GHz
)
an
d
8
GB
o
f
R
AM
,
r
u
n
n
i
n
g
W
in
d
o
ws
1
0
.
A
co
lo
n
y
o
f
3
0
b
ats
was
u
s
ed
th
r
o
u
g
h
o
u
t,
with
th
e
lo
u
d
n
ess
an
d
p
u
ls
e
r
ate
b
o
th
in
itialized
to
0
.
9
.
E
ac
h
in
s
tan
ce
was
allo
ca
ted
a
n
u
m
b
e
r
o
f
iter
atio
n
s
eq
u
al
to
its
d
im
en
s
i
o
n
a
n
d
s
o
lv
ed
o
v
e
r
3
0
in
d
ep
e
n
d
en
t
r
u
n
s
,
f
r
o
m
w
h
ich
t
h
e
b
e
s
t,
m
ea
n
a
n
d
wo
r
s
t
p
r
o
f
its
ar
e
r
e
p
o
r
ted
alo
n
g
s
id
e
t
h
e
s
tan
d
ar
d
d
ev
iatio
n
.
3
.
2
.
Co
nv
er
g
ence
beha
v
io
r
Fig
u
r
e
1
tr
ac
es
th
e
m
ea
n
b
est
-
so
-
f
ar
p
r
o
f
it
ag
ain
s
t
th
e
iter
atio
n
co
u
n
t
f
o
r
two
r
e
p
r
esen
tativ
e
in
s
tan
ce
s
.
Fig
u
r
e
1
(
a)
s
h
o
ws
I
DKP1
an
d
Fig
u
r
e
1
(
b
)
s
h
o
ws
I
DKP5
.
On
b
o
th
i
n
s
tan
ce
s
th
e
cu
r
v
e
r
is
es
s
teep
ly
o
v
er
th
e
f
ir
s
t
5
0
to
1
0
0
iter
atio
n
s
an
d
t
h
en
f
latten
s
,
r
ec
o
v
e
r
in
g
th
e
b
u
lk
o
f
th
e
attain
ab
le
p
r
o
f
it
ea
r
ly
in
th
e
r
u
n
.
T
h
e
r
a
p
id
in
itial
clim
b
is
attr
ib
u
tab
le
to
th
e
r
ep
air
o
p
e
r
a
to
r
,
wh
ich
lifts
ev
er
y
r
an
d
o
m
s
tar
tin
g
v
ec
to
r
to
a
lo
ca
lly
s
en
s
ib
le
co
n
f
ig
u
r
atio
n
b
ef
o
r
e
t
h
e
b
at
d
y
n
am
ics b
eg
i
n
to
ac
t.
T
h
e
f
lat
tail
is
less
f
av
o
r
a
b
le.
Af
ter
r
o
u
g
h
l
y
iter
atio
n
1
5
0
t
h
e
m
ea
n
b
est
-
so
-
f
ar
p
r
o
f
it
is
ess
en
tiall
y
s
tatic,
wh
ich
in
d
icate
s
th
at
th
e
co
lo
n
y
h
as
c
o
n
v
e
r
g
ed
an
d
th
a
t
th
e
r
em
ai
n
in
g
b
u
d
g
et
y
ield
s
litt
le
r
etu
r
n
.
T
h
is
is
co
n
s
is
ten
t
with
th
e
lo
u
d
n
ess
d
ec
ay
in
(
9
)
:
o
n
ce
Aᵢ
h
as
f
al
len
,
f
ew
ca
n
d
id
ate
m
o
v
es
a
r
e
ac
ce
p
ted
a
n
d
th
e
p
o
p
u
latio
n
lo
s
es
th
e
d
iv
er
s
ity
n
ee
d
ed
to
escap
e
th
e
b
asin
it
o
cc
u
p
ies.
T
h
e
o
b
s
er
v
atio
n
s
u
g
g
ests
th
at
a
r
estar
t
m
ec
h
an
is
m
o
r
a
lo
u
d
n
ess
f
lo
o
r
wo
u
ld
m
ak
e
b
etter
u
s
e
o
f
th
e
iter
atio
n
b
u
d
g
et,
a
p
o
in
t ta
k
e
n
u
p
in
s
ec
tio
n
4.
3
.
3
.
Resul
t
s
o
n inv
er
s
e
s
t
ro
ng
ly
co
rr
ela
t
ed
ins
t
a
nces
T
ab
le
1
co
m
p
a
r
es
th
e
th
r
ee
a
lg
o
r
ith
m
s
o
n
I
DKP1
to
I
DKP
7
.
B
B
AT
d
o
m
in
ates
SecE
GA
o
n
ev
er
y
in
s
tan
ce
an
d
b
y
a
wid
e
m
ar
g
i
n
,
th
e
g
ap
in
m
ea
n
p
r
o
f
it
r
an
g
in
g
f
r
o
m
2
.
9
%
o
n
I
DKP1
to
9
.
8
%
o
n
I
DKP7
.
T
h
e
co
m
p
ar
is
o
n
a
g
ain
s
t
FirE
GA
is
clo
s
er
b
u
t
s
till
f
av
o
r
ab
le:
B
B
AT
attain
s
a
h
ig
h
er
b
est
p
r
o
f
it
o
n
s
ix
o
f
t
h
e
s
ev
en
in
s
tan
ce
s
an
d
a
h
ig
h
er
m
ea
n
p
r
o
f
it
o
n
t
h
e
s
am
e
s
ix
,
th
e
s
in
g
le
ex
ce
p
tio
n
in
b
o
th
ca
s
es
b
ein
g
I
DKP1
,
wh
er
e
FirE
GA
r
ea
ch
es th
e
k
n
o
wn
o
p
tim
u
m
o
f
7
0
,
1
0
6
a
n
d
B
B
AT
s
t
o
p
s
f
iv
e
u
n
its
s
h
o
r
t.
T
h
e
m
ar
g
in
wid
en
s
with
in
s
tan
ce
s
ize.
On
I
DKP7
,
th
e
lar
g
est
in
s
tan
ce
in
th
e
f
am
il
y
,
B
B
AT
im
p
r
o
v
es
th
e
m
ea
n
p
r
o
f
it
b
y
2
,
2
9
0
u
n
its
o
v
er
FirE
GA
wh
il
e
s
im
u
ltan
eo
u
s
ly
r
e
d
u
cin
g
th
e
s
tan
d
ar
d
d
ev
iatio
n
f
r
o
m
2
,
2
9
4
.
3
t
o
9
3
6
.
3
,
s
o
th
e
g
ain
is
n
o
t
p
u
r
ch
ased
with
a
d
d
itio
n
al
in
s
tab
ilit
y
.
On
I
DKP5
an
d
I
DKP7
B
B
AT
also
r
aises
th
e
wo
r
s
t
-
ca
s
e
p
r
o
f
it
ab
o
v
e
th
at
o
f
FirE
GA,
alt
h
o
u
g
h
o
n
th
e
o
th
er
f
iv
e
i
n
s
tan
ce
s
o
f
th
is
f
a
m
ily
FirE
GA
s
till
g
u
ar
an
tees th
e
h
ig
h
er
f
l
o
o
r
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
16
,
No
.
5
,
Octo
b
e
r
20
26
:
2
6
8
0
-
2
6
8
7
2684
(
a)
(
b
)
Fig
u
r
e
1
.
Me
an
b
est
-
so
-
f
ar
p
r
o
f
it o
v
er
5
0
0
iter
atio
n
s
f
o
r
(
a)
i
n
s
tan
ce
I
DKP1
an
d
(
b
)
in
s
tan
c
e
I
DKP5
T
ab
le
1
.
C
o
m
p
a
r
is
o
n
o
f
B
B
A
T
,
FirE
GA
an
d
SecE
GA
o
n
th
e
in
v
er
s
e
s
tr
o
n
g
l
y
co
r
r
elate
d
i
n
s
tan
ce
s
I
n
st
a
n
c
e
O
P
T
A
l
g
o
r
i
t
h
m
B
e
st
M
e
a
n
W
o
r
st
SD
I
D
K
P
1
7
0
1
0
6
F
i
r
EG
A
7
0
1
0
6
7
0
0
9
9
7
0
0
9
0
7
S
e
c
EG
A
6
8
6
6
3
6
8
0
0
0
6
7
3
6
9
3
2
8
B
B
A
T
7
0
1
0
1
6
9
9
9
9
.
4
6
9
7
5
5
8
6
.
0
I
D
K
P
2
1
1
8
2
6
8
F
i
r
EG
A
1
1
8
1
6
9
1
1
7
8
6
9
1
1
7
6
2
5
1
0
2
.
6
S
e
c
EG
A
1
1
4
4
3
4
1
1
3
3
8
5
1
1
2
3
0
7
7
4
4
6
.
7
B
B
A
T
1
1
8
2
4
0
1
1
8
0
7
6
1
1
7
4
9
0
1
7
7
.
7
I
D
K
P
3
2
3
4
8
0
4
F
i
r
EG
A
2
3
4
4
9
7
2
3
3
9
9
7
2
3
3
6
6
6
1
7
5
.
4
S
e
c
EG
A
2
2
0
0
9
6
2
1
7
9
8
2
2
1
6
3
1
3
8
3
5
.
8
B
B
A
T
2
3
4
7
9
0
2
3
4
1
5
4
.
3
2
3
1
2
8
0
7
7
4
.
0
I
D
K
P
4
2
8
2
5
9
1
F
i
r
EG
A
2
8
2
1
4
8
2
8
0
6
9
5
2
7
8
8
8
1
8
2
7
.
6
S
e
c
EG
A
2
6
3
2
3
8
2
6
0
4
2
5
2
5
8
9
2
2
9
3
3
.
4
B
B
A
T
2
8
2
5
5
0
2
8
1
5
5
4
2
7
8
7
3
0
9
6
7
.
1
I
D
K
P
5
3
3
5
5
8
4
F
i
r
EG
A
3
3
5
0
0
4
3
3
3
4
8
4
3
2
9
6
2
1
1
1
7
3
.
9
S
e
c
EG
A
3
0
9
5
7
3
3
0
6
8
7
8
3
0
4
8
8
1
9
0
7
.
2
B
B
A
T
3
3
5
5
0
0
3
3
4
7
6
7
.
3
3
3
1
1
3
0
9
2
1
.
7
I
D
K
P
6
4
5
2
4
6
3
F
i
r
EG
A
4
5
1
6
8
0
4
4
9
8
6
3
4
4
6
7
0
4
1
1
6
1
.
5
S
e
c
EG
A
4
1
4
0
9
0
4
1
1
3
6
7
4
0
8
7
8
8
1
0
9
9
.
3
B
B
A
T
4
5
2
3
6
0
4
5
1
1
8
5
.
7
4
4
6
6
4
0
1
1
9
5
.
5
I
D
K
P
7
4
8
9
1
4
9
F
i
r
EG
A
4
8
8
0
0
9
4
8
5
5
9
2
4
7
6
3
8
5
2
2
9
4
.
3
S
e
c
EG
A
4
5
1
5
2
8
4
4
4
3
1
6
4
4
2
1
3
3
1
2
8
0
.
3
B
B
A
T
4
8
8
9
7
0
4
8
7
8
8
2
4
8
5
3
4
0
9
3
6
.
3
3
.
4
.
Resul
t
s
o
n str
o
ng
ly
co
rr
ela
t
ed
ins
t
a
nces
T
ab
le
2
r
e
p
o
r
ts
th
e
s
tr
o
n
g
ly
c
o
r
r
elate
d
f
a
m
ily
,
an
d
th
e
p
atter
n
d
if
f
er
s
s
h
ar
p
ly
.
B
B
AT
ag
ain
r
ea
ch
es
a
h
ig
h
er
b
est
p
r
o
f
it
th
a
n
FirE
G
A
o
n
s
ix
o
f
s
ev
en
in
s
tan
ce
s
,
with
th
e
lar
g
est
s
in
g
le
im
p
r
o
v
em
en
t
o
n
SDKP7
,
wh
er
e
it
f
in
d
s
6
0
4
,
2
5
0
ag
ain
s
t
5
9
9
,
3
6
1
.
On
m
ea
n
p
r
o
f
it,
h
o
wev
er
,
FirE
GA
is
ah
ea
d
o
n
s
ix
o
f
t
h
e
s
ev
en
in
s
tan
ce
s
,
an
d
o
n
SDKP6
th
e
two
ar
e
s
ep
ar
ated
b
y
o
n
ly
3
6
u
n
its
.
T
h
e
r
ev
e
r
s
al
is
ex
p
lain
ed
b
y
th
e
s
tan
d
ar
d
d
ev
iatio
n
s
:
o
n
SDKP1
to
SD
KP4
th
e
FirE
GA
s
tan
d
ar
d
d
e
v
iatio
n
lies
b
etwe
en
4
2
an
d
1
2
3
,
wh
er
ea
s
B
B
AT
r
an
g
es
f
r
o
m
3
1
4
to
9
6
5
.
B
B
A
T
ex
p
lo
r
es
m
o
r
e
wid
ely
a
n
d
c
o
n
s
eq
u
en
tly
f
in
d
s
b
etter
p
ea
k
s
,
b
u
t
its
in
d
iv
id
u
a
l
r
u
n
s
ar
e
less
r
eliab
le.
SDKP5
is
th
e
o
n
e
in
s
tan
ce
wh
er
e
B
B
AT
is
b
ea
ten
o
n
ev
er
y
cr
iter
io
n
,
a
n
d
it
is
also
t
h
e
in
s
t
an
ce
with
th
e
lar
g
est
o
p
tim
ality
g
a
p
f
o
r
all
th
r
ee
alg
o
r
ith
m
s
,
FirE
GA
f
allin
g
2
.
2
%
s
h
o
r
t
o
f
th
e
o
p
tim
u
m
an
d
B
B
AT
3
.
0
%.
T
h
e
ex
ce
p
tio
n
is
in
s
tr
u
ctiv
e
r
ath
er
t
h
an
in
ci
d
en
tal:
s
tr
o
n
g
ly
co
r
r
elate
d
in
s
tan
ce
s
m
ak
e
p
r
o
f
it
d
e
n
s
ity
n
ea
r
ly
u
n
if
o
r
m
ac
r
o
s
s
item
s
,
s
o
th
e
g
r
ee
d
y
s
tag
e
o
f
th
e
r
ep
ai
r
o
p
er
ato
r
h
as littl
e
b
asis
o
n
w
h
ich
to
ch
o
o
s
e,
an
d
th
e
s
ea
r
ch
is
lef
t to
r
ely
o
n
th
e
b
at
d
y
n
am
ics alo
n
e.
3
.
5
.
Dis
cus
s
io
n
T
ab
le
3
a
g
g
r
e
g
ates
th
e
two
f
a
m
ilies
.
Acr
o
s
s
all
1
4
in
s
tan
ce
s
B
B
AT
ac
h
iev
es
th
e
b
est
p
r
o
f
it
o
n
1
2
b
u
t
th
e
b
etter
m
ea
n
p
r
o
f
it
o
n
o
n
ly
7
,
s
o
th
e
claim
th
at
B
B
AT
is
co
m
p
etitiv
e
with
th
e
elite
g
en
etic
alg
o
r
ith
m
s
is
s
u
p
p
o
r
ted
,
b
u
t
th
e
q
u
alif
ica
tio
n
m
atter
s
:
th
e
ad
v
an
tag
e
in
m
ea
n
p
r
o
f
it
r
ests
alm
o
s
t
en
tire
ly
o
n
th
e
in
v
er
s
e
s
tr
o
n
g
ly
co
r
r
elate
d
f
am
ily
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
B
in
a
r
y
b
a
t
a
lg
o
r
ith
m
w
ith
g
r
ee
d
y
r
ep
a
ir
fo
r
th
e
d
is
co
u
n
te
d
0
-
1
kn
a
p
s
a
ck
p
r
o
b
lem
(
Tu
n
g
K
h
a
c
Tr
u
o
n
g
)
2685
T
wo
lim
itatio
n
s
s
h
o
u
ld
b
e
s
tated
p
lain
ly
.
First,
th
e
co
m
p
a
r
is
o
n
is
ag
ain
s
t
alg
o
r
ith
m
s
p
u
b
lis
h
ed
in
2
0
1
6
an
d
2
0
1
9
.
T
h
e
ex
ac
t
r
e
d
u
ctio
n
p
r
o
ce
d
u
r
es
o
f
W
ilb
au
t
et
a
l.
[
1
2
]
s
o
lv
e
th
ese
in
s
tan
ce
s
to
o
p
tim
ality
,
an
d
r
ec
en
t
m
etah
e
u
r
is
tics
[
1
0
]
,
[
2
5
]
r
ep
o
r
t
s
tr
o
n
g
er
r
esu
lts
th
an
e
ith
er
b
aselin
e
u
s
ed
h
e
r
e,
s
o
B
B
AT
is
n
o
t
claim
ed
to
b
e
s
tate
o
f
th
e
ar
t;
th
e
co
n
tr
ib
u
tio
n
is
a
d
em
o
n
s
tr
atio
n
th
at
a
b
at
f
o
r
m
u
latio
n
with
a
s
m
all
p
ar
am
eter
s
et
r
ea
ch
es
a
co
m
p
etitiv
e
r
eg
io
n
o
f
th
e
s
ea
r
c
h
s
p
ac
e.
Seco
n
d
,
t
h
e
co
m
p
ar
is
o
n
r
ests
o
n
d
escr
i
p
tiv
e
s
tatis
tics
o
v
er
3
0
r
u
n
s
an
d
n
o
s
ig
n
i
f
ican
ce
te
s
t
was
ap
p
lied
.
Giv
en
th
e
o
v
er
lap
in
th
e
d
is
tr
ib
u
tio
n
s
o
n
th
e
s
tr
o
n
g
ly
co
r
r
elate
d
f
am
ily
,
a
W
ilco
x
o
n
s
ig
n
ed
-
r
a
n
k
test
,
as
a
p
p
lied
to
th
is
b
e
n
ch
m
ar
k
in
[
2
5
]
,
wo
u
ld
b
e
r
eq
u
ir
ed
b
ef
o
r
e
a
n
y
claim
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1
T
ab
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3
.
Nu
m
b
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f
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s
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wh
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B
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tp
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D
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1
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A
l
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B
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f
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t
6
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7
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1
2
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1
4
M
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n
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t
6
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1
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7
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1
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2
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1
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3
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1
4
S
t
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n
d
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r
d
d
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a
t
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2
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1
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1
4
T
h
e
v
ar
ian
ce
p
atter
n
p
o
in
ts
to
a
co
n
cr
ete
im
p
r
o
v
em
en
t.
T
h
e
s
tan
d
ar
d
d
ev
iatio
n
s
in
T
ab
le
2
ar
e
th
r
ee
to
eig
h
t
tim
es
th
o
s
e
o
f
FirE
G
A
o
n
th
e
s
m
aller
in
s
tan
ce
s
,
a
n
d
th
e
c
o
n
v
e
r
g
en
ce
cu
r
v
es
in
Fig
u
r
e
1
s
h
o
w
th
e
co
lo
n
y
s
ettlin
g
well
b
ef
o
r
e
th
e
iter
atio
n
b
u
d
g
et
ex
p
ir
es.
B
o
th
o
b
s
er
v
atio
n
s
im
p
licate
th
e
lo
u
d
n
ess
d
ec
ay
s
ch
ed
u
le
o
f
(
9
)
,
wh
ich
s
u
p
p
r
e
s
s
es
ac
ce
p
tan
ce
o
f
n
ew
ca
n
d
id
ates
in
th
e
later
p
a
r
t
o
f
th
e
r
u
n
.
I
m
p
o
s
in
g
a
lo
we
r
b
o
u
n
d
o
n
Aᵢ
,
o
r
r
ein
itializin
g
a
f
r
ac
tio
n
o
f
th
e
co
lo
n
y
wh
en
th
e
in
cu
m
b
en
t
s
talls
,
wo
u
ld
ad
d
r
ess
th
e
two
s
y
m
p
to
m
s
to
g
eth
er
.
4.
CO
NCLU
SI
O
N
T
h
is
p
ap
er
p
r
esen
ted
B
B
AT
,
a
b
in
ar
y
b
at
alg
o
r
ith
m
f
o
r
th
e
d
is
co
u
n
ted
0
-
1
k
n
ap
s
ac
k
p
r
o
b
lem
.
C
o
n
tin
u
o
u
s
b
at
v
elo
cities
ar
e
co
n
v
er
ted
in
to
b
it
-
s
elec
tio
n
p
r
o
b
ab
ilit
ies
b
y
a
s
ig
m
o
id
tr
an
s
f
er
f
u
n
ctio
n
,
an
d
a
two
-
s
tag
e
g
r
ee
d
y
o
p
e
r
ato
r
r
ep
air
s
th
e
ex
clu
s
iv
ity
an
d
ca
p
ac
ity
v
io
latio
n
s
th
at
th
is
co
n
v
er
s
io
n
p
r
o
d
u
ce
s
wh
ile
r
aisi
n
g
th
e
p
r
o
f
it
o
f
th
e
r
esu
lt
in
g
f
ea
s
ib
le
s
o
lu
tio
n
.
T
h
e
alg
o
r
ith
m
in
h
er
its
th
e
co
m
p
ac
t
p
ar
am
eter
s
et
o
f
th
e
o
r
ig
in
al
b
at
m
eta
h
eu
r
is
tic,
r
eq
u
ir
in
g
o
n
ly
a
p
o
p
u
latio
n
s
ize,
an
in
itial lo
u
d
n
ess
an
d
an
in
iti
al
p
u
ls
e
r
ate.
On
1
4
b
e
n
ch
m
ar
k
in
s
tan
ce
s
s
o
lv
ed
3
0
tim
es
ea
ch
,
B
B
AT
o
u
tp
er
f
o
r
m
ed
SecE
GA
o
n
e
v
er
y
in
s
tan
ce
an
d
e
v
er
y
cr
iter
io
n
.
Ag
ai
n
s
t
FirE
GA
it
o
b
tain
ed
a
h
ig
h
e
r
b
est
p
r
o
f
it
o
n
1
2
o
f
t
h
e
1
4
i
n
s
tan
ce
s
b
u
t
a
h
ig
h
e
r
m
ea
n
p
r
o
f
it
o
n
o
n
ly
7
.
T
h
e
a
d
v
an
tag
e
in
m
ea
n
p
r
o
f
it
is
co
n
ce
n
tr
ated
alm
o
s
t
en
tire
ly
o
n
th
e
in
v
er
s
e
s
tr
o
n
g
ly
co
r
r
elate
d
f
am
ily
,
wh
er
e
B
B
AT
wo
n
6
o
f
7
co
m
p
ar
is
o
n
s
an
d
r
ed
u
ce
d
th
e
s
tan
d
ar
d
d
e
v
iatio
n
o
n
t
h
e
two
lar
g
est
in
s
tan
ce
s
;
o
n
th
e
s
tr
o
n
g
ly
co
r
r
elate
d
f
am
ily
it
r
ea
ch
ed
b
etter
p
ea
k
s
b
u
t
wit
h
h
ig
h
er
r
u
n
-
to
-
r
u
n
v
ar
ian
ce
,
an
d
FirE
GA
r
etain
ed
th
e
b
etter
m
ea
n
o
n
s
ix
o
f
s
ev
en
in
s
tan
ce
s
.
B
B
AT
is
th
er
ef
o
r
e
b
est
ch
ar
ac
ter
ized
as a
co
m
p
etitiv
e
s
o
lv
er
wh
o
s
e
wea
k
n
ess
is
s
tab
ilit
y
r
ath
er
th
a
n
s
ea
r
ch
p
o
wer
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
2
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8
8
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8
7
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I
n
t J E
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&
C
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p
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,
Vo
l.
16
,
No
.
5
,
Octo
b
e
r
20
26
:
2
6
8
0
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2
6
8
7
2686
T
h
r
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d
ir
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tio
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