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[
1
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2
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4
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[
5
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.
W
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I
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8
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3
8
A
r
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.
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r
o
b
le
m
s
h
av
e
m
a
d
e
it
a
p
o
p
u
lar
ch
o
ice
am
o
n
g
r
esear
ch
er
s
[
1
0
]
.
I
n
a
c
o
m
p
a
r
a
t
i
v
e
s
t
u
d
y
i
n
v
o
l
v
i
n
g
5
0
b
e
n
c
h
m
a
r
k
f
u
n
c
t
i
o
n
s
,
K
a
y
a
e
t
a
l
.
[
1
1
]
d
e
m
o
n
s
t
r
ate
d
A
B
C
’
s
s
u
p
e
r
i
o
r
p
e
r
f
o
r
m
a
n
c
e
o
v
e
r
o
t
h
e
r
w
e
l
l
-
e
s
t
a
b
li
s
h
e
d
a
l
g
o
r
it
h
m
s
s
u
c
h
as
t
h
e
g
e
n
e
t
i
c
a
l
g
o
r
i
t
h
m
(
GA
)
,
d
if
f
e
r
e
n
t
i
a
l
e
v
o
l
u
t
i
o
n
(
D
E
)
,
e
v
o
l
u
t
i
o
n
a
r
y
s
t
r
a
t
e
g
i
es
(
E
S
)
,
a
n
d
p
a
r
t
i
c
le
s
w
a
r
m
o
p
t
i
m
i
z
a
ti
o
n
(
P
SO
)
,
r
e
p
o
r
t
i
n
g
c
o
n
s
i
s
t
e
n
t
l
y
b
et
t
e
r
o
b
j
e
c
t
i
v
e
v
a
l
u
e
s
a
n
d
l
o
w
e
r
s
t
an
d
a
r
d
d
e
v
i
a
t
i
o
n
s
.
A
d
d
i
t
i
o
n
a
l
v
a
l
i
d
a
t
i
o
n
w
as
p
r
o
v
i
d
e
d
b
y
K
h
o
s
r
a
v
a
n
i
a
n
e
t
a
l
.
[
1
2
]
,
w
h
o
f
o
u
n
d
A
B
C
t
o
b
e
m
o
r
e
e
f
f
e
c
t
i
v
e
t
h
a
n
h
a
r
m
o
n
y
s
e
a
r
c
h
(
H
S
)
,
a
n
t
c
o
l
o
n
y
o
p
t
i
m
i
z
at
i
o
n
(
A
C
O
)
,
a
n
d
GA
i
n
o
p
t
i
m
i
z
i
n
g
o
i
l
-
w
el
l
d
e
s
i
g
n
s
.
Similar
ly
,
Ag
ar
wal
et
a
l.
[
1
3
]
s
h
o
we
d
th
at
AB
C
o
u
tp
er
f
o
r
m
ed
th
e
f
ir
ef
ly
alg
o
r
ith
m
in
s
o
lv
in
g
th
e
R
astrig
in
f
u
n
ctio
n
,
h
ig
h
lig
h
tin
g
its
f
aster
co
n
v
er
g
en
ce
.
T
h
ese
s
tu
d
ies
af
f
ir
m
AB
C
's
r
o
b
u
s
tn
ess
[
1
1
]
,
co
m
p
u
tatio
n
a
l e
f
f
icien
cy
[
1
4
]
,
a
n
d
r
eliab
le
p
er
f
o
r
m
an
ce
d
esp
ite
h
a
v
in
g
r
e
lativ
ely
f
ew
co
n
tr
o
l
p
ar
am
eter
s
.
T
o
f
u
r
th
er
en
h
a
n
ce
AB
C
's
ca
p
ab
ilit
ies,
L
ee
an
d
Hash
im
[
1
5
]
in
tr
o
d
u
ce
d
th
e
h
y
b
r
i
d
AB
C
alg
o
r
ith
m
with
ar
tific
ial
r
a
b
b
it
alg
o
r
ith
m
,
w
h
ich
ac
ce
le
r
ates
co
n
v
er
g
en
ce
b
y
r
e
f
in
in
g
th
e
s
tr
u
ctu
r
e
o
f
s
ea
r
ch
in
g
b
ee
p
h
ase
.
N
u
m
er
o
u
s
en
h
an
ce
m
e
n
ts
s
in
ce
th
en
h
av
e
f
o
c
u
s
ed
o
n
im
p
r
o
v
in
g
th
e
alg
o
r
ith
m
’
s
b
ala
n
ce
b
etwe
en
ex
p
l
o
r
atio
n
an
d
ex
p
lo
itatio
n
[
1
6
]
.
B
u
ild
in
g
o
n
th
ese
d
ev
elo
p
m
en
ts
,
th
e
cu
r
r
en
t
s
t
u
d
y
p
r
esen
ts
a
n
ew
m
o
d
if
icatio
n
th
at
in
te
g
r
ates
th
e
ar
ith
m
etic
o
p
tim
izatio
n
al
g
o
r
ith
m
(
AOA)
[
1
7
]
in
t
o
th
e
AB
C
s
tr
u
ctu
r
e.
T
h
is
h
y
b
r
id
,
ter
m
ed
th
e
ar
ith
m
etic
ar
tific
ial
b
ee
co
lo
n
y
(
AABC
)
alg
o
r
ith
m
,
is
d
esig
n
e
d
to
s
tr
e
n
g
th
en
b
o
th
g
lo
b
al
ex
p
lo
r
atio
n
an
d
l
o
ca
l e
x
p
l
o
itatio
n
ef
f
icien
c
y
.
T
h
e
p
r
o
p
o
s
ed
A
A
B
C
a
l
g
o
r
i
t
h
m
en
h
an
c
e
s
t
h
e
e
x
p
l
o
r
a
ti
o
n
c
ap
ab
i
l
i
t
y
o
f
th
e
s
t
a
n
d
a
r
d
A
B
C
a
p
p
r
o
a
ch
b
y
em
b
ed
d
in
g
th
e
s
e
a
r
c
h
d
y
n
a
m
i
c
s
o
f
th
e
A
OA
i
n
t
o
th
e
e
m
p
l
o
y
ed
b
e
e
p
h
a
s
e
.
T
o
s
t
r
e
n
g
t
h
en
e
x
p
lo
i
t
a
t
i
o
n
,
t
h
e
o
n
l
o
o
k
e
r
b
ee
p
h
a
s
e
i
s
r
ef
i
n
ed
w
i
th
in
n
o
v
a
t
i
v
e
s
tr
a
t
e
g
ie
s
,
in
c
l
u
d
i
n
g
le
v
e
r
a
g
in
g
t
h
e
g
lo
b
a
l
b
e
s
t
s
o
l
u
t
io
n
a
s
a
g
u
id
i
n
g
r
ef
e
r
e
n
ce
a
n
d
i
m
p
l
e
m
en
t
i
n
g
a
n
e
w
l
y
d
e
s
ig
n
ed
s
t
e
p
-
s
i
z
e
c
o
n
t
r
o
l
m
e
ch
a
n
i
s
m
.
T
h
e
a
l
g
o
r
i
t
h
m
's
ef
f
e
c
t
iv
en
e
s
s
i
s
th
o
r
o
u
g
h
ly
e
v
a
l
u
a
t
ed
u
s
i
n
g
a
s
e
t
o
f
t
en
b
en
c
h
m
a
r
k
f
u
n
c
t
io
n
s
.
M
o
r
e
o
v
er
,
t
h
e
A
A
B
C
i
s
a
p
p
l
i
e
d
t
o
a
f
l
ex
i
b
le
m
a
n
ip
u
l
a
to
r
s
y
s
t
e
m
(
F
M
S
)
t
o
a
s
s
e
s
s
i
t
s
p
e
r
f
o
r
m
a
n
ce
i
n
r
e
g
u
l
a
t
i
n
g
t
h
e
h
u
b
a
n
g
l
e
w
i
t
h
in
a
r
e
a
l
-
wo
r
ld
co
n
t
r
o
l
c
o
n
t
e
x
t.
A
d
e
ta
i
l
e
d
co
m
p
a
r
a
t
i
v
e
s
t
u
d
y
b
e
t
we
e
n
t
h
e
p
r
o
p
o
s
e
d
A
A
B
C
a
n
d
t
h
e
o
r
ig
i
n
a
l
A
B
C
a
l
g
o
r
i
th
m
i
s
c
o
n
d
u
c
t
e
d
to
d
em
o
n
s
t
r
a
te
th
e
p
er
f
o
r
m
an
c
e
g
a
i
n
s
a
ch
i
e
v
ed
t
h
r
o
u
g
h
th
e
i
n
t
r
o
d
u
c
e
d
e
n
h
a
n
c
e
m
en
t
s
.
T
h
e
s
tr
u
ctu
r
e
o
f
th
e
p
ap
er
is
a
s
f
o
llo
ws
:
s
ec
tio
n
2
p
r
esen
ts
th
e
f
u
n
d
am
en
tals
o
f
t
h
e
AB
C
alg
o
r
ith
m
.
Sectio
n
3
d
is
cu
s
s
es
th
e
AOA
alg
o
r
ith
m
an
d
th
e
FMS
m
o
d
e
l,
f
o
llo
wed
b
y
s
ec
tio
n
4
,
wh
ic
h
d
etails
th
e
latter
.
Sectio
n
5
d
escr
ib
es
th
e
f
o
r
m
u
latio
n
an
d
co
m
p
o
n
en
ts
o
f
th
e
AAB
C
alg
o
r
ith
m
.
Sectio
n
6
r
ep
o
r
ts
th
e
r
esu
lts
o
f
n
u
m
er
ical
ex
p
e
r
im
en
ts
o
n
b
en
ch
m
ar
k
f
u
n
ctio
n
s
an
d
th
e
ap
p
licatio
n
o
f
AABC
to
th
e
FMS.
Sect
io
n
7
co
n
clu
d
es with
a
s
u
m
m
a
r
y
o
f
k
ey
f
in
d
in
g
s
an
d
r
ec
o
m
m
en
d
a
tio
n
s
f
o
r
f
u
tu
r
e
r
esear
ch
.
2.
ARTI
F
I
CI
AL
B
E
E
CO
L
O
N
Y
AL
G
O
RI
T
H
M
I
n
s
p
ir
ed
b
y
th
e
in
tellig
en
t
f
o
r
ag
in
g
d
y
n
am
ics
o
f
h
o
n
e
y
b
ee
s
war
m
s
,
th
e
A
B
C
a
lg
o
r
ith
m
,
d
ev
elo
p
e
d
by
Kar
ab
o
g
a
[
8
]
,
tr
an
s
f
o
r
m
s
th
e
o
p
tim
izatio
n
p
r
o
ce
s
s
in
to
a
m
etap
h
o
r
ical
s
ea
r
ch
f
o
r
n
ec
tar
.
I
n
t
h
is
n
atu
r
e
-
in
s
p
ir
ed
f
r
am
ewo
r
k
,
ea
ch
f
o
o
d
s
o
u
r
ce
s
y
m
b
o
lizes
a
p
o
ten
t
ial
s
o
lu
tio
n
,
s
ca
tter
ed
ac
r
o
s
s
a
v
ir
tu
al
lan
d
s
ca
p
e
r
ep
r
esen
tin
g
t
h
e
p
r
o
b
lem
’
s
s
e
ar
ch
s
p
ac
e.
T
h
e
alg
o
r
ith
m
s
i
m
u
lates
th
e
co
o
r
d
in
ated
ef
f
o
r
ts
o
f
th
r
ee
t
y
p
es
o
f
b
ee
s
:
em
p
lo
y
ed
b
ee
s
,
o
n
lo
o
k
e
r
b
ee
s
,
an
d
s
co
u
t
b
ee
s
,
ea
c
h
c
o
n
tr
ib
u
tin
g
d
is
tin
ctiv
ely
to
th
e
b
alan
ce
b
etwe
en
ex
p
lo
r
atio
n
(
s
ea
r
c
h
in
g
n
ew
r
e
g
io
n
s
)
a
n
d
ex
p
lo
itatio
n
(
r
ef
in
i
n
g
k
n
o
wn
g
o
o
d
ar
ea
s
)
.
T
h
e
jo
u
r
n
ey
b
e
g
in
s
with
a
r
an
d
o
m
in
itializatio
n
p
h
ase,
w
h
er
e
a
s
war
m
o
f
s
o
lu
tio
n
ca
n
d
id
ates
is
d
is
p
er
s
ed
th
r
o
u
g
h
o
u
t th
e
s
ea
r
ch
d
o
m
ain
.
T
h
is
in
itial
p
o
p
u
latio
n
,
ty
p
ica
lly
r
ep
r
esen
ted
b
y
SN,
m
ir
r
o
r
s
th
e
n
u
m
b
er
o
f
em
p
lo
y
e
d
b
e
es
an
d
is
p
o
s
itio
n
e
d
u
s
in
g
(
1
)
to
s
ee
d
th
e
al
g
o
r
ith
m
’
s
f
ir
s
t step
s
.
,
=
,
+
(
0
,
1
)
(
,
−
,
)
(
1
)
W
h
er
e
,
r
ep
r
esen
ts
th
e
s
o
lu
tio
n
in
ℎ
f
o
o
d
s
o
u
r
ce
in
ℎ
d
im
en
s
i
o
n
,
,
in
wh
ich
=
1
,
2
,
3
,
…
,
an
d
=
1
,
2
,
3
,
4
,
…
,
.
E
ac
h
o
f
th
e
f
o
o
d
s
o
u
r
ce
is
r
an
d
o
m
ly
ass
ig
n
ed
t
o
th
e
S
N
n
u
m
b
er
o
f
em
p
lo
y
ed
b
ee
s
f
o
r
t
h
e
p
u
r
p
o
s
e
o
f
f
o
o
d
q
u
ality
ev
alu
a
tio
n
.
I
n
em
p
lo
y
e
d
b
ee
p
h
ase,
th
e
i
n
f
o
r
m
atio
n
o
f
th
e
cu
r
r
en
t
f
o
o
d
s
o
u
r
ce
is
u
s
ed
b
y
th
e
em
p
l
o
y
ed
b
ee
to
ad
ju
s
t th
em
s
elv
es to
an
o
th
er
r
an
d
o
m
f
o
o
d
s
o
u
r
ce
to
im
p
r
o
v
e
th
e
f
o
o
d
s
o
u
r
ce
q
u
ality
.
T
h
e
n
ew
s
o
lu
tio
n
,
,
is
g
en
er
ated
u
s
in
g
(
2
)
.
,
=
,
+
(
−
1
,
1
)
(
,
−
,
)
(
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
9
3
8
I
n
t J Ar
tif
I
n
tell
,
Vo
l.
14
,
No
.
3
,
Octo
b
er
20
25
:
3
7
9
0
-
3
8
0
1
3792
W
h
er
e
,
is
r
an
d
o
m
ly
ch
o
s
en
s
o
lu
tio
n
.
,
is
r
an
d
o
m
ly
ch
o
s
en
n
eig
h
b
o
r
p
ar
tn
er
s
o
lu
tio
n
in
wh
ich
=
1
,
2
,
3
,
…
,
an
d
m
u
s
t
b
e
d
if
f
er
e
n
t
f
r
o
m
.
T
h
e
em
p
lo
y
ed
b
ee
s
will
th
en
co
m
p
ar
e
th
e
q
u
ality
o
f
n
ew
s
o
lu
tio
n
,
,
an
d
th
e
p
r
ev
i
o
u
s
s
o
l
u
tio
n
,
,
.
I
f
th
e
n
ewly
d
is
co
v
er
e
d
s
o
lu
tio
n
is
s
u
p
er
io
r
to
th
e
p
r
ev
io
u
s
o
n
e,
th
e
em
p
lo
y
ed
b
ee
r
ep
lace
s
th
e
o
ld
s
o
l
u
tio
n
with
th
e
n
ew
o
n
e.
T
h
e
f
itn
ess
o
f
th
is
u
p
d
at
ed
s
o
lu
tio
n
is
th
en
ev
alu
ated
u
s
in
g
(
3
)
.
=
{
1
1
+
(
,
)
(
,
)
≥
0
1
+
|
(
,
)
|
(
,
)
≤
0
(
3
)
I
n
th
is
co
n
tex
t,
(
,
)
r
ep
r
esen
ts
th
e
o
b
jectiv
e
v
alu
e
o
f
th
e
n
ewly
g
en
er
ated
s
o
lu
tio
n
.
Af
ter
co
m
p
letin
g
th
eir
s
ea
r
c
h
,
em
p
l
o
y
ed
b
ee
s
co
m
m
u
n
icate
th
e
q
u
ality
o
f
th
e
f
o
o
d
s
o
u
r
ce
s
t
o
th
e
o
n
lo
o
k
er
b
ee
s
th
r
o
u
g
h
a
m
ec
h
a
n
is
m
ak
in
to
th
e
wag
g
le
d
an
ce
o
b
s
er
v
e
d
in
n
atu
r
e.
T
h
e
q
u
ality
o
f
th
e
wag
g
le
d
a
n
ce
r
e
f
lects
th
e
f
itn
ess
o
f
th
e
co
r
r
esp
o
n
d
i
n
g
f
o
o
d
s
o
u
r
ce
—
th
e
m
o
r
e
f
a
v
o
r
ab
le
th
e
f
o
o
d
s
o
u
r
ce
,
th
e
m
o
r
e
ex
p
r
ess
iv
e
th
e
d
an
ce
.
T
h
is
q
u
ality
ass
ess
m
en
t is q
u
an
tifie
d
u
s
in
g
(
4
)
.
=
∑
=
1
(
4
)
I
n
th
is
co
n
tex
t,
t
h
e
p
r
o
b
a
b
ilit
y
v
alu
e
s
ig
n
if
ies
th
e
q
u
alit
y
o
f
th
e
f
o
o
d
s
o
u
r
ce
.
On
lo
o
k
er
b
ee
s
th
en
r
a
n
d
o
m
l
y
ch
o
o
s
e
a
f
o
o
d
s
o
u
r
ce
b
ased
o
n
its
ass
o
ciate
d
p
r
o
b
ab
ilit
y
v
alu
e
.
Fo
llo
win
g
th
e
s
elec
tio
n
o
f
a
f
o
o
d
s
o
u
r
ce
,
o
n
lo
o
k
er
b
e
es r
ef
in
e
th
e
s
o
lu
tio
n
u
s
in
g
(
2
)
.
T
h
i
s
s
elec
tio
n
m
ec
h
an
is
m
m
ir
r
o
r
s
a
r
o
u
lette
wh
ee
l in
th
e
AB
C
alg
o
r
ith
m
.
I
n
i
n
s
tan
ce
s
wh
er
e
a
f
o
o
d
s
o
u
r
ce
f
ails
to
ex
h
ib
it
im
p
r
o
v
em
en
t
with
in
a
s
p
ec
if
ied
tim
ef
r
am
e,
as
in
d
icate
d
b
y
tr
ial
lim
its
,
th
e
s
aid
f
o
o
d
s
o
u
r
ce
is
d
ee
m
ed
u
n
s
u
cc
ess
f
u
l
an
d
ab
an
d
o
n
e
d
.
E
m
p
lo
y
ed
b
ee
s
th
en
tr
an
s
itio
n
in
to
s
co
u
t
b
ee
s
,
task
ed
with
ex
p
lo
r
in
g
f
o
r
n
ew
f
o
o
d
s
o
u
r
ce
s
,
a
p
r
o
ce
s
s
f
ac
ilit
ated
b
y
(
1
)
.
3.
ARIT
H
M
E
T
I
C
O
P
T
I
M
I
Z
A
T
I
O
N
A
L
G
O
RIT
H
M
I
n
tr
o
d
u
ce
d
b
y
Hu
et
a
l.
[
1
7
]
,
t
h
e
AOA
is
b
u
ilt
u
p
o
n
f
u
n
d
am
en
tal
ar
ith
m
etic
p
r
in
ci
p
les
:
d
iv
is
io
n
(
D)
,
m
u
ltip
licatio
n
(
M)
,
s
u
b
tr
ac
tio
n
(
S),
an
d
ad
d
itio
n
(
A
)
,
wh
i
ch
f
o
r
m
t
h
e
co
r
e
o
f
c
o
n
v
e
n
tio
n
al
m
ath
e
m
atica
l
p
r
o
b
lem
-
s
o
lv
in
g
.
L
ik
e
o
th
er
m
etah
eu
r
is
tic
alg
o
r
ith
m
s
,
AOA
is
d
esig
n
ed
to
ef
f
ec
tiv
ely
b
alan
ce
ex
p
lo
r
atio
n
an
d
ex
p
lo
itatio
n
to
lo
ca
te
th
e
g
lo
b
al
o
p
tim
u
m
.
T
h
e
alg
o
r
ith
m
f
o
llo
ws
th
e
B
ODM
AS
p
r
in
cip
le
(
b
r
ac
k
ets,
o
r
d
er
s
,
d
iv
is
io
n
/m
u
ltip
licatio
n
,
ad
d
itio
n
/s
u
b
tr
ac
tio
n
)
,
p
r
io
r
itizin
g
d
iv
is
io
n
a
n
d
m
u
ltip
licatio
n
o
v
e
r
ad
d
itio
n
an
d
s
u
b
tr
ac
tio
n
t
o
en
s
u
r
e
a
lo
g
ically
co
h
er
e
n
t
ex
ec
u
tio
n
o
f
m
ath
em
atica
l
o
p
er
atio
n
s
.
T
h
is
h
ier
ar
ch
y
e
n
s
u
r
es
th
at
ar
ith
m
etic
o
p
er
ati
o
n
s
ar
e
ex
ec
u
ted
in
a
lo
g
ical
a
n
d
s
tr
u
ctu
r
ed
s
eq
u
en
ce
wh
e
n
m
u
lt
ip
le
o
p
er
atio
n
s
a
r
e
p
r
esen
t in
a
co
m
p
u
tatio
n
.
AOA
b
eg
in
s
b
y
in
itializin
g
a
p
o
p
u
latio
n
o
f
ca
n
d
id
ate
s
o
lu
tio
n
s
(
r
e
f
er
r
ed
to
as
f
o
o
d
s
o
u
r
ce
s
)
r
an
d
o
m
l
y
ac
r
o
s
s
th
e
s
ea
r
ch
s
p
ac
e.
T
h
e
alg
o
r
ith
m
th
e
n
em
p
l
o
y
s
a
d
y
n
am
ic
m
ath
em
atica
l
f
u
n
ctio
n
,
k
n
o
wn
as
th
e
m
ath
o
p
tim
izer
ac
ce
ler
at
io
n
(
MO
A)
,
to
g
o
v
er
n
th
e
t
r
an
s
itio
n
b
etwe
en
e
x
p
lo
r
atio
n
an
d
ex
p
lo
itatio
n
p
h
ases
.
T
h
is
s
witch
in
g
b
eh
av
io
r
is
f
o
r
m
u
lated
in
(
5
)
,
wh
ich
p
lay
s
a
cr
itical
r
o
le
in
co
n
tr
o
ll
in
g
th
e
alg
o
r
ith
m
'
s
co
n
v
er
g
en
ce
d
y
n
am
ics.
(
)
=
+
×
(
−
)
(
5
)
Her
e,
r
ep
r
esen
ts
th
e
m
ax
im
u
m
n
u
m
b
e
r
o
f
iter
atio
n
s
,
is
th
e
cu
r
r
en
t
iter
atio
n
co
u
n
t,
is
th
e
m
ax
im
u
m
v
alu
e
o
f
MO
A,
an
d
is
th
e
m
in
im
u
m
v
alu
e
o
f
MO
A.
T
h
e
ter
m
(
)
co
r
r
esp
o
n
d
s
to
th
e
MO
A
v
alu
e
at
th
e
cu
r
r
en
t
iter
atio
n
.
T
h
e
d
ec
is
io
n
to
s
witch
b
etwe
en
th
e
ex
p
lo
r
atio
n
a
n
d
ex
p
lo
itatio
n
p
r
o
ce
s
s
es
is
d
eter
m
in
ed
b
y
c
o
m
p
ar
in
g
a
r
an
d
o
m
n
u
m
b
er
1
with
th
e
cu
r
r
en
t
MO
A
v
alu
e.
I
f
(
)
<
1
,
t
h
e
ex
p
l
o
r
atio
n
p
r
o
ce
s
s
u
n
f
o
ld
s
,
in
v
o
l
v
in
g
th
e
u
s
e
o
f
d
i
v
is
io
n
an
d
m
u
ltip
licatio
n
o
p
er
ato
r
s
.
C
o
n
v
er
s
ely
,
if
(
)
≥
1
,
th
e
e
x
p
lo
itatio
n
p
r
o
ce
s
s
tak
es
p
lace
,
em
p
lo
y
i
n
g
s
u
b
tr
ac
tio
n
an
d
ad
d
itio
n
o
p
e
r
a
to
r
s
.
T
h
e
ex
p
lo
r
atio
n
p
h
ase
in
th
e
AOA
lev
er
ag
es
m
u
ltip
licati
o
n
an
d
d
iv
is
io
n
o
p
er
ato
r
s
d
u
e
to
th
eir
s
tr
o
n
g
s
ca
tter
in
g
ch
ar
ac
ter
is
tics
,
wh
ich
en
a
b
le
b
r
o
ad
co
v
e
r
ag
e
o
f
th
e
s
ea
r
ch
s
p
ac
e.
T
h
ese
o
p
er
atio
n
s
f
ac
ilit
ate
th
e
g
en
er
atio
n
o
f
d
i
v
er
s
e
ca
n
d
id
ate
s
o
lu
tio
n
s
ac
r
o
s
s
wid
e
r
eg
io
n
s
.
T
h
e
u
p
d
ated
p
o
s
itio
n
s
o
f
n
ew
ca
n
d
i
d
ate
s
o
lu
tio
n
s
d
u
r
in
g
ex
p
l
o
r
atio
n
a
r
e
ca
lcu
lated
u
s
in
g
(
6
)
a
n
d
(
7
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ar
tif
I
n
tell
I
SS
N:
2252
-
8
9
3
8
A
r
ith
metic
a
r
tifi
cia
l b
ee
co
lo
n
y
o
p
timiz
a
tio
n
a
lg
o
r
ith
m
w
ith
flexib
le
ma
n
ip
u
la
to
r
…
(
Mo
h
d
R
u
z
a
in
i H
a
s
h
im
)
3793
,
=
(
)
÷
(
+
)
(
(
−
)
+
)
,
2
>
0
.
5
(
6
)
,
=
(
)
×
×
(
(
−
)
+
)
,
ℎ
(
7
)
I
n
th
is
co
n
tex
t,
(
)
d
en
o
tes
th
e
b
est
s
o
lu
tio
n
f
o
u
n
d
s
o
f
ar
in
th
e
ℎ
d
im
en
s
io
n
.
T
h
e
ter
m
r
ep
r
esen
ts
a
s
m
all
f
lo
atin
g
-
p
o
in
t
c
o
n
s
tan
t
in
tr
o
d
u
ce
d
to
p
r
ev
en
t
d
iv
is
io
n
b
y
ze
r
o
o
r
s
in
g
u
lar
ity
.
T
h
e
p
ar
am
eter
s
er
v
es
as
a
co
n
t
r
o
l
f
ac
to
r
f
o
r
ad
j
u
s
tin
g
th
e
s
ea
r
c
h
b
eh
av
i
o
r
.
an
d
co
r
r
esp
o
n
d
to
th
e
u
p
p
er
an
d
lo
wer
b
o
u
n
d
s
o
f
th
e
s
ea
r
ch
s
p
ac
e,
r
esp
ec
tiv
el
y
,
wh
ile
2
is
a
r
an
d
o
m
ly
g
en
er
ate
d
n
u
m
b
er
with
in
t
h
e
in
ter
v
al
[
0
,
1
]
.
T
h
e
m
ath
o
p
ti
m
izer
p
r
o
b
ab
ilit
y
(
MO
P)
is
co
m
p
u
ted
u
s
in
g
(
8
)
.
(
)
=
1
−
(
)
1
(
8
)
Her
e,
th
e
p
ar
am
eter
α
p
lay
s
a
p
iv
o
tal
r
o
le,
d
y
n
am
ically
t
u
n
in
g
th
e
p
r
ec
is
io
n
o
f
t
h
e
e
x
p
lo
itatio
n
p
r
o
ce
s
s
as
th
e
alg
o
r
ith
m
p
r
o
g
r
ess
es
th
r
o
u
g
h
its
iter
atio
n
s
.
T
h
e
MO
P,
ev
al
u
ated
at
th
e
cu
r
r
en
t
iter
atio
n
M
(
)
f
u
r
th
e
r
in
f
lu
e
n
ce
s
th
is
b
al
an
ce
.
W
h
en
th
e
r
an
d
o
m
ly
g
e
n
er
ated
v
al
u
e
2
>
0
.
5
,
th
e
alg
o
r
ith
m
v
en
tu
r
es
in
to
e
x
p
lo
r
ati
o
n
u
s
in
g
th
e
d
iv
is
io
n
o
p
er
at
o
r
;
o
th
e
r
wis
e,
it
o
p
ts
f
o
r
th
e
m
u
ltip
licatio
n
o
p
er
at
o
r
,
b
o
th
k
n
o
wn
f
o
r
th
ei
r
b
r
o
ad
s
ea
r
ch
d
is
p
er
s
io
n
,
en
ab
lin
g
th
e
d
is
co
v
er
y
o
f
d
iv
e
r
s
e
r
eg
io
n
s
in
t
h
e
s
o
lu
tio
n
s
p
ac
e.
Ack
n
o
wled
g
in
g
th
at
d
iv
is
io
n
an
d
m
u
ltip
licatio
n
o
p
er
ato
r
s
p
o
s
s
ess
h
ig
h
d
is
p
er
s
io
n
ch
ar
ac
t
er
is
tics
—
wh
ich
ca
n
h
in
d
er
th
e
al
g
o
r
it
h
m
’
s
ab
ilit
y
to
c
o
n
v
e
r
g
e
to
war
d
th
e
o
p
tim
al
s
o
lu
tio
n
in
later
s
tag
es
—
AOA
s
tr
ateg
ically
u
tili
ze
s
s
u
b
tr
ac
ti
o
n
an
d
ad
d
itio
n
o
p
e
r
atio
n
s
t
o
en
h
a
n
ce
th
e
ex
p
lo
itatio
n
p
h
ase.
T
h
is
lo
ca
lized
s
ea
r
ch
p
r
o
ce
s
s
is
g
o
v
er
n
ed
b
y
(
9
)
an
d
(
1
0
)
.
,
=
(
)
−
×
(
(
−
)
+
)
,
3
>
0
.
5
(
9
)
,
=
(
)
+
×
(
(
−
)
+
)
,
ℎ
(
1
0
)
Her
e,
3
r
ep
r
esen
ts
a
r
an
d
o
m
ly
g
en
er
ated
n
u
m
b
er
with
in
th
e
r
an
g
e
[
0
,
1
]
.
I
f
3
<
0
.
5
,
th
e
s
u
b
tr
ac
tio
n
o
p
er
ato
r
is
ap
p
lied
d
u
r
in
g
th
e
ex
p
lo
itatio
n
p
h
ase;
o
th
er
wis
e,
th
e
ad
d
i
tio
n
o
p
er
ato
r
is
u
s
ed
.
T
h
ese
o
p
er
ato
r
s
in
tr
o
d
u
ce
o
n
ly
m
i
n
o
r
ad
ju
s
tm
en
ts
to
th
e
s
o
lu
tio
n
’
s
p
o
s
itio
n
,
allo
win
g
th
e
al
g
o
r
ith
m
to
m
ain
tain
f
o
cu
s
o
n
p
r
o
m
is
in
g
r
eg
io
n
s
o
f
th
e
s
ea
r
ch
s
p
ac
e
a
n
d
r
ed
u
ci
n
g
th
e
r
is
k
o
f
d
r
if
tin
g
awa
y
f
r
o
m
p
o
ten
tial o
p
tim
a.
4.
F
L
E
X
I
B
L
E
M
AN
I
P
UL
AT
O
R
SYST
E
M
A
m
an
ip
u
lato
r
is
a
m
ec
h
an
ic
al
ass
em
b
ly
co
n
s
is
tin
g
o
f
m
u
ltip
le
in
ter
co
n
n
ec
ted
lin
k
s
,
d
e
s
ig
n
ed
to
ex
ec
u
te
a
d
iv
er
s
e
ar
r
ay
o
f
t
ask
s
ac
r
o
s
s
d
if
f
er
en
t
ap
p
lica
tio
n
f
ield
s
[
1
8
]
.
I
ts
s
eg
m
en
t
ed
s
tr
u
ctu
r
e
d
r
aws
in
s
p
ir
atio
n
f
r
o
m
th
e
v
er
s
atility
an
d
p
r
ec
is
io
n
o
f
th
e
h
u
m
a
n
ar
m
,
wh
ich
en
ab
les
co
m
p
l
ex
an
d
co
o
r
d
in
ated
m
o
tio
n
.
T
r
ad
itio
n
al
m
an
i
p
u
lat
o
r
d
esig
n
s
em
p
h
asize
h
ig
h
s
tr
u
ctu
r
al
s
tiff
n
ess
to
r
ed
u
ce
s
y
s
tem
v
ib
r
atio
n
s
an
d
en
h
an
ce
p
o
s
itio
n
al
ac
c
u
r
ac
y
[
1
9
]
.
T
h
is
r
i
g
id
ity
is
ty
p
ically
ac
h
iev
e
d
th
r
o
u
g
h
th
e
u
s
e
o
f
d
e
n
s
e
an
d
h
ea
v
y
m
ater
ials
.
W
h
ile
ef
f
ec
tiv
e
in
d
am
p
in
g
o
s
cillatio
n
s
,
th
is
ap
p
r
o
ac
h
in
tr
o
d
u
ce
s
s
ig
n
if
ican
t
d
r
awb
ac
k
s
,
in
clu
d
in
g
in
cr
ea
s
ed
s
y
s
tem
weig
h
t,
lim
i
ted
m
an
e
u
v
er
a
b
ilit
y
,
th
e
n
ec
e
s
s
ity
f
o
r
lar
g
er
ac
tu
ato
r
s
,
h
ig
h
er
en
er
g
y
d
em
a
n
d
s
,
an
d
elev
ated
o
p
er
atio
n
al
co
s
ts
[
2
0
]
.
T
o
m
itig
ate
th
ese
i
s
s
u
es,
th
e
FMS
h
as
em
er
g
ed
as
a
p
r
o
m
is
in
g
alter
n
ativ
e.
An
FMS
g
en
er
ally
co
m
p
r
is
es
k
ey
c
o
m
p
o
n
en
ts
s
u
ch
as
a
s
tr
ain
g
au
g
e
,
s
h
af
t
en
co
d
er
,
ac
ce
ler
o
m
eter
,
tach
o
g
en
er
ato
r
,
r
ed
u
ctio
n
g
ea
r
b
o
x
,
an
d
d
ir
ec
t
cu
r
r
en
t
(
DC
)
m
o
t
o
r
[
2
1
]
.
I
n
co
m
p
ar
is
o
n
to
r
ig
id
m
an
ip
u
lato
r
s
,
FMSs
o
f
f
er
s
ev
er
al
b
en
ef
its
:
lig
h
ter
o
v
er
all
weig
h
t,
im
p
r
o
v
e
d
m
o
b
ilit
y
,
s
m
aller
ac
tu
ato
r
s
ize,
lo
wer
p
o
wer
c
o
n
s
u
m
p
tio
n
,
r
ed
u
ce
d
m
a
n
u
f
ac
tu
r
in
g
c
o
s
ts
,
a
h
ig
h
er
p
ay
lo
ad
-
to
-
weig
h
t
r
atio
,
an
d
en
h
an
ce
d
s
af
ety
,
p
ar
ticu
lar
l
y
in
co
llab
o
r
ativ
e
en
v
i
r
o
n
m
e
n
ts
in
v
o
l
v
in
g
h
u
m
an
i
n
ter
ac
tio
n
[
2
1
]
.
H
o
wev
er
,
d
u
e
to
th
eir
in
h
er
en
tly
lig
h
tweig
h
t
an
d
c
o
m
p
lian
t
s
tr
u
ctu
r
e,
FMSs
ar
e
m
o
r
e
p
r
o
n
e
to
v
ib
r
atio
n
s
wh
en
s
u
b
jecte
d
t
o
ex
ter
n
al
f
o
r
ce
s
o
r
d
is
tu
r
b
an
ce
s
[
2
2
]
.
T
h
ese
o
s
cillatio
n
s
ca
n
co
m
p
r
o
m
is
e
th
e
s
y
s
tem
’
s
p
r
ec
is
io
n
an
d
co
n
tr
o
l
ac
cu
r
ac
y
.
T
o
ad
d
r
ess
th
is
c
h
allen
g
e,
n
u
m
er
o
u
s
co
n
tr
o
l
tech
n
iq
u
es
h
av
e
b
ee
n
in
v
esti
g
ated
to
s
u
p
p
r
ess
v
ib
r
atio
n
s
in
FMSs
.
Am
o
n
g
th
e
m
o
s
t
n
o
ta
b
le
ar
e
t
h
e
p
r
o
p
o
r
tio
n
al
-
i
n
teg
r
al
-
d
e
r
iv
ativ
e
(
PID
)
co
n
tr
o
l
[
2
3
]
,
n
o
n
lin
ea
r
a
d
ap
tiv
e
co
n
t
r
o
l
[
2
4
]
,
tim
e
-
d
elay
c
o
n
tr
o
l
[
2
5
]
,
l
in
ea
r
q
u
ad
r
atic
r
eg
u
lato
r
(
L
Q
R
)
[
2
6
]
,
an
d
i
n
p
u
t
s
h
ap
in
g
[
2
7
]
.
Of
th
ese,
PID
c
o
n
tr
o
l
r
e
m
ain
s
th
e
m
o
s
t
co
m
m
o
n
ly
em
p
lo
y
e
d
d
u
e
to
its
ea
s
e
o
f
im
p
lem
en
tatio
n
an
d
r
o
b
u
s
t
p
er
f
o
r
m
an
ce
.
I
n
th
e
p
r
esen
t
s
tu
d
y
,
b
o
th
th
e
m
o
d
if
ied
o
p
tim
izatio
n
alg
o
r
ith
m
an
d
th
e
s
tan
d
ar
d
AB
C
alg
o
r
ith
m
ar
e
ap
p
lied
to
f
in
e
-
tu
n
e
th
e
PID
co
n
tr
o
ller
p
ar
am
eter
s
f
o
r
th
e
FMS
,
as
illu
s
tr
ated
in
Fig
u
r
e
1
.
Fig
u
r
e
1
(
a)
d
ep
icts
th
e
s
ch
em
atic
d
iag
r
am
o
f
th
e
s
in
g
le
-
lin
k
f
lex
ib
le
m
an
ip
u
lato
r
,
wh
ile
Fig
u
r
e
1
(
b
)
s
h
o
ws
th
e
co
n
tr
o
l sy
s
tem
ar
c
h
itectu
r
e
u
s
ed
f
o
r
th
e
FMS.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
9
3
8
I
n
t J Ar
tif
I
n
tell
,
Vo
l.
14
,
No
.
3
,
Octo
b
er
20
25
:
3
7
9
0
-
3
8
0
1
3794
(
a)
(
b
)
Fig
u
r
e
1
.
Flex
ib
le
m
a
n
ip
u
lato
r
s
y
s
tem
: (
a)
s
in
g
le
lin
k
m
an
i
p
u
lato
r
s
y
s
tem
[
2
5
]
an
d
(
b
)
FMS b
lo
ck
d
iag
r
am
5.
ARIT
H
M
E
T
I
C
ART
I
F
I
C
I
A
L
B
E
E
CO
L
O
NY
AL
G
O
R
I
T
H
M
T
h
e
AABC
a
lg
o
r
ith
m
wa
s
d
ev
elo
p
ed
b
y
in
teg
r
atin
g
th
e
A
OA
in
to
th
e
f
r
am
ewo
r
k
o
f
th
e
o
r
ig
in
al
AB
C
alg
o
r
ith
m
.
T
h
is
h
y
b
r
id
i
za
tio
n
is
m
o
tiv
ated
b
y
th
e
n
ee
d
to
o
v
er
co
m
e
s
ev
er
al
k
ey
lim
itatio
n
s
o
f
th
e
co
n
v
en
tio
n
al
AB
C
a
lg
o
r
ith
m
,
in
clu
d
in
g
its
in
ad
eq
u
ate
e
x
p
lo
r
atio
n
ca
p
ab
ilit
y
,
s
lo
w
co
n
v
er
g
en
ce
s
p
ee
d
,
ten
d
en
cy
to
b
ec
o
m
e
tr
ap
p
ed
in
lo
ca
l
o
p
tim
a,
an
d
wea
k
ex
p
lo
itatio
n
p
er
f
o
r
m
a
n
ce
.
I
n
th
e
s
tan
d
ar
d
AB
C
alg
o
r
ith
m
,
o
n
l
y
o
n
e
em
p
lo
y
ed
b
ee
is
r
esp
o
n
s
ib
le
f
o
r
d
is
co
v
er
in
g
a
p
o
ten
tial
s
o
lu
tio
n
,
wh
ich
is
th
en
co
m
m
u
n
icate
d
to
th
e
o
n
l
o
o
k
e
r
b
ee
s
.
T
h
e
s
ea
r
ch
m
o
v
em
e
n
t
is
co
n
tr
o
lled
b
y
(
2
)
,
wh
ich
r
e
lies
o
n
a
r
a
n
d
o
m
l
y
ch
o
s
en
s
o
lu
tio
n
as
a
r
ef
er
e
n
ce
p
o
in
t.
H
o
wev
er
,
t
h
e
ab
s
en
ce
o
f
a
g
u
id
in
g
m
ec
h
a
n
is
m
in
th
i
s
p
r
o
ce
s
s
r
esu
lts
in
er
r
atic
ex
p
lo
r
atio
n
,
h
in
d
e
r
in
g
th
e
alg
o
r
ith
m
’
s
ab
ilit
y
to
ef
f
ec
tiv
ely
f
o
c
u
s
o
n
p
r
o
m
is
in
g
r
eg
io
n
s
a
n
d
th
u
s
s
lo
win
g
d
o
wn
c
o
n
v
er
g
en
ce
.
Fu
r
th
er
m
o
r
e
,
with
o
u
t
a
s
tr
u
ctu
r
ed
s
elec
tio
n
ap
p
r
o
ac
h
,
th
e
alg
o
r
ith
m
h
as
an
eq
u
al
p
r
o
b
ab
ilit
y
o
f
ch
o
o
s
in
g
eith
e
r
th
e
b
est
o
r
wo
r
s
t
r
ef
er
en
ce
s
o
lu
tio
n
s
,
r
ed
u
ci
n
g
its
ef
f
ec
tiv
en
ess
in
c
o
n
v
e
r
g
in
g
to
war
d
o
p
tim
al
s
o
lu
tio
n
s
an
d
in
cr
ea
s
in
g
th
e
li
k
elih
o
o
d
o
f
b
ec
o
m
in
g
tr
a
p
p
ed
in
lo
ca
l
o
p
tim
a.
T
h
e
u
s
e
o
f
th
e
ad
d
itio
n
o
p
e
r
ato
r
in
(
2
)
also
lim
its
th
e
s
tep
s
ize
o
f
t
h
e
s
ea
r
ch
ag
en
ts
,
t
h
er
eb
y
r
estrictin
g
t
h
eir
ca
p
ac
ity
to
ex
p
lo
r
e
d
is
tan
t
o
r
b
o
u
n
d
ar
y
r
eg
io
n
s
o
f
th
e
s
ea
r
ch
s
p
ac
e.
T
h
is
lim
itatio
n
d
i
m
in
is
h
es
th
e
alg
o
r
ith
m
’
s
ex
p
lo
r
ato
r
y
s
tr
en
g
th
.
I
n
ter
m
s
o
f
ex
p
lo
itatio
n
,
th
e
o
r
i
g
in
al
AB
C
alg
o
r
ith
m
lack
s
a
m
ec
h
an
is
m
to
ad
ap
tiv
el
y
co
n
tr
o
l
th
e
s
tep
s
ize,
wh
ich
ca
n
lead
to
in
ef
f
icien
t
lo
ca
l
s
ea
r
ch
es
an
d
m
is
s
ed
o
p
p
o
r
tu
n
ities
in
p
r
o
m
is
in
g
ar
ea
s
.
Ad
d
itio
n
ally
,
th
e
alg
o
r
ith
m
ex
h
ib
its
a
n
im
b
ala
n
ce
b
etwe
en
ex
p
lo
r
atio
n
an
d
ex
p
lo
itatio
n
a
g
en
ts
,
with
a
g
r
ea
ter
e
m
p
h
asis
o
n
ex
p
lo
r
atio
n
(
em
p
lo
y
ed
an
d
s
co
u
t
b
ee
s
)
co
m
p
a
r
ed
to
ex
p
lo
itatio
n
(
o
n
lo
o
k
er
b
e
es),
f
u
r
th
e
r
wea
k
en
in
g
its
lo
ca
l
s
ea
r
ch
p
er
f
o
r
m
an
ce
.
T
o
ad
d
r
ess
th
e
lim
itatio
n
s
o
f
t
h
e
o
r
ig
in
al
AB
C
alg
o
r
ith
m
,
s
ev
er
al
en
h
a
n
ce
m
en
t
s
tr
ateg
ies
h
av
e
b
ee
n
in
tr
o
d
u
ce
d
in
th
e
p
r
o
p
o
s
ed
AABC
a
lg
o
r
ith
m
.
I
n
th
is
im
p
r
o
v
ed
v
e
r
s
io
n
,
th
e
ex
p
lo
r
atio
n
p
h
ase
tr
ad
itio
n
all
y
p
er
f
o
r
m
ed
b
y
th
e
em
p
lo
y
e
d
b
ee
s
in
AB
C
is
r
ep
lace
d
with
t
h
e
ex
p
lo
r
atio
n
m
ec
h
a
n
is
m
s
f
r
o
m
th
e
AOA.
T
h
is
s
u
b
s
titu
tio
n
lev
er
ag
es
AOA’
s
s
tr
o
n
g
ex
p
lo
r
ato
r
y
ca
p
ab
i
liti
es
th
r
o
u
g
h
its
d
iv
is
io
n
an
d
m
u
ltip
licatio
n
o
p
er
ato
r
s
,
e
n
ab
lin
g
a
d
u
al
-
m
o
d
e
s
ea
r
ch
th
at
en
h
a
n
ce
s
s
o
lu
tio
n
d
i
v
er
s
ity
.
Ad
d
itio
n
ally
,
th
e
o
n
lo
o
k
er
b
ee
p
h
ase
is
s
p
lit
in
to
two
d
is
tin
ct
s
tag
es.
T
h
e
f
ir
s
t
s
tag
e,
r
e
f
er
r
ed
to
as
th
e
b
ar
o
n
o
n
lo
o
k
er
b
ee
p
h
ase,
ad
o
p
ts
AOA’
s
ex
p
lo
itatio
n
s
tr
ateg
ies,
u
tili
zin
g
ad
d
itio
n
a
n
d
s
u
b
tr
ac
tio
n
o
p
er
ato
r
s
to
allo
w
b
id
ir
ec
tio
n
a
l
s
ea
r
ch
m
o
v
em
en
t.
T
h
e
s
ec
o
n
d
s
tag
e,
ter
m
ed
th
e
d
u
k
e
o
n
lo
o
k
er
b
ee
p
h
ase,
ap
p
lies
a
m
o
d
if
ie
d
v
er
s
io
n
o
f
th
e
s
tan
d
ar
d
o
n
lo
o
k
e
r
b
ee
eq
u
atio
n
,
as d
etailed
in
(
1
1
)
.
,
=
(
)
+
(
−
1
,
1
)
(
,
−
,
)
(
1
1
)
T
h
e
b
est
-
so
-
f
ar
s
o
l
u
tio
n
,
d
en
o
ted
as
(
)
,
is
u
tili
ze
d
as
th
e
r
ef
er
en
ce
p
o
in
t
f
o
r
th
e
s
ea
r
c
h
p
r
o
ce
s
s
with
in
th
e
jjj
-
th
d
im
e
n
s
io
n
.
T
o
en
h
an
ce
th
e
ac
cu
r
a
cy
o
f
th
e
ex
p
l
o
itatio
n
p
h
ase,
a
s
tep
s
ize
co
n
tr
o
l
p
ar
am
eter
,
,
is
in
tr
o
d
u
ce
d
.
T
h
is
p
ar
am
eter
g
o
v
e
r
n
s
th
e
m
ag
n
itu
d
e
o
f
p
o
s
itio
n
al
u
p
d
ate
s
n
ea
r
th
e
o
p
tim
al
s
o
lu
tio
n
,
th
er
e
b
y
im
p
r
o
v
in
g
lo
ca
l sear
ch
r
ef
in
em
e
n
t.
T
h
e
v
al
u
e
o
f
is
co
m
p
u
ted
u
s
in
g
(
1
2
)
.
(
)
=
1
(
1
−
(
−
)
)
(
1
2
)
W
h
er
e
(
)
r
ep
r
esen
ts
th
e
s
tep
s
ize
co
ef
f
icien
t
at
th
e
cu
r
r
en
t
iter
a
tio
n
,
with
t
h
e
s
tep
s
ize
v
alu
e
d
ec
r
ea
s
in
g
ex
p
o
n
e
n
tially
as
th
e
iter
atio
n
n
u
m
b
er
s
in
cr
ea
s
e.
T
h
e
s
elec
tio
n
o
f
th
e
ex
p
o
n
e
n
tial
f
u
n
ctio
n
f
o
r
th
e
s
tep
s
ize
p
ar
am
eter
is
m
o
tiv
ated
b
y
its
h
ig
h
r
ate
o
f
c
h
an
g
e.
T
h
e
b
ar
o
n
o
n
l
o
o
k
e
r
b
ee
ev
alu
ate
s
f
ea
s
ib
le
s
o
lu
tio
n
s
with
o
u
t
u
s
in
g
a
p
r
o
b
ab
ilit
y
eq
u
atio
n
,
wh
ile
th
e
d
u
k
e
o
n
lo
o
k
er
b
ee
'
s
ev
alu
atio
n
o
f
f
e
asib
le
s
o
lu
tio
n
s
is
d
eter
m
in
ed
b
y
th
e
p
r
o
b
ab
ilit
y
v
alu
e
ca
lcu
lated
u
s
in
g
(
4
)
.
T
h
e
d
u
k
e
o
n
l
o
o
k
er
b
ee
o
n
ly
ev
alu
ates
th
e
h
ig
h
est
-
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ar
tif
I
n
tell
I
SS
N:
2252
-
8
9
3
8
A
r
ith
metic
a
r
tifi
cia
l b
ee
co
lo
n
y
o
p
timiz
a
tio
n
a
lg
o
r
ith
m
w
ith
flexib
le
ma
n
ip
u
la
to
r
…
(
Mo
h
d
R
u
z
a
in
i H
a
s
h
im
)
3795
q
u
ality
f
o
o
d
b
ased
o
n
th
e
p
r
o
b
ab
ilit
y
o
f
th
e
f
o
o
d
.
T
h
e
o
n
l
o
o
k
er
b
ee
p
h
ase
in
th
e
p
r
o
p
o
s
ed
AAB
C
alg
o
r
ith
m
is
d
iv
id
ed
i
n
to
two
ca
teg
o
r
ies
—
b
ar
o
n
an
d
d
u
k
e
o
n
lo
o
k
er
b
ee
s
—
to
f
u
r
th
er
s
tr
en
g
th
e
n
its
ex
p
lo
itatio
n
ca
p
ab
ilit
y
.
T
o
en
s
u
r
e
d
iv
er
s
ity
in
th
e
s
ea
r
ch
p
r
o
ce
s
s
,
th
e
o
r
ig
in
al
s
co
u
t
b
ee
eq
u
atio
n
f
r
o
m
th
e
AB
C
alg
o
r
ith
m
is
r
etain
e
d
in
AABC
f
o
r
g
en
er
atin
g
n
ew
f
ea
s
ib
le
s
o
lu
tio
n
s
o
n
ce
th
e
cu
r
r
en
t
s
o
lu
tio
n
h
as
b
ee
n
f
u
lly
ex
p
lo
ited
.
B
o
th
th
e
ex
p
lo
r
atio
n
an
d
ex
p
lo
itatio
n
p
h
ases
in
AABC
ar
e
g
u
id
ed
b
y
th
e
b
est
s
o
lu
tio
n
id
en
tifie
d
s
o
f
ar
,
wh
ich
s
er
v
es
as
a
r
ef
e
r
en
ce
p
o
in
t
to
d
ir
ec
t
th
e
s
ea
r
ch
to
war
d
th
e
g
lo
b
al
o
p
tim
u
m
.
Mo
r
eo
v
e
r
,
t
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
m
ain
tain
s
an
eq
u
al
n
u
m
b
er
o
f
ex
p
lo
r
atio
n
an
d
ex
p
lo
itati
o
n
ag
e
n
ts
,
th
er
eb
y
ac
h
iev
i
n
g
a
b
alan
ce
d
s
ea
r
ch
p
r
o
ce
s
s
.
T
h
e
o
v
e
r
all
s
tep
s
o
f
th
e
AABC
alg
o
r
ith
m
ar
e
illu
s
t
r
ated
in
Fig
u
r
e
1
,
wh
ile
its
d
etailed
f
r
am
ewo
r
k
is
p
r
esen
ted
in
Alg
o
r
ith
m
1
.
Alg
o
r
ith
m
1
: A
r
ith
m
etic
ar
tific
ial
b
ee
co
lo
n
y
alg
o
r
it
h
m
1:
Initialize population FS using (1)
2:
Evaluate fitness of each candidate solution using (3)
3:
Identify best solution so far
4:
Compute MOA and MOP using (5) and (8)
5:
Set iteration counter C_iter ← 0
6:
while C_iter < M_iter do
7:
Generate random numbers r1, r2, r3
8:
for each candidate solution in FS do
9:
if r1 > MOA then
10:
if r2 > 0.5 then
11:
Update solution using Equation (6)
12:
else
13:
Update solution using Equation (7)
14:
end if
15:
else
16:
if r3 > 0.5 then
17:
Update solution using Equation (9)
18:
else
19:
Update solution using Equation (10)
20:
end if
21:
Evaluate fitness of updated solution
22:
Apply greedy selection
23:
Memorize best solution
24:
trial_iter ← trial_iter + 1
25:
end if
26:
end for
27:
Calculate selection probability Pi using Equation (4)
28:
Set iter ← 1, t ← 0
29:
while t < FS do
30:
if rand() < Pi then
31:
Update step size using Equation (12)
32:
Update solution using Equation (11)
33:
Evaluate fitness of updated solution
34:
Apply greedy selection
35:
Memorize best solution
36:
trial_iter ← trial_iter + 1
37:
t ← t + 1
38:
end if
39:
if trial_iter > limit then
40:
Replace solution using Equation (1)
41:
end if
42:
Memorize best solution
43:
C_iter ← C_iter + 1
44:
end while
45:
end while
46:
Return best solution found
6.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
p
r
o
p
o
s
ed
AABC
a
lg
o
r
ith
m
is
co
m
p
r
eh
en
s
iv
ely
ev
alu
at
ed
b
y
co
n
d
u
ctin
g
ex
p
er
im
en
ts
u
s
in
g
f
iv
e
wid
ely
r
ec
o
g
n
ized
b
en
c
h
m
ar
k
f
u
n
ctio
n
s
,
ea
c
h
f
ea
tu
r
in
g
d
is
tin
ct
an
d
d
iv
er
s
e
lan
d
s
ca
p
e
ch
ar
ac
ter
is
tics
as
r
ef
er
en
ce
d
in
[
2
8
]
.
A
d
d
itio
n
al
ly
,
th
e
alg
o
r
ith
m
is
ap
p
lied
to
a
r
ea
l
-
w
o
r
ld
a
p
p
licatio
n
in
v
o
lv
in
g
a
s
in
g
le
-
lin
k
m
an
ip
u
lato
r
s
y
s
tem
,
as
d
etail
ed
in
[
1
8
]
.
T
h
e
p
r
im
ar
y
o
b
jectiv
e
o
f
th
ese
ex
p
er
im
en
ts
is
t
o
th
o
r
o
u
g
h
ly
ass
ess
th
e
alg
o
r
ith
m
'
s
p
er
f
o
r
m
an
ce
in
ter
m
s
o
f
its
co
n
v
er
g
en
ce
s
p
ee
d
,
r
o
b
u
s
tn
ess
ag
ain
s
t
v
ar
iatio
n
s
in
in
p
u
t
o
r
co
n
d
itio
n
s
,
an
d
o
v
er
all
ac
cu
r
a
cy
in
r
ea
ch
i
n
g
o
p
tim
al
s
o
lu
tio
n
s
.
6
.
1
.
A
rit
hm
e
t
ic
a
rt
if
icia
l bee
co
lo
ny
ev
a
lua
t
io
n us
ing
ben
chm
a
rk
f
un
ct
io
ns
T
o
ass
ess
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
p
r
o
p
o
s
ed
AABC
alg
o
r
ith
m
,
a
s
et
o
f
f
iv
e
wid
ely
r
ec
o
g
n
ized
b
en
ch
m
ar
k
f
u
n
ctio
n
s
is
em
p
lo
y
ed
—
th
ese
f
u
n
ctio
n
s
ar
e
c
o
m
m
o
n
ly
u
tili
ze
d
in
o
p
tim
izatio
n
r
esear
ch
[
2
8
]
.
T
h
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
9
3
8
I
n
t J Ar
tif
I
n
tell
,
Vo
l.
14
,
No
.
3
,
Octo
b
er
20
25
:
3
7
9
0
-
3
8
0
1
3796
alg
o
r
ith
m
is
test
ed
o
n
b
o
th
1
0
-
d
im
e
n
s
io
n
al
an
d
1
0
0
-
d
i
m
en
s
io
n
al
v
er
s
io
n
s
o
f
th
e
b
en
ch
m
ar
k
f
u
n
ctio
n
s
to
ev
alu
ate
its
s
ca
lab
ili
ty
an
d
ef
f
ec
tiv
en
ess
.
Fo
r
th
is
ex
p
er
im
en
t,
th
e
p
o
p
u
latio
n
s
ize
is
s
et
to
8
0
,
with
a
tr
ial
lim
it
o
f
5
0
,
an
d
t
h
e
s
to
p
p
in
g
c
o
n
d
itio
n
is
d
ef
in
e
d
as
a
m
ax
im
u
m
o
f
3
,
0
0
0
cy
cles.
T
h
e
co
m
p
ar
ativ
e
r
esu
lts
f
o
r
b
o
th
th
e
o
r
ig
in
al
AB
C
alg
o
r
it
h
m
an
d
th
e
p
r
o
p
o
s
ed
AABC
alg
o
r
ith
m
ac
r
o
s
s
th
e
1
0
D
an
d
1
0
0
D
test
ca
s
es
ar
e
s
u
m
m
ar
ized
in
T
a
b
le
1
.
T
ab
le
1
.
C
o
m
p
a
r
is
o
n
o
f
r
esu
lts
o
b
tain
ed
b
y
AB
C
an
d
AAB
C
o
n
b
en
ch
m
ar
k
p
r
o
b
lem
s
with
1
0
a
n
d
100
-
d
im
en
s
io
n
s
F
u
n
c
t
i
o
n
A
l
g
o
r
i
t
h
m
1
0
D
i
m
e
n
s
i
o
n
1
0
0
D
i
me
n
si
o
n
A
v
e
r
a
g
e
S
TD
A
v
e
r
a
g
e
S
TD
F
1
S
p
h
e
r
e
A
B
C
8
.
4
4
E
-
17
1
.
8
5
E
-
17
1
.
2
0
E
-
11
1
.
0
2
E
-
11
A
A
B
C
0
0
5
.
0
3
E
-
15
1
.
0
3
E
-
14
F
2
A
c
k
l
e
y
A
B
C
9
.
4
1
E
-
15
2
.
5
7
E
-
15
7
.
1
1
E
-
05
3
.
2
5
E
-
05
A
A
B
C
8
.
8
8
E
-
16
8
.
8
8
E
-
16
1
.
5
8
E
-
13
5
.
3
2
E
-
14
F
3
R
o
s
e
n
b
r
o
c
k
A
B
C
2
.
6
4
E
-
02
1
.
8
0
E
-
02
2
.
1
1
E+
0
0
1
.
5
8
E+
0
0
A
A
B
C
2
.
4
5
E
-
03
2
.
7
8
E
-
03
1
.
4
8
E+
0
2
6
.
6
2
E+
0
1
F
4
G
r
i
e
w
a
n
k
A
B
C
1
.
4
8
E
-
11
5
.
8
1
E
-
11
2
.
4
7
E
-
07
1
.
1
0
E
-
06
A
A
B
C
0
.
0
0
E+
0
0
0
.
0
0
E+
0
0
2
.
3
4
E
-
15
2
.
6
0
E
-
15
F
5
R
a
st
r
i
g
i
n
A
B
C
0
.
0
0
E+
0
0
0
.
0
0
E+
0
0
3
.
4
0
E+
0
0
1
.
9
1
E+
0
0
A
A
B
C
0
.
0
0
E+
0
0
0
.
0
0
E+
0
0
5
.
0
0
E
-
12
7
.
5
9
E
-
12
T
h
e
tab
les
p
r
esen
t
th
e
b
est,
av
er
ag
e,
m
ed
ian
,
wo
r
s
t,
an
d
s
tan
d
ar
d
d
ev
iatio
n
v
alu
es
o
f
th
e
b
en
ch
m
ar
k
f
u
n
ctio
n
s
ac
r
o
s
s
3
0
in
d
ep
e
n
d
en
t
r
u
n
s
.
Valu
es
th
at
s
h
o
w
s
u
p
er
io
r
p
er
f
o
r
m
an
ce
f
o
r
ei
th
er
alg
o
r
ith
m
ar
e
h
ig
h
lig
h
ted
in
b
o
ld
.
T
h
e
b
en
ch
m
ar
k
s
et
in
clu
d
es
f
u
n
ctio
n
s
F1
an
d
F3
,
wh
ich
ar
e
u
n
im
o
d
al
with
a
s
in
g
le
g
lo
b
al
m
in
im
u
m
.
T
h
ese
f
u
n
ctio
n
s
ar
e
s
p
ec
if
ically
d
esig
n
ed
to
ev
alu
ate
t
h
e
alg
o
r
ith
m
s
’
ex
p
lo
itatio
n
ca
p
ab
ilit
ies an
d
co
n
v
er
g
en
ce
s
p
ee
d
.
T
ab
le
2
d
em
o
n
s
tr
ates
th
at
th
e
AABC
alg
o
r
ith
m
o
u
tp
er
f
o
r
m
s
th
e
o
r
ig
in
al
AB
C
alg
o
r
ith
m
o
n
th
e
F1
b
en
ch
m
ar
k
f
u
n
ctio
n
.
AABC
s
u
cc
es
s
f
u
lly
r
ea
ch
es
th
e
g
l
o
b
al
m
in
im
u
m
o
f
F1
(
i.e
.
,
0
)
,
co
n
s
is
ten
tly
ac
r
o
s
s
m
u
ltip
le
r
u
n
s
.
T
h
is
s
u
p
er
io
r
p
er
f
o
r
m
a
n
ce
is
also
o
b
s
er
v
ed
i
n
th
e
3
0
-
d
im
en
s
io
n
al
v
er
s
io
n
o
f
F1
,
wh
er
e
AABC
ac
h
iev
es
b
etter
av
er
ag
e
an
d
wo
r
s
t
-
ca
s
e
r
esu
lts
co
m
p
ar
ed
to
th
e
o
r
ig
in
al
AB
C
.
Fu
r
th
er
m
o
r
e,
AABC
ex
h
ib
its
g
r
ea
ter
s
tab
ilit
y
,
as
in
d
icate
d
b
y
its
lo
wer
s
tan
d
ar
d
d
ev
iatio
n
.
T
h
is
im
p
r
o
v
em
e
n
t
in
ex
p
lo
i
tatio
n
p
r
ec
is
io
n
ca
n
b
e
attr
ib
u
te
d
to
th
e
s
tep
s
ize
co
n
tr
o
l
m
ec
h
an
is
m
em
b
ed
d
ed
in
th
e
d
u
k
e
o
n
lo
o
k
er
b
ee
p
h
ase.
Fo
r
t
h
e
F3
b
en
ch
m
ar
k
f
u
n
cti
o
n
,
AABC
s
u
r
p
ass
es
A
B
C
in
th
e
1
0
-
d
im
en
s
io
n
al
ca
s
e,
d
eliv
er
in
g
a
b
etter
av
er
ag
e
p
er
f
o
r
m
an
ce
.
T
h
e
i
m
p
r
o
v
e
d
r
e
s
u
l
ts
c
a
n
b
e
li
n
k
e
d
t
o
t
h
e
r
el
a
t
i
v
e
l
y
l
o
w
c
o
m
p
l
e
x
it
y
o
f
t
h
e
p
r
o
b
l
e
m
i
n
l
o
w
e
r
d
i
m
e
n
s
i
o
n
s
,
w
h
i
c
h
m
a
k
e
s
i
t
ea
s
i
e
r
f
o
r
a
l
g
o
r
i
t
h
m
s
t
o
c
o
n
v
e
r
g
e
t
o
o
p
t
i
m
al
s
o
l
u
t
i
o
n
s
.
H
o
w
ev
e
r
,
a
s
t
h
e
p
r
o
b
l
e
m
d
i
m
e
n
s
i
o
n
i
n
c
r
e
as
e
s
,
t
h
e
c
o
m
p
l
e
x
i
t
y
g
r
o
w
s
—
d
u
e
t
o
t
r
a
n
s
f
o
r
m
a
t
i
o
n
s
s
u
c
h
as
r
o
t
a
t
i
o
n
a
n
d
c
o
n
v
o
l
u
t
i
o
n
—
m
a
k
i
n
g
i
t
m
o
r
e
c
h
a
l
l
e
n
g
i
n
g
.
I
n
th
e
1
0
0
-
d
im
en
s
io
n
al
F3
f
u
n
ctio
n
,
A
B
C
o
u
tp
er
f
o
r
m
s
AABC
.
T
h
e
d
ec
lin
e
in
AABC
’
s
p
er
f
o
r
m
an
ce
at
h
ig
h
er
d
im
en
s
io
n
s
is
p
r
im
ar
ily
d
u
e
to
its
ex
p
lo
itatio
n
m
ec
h
an
is
m
,
wh
ich
u
s
es
th
e
g
lo
b
al
b
est
s
o
lu
tio
n
as
a
r
ef
er
en
ce
p
o
in
t.
W
h
ile
th
is
ap
p
r
o
ac
h
ef
f
ec
tiv
el
y
g
u
id
es
th
e
s
ea
r
ch
t
o
war
d
p
r
o
m
is
in
g
r
eg
i
o
n
s
,
it
also
r
ed
u
ce
s
p
o
p
u
latio
n
d
iv
e
r
s
ity
.
T
h
is
lo
s
s
in
d
iv
e
r
s
ity
is
f
u
r
th
er
ex
ac
e
r
b
ated
b
y
th
e
r
o
u
le
tte
wh
ee
l
s
elec
tio
n
m
ec
h
an
is
m
,
wh
ich
ten
d
s
to
f
av
o
r
‘
s
u
p
er
in
d
iv
i
d
u
als’
—
i.e
.
,
h
ig
h
ly
f
it
s
o
lu
ti
o
n
s
—
ca
u
s
in
g
th
e
s
ea
r
ch
to
co
n
v
er
g
e
p
r
em
at
u
r
ely
ar
o
u
n
d
lim
ited
ar
ea
s
o
f
th
e
s
o
lu
tio
n
s
p
ac
e.
I
n
co
n
t
r
ast,
th
e
AB
C
alg
o
r
ith
m
,
d
esp
ite
u
s
in
g
th
e
s
am
e
s
elec
tio
n
s
tr
a
teg
y
,
m
ain
tain
s
g
r
ea
ter
d
i
v
er
s
ity
b
y
r
ef
e
r
en
cin
g
r
an
d
o
m
ly
s
elec
ted
s
o
lu
tio
n
s
d
u
r
in
g
th
e
s
ea
r
ch
p
r
o
ce
s
s
,
wh
i
ch
co
n
tr
ib
u
tes to
its
b
etter
p
er
f
o
r
m
an
ce
in
h
ig
h
-
d
im
en
s
io
n
al
p
r
o
b
lem
s
.
T
ab
le
2
.
Sta
tis
tical
r
esu
lts
o
f
W
ilco
x
o
n
s
ig
n
ed
-
r
a
n
k
test
f
o
r
1
0
-
an
d
1
0
0
-
d
im
en
s
io
n
al
b
e
n
c
h
m
ar
k
p
r
o
b
le
m
s
P
r
o
b
l
e
m
c
o
mp
l
e
x
i
t
y
10
-
d
i
m
e
n
si
o
n
a
l
1
0
0
-
d
i
me
n
s
i
o
n
a
l
F
u
n
c
t
i
o
n
S
i
g
n
p
-
v
a
l
u
e
S
i
g
n
p
-
v
a
l
u
e
F1
+
2
.
0
0
E
-
06
+
2
.
0
0
E
-
06
F2
+
7
.
7
5
E
-
07
+
2
.
0
0
E
-
06
F3
+
2
.
0
0
E
-
06
-
2
.
0
0
E
-
06
F4
+
2
.
0
0
E
-
06
+
2
.
0
0
E
-
06
F5
=
1
.
0
0
E+
0
0
+
2
.
0
0
E
-
06
O
v
e
r
a
l
l
o
u
t
c
o
m
e
+
/
-
/=
4
/
0
/
1
4
/
1
/
0
T
h
e
p
er
f
o
r
m
an
ce
o
f
th
e
p
r
o
p
o
s
ed
AABC
alg
o
r
ith
m
is
f
u
r
th
er
ev
al
u
ated
u
s
in
g
m
u
ltimo
d
al
b
en
ch
m
ar
k
f
u
n
ctio
n
s
F2
,
F4
,
a
n
d
F5
.
Fu
n
ctio
n
F2
p
r
esen
ts
a
ch
allen
g
in
g
lan
d
s
ca
p
e,
ch
a
r
ac
ter
ized
b
y
a
n
ea
r
ly
f
lat
o
u
ter
r
eg
i
o
n
an
d
a
lar
g
e
ce
n
tr
al
b
asin
.
T
h
is
s
tr
u
ctu
r
e
i
n
cr
ea
s
es
th
e
r
is
k
o
f
alg
o
r
ith
m
s
g
ettin
g
tr
ap
p
ed
in
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ar
tif
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n
tell
I
SS
N:
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8
9
3
8
A
r
ith
metic
a
r
tifi
cia
l b
ee
co
lo
n
y
o
p
timiz
a
tio
n
a
lg
o
r
ith
m
w
ith
flexib
le
ma
n
ip
u
la
to
r
…
(
Mo
h
d
R
u
z
a
in
i H
a
s
h
im
)
3797
lo
ca
l
m
in
im
a.
Desp
ite
th
is
,
A
AB
C
d
em
o
n
s
tr
ates
s
tr
o
n
g
p
er
f
o
r
m
an
ce
o
n
F2
,
ac
h
ie
v
in
g
b
e
tter
o
b
jectiv
e
v
alu
es
th
an
th
e
o
r
ig
in
al
AB
C
alg
o
r
ith
m
.
Similar
ly
,
F5
p
o
s
es
a
h
ig
h
r
is
k
d
u
e
to
its
n
u
m
er
o
u
s
lo
ca
l
o
p
tim
a.
On
th
is
f
u
n
ctio
n
,
AABC
o
u
tp
er
f
o
r
m
s
AB
C
in
ter
m
s
o
f
av
er
ag
e,
wo
r
s
t
-
ca
s
e,
an
d
s
tan
d
ar
d
d
ev
iatio
n
v
alu
es,
in
d
icatin
g
g
r
ea
ter
r
o
b
u
s
tn
ess
an
d
co
n
s
is
ten
cy
.
T
h
e
im
p
r
o
v
e
d
p
er
f
o
r
m
a
n
ce
o
f
AABC
o
n
th
ese
co
m
p
l
ex
lan
d
s
ca
p
es
ca
n
b
e
attr
ib
u
ted
to
t
h
e
en
h
an
ce
d
ex
p
lo
r
atio
n
ca
p
a
b
ilit
y
in
tr
o
d
u
ce
d
b
y
th
e
d
iv
is
io
n
a
n
d
m
u
ltip
licatio
n
o
p
e
r
ato
r
s
.
R
an
d
o
m
ly
alter
n
atin
g
b
etwe
en
th
ese
o
p
er
ato
r
s
in
ea
ch
ite
r
atio
n
h
elp
s
m
ain
tain
p
o
p
u
la
tio
n
d
iv
er
s
ity
an
d
r
ed
u
ce
s
th
e
r
is
k
o
f
p
r
e
m
atu
r
e
co
n
v
er
g
en
ce
.
Fo
r
f
u
n
ctio
n
F4
,
wh
ich
co
n
tain
s
n
u
m
er
o
u
s
wid
ely
s
ca
tter
ed
lo
ca
l
m
in
im
a,
AABC
co
n
s
is
ten
tly
p
r
o
d
u
ce
s
b
etter
m
ed
ian
v
alu
e
s
th
an
AB
C
.
T
h
e
AB
C
alg
o
r
i
th
m
r
elies
s
o
lely
o
n
th
e
ad
d
itio
n
o
p
er
ato
r
d
u
r
in
g
its
s
ea
r
ch
p
r
o
ce
s
s
,
wh
ich
l
im
its
its
ab
ilit
y
to
escap
e
lo
ca
l
o
p
tim
a
d
u
e
to
in
s
u
f
f
icien
t
d
ir
ec
tio
n
al
g
u
i
d
a
n
ce
.
I
n
co
n
tr
ast,
AABC
s
h
o
ws
s
ig
n
if
ican
tly
im
p
r
o
v
ed
r
e
s
u
lts
,
p
ar
ticu
lar
ly
in
h
ig
h
er
-
d
im
en
s
io
n
al
in
s
tan
ce
s
o
f
F4
,
wh
er
e
it
ac
h
ie
v
es
s
u
p
er
io
r
a
v
er
ag
e
a
n
d
b
est
o
b
jectiv
e
v
alu
es.
T
h
is
h
ig
h
lig
h
ts
th
e
alg
o
r
ith
m
’
s
e
n
h
an
ce
d
ex
p
lo
r
atio
n
ab
ilit
y
wh
en
tack
lin
g
c
o
m
p
lex
m
u
l
tim
o
d
al
p
r
o
b
lem
s
.
Ov
er
all,
th
e
co
m
p
ar
is
o
n
r
esu
l
ts
p
r
esen
ted
in
T
a
b
le
1
clea
r
l
y
d
em
o
n
s
tr
ate
th
at
th
e
AABC
alg
o
r
ith
m
ex
h
ib
its
s
u
p
er
io
r
s
ea
r
c
h
ca
p
a
b
ilit
ies
co
m
p
ar
ed
to
th
e
o
r
ig
i
n
al
AB
C
.
T
h
e
m
o
d
if
icatio
n
s
in
tr
o
d
u
ce
d
in
AABC
lead
to
a
m
o
r
e
ef
f
ec
tiv
e
b
alan
ce
b
etwe
en
ex
p
lo
r
atio
n
an
d
ex
p
lo
itatio
n
,
en
ab
lin
g
it
to
n
av
ig
ate
c
o
m
p
lex
s
ea
r
ch
s
p
ac
es
m
o
r
e
ef
f
icien
tly
.
T
o
v
er
if
y
th
e
s
ig
n
if
ican
ce
o
f
th
e
p
er
f
o
r
m
an
c
e
d
if
f
er
en
ce
s
b
etwe
en
th
e
p
r
o
p
o
s
ed
AABC
alg
o
r
ith
m
an
d
th
e
o
r
ig
in
al
AB
C
alg
o
r
ith
m
,
a
s
tatis
tical
s
ig
n
if
ican
ce
test
is
co
n
d
u
cted
.
T
h
e
W
ilco
x
o
n
s
ig
n
ed
-
r
an
k
test
—
a
wid
ely
u
s
ed
n
o
n
-
p
ar
am
etr
ic
m
eth
o
d
—
is
s
elec
ted
d
u
e
to
i
ts
ef
f
ec
tiv
en
ess
in
h
an
d
lin
g
d
ata
s
ets
th
at
d
o
n
o
t
r
eq
u
ir
e
ass
u
m
p
tio
n
s
a
b
o
u
t
n
o
r
m
ality
.
T
h
e
test
is
p
er
f
o
r
m
e
d
at
a
5
%
s
ig
n
if
ican
ce
lev
el
t
o
en
s
u
r
e
a
r
elia
b
le
co
m
p
ar
is
o
n
.
T
a
b
le
2
p
r
esen
ts
th
e
co
r
r
esp
o
n
d
in
g
p
-
v
alu
es
an
d
o
u
tco
m
es
o
f
th
e
test
.
I
n
th
is
tab
le,
th
e
s
y
m
b
o
ls
‘
+’
,
‘
−
’
,
an
d
‘
=’
r
ep
r
esen
t
c
ases
wh
er
e
AABC
is
s
tati
s
ti
ca
lly
s
u
p
er
io
r
,
in
f
er
io
r
,
o
r
c
o
m
p
ar
ab
le
to
AB
C
,
r
esp
ec
tiv
ely
.
T
h
is
s
tati
s
tical
a
n
aly
s
is
s
er
v
es
a
s
a
r
ig
o
r
o
u
s
v
alid
atio
n
o
f
th
e
im
p
r
o
v
em
en
t
s
in
tr
o
d
u
ce
d
in
th
e
AAB
C
alg
o
r
ith
m
.
6
.
2
.
A
rit
hm
e
t
ic
a
rt
if
icia
l bee
co
lo
ny
ev
a
lua
t
io
n f
o
r
f
lex
ibl
e
m
a
nip
ula
t
o
r
s
y
s
t
em
c
o
ntr
o
ller
T
h
e
AABC
alg
o
r
ith
m
is
em
p
lo
y
ed
to
o
p
tim
ize
th
e
tr
ajec
to
r
y
o
f
FMS.
I
n
th
is
ap
p
licatio
n
,
th
e
g
ain
v
alu
es
o
b
tain
e
d
f
r
o
m
th
e
A
AB
C
alg
o
r
ith
m
ar
e
in
teg
r
ate
d
in
to
a
PID
co
n
tr
o
ller
to
i
m
p
r
o
v
e
th
e
s
y
s
tem
’
s
d
y
n
am
ic
r
esp
o
n
s
e.
T
h
e
ef
f
ec
tiv
en
ess
o
f
th
e
alg
o
r
ith
m
is
ass
es
s
ed
u
s
in
g
s
ev
er
al
er
r
o
r
-
b
ased
p
er
f
o
r
m
an
ce
m
etr
ics.
T
h
e
ev
alu
atio
n
p
r
o
ce
s
s
co
m
p
r
is
es
a
s
er
ie
s
o
f
s
im
u
l
atio
n
ex
p
er
im
e
n
ts
,
in
clu
d
in
g
er
r
o
r
m
in
im
izatio
n
,
tr
an
s
ien
t
r
esp
o
n
s
e
an
aly
s
is
,
h
u
b
an
g
le
p
er
f
o
r
m
a
n
ce
ass
ess
m
en
t,
an
d
s
in
g
le
-
o
b
jectiv
e
o
p
tim
izatio
n
in
v
o
lv
in
g
m
u
ltip
le
co
n
tr
o
l
p
ar
a
m
eter
s
.
Fo
r
all
s
im
u
latio
n
s
,
th
e
p
o
p
u
latio
n
s
ize
is
s
et
to
3
0
,
with
a
p
r
o
b
lem
d
im
en
s
io
n
ality
o
f
3
.
T
h
e
alg
o
r
ith
m
is
ex
ec
u
ted
f
o
r
1
0
0
iter
at
io
n
s
,
with
a
tr
ial
lim
it o
f
5
0
.
T
h
e
s
ea
r
ch
s
p
ac
e
f
o
r
th
e
o
p
tim
izatio
n
p
r
o
ce
s
s
is
co
n
s
tr
ain
ed
with
in
th
e
r
a
n
g
e
o
f
[
0
,
1
0
]
.
T
o
ev
alu
ate
th
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
PID
co
n
tr
o
ller
,
t
h
r
ee
er
r
o
r
m
etr
ics
ar
e
em
p
lo
y
ed
:
in
t
eg
r
al
tim
e
ab
s
o
lu
te
er
r
o
r
(
I
T
AE
)
,
in
teg
r
al
ab
s
o
lu
te
er
r
o
r
(
I
AE
)
,
an
d
i
n
teg
r
al
s
q
u
ar
e
er
r
o
r
(
I
SE)
.
T
h
e
p
r
o
p
o
s
ed
AAB
C
alg
o
r
ith
m
is
ex
ec
u
ted
o
v
er
1
0
in
d
e
p
en
d
e
n
t
tr
ials
to
d
eter
m
in
e
th
e
o
p
tim
al
v
alu
es
o
f
t
h
e
p
r
o
p
o
r
tio
n
al
g
ain
(
)
in
teg
r
al
g
ain
(
)
,
an
d
d
e
r
iv
ativ
e
g
ain
(
)
o
f
th
e
PID
co
n
tr
o
ller
.
F
o
r
ea
ch
er
r
o
r
m
etr
ic,
th
e
b
est
r
esu
lt
am
o
n
g
th
e
1
0
t
r
ials
is
s
elec
te
d
f
o
r
p
e
r
f
o
r
m
an
ce
ev
alu
atio
n
.
Ad
d
itio
n
ally
,
th
e
c
o
m
p
u
tatio
n
al
tim
e
r
e
q
u
ir
ed
b
y
th
e
alg
o
r
ith
m
is
r
ec
o
r
d
e
d
to
as
s
ess
it
s
ef
f
icien
cy
in
m
in
im
izi
n
g
th
e
er
r
o
r
c
r
iter
ia.
T
h
e
r
esu
lts
,
s
u
m
m
ar
ized
in
T
ab
le
3
an
d
illu
s
tr
ated
in
Fi
g
u
r
e
2
,
co
m
p
ar
e
t
h
e
p
er
f
o
r
m
an
ce
o
f
th
e
AAB
C
alg
o
r
ith
m
with
th
e
o
r
ig
in
al
AB
C
a
lg
o
r
ith
m
.
I
n
th
e
tab
le,
b
o
ld
f
ac
e
v
alu
es
in
d
ica
te
th
e
lo
west
er
r
o
r
ac
h
iev
ed
f
o
r
ea
c
h
m
etr
ic.
T
h
e
f
in
d
in
g
s
clea
r
l
y
s
h
o
w
th
at
AAB
C
o
u
tp
er
f
o
r
m
s
AB
C
ac
r
o
s
s
all
th
r
ee
er
r
o
r
cr
iter
ia.
Fu
r
th
er
m
o
r
e,
AABC
d
em
o
n
s
tr
ates
s
h
o
r
ter
co
m
p
u
ta
tio
n
al
tim
es,
in
d
icatin
g
im
p
r
o
v
ed
ef
f
icien
cy
.
T
h
e
s
u
p
er
io
r
p
er
f
o
r
m
an
ce
o
f
AABC
ca
n
b
e
attr
ib
u
ted
to
its
e
n
h
an
ce
d
ex
p
l
o
r
atio
n
ca
p
ab
ilit
y
,
wh
ich
allo
ws
th
e
s
ea
r
ch
ag
en
ts
to
ex
p
lo
r
e
th
e
s
o
lu
tio
n
s
p
ac
e
m
o
r
e
b
r
o
ad
ly
,
t
h
u
s
in
cr
ea
s
in
g
p
o
p
u
latio
n
d
iv
er
s
ity
.
At
th
e
s
am
e
tim
e,
AABC
ex
h
ib
its
s
tr
o
n
g
e
x
p
lo
itatio
n
ca
p
ab
ilit
ies,
en
ab
li
n
g
it
to
co
n
v
er
g
e
to
lo
wer
e
r
r
o
r
v
al
u
es
co
m
p
a
r
ed
to
AB
C
.
W
h
ile
co
m
p
u
tatio
n
al
tim
e
ten
d
s
to
in
cr
ea
s
e
wit
h
p
o
p
u
latio
n
s
ize
d
u
e
to
th
e
h
ig
h
er
n
u
m
b
er
o
f
ca
n
d
id
ate
s
o
lu
tio
n
s
b
ein
g
e
v
a
lu
ated
,
AABC
s
till
m
ain
tain
s
f
aster
p
e
r
f
o
r
m
an
ce
u
n
d
er
th
e
g
iv
en
s
ettin
g
s
.
I
n
ter
m
s
o
f
PID
tu
n
in
g
,
AABC
c
o
n
s
is
ten
tly
p
r
o
d
u
ce
s
s
m
aller
g
ain
v
alu
es
th
an
AB
C
,
r
e
s
u
ltin
g
in
im
p
r
o
v
e
d
er
r
o
r
m
etr
ics
f
o
r
th
e
PID
co
n
tr
o
ller
.
T
h
e
co
n
v
er
g
en
ce
p
lo
ts
i
n
Fig
u
r
e
2
f
u
r
th
er
c
o
n
f
ir
m
AAB
C
'
s
ad
v
an
tag
e,
s
h
o
win
g
th
at
it
s
tar
ts
f
r
o
m
a
l
o
wer
in
itial
er
r
o
r
an
d
co
n
v
er
g
es
m
o
r
e
r
ap
id
ly
.
T
h
is
is
d
u
e
t
o
AABC
’
s
g
u
id
ed
s
ea
r
ch
m
ec
h
an
is
m
,
w
h
ich
s
el
ec
ts
th
e
b
est
-
p
er
f
o
r
m
in
g
in
d
iv
id
u
al
in
th
e
p
o
p
u
latio
n
as
a
r
e
f
er
en
ce
p
o
in
t
f
r
o
m
th
e
v
er
y
f
ir
s
t iter
atio
n
.
Un
d
er
t
h
e
I
AE
cr
iter
io
n
,
t
h
e
AB
C
alg
o
r
ith
m
ex
h
i
b
its
a
s
h
o
r
ter
s
ettlin
g
tim
e
(
)
co
m
p
a
r
ed
to
t
h
e
AAB
C
alg
o
r
ith
m
.
T
h
is
is
p
r
i
m
ar
ily
d
u
e
to
th
e
in
f
lu
e
n
ce
o
f
th
e
in
te
g
r
al
g
ain
,
wh
ich
p
lay
s
a
s
ig
n
if
ica
n
t
r
o
le
in
th
e
ac
cu
m
u
latio
n
o
f
er
r
o
r
o
v
e
r
tim
e.
As
th
e
in
teg
r
al
co
m
p
o
n
en
t in
cr
ea
s
es in
r
esp
o
n
s
e
to
ev
en
s
m
all
er
r
o
r
s
,
th
e
s
y
s
tem
ten
d
s
to
tak
e
lo
n
g
e
r
to
s
tab
ilize.
T
h
e
AB
C
alg
o
r
ith
m
f
ea
tu
r
es
a
h
i
g
h
er
i
n
teg
r
al
g
ain
th
an
AABC
,
co
n
tr
ib
u
tin
g
to
th
is
f
aster
s
ettlin
g
tim
e.
Ho
wev
er
,
AB
C
also
in
co
r
p
o
r
ates
a
h
ig
h
er
d
er
i
v
ativ
e
g
ain
,
wh
ic
h
co
u
n
ter
ac
ts
th
e
ef
f
ec
ts
o
f
its
l
ar
g
er
in
teg
r
al
g
ain
.
Ad
d
itio
n
a
lly
,
b
ec
au
s
e
th
e
I
AE
cr
iter
io
n
in
h
er
en
tly
lead
s
to
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
9
3
8
I
n
t J Ar
tif
I
n
tell
,
Vo
l.
14
,
No
.
3
,
Octo
b
er
20
25
:
3
7
9
0
-
3
8
0
1
3798
s
lo
wer
s
y
s
tem
r
esp
o
n
s
es,
th
e
in
clu
s
io
n
o
f
a
s
tr
o
n
g
er
d
er
iv
a
tiv
e
co
m
p
o
n
e
n
t
h
elp
s
m
itig
ate
th
is
d
r
awb
ac
k
b
y
ac
ce
ler
atin
g
s
y
s
tem
co
r
r
ec
tio
n
.
I
n
ter
m
s
o
f
o
v
er
s
h
o
o
t
(
O
S),
th
e
AABC
alg
o
r
ith
m
o
u
t
p
er
f
o
r
m
s
AB
C
b
y
p
r
o
d
u
cin
g
a
lo
wer
OS
v
al
u
e.
T
h
is
im
p
r
o
v
em
e
n
t
is
attr
ib
u
ted
to
AABC
’
s
s
m
al
ler
p
r
o
p
o
r
tio
n
al
an
d
in
te
g
r
al
g
ain
s
,
wh
ich
h
elp
s
u
p
p
r
ess
o
s
cillato
r
y
b
eh
a
v
io
r
an
d
en
h
an
c
e
s
y
s
tem
s
tab
ilit
y
.
W
h
en
ev
al
u
atin
g
th
e
r
is
e
tim
e
(
)
,
AABC
d
em
o
n
s
tr
ates
a
f
aste
r
r
esp
o
n
s
e
co
m
p
ar
ed
to
AB
C
,
in
d
icatin
g
th
at
it
r
ea
c
h
es
th
e
d
esire
d
o
u
tp
u
t
lev
el
m
o
r
e
q
u
ick
ly
.
W
h
ile
f
o
r
I
SE
cr
iter
ia,
t
h
e
tw
o
alg
o
r
ith
m
s
p
er
f
o
r
m
e
q
u
ally
well
in
s
ettlin
g
tim
e
b
ec
au
s
e
th
ey
h
av
e
th
e
lo
west
v
alu
es
o
f
in
teg
r
al
an
d
d
er
iv
ativ
e
g
ai
n
.
Ho
wev
er
,
AB
C
alg
o
r
ith
m
b
ea
ts
AAB
C
alg
o
r
ith
m
in
OS
b
ec
au
s
e
AABC
a
lg
o
r
ith
m
d
o
e
s
n
o
t
h
av
e
en
o
u
g
h
in
te
g
r
al
g
a
in
to
b
alan
ce
th
e
h
ig
h
p
r
o
p
o
r
tio
n
al
g
ain
.
AABC
alg
o
r
ith
m
p
e
r
f
o
r
m
b
etter
wh
e
r
e
it
r
ea
cts
f
aster
in
ter
m
o
f
r
is
e
tim
e
th
an
o
r
ig
in
al
AB
C
alg
o
r
ith
m
.
Fo
r
th
e
I
T
AE
cr
iter
ia,
AABC
alg
o
r
ith
m
o
u
tp
er
f
o
r
m
s
AB
C
alg
o
r
ith
m
in
s
ettlin
g
tim
e
an
d
OS
.
B
u
t
AABC
alg
o
r
ith
m
h
as
th
e
s
lo
west
r
is
e
tim
e
b
ec
a
u
s
e
it
s
tar
ts
f
r
o
m
t
h
e
h
ig
h
est
v
alu
e
co
m
p
a
r
ed
t
o
AB
C
alg
o
r
it
h
m
,
wh
ich
h
in
d
er
s
its
co
n
v
er
g
en
ce
.
T
h
is
is
b
ec
au
s
e
I
T
AE
h
as th
e
m
o
s
t slu
g
g
is
h
in
itial r
esp
o
n
s
e.
T
ab
le
3
.
Ou
tco
m
es f
o
r
o
u
tp
u
t
r
esp
o
n
s
e
f
lex
ib
le
m
a
n
ip
u
lato
r
s
y
s
tem
ex
p
er
im
en
t
Er
r
o
r
c
r
i
t
e
r
i
a
I
A
E
I
S
E
I
TA
E
P
a
r
a
me
t
e
r
A
B
C
A
A
B
C
A
B
C
A
A
B
C
A
B
C
A
A
B
C
2
.
8
1
8
1
.
8
8
7
9
.
3
7
7
9
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4
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5
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Er
r
o
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0
.
1
1
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Fig
u
r
e
2
.
Ou
t
p
u
t r
esp
o
n
s
e
f
lex
ib
le
m
an
ip
u
lato
r
s
y
s
tem
ex
p
er
im
en
t w
ith
d
if
f
er
e
n
t e
r
r
o
r
cr
ite
r
ia
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ar
tif
I
n
tell
I
SS
N:
2252
-
8
9
3
8
A
r
ith
metic
a
r
tifi
cia
l b
ee
co
lo
n
y
o
p
timiz
a
tio
n
a
lg
o
r
ith
m
w
ith
flexib
le
ma
n
ip
u
la
to
r
…
(
Mo
h
d
R
u
z
a
in
i H
a
s
h
im
)
3799
7.
CO
NCLU
SI
O
N
T
h
e
AABC
alg
o
r
ith
m
is
a
r
ef
in
ed
v
ar
ian
t
o
f
th
e
s
tan
d
ar
d
AB
C
a
lg
o
r
ith
m
,
d
esig
n
ed
s
p
e
cif
ically
to
en
h
an
ce
t
h
e
o
p
tim
izatio
n
p
er
f
o
r
m
an
ce
o
f
FMS
.
T
h
is
im
p
r
o
v
em
en
t
aim
s
to
o
v
er
co
m
e
k
ey
s
h
o
r
tco
m
in
g
s
o
f
th
e
o
r
ig
in
al
AB
C
,
p
ar
ticu
lar
ly
b
y
s
tr
en
g
t
h
en
in
g
g
lo
b
al
ex
p
lo
r
atio
n
a
n
d
r
ed
u
ci
n
g
th
e
r
is
k
o
f
p
r
em
at
u
r
e
co
n
v
er
g
en
ce
to
s
u
b
o
p
tim
al
s
o
l
u
tio
n
s
.
I
n
th
is
m
o
d
if
ied
ap
p
r
o
ac
h
,
th
e
em
p
l
o
y
ed
b
ee
p
h
ase
is
r
ep
lace
d
with
th
e
ex
p
lo
r
atio
n
m
ec
h
a
n
is
m
d
er
i
v
ed
f
r
o
m
th
e
AOA,
in
tr
o
d
u
cin
g
a
m
o
r
e
s
y
s
tem
atic
a
n
d
ef
f
icien
t
s
ea
r
ch
m
eth
o
d
o
l
o
g
y
.
Ad
d
itio
n
ally
,
th
e
AAB
C
alg
o
r
ith
m
in
co
r
p
o
r
at
es th
e
g
lo
b
al
b
est s
o
lu
tio
n
as a
d
y
n
am
ic
r
ef
e
r
en
ce
p
o
in
t
th
r
o
u
g
h
o
u
t
th
e
o
p
tim
iz
atio
n
p
r
o
ce
s
s
to
ac
ce
ler
ate
c
o
n
v
er
g
en
ce
.
T
o
e
n
h
an
ce
lo
c
al
ex
p
lo
itatio
n
,
th
e
o
n
lo
o
k
er
b
ee
p
h
ase
is
r
estru
ctu
r
ed
in
to
two
d
is
tin
ct
co
m
p
o
n
en
ts
,
co
u
p
led
with
a
s
tep
-
s
ize
co
n
tr
o
l
m
ec
h
an
is
m
th
at
en
ab
les
p
r
ec
is
e
f
i
n
e
-
tu
n
i
n
g
d
u
r
in
g
th
e
lo
ca
l
s
ea
r
ch
p
h
ase.
T
h
ese
en
h
an
ce
m
en
ts
co
ll
ec
tiv
ely
r
esu
lt
in
a
m
o
r
e
b
ala
n
ce
d
a
n
d
e
f
f
ec
tiv
e
s
ea
r
ch
s
tr
ateg
y
co
m
p
ar
ed
to
t
h
e
o
r
ig
i
n
al
AB
C
alg
o
r
ith
m
.
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
AAB
C
h
as
b
ee
n
r
ig
o
r
o
u
s
ly
v
alid
ated
th
r
o
u
g
h
c
o
m
p
r
eh
en
s
i
v
e
test
in
g
u
s
in
g
ten
wid
ely
a
cc
ep
ted
b
en
c
h
m
ar
k
f
u
n
ctio
n
s
.
Acr
o
s
s
th
ese
f
u
n
cti
o
n
s
,
AABC
co
n
s
is
ten
tly
d
em
o
n
s
tr
ated
s
u
p
er
io
r
r
esu
lts
in
ter
m
s
o
f
co
n
v
e
r
g
en
ce
s
p
ee
d
,
s
o
lu
tio
n
ac
cu
r
ac
y
,
an
d
r
esu
lt
s
tab
ilit
y
.
Fu
r
t
h
er
i
n
s
ig
h
ts
in
to
its
co
n
v
er
g
en
ce
d
y
n
a
m
ics
an
d
s
tatis
tical
p
er
f
o
r
m
an
ce
m
etr
ics
af
f
ir
m
i
ts
ef
f
ec
tiv
en
ess
.
T
o
ex
am
in
e
th
e
alg
o
r
ith
m
'
s
p
r
ac
tical
r
elev
an
ce
,
th
e
AABC
alg
o
r
ith
m
was
ap
p
lied
to
o
p
ti
m
ize
th
e
co
n
tr
o
l
p
ar
a
m
eter
s
o
f
FMS
.
E
x
p
er
im
en
tal
ev
alu
a
tio
n
s
u
s
in
g
v
ar
io
u
s
p
er
f
o
r
m
an
ce
in
d
icato
r
s
r
ev
ea
led
th
at
AABC
o
u
tp
e
r
f
o
r
m
e
d
th
e
co
n
v
en
tio
n
al
AB
C
alg
o
r
ith
m
,
d
eliv
er
in
g
n
o
tab
le
im
p
r
o
v
em
e
n
ts
in
co
n
tr
o
l
p
r
ec
is
io
n
.
C
o
m
p
a
r
ativ
e
a
s
s
es
s
m
en
ts
with
o
th
er
AB
C
-
b
ased
v
ar
ian
ts
also
co
n
f
ir
m
e
d
th
e
AABC
’
s
co
m
p
e
titi
v
e
ed
g
e.
T
h
ese
o
u
tco
m
es
h
i
g
h
lig
h
t
t
h
e
alg
o
r
ith
m
'
s
r
o
b
u
s
tn
ess
an
d
e
f
f
icien
cy
as
an
o
p
tim
izatio
n
to
o
l.
Fu
tu
r
e
r
esear
ch
m
ay
ex
p
l
o
r
e
h
y
b
r
id
izin
g
AABC
with
o
th
er
m
etah
eu
r
is
tic
tech
n
iq
u
es
o
r
in
tellig
en
t
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.
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ax
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im
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Ah
m
ad
Fit
r
i M
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o
h
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m
m
a
d
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s
m
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:
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o
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tate
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t
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est.
I
NF
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CO
NS
E
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T
No
t a
p
p
licab
le.
E
T
H
I
CAL AP
P
RO
V
AL
No
t a
p
p
licab
le.
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