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task
n
a
,
ca
n
b
e
s
c
h
ed
u
l
ed
,
all
o
f
its
p
ar
en
t
n
o
d
es
m
u
s
t
f
ir
s
t
b
e
s
c
h
ed
u
led
.
A
d
d
itio
n
al
l
y
,
t
h
e
cr
itical
p
at
h
o
f
a
DAG
is
t
h
e
lo
n
g
est
p
at
h
f
r
o
m
t
h
e
en
tr
y
n
o
d
e
to
th
e
e
x
it
n
o
d
e,
co
n
s
id
er
i
n
g
b
o
th
t
h
e
co
m
p
u
tatio
n
a
n
d
co
m
m
u
n
icatio
n
co
s
ts
b
et
w
ee
n
th
e
tas
k
s
[
5
]
.
I
t
is
as
s
u
m
ed
t
h
at
t
h
er
e
is
o
n
e
e
n
tr
y
tas
k
(n
e
ntry
)
w
h
ic
h
h
a
s
n
o
p
r
ed
ec
ess
o
r
n
o
d
es,
an
d
o
n
e
e
x
it
tas
k
(
n
exit
)
,
w
h
ic
h
is
a
n
o
d
e
w
it
h
n
o
s
u
cc
es
s
o
r
s
f
o
r
th
e
DA
G.
I
f
a
D
AG
co
n
tain
s
m
u
ltip
le
e
n
tr
y
o
r
ex
i
t
task
s
,
a
d
u
m
m
y
en
tr
y
o
r
ex
i
t
n
o
d
e
w
it
h
ze
r
o
co
m
p
u
tatio
n
co
s
t,
alo
n
g
w
it
h
a
ze
r
o
-
co
m
m
u
n
icatio
n
co
s
t
,
ca
n
b
e
co
n
n
ec
ted
,
th
er
ef
o
r
e
m
a
k
in
g
o
u
r
a
lg
o
r
it
h
m
ap
p
licab
le
f
o
r
DA
Gs
o
f
an
y
k
in
d
.
T
h
e
f
o
cu
s
o
f
o
u
r
r
esear
ch
is
s
tatic
ta
s
k
s
ch
ed
u
li
n
g
,
w
h
er
e
in
f
o
r
m
atio
n
ab
o
u
t
av
a
ilab
le
r
eso
u
r
ce
s
i
s
k
n
o
w
n
b
e
f
o
r
e
ex
ec
u
tio
n
a
n
d
s
ch
ed
u
li
n
g
m
a
y
b
e
d
o
n
e
at
co
m
p
ile
t
i
m
e.
W
h
et
h
er
s
ta
ti
c
o
r
d
y
n
a
m
ic,
tas
k
s
ch
ed
u
lin
g
is
c
la
s
s
i
f
ied
as
an
NP
-
Har
d
p
r
o
b
lem
[
4
,
6
]
.
Ho
w
e
v
er
,
th
e
tas
k
s
c
h
ed
u
li
n
g
p
r
o
b
lem
h
as
b
ee
n
w
ell
s
tu
d
ied
an
d
a
n
u
m
b
er
o
f
s
u
b
o
p
ti
m
al
h
e
u
r
is
t
ic
-
b
ased
s
o
l
u
tio
n
s
h
a
v
e
b
e
en
p
r
o
p
o
s
ed
.
T
h
ese
s
o
lu
tio
n
s
m
a
y
b
e
ca
teg
o
r
ized
as lis
t sc
h
ed
u
l
in
g
,
clu
s
ter
i
n
g
,
tas
k
d
u
p
licatio
n
a
n
d
g
u
id
ed
r
an
d
o
m
s
ea
r
ch
m
et
h
o
d
s
.
L
is
t
s
c
h
ed
u
lin
g
alg
o
r
it
h
m
s
[
7
]
,
[
8
]
,
[
9
]
,
[
1
0
]
f
ir
s
t
p
r
io
r
itize
tas
k
s
,
b
a
s
ed
o
n
v
ar
io
u
s
cr
iter
ia,
in
to
a
n
o
r
d
er
e
d
lis
t
b
ef
o
r
e
m
ap
p
in
g
th
e
m
o
n
to
th
e
p
r
o
ce
s
s
o
r
s
.
G
en
er
all
y
,
li
s
t
s
c
h
ed
u
lin
g
al
g
o
r
ith
m
s
h
av
e
g
o
o
d
p
er
f
o
r
m
a
n
ce
-
to
-
co
s
t
tr
ad
eo
f
f
s
.
C
l
u
s
ter
in
g
al
g
o
r
ith
m
s
[
4
]
,
[
1
1
]
,
[
1
2
]
,
[
1
3
]
atte
m
p
t
to
r
ed
u
ce
th
e
co
m
m
u
n
icatio
n
co
s
t
as
s
o
ciate
d
w
ith
d
ep
en
d
en
t
tas
k
s
b
y
g
r
o
u
p
in
g
co
m
m
u
n
icati
n
g
n
o
d
es
to
g
eth
er
in
cl
u
s
ter
s
f
o
r
s
c
h
ed
u
li
n
g
o
n
to
t
h
e
s
a
m
e
p
r
o
ce
s
s
o
r
.
T
h
e
f
o
u
n
d
ati
o
n
o
f
t
h
is
ap
p
r
o
ac
h
is
th
e
f
ac
t
th
at
w
h
en
t
w
o
co
m
m
u
n
icati
n
g
tas
k
s
ar
e
p
lace
d
o
n
th
e
s
a
m
e
p
r
o
ce
s
s
o
r
,
th
e
co
m
m
u
n
icatio
n
co
s
t
b
et
wee
n
t
h
e
m
b
ec
o
m
e
s
n
eg
l
ig
ib
le.
T
h
e
b
asi
s
o
f
tas
k
d
u
p
licatio
n
al
g
o
r
ith
m
s
[
1
4
]
,
[
1
5
]
,
[
1
6
]
,
[
1
7
]
is
to
,
w
h
er
e
p
o
s
s
ib
le,
r
e
m
o
v
e
t
h
e
co
s
t
ass
o
ciate
d
w
i
th
i
n
ter
-
p
r
o
ce
s
s
o
r
co
m
m
u
n
icatio
n
,
an
d
th
u
s
r
ed
u
ce
t
h
e
o
v
er
all
s
c
h
ed
u
le
len
g
t
h
,
b
y
d
u
p
licatin
g
p
r
ed
ec
ess
o
r
n
o
d
es
[
4
]
.
T
ask
d
u
p
licatio
n
,
li
k
e
cl
u
s
ter
in
g
,
ta
k
es
ad
v
a
n
ta
g
e
o
f
t
h
e
ze
r
o
o
r
n
eg
lig
ib
le
co
m
m
u
n
icatio
n
co
s
t
w
h
e
n
t
wo
d
ep
en
d
en
t
tas
k
s
ar
e
p
lace
d
o
n
t
h
e
s
a
m
e
p
r
o
ce
s
s
o
r
.
Gu
i
d
ed
r
an
d
o
m
s
ea
r
c
h
alg
o
r
ith
m
s
[
5
]
,
[1
8]
,
[
1
9
]
,
[
2
0
]
,
[
2
1
]
,
[
2
2
]
,
o
n
th
e
o
th
er
h
an
d
,
ex
a
m
i
n
e
m
u
l
tip
le
s
o
lu
tio
n
s
in
t
h
e
s
ea
r
ch
s
p
ac
e
an
d
co
n
v
er
g
e
to
a
n
e
f
f
icie
n
t
s
o
l
u
tio
n
.
S
u
c
h
al
g
o
r
ith
m
s
,
lik
e
Ge
n
etic
Alg
o
r
it
h
m
s
an
d
An
t
C
o
lo
n
y
Op
ti
m
izatio
n
(
AC
O)
h
a
v
e
b
ee
n
ap
p
lied
to
th
e
task
s
ch
ed
u
li
n
g
p
r
o
b
le
m
p
r
o
d
u
cin
g
s
o
m
e
v
er
y
g
o
o
d
r
esu
lts
.
I
n
p
ar
ticu
lar
,
th
e
A
C
O
tech
n
iq
u
e
,
w
h
ich
f
o
r
m
s
th
e
b
as
is
o
f
o
u
r
alg
o
r
ith
m
,
is
co
n
s
id
er
ed
an
ad
ap
tab
le
s
o
lu
tio
n
,
an
d
h
as b
ee
n
s
u
cc
e
s
s
f
u
ll
y
ap
p
l
ied
to
m
u
ltip
le
p
r
o
b
le
m
s
[
2
3
]
,
[
2
4
]
,
[
2
5
]
.
1
.
1
.
T
he
ACO
M
et
a
heuris
t
ic
An
t
C
o
lo
n
y
Op
ti
m
izatio
n
(
AC
O)
alg
o
r
ith
m
s
w
er
e
f
ir
s
t
in
tr
o
d
u
ce
d
b
y
Do
r
ig
o
an
d
h
is
co
lleag
u
e
s
in
th
e
ea
r
l
y
1
9
9
0
s
,
an
d
f
o
r
m
p
ar
t o
f
a
w
id
er
r
esear
ch
ar
ea
k
n
o
w
n
as
S
w
ar
m
I
n
telli
g
e
n
ce
,
w
h
ich
m
o
d
el
s
s
o
l
u
tio
n
s
to
co
m
b
i
n
ato
r
ial,
an
d
o
p
ti
m
iz
atio
n
p
r
o
b
lem
s
,
b
ased
o
n
t
h
e
b
eh
av
io
r
an
d
p
r
o
ce
s
s
es
e
x
h
ib
ited
in
n
a
tu
r
e
[
2
5
]
.
AC
O
i
s
i
n
s
p
ir
ed
b
y
t
h
e
i
n
d
ir
ec
t
co
m
m
u
n
icati
o
n
o
f
a
f
o
r
ag
in
g
an
t
co
lo
n
y
,
w
h
er
e
th
e
s
u
r
v
iv
a
l
o
f
th
e
en
tire
co
lo
n
y
g
o
v
er
n
s
t
h
e
a
n
ts
’
b
e
h
a
v
io
r
an
d
n
o
t si
m
p
l
y
i
n
d
iv
id
u
al
s
u
r
v
i
v
al.
T
h
is
i
n
d
ir
ec
t c
o
m
m
u
n
ica
tio
n
,
k
n
o
w
n
a
s
s
tig
m
er
g
y
,
e
n
ab
les an
ts
to
f
i
n
d
v
er
y
s
h
o
r
t p
ath
s
b
et
w
ee
n
f
o
o
d
s
o
u
r
ce
s
an
d
th
eir
n
est
[
2
6
]
.
I
n
th
e
in
i
tial
s
ta
g
es
o
f
f
o
r
ag
in
g
,
th
e
an
t
s
ex
p
lo
r
e
th
e
ar
ea
r
a
n
d
o
m
l
y
,
d
ep
o
s
iti
n
g
c
h
e
m
ical
p
h
er
o
m
o
n
e
tr
ails
as
th
e
y
tr
a
v
er
s
e.
W
h
e
n
f
o
o
d
is
en
co
u
n
ter
ed
,
th
e
q
u
alit
y
a
n
d
q
u
an
tit
y
is
ass
e
s
s
ed
a
n
d
p
h
er
o
m
o
n
e
,
f
r
o
m
th
e
f
o
o
d
s
o
u
r
ce
to
t
h
e
n
est
,
i
s
d
ep
o
s
ited
.
Su
b
s
eq
u
en
t
f
o
r
ag
in
g
a
n
t
s
u
tili
ze
th
e
s
e
p
h
er
o
m
o
n
e
tr
ails
to
g
u
id
e
th
e
m
to
th
e
f
o
o
d
,
w
it
h
t
h
e
p
r
o
b
ab
ilit
y
of
u
t
ilizi
n
g
p
at
h
s
m
ar
k
ed
b
y
s
tr
o
n
g
p
h
er
o
m
o
n
e
co
n
ce
n
tr
atio
n
s
,
w
h
ic
h
r
ein
f
o
r
ce
s
t
h
e
p
h
er
o
m
o
n
e
d
e
n
s
it
y
an
d
t
h
u
s
in
cr
ea
s
e
s
th
eir
attr
ac
tiv
en
e
s
s
f
o
r
later
an
ts
.
T
h
is
r
ein
f
o
r
ce
m
e
n
t
lead
s
to
co
n
v
er
g
e
n
ce
to
t
h
e
m
o
s
t
attr
ac
ti
v
e
p
at
h
.
E
v
ap
o
r
atio
n
o
f
p
h
er
o
m
o
n
es
o
n
th
e
tr
ails
p
r
o
v
id
es
th
e
li
m
it
in
g
m
ec
h
a
n
i
s
m
f
o
r
th
i
s
p
o
s
itiv
e
f
ee
d
b
ac
k
,
s
o
less
f
r
eq
u
en
ted
p
ath
s
h
av
e
d
ec
r
ea
s
ed
p
h
er
o
m
o
n
e
co
n
ce
n
tr
atio
n
.
T
h
e
A
C
O
m
eta
h
eu
r
i
s
tic
(
Fi
g
.
1
)
ap
p
lies
th
e
f
o
r
ag
in
g
b
eh
a
v
io
r
o
f
n
at
u
r
al
an
t
s
in
a
co
m
p
u
tat
io
n
al
en
v
ir
o
n
m
e
n
t
a
n
d
iter
ativ
el
y
c
o
n
s
tr
u
ct
s
ca
n
d
id
ate
s
o
lu
tio
n
s
u
s
i
n
g
ar
tif
icia
l
p
h
er
o
m
o
n
e
an
d
lo
ca
l
h
eu
r
is
tics
t
o
g
u
id
e
t
h
e
ar
ti
f
icial
a
g
en
ts
(
a
n
ts
)
t
h
r
o
u
g
h
t
h
e
i
n
v
e
s
ti
g
a
ted
s
ea
r
ch
s
p
ac
e.
T
h
e
p
h
er
o
m
o
n
e
tr
ails
b
ias
f
u
t
u
r
e
ag
en
t
s
to
w
ar
d
h
ig
h
q
u
al
it
y
s
o
l
u
tio
n
s
,
u
n
til a
ter
m
in
a
tio
n
co
n
d
itio
n
is
s
ati
s
f
ied
.
C
o
n
tr
ar
y
to
f
o
r
ag
i
n
g
an
t
s
i
n
n
atu
r
e
w
h
ic
h
d
ep
o
s
it
a
co
n
ti
n
u
o
u
s
tr
ail
o
f
p
h
er
o
m
o
n
e,
AC
O
ap
p
r
o
ac
h
es
h
av
e
i
m
p
le
m
e
n
ted
v
ar
io
u
s
alt
er
n
ativ
e
s
[
2
7
]
.
Fo
r
ex
a
m
p
le,
i
n
t
h
e
o
r
ig
in
al
An
t
S
y
s
te
m
(
AS)
[
2
8
]
an
ts
d
ep
o
s
it
p
h
er
o
m
o
n
e
to
o
n
l
y
co
m
p
lete
d
s
o
lu
tio
n
s
.
A
lter
n
ati
v
el
y
,
t
h
e
A
n
t
C
o
lo
n
y
S
y
s
te
m
(
AC
S)
[
2
9
]
m
ak
e
s
s
tep
-
by
-
s
tep
o
n
lin
e
(
lo
ca
l)
p
h
er
o
m
o
n
e
d
ep
o
s
its
b
y
ev
er
y
a
g
en
t
d
u
r
i
n
g
t
h
e
co
n
s
tr
u
ctio
n
o
f
s
o
l
u
tio
n
s
an
d
in
tr
o
d
u
ce
s
a
f
u
r
t
h
er
o
f
f
lin
e
(
g
lo
b
al)
u
p
d
ate
o
f
p
h
er
o
m
o
n
e
s
to
th
e
b
est
s
o
l
u
tio
n
o
f
t
h
e
iter
atio
n
.
A
d
d
itio
n
all
y
,
s
o
m
e
k
i
n
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o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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C
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Vo
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No
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1
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r
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1
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3
2
9
322
ev
ap
o
r
atio
n
m
ec
h
an
is
m
is
i
m
p
le
m
en
ted
,
allo
w
i
n
g
th
e
a
n
ts
to
co
n
s
id
er
n
e
w
ar
ea
s
o
f
t
h
e
s
ea
r
ch
s
p
ac
e
[
2
7
]
.
Fu
r
t
h
er
m
o
r
e,
s
o
m
e
AC
O
tech
n
iq
u
e
s
e
m
p
lo
y
lo
ca
l
an
d
g
lo
b
al
o
p
tim
iza
tio
n
s
tr
ate
g
ie
s
to
f
u
r
th
er
i
n
cr
ea
s
e
th
e
q
u
alit
y
o
f
th
e
s
o
lu
tio
n
s
p
r
o
d
u
ce
d
.
T
h
e
A
C
O
tech
n
iq
u
e
h
as
b
e
en
ap
p
lied
to
v
ar
io
u
s
o
p
ti
m
izatio
n
,
class
i
f
icatio
n
an
d
s
ch
ed
u
lin
g
p
r
o
b
lem
s
[
2
5
]
.
I
t
h
as
b
ee
n
co
m
b
i
n
ed
w
it
h
o
t
h
er
r
an
d
o
m
s
ea
r
c
h
al
g
o
r
ith
m
s
,
f
o
r
e
x
a
m
p
le,
th
e
Ge
n
etic
A
l
g
o
r
ith
m
a
n
d
T
ab
u
Sear
ch
.
AC
O
h
as
also
b
ee
n
co
m
b
in
e
d
w
it
h
lis
t
s
c
h
e
d
u
li
n
g
,
f
o
r
in
s
tan
ce
,
th
e
ANT
-
L
S
alg
o
r
ith
m
[
2
7
]
an
d
th
e
AC
O
-
T
MS
[
3
0
]
.
T
h
is
co
m
b
in
atio
n
o
f
p
h
er
o
m
o
n
e
tr
ail
s
a
n
d
lis
t
s
ch
ed
u
li
n
g
h
e
u
r
is
t
ics
f
ac
ilit
ate
s
f
u
r
t
h
er
g
u
id
an
ce
f
o
r
th
e
an
t
s
to
w
ar
d
g
o
o
d
q
u
alit
y
s
ch
ed
u
le
s
.
Fig
u
r
e
1
.
T
h
e
A
C
O
Me
ta
h
e
u
r
is
tic
Giv
e
n
th
e
v
er
s
atil
it
y
o
f
A
C
O
alg
o
r
ith
m
s
,
w
e
p
r
ese
n
t
an
AC
O
-
b
ased
alg
o
r
ith
m
w
h
ic
h
u
s
es
t
h
e
f
o
u
n
d
atio
n
o
f
th
e
AC
O
.
Ou
r
p
r
o
p
o
s
ed
alg
o
r
ith
m
i
n
co
r
p
o
r
ates
th
e
u
p
w
ar
d
r
an
k
i
n
g
co
n
ce
p
t
u
s
ed
in
t
h
e
HE
FT
alg
o
r
ith
m
[
8
]
i
n
o
u
r
p
r
io
r
itiz
atio
n
m
et
h
o
d
o
lo
g
y
,
a
n
i
n
s
er
ti
o
n
-
b
ased
p
o
lic
y
alo
n
g
w
i
th
p
h
er
o
m
o
n
e
ag
i
n
g
,
to
p
r
o
d
u
ce
ef
f
icie
n
t
s
c
h
ed
u
le
s
.
O
u
r
r
esear
ch
in
v
e
s
ti
g
ates
t
h
e
ap
p
licatio
n
o
f
an
e
f
f
icie
n
t
s
o
l
u
ti
o
n
to
th
e
s
tatic
ta
s
k
s
ch
ed
u
lin
g
p
r
o
b
le
m
in
a
h
ete
r
o
g
en
eo
u
s
e
n
v
ir
o
n
m
e
n
t
w
h
er
e
d
ep
en
d
en
cies
b
et
w
ee
n
t
h
e
t
ask
s
ar
e
ta
k
e
n
i
n
to
co
n
s
id
er
atio
n
.
Fo
r
o
u
r
s
ch
ed
u
li
n
g
s
y
s
te
m
m
o
d
el,
th
e
tar
g
et
co
m
p
u
ti
n
g
e
n
v
ir
o
n
m
en
t
co
n
s
i
s
ts
o
f
a
s
et
o
f
p
r
o
ce
s
s
o
r
s
P
,
w
h
er
e
P
=
{
p
1
,
p
2
,
p
3
,
…p
|P
|
},
an
d
|
P
|
d
e
n
o
tes
t
h
e
n
u
m
b
er
o
f
p
r
o
ce
s
s
o
r
s
.
O
u
r
m
o
d
el
a
s
s
u
m
e
s
h
eter
o
g
e
n
eo
u
s
n
o
n
-
p
r
ee
m
p
t
iv
e
p
r
o
ce
s
s
o
r
s
th
at
ar
e
co
n
n
e
cted
in
a
f
u
ll
y
co
n
n
ec
ted
t
o
p
o
lo
g
y
a
n
d
i
n
ter
-
p
r
o
ce
s
s
o
r
co
m
m
u
n
icatio
n
is
co
n
ten
t
io
n
-
f
r
ee
.
T
h
e
m
ai
n
o
b
j
ec
tiv
e
o
f
t
h
e
tas
k
s
c
h
ed
u
lin
g
p
r
o
b
lem
is
t
o
d
eter
m
in
e
a
m
ap
p
in
g
o
f
tas
k
s
o
f
a
g
i
v
en
ap
p
licatio
n
to
p
r
o
ce
s
s
o
r
s
th
a
t
m
i
n
i
m
ize
s
th
e
s
c
h
ed
u
le
len
g
t
h
.
T
h
e
r
em
ai
n
d
er
o
f
t
h
e
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
w
s
:
W
e
d
es
cr
ib
e
o
u
r
p
r
o
p
o
s
ed
alg
o
r
ith
m
in
Sect
io
n
2
an
d
o
u
tlin
e
o
u
r
m
e
th
o
d
o
lo
g
y
f
o
r
p
er
f
o
r
m
a
n
ce
ev
al
u
atio
n
in
Sectio
n
3
.
R
esu
l
ts
o
b
tain
ed
f
r
o
m
a
p
er
f
o
r
m
an
ce
co
m
p
ar
is
o
n
o
f
th
e
AC
S
[
2
9
]
an
d
AC
O
-
T
MS
[
3
0
]
w
i
th
o
u
r
p
r
o
p
o
s
ed
w
o
r
k
ar
e
p
r
esen
te
d
an
d
d
is
cu
s
s
ed
in
Sectio
n
4
an
d
w
e
s
u
m
m
ar
ize
o
u
r
co
n
clu
s
io
n
s
an
d
f
u
t
u
r
e
w
o
r
k
s
i
n
Sectio
n
V.
2.
T
H
E
P
RO
P
O
SE
D
AL
G
O
RI
T
H
M
2
.
1
.
O
v
er
v
ie
w
o
f
O
ur
Alg
o
rit
h
m
Ou
r
p
r
o
p
o
s
ed
alg
o
r
ith
m
(
F
ig
.
2
)
is
k
n
o
w
n
as
th
e
r
a
n
k
in
g
-
An
t
C
o
lo
n
y
S
y
s
te
m
(
r
AC
S)
a
n
d
co
m
b
in
es
th
e
f
o
u
n
d
atio
n
o
f
t
h
e
A
n
t
C
o
lo
n
y
S
y
s
te
m
(
AC
S)
w
it
h
t
h
e
h
eu
r
i
s
tic
f
u
n
ctio
n
w
h
ic
h
w
a
s
in
s
p
ir
ed
b
y
th
e
l
is
t
s
ch
ed
u
lin
g
al
g
o
r
ith
m
HE
FT
.
AC
S
e
x
h
ib
its
f
le
x
ib
ilit
y
w
it
h
t
h
e
u
tili
za
tio
n
o
f
t
h
e
o
f
f
li
n
e
p
h
er
o
m
o
n
e
u
p
d
ate
an
d
HE
FT
h
as
y
ield
ed
g
o
o
d
p
er
f
o
r
m
an
ce
as
a
lis
t
s
c
h
ed
u
l
in
g
alg
o
r
ith
m
,
w
it
h
th
e
u
s
e
o
f
th
e
u
p
w
ar
d
r
an
k
v
a
lu
e
f
o
r
p
r
io
r
itizatio
n
.
Firstl
y
,
w
e
i
n
itial
ize
o
u
r
t
w
o
m
atr
ices
f
o
r
o
u
r
p
h
er
o
m
o
n
e
r
ep
r
esen
tatio
n
.
V
×
P
,
w
h
ic
h
we
d
en
o
te
as
τ
,
an
d
P
×
V
w
h
ic
h
w
e
d
en
o
te
as τ
1
.
T
h
e
e
n
tr
y
)
,
(
p
i
in
d
icate
s
t
h
e
p
h
er
o
m
o
n
e
o
n
t
h
e
ed
g
e
b
et
w
e
en
ta
s
k
i
an
d
p
r
o
ce
s
s
o
r
elem
e
n
t
p
,
w
h
er
ea
s
)
,
(
1
j
p
in
d
icate
s
th
e
p
h
er
o
m
o
n
e
o
n
t
h
e
ed
g
e
b
et
w
ee
n
p
r
o
ce
s
s
o
r
ele
m
en
t
p
an
d
task
j
.
T
h
er
ef
o
r
e,
if
n
e
nt
r
y
→
p
2
→
n
3
→
p
1
→
n
2
→
p
|P|
→….
→
n
e
x
i
t
→
p
1
is
a
p
o
s
s
ib
le
s
o
lu
tio
n
(
a
co
m
p
lete
m
ap
p
in
g
o
f
th
e
tas
k
g
r
ap
h
w
it
h
in
t
h
e
s
ea
r
ch
s
p
ac
e
w
h
er
e
an
a
n
t,
s
ta
r
ts
at
th
e
en
tr
y
n
o
d
e
(
n
entry
)
m
o
v
e
s
f
r
o
m
tas
k
to
p
r
o
ce
s
s
o
r
an
d
f
r
o
m
p
r
o
ce
s
s
o
r
to
task
,
u
n
til
a
p
r
o
ce
s
s
o
r
h
a
s
b
ee
n
s
elec
ted
f
o
r
t
h
e
ex
it
n
o
d
e
(
n
exit
)
)
,
th
en
τ
(
n
3
,
p
1
)
ϵ
V
×
P
an
d
τ
1
(
p
1
,
n
2
)
ϵ
V
×
P
.
I
n
itiall
y
,
a
s
m
al
l
p
h
er
o
m
o
n
e
d
ep
o
s
it
is
m
ad
e
to
all
ele
m
en
ts
o
f
ea
c
h
m
atr
ix
an
d
th
e
r
ea
d
y
lis
t
(R
L)
is
i
n
itia
lized
co
n
tain
i
n
g
th
e
e
n
tr
y
n
o
d
e.
Ou
r
iter
ativ
e
a
n
t
co
lo
n
y
al
g
o
r
ith
m
th
e
n
,
ex
ec
u
tes
a
s
f
o
llo
ws:
f
o
r
ea
ch
an
t,
i
n
ea
ch
iter
ati
o
n
,
an
an
t
lis
t
o
f
len
g
t
h
V
th
at
s
to
r
es
b
o
th
a
task
an
d
its
s
e
lecte
d
p
r
o
c
ess
o
r
is
cr
ea
ted
.
T
h
e
an
t
s
elec
ts
a
task
f
r
o
m
t
h
e
r
ea
d
y
l
is
t
u
s
in
g
t
h
e
s
tate
tr
a
n
s
itio
n
(
ST
)
r
u
le
(
1
)
an
d
a
p
r
o
ce
s
s
o
r
u
s
in
g
th
e
s
tate
tr
an
s
iti
o
n
(
ST
)
r
u
le
(
2
)
to
co
n
s
tr
u
ct
a
s
c
h
ed
u
le.
T
h
e
s
e
lecte
d
task
is
r
e
m
o
v
ed
f
r
o
m
th
e
r
ea
d
y
lis
t,
an
d
ap
p
en
d
e
d
,
alo
n
g
w
i
th
th
e
p
r
o
ce
s
s
o
r
,
to
th
e
a
n
t
lis
t.
T
h
e
r
ea
d
y
l
i
s
t
i
s
t
h
e
n
u
p
d
ated
to
co
n
tai
n
all
t
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ltip
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o
ce
s
s
o
r
E
n
viro
n
men
ts
–
A
n
E
fficien
t
…
(
Je
ffr
e
y
E
lco
ck
)
325
an
d
)
(
b
e
s
t
FT
is
t
h
e
f
i
n
is
h
ti
m
e
o
f
t
h
e
b
est
a
n
t
o
f
th
e
iter
atio
n
w
h
il
e
a
d
en
o
te
s
t
h
e
p
h
er
o
m
o
n
e
ev
ap
o
r
atio
n
p
ar
am
eter
)
1
0
(
a
.
3.
RE
S
E
ARCH
M
E
T
H
O
D
W
e
co
n
d
u
cted
a
co
m
p
r
eh
e
n
s
i
v
e
p
er
f
o
r
m
a
n
ce
e
v
alu
a
tio
n
o
f
o
u
r
alg
o
r
ith
m
b
y
u
tili
zi
n
g
a
t
w
o
-
p
r
o
n
g
ed
ap
p
r
o
ac
h
:
(
1
)
an
ev
alu
atio
n
o
f
s
o
m
e
o
f
t
h
e
attr
ib
u
tes
o
f
o
u
r
alg
o
r
ith
m
a
n
d
(
2
)
a
co
m
p
ar
is
o
n
o
f
o
u
r
p
r
o
p
o
s
ed
w
o
r
k
w
i
th
t
w
o
p
u
b
li
s
h
ed
AC
O
-
b
ased
alg
o
r
it
h
m
s
.
Du
r
in
g
t
h
e
an
al
y
s
is
o
f
o
u
r
p
r
o
p
o
s
ed
alg
o
r
ith
m
,
w
e
i
n
v
e
s
ti
g
at
ed
th
e
ef
f
icie
n
c
y
o
f
th
e
f
o
llo
win
g
p
r
o
p
er
ties
:
Utilizatio
n
o
f
I
d
le
P
r
o
ce
s
s
o
r
T
i
m
e
R
an
d
o
m
n
e
s
s
w
it
h
Firs
t I
ter
atio
n
E
f
f
icien
c
y
o
f
P
h
er
o
m
o
n
e
A
g
i
n
g
Me
c
h
a
n
is
m
W
ith
t
h
e
e
x
p
er
i
m
e
n
tatio
n
o
f
r
an
d
o
m
n
e
s
s
o
n
th
e
f
ir
s
t
i
ter
ati
o
n
,
w
e
i
n
v
esti
g
ated
t
h
e
in
f
l
u
e
n
ce
o
f
t
h
e
g
u
id
a
n
ce
v
s
r
an
d
o
m
n
es
s
d
u
r
i
n
g
t
h
e
f
ir
s
t
iter
atio
n
.
T
o
test
th
is
,
w
e
s
ea
r
c
h
ed
th
e
liter
at
u
r
e
f
o
r
DA
G
i
n
s
tan
ce
s
p
u
b
lis
h
ed
i
n
t
h
e
liter
at
u
r
e
[
8
]
,
[
2
2
]
,
[
3
]
.
T
h
is
w
as
d
o
n
e
s
o
as
to
av
o
id
b
iasi
n
g
a
n
y
s
p
ec
if
ic
D
AG.
T
ab
le
1
s
h
o
w
s
t
h
e
p
u
b
li
s
h
ed
m
ak
e
s
p
an
s
o
f
t
h
e
t
h
e
s
elec
ted
D
A
G
s
.
T
ab
le
1
.
P
u
b
lis
h
ed
Ma
k
e
s
p
an
s
o
f
th
e
Selecte
d
D
A
G
s
G
r
a
p
h
P
u
b
l
i
s
h
e
d
M
a
k
e
sp
a
n
D
A
G
1
[
8
]
8
0
D
A
G
2
[
2
2
]
31
D
A
G
3
[
3
]
1
3
5
I
n
th
e
s
ec
o
n
d
p
h
ase
o
f
o
u
r
ev
alu
a
tio
n
,
w
e
co
m
p
ar
ed
o
u
r
p
r
o
p
o
s
ed
w
o
r
k
w
it
h
th
e
AC
S
[
2
9
]
an
d
AC
O
-
T
MS
[
3
0
]
alg
o
r
ith
m
s
b
y
u
til
izin
g
r
an
d
o
m
l
y
g
e
n
er
ate
d
task
g
r
ap
h
s
.
Fo
r
t
h
is
co
m
p
ar
i
s
o
n
,
a
to
tal
o
f
1
3
,
5
0
0
r
an
d
o
m
g
r
ap
h
s
w
it
h
t
h
e
v
ar
io
u
s
c
h
ar
ac
ter
is
t
ics
w
e
r
e
g
en
er
ated
a
n
d
th
e
n
e
x
ec
u
t
ed
.
T
h
e
alg
o
r
ith
m
s
w
er
e
t
h
en
co
m
p
ar
ed
b
ased
o
n
s
elec
ted
co
m
p
ar
ativ
e
m
etr
ics.
3
.
1
.
At
t
ribute
s
o
f
Ra
nd
o
m
ly
G
ener
a
t
ed
DA
G
s
I
n
o
u
r
ex
p
er
i
m
e
n
t,
t
h
e
f
o
llo
w
i
n
g
i
n
p
u
t p
ar
a
m
eter
s
w
er
e
u
s
ed
f
o
r
th
e
g
e
n
er
atio
n
o
f
t
h
e
ta
s
k
g
r
ap
h
,
w
h
ic
h
w
er
e
also
u
til
ized
in
[
8
]
:
Nu
m
b
er
o
f
ta
s
k
s
i
n
th
e
D
AG
(
|
V|
).
Ou
tDe
g
r
ee
o
f
a
n
o
d
e
(
O
deg
)
.
T
h
is
i
s
th
e
m
a
x
i
m
u
m
n
u
m
b
er
o
f
ch
ild
r
en
o
f
a
n
o
d
e.
Sh
a
p
e
p
ar
a
m
eter
o
f
t
h
e
g
r
ap
h
(
α
)
.
C
o
m
m
u
n
ica
tio
n
to
co
m
p
u
ta
tio
n
r
atio
(
CCR
)
.
I
t
is
th
e
r
atio
b
et
w
ee
n
t
h
e
av
er
ag
e
co
m
m
u
n
ic
atio
n
co
s
t a
n
d
th
e
a
v
er
ag
e
co
m
p
u
tat
io
n
co
s
t.
R
an
g
e
p
er
ce
n
ta
g
e
o
f
co
m
p
u
t
atio
n
co
s
ts
o
n
p
r
o
ce
s
s
o
r
s
(
β
)
.
I
t
is
t
h
e
h
eter
o
g
en
eit
y
f
ac
t
o
r
f
o
r
pr
o
ce
s
s
o
r
s
.
A
h
i
g
h
er
p
er
ce
n
tag
e
v
al
u
e
i
n
d
icate
s
a
s
i
g
n
i
f
ican
t
d
if
f
er
e
n
ce
in
t
h
e
co
m
p
u
tatio
n
co
s
t
ac
r
o
s
s
th
e
p
r
o
ce
s
s
o
r
s
,
w
h
ile
lo
w
er
v
al
u
es
ar
e
i
n
d
icati
v
e
o
f
m
o
r
e
s
u
b
tle
d
i
f
f
e
r
en
ce
s
i
n
co
m
p
u
tatio
n
co
s
ts
.
Fo
r
ea
ch
ex
p
er
i
m
e
n
t,
th
e
v
al
u
es d
is
cu
s
s
ed
ab
o
v
e,
w
er
e
as
s
i
g
n
ed
f
r
o
m
t
h
e
s
et
s
g
i
v
e
n
b
elo
w
.
Set o
f
No
d
es (
V
)
=
{2
0
,
4
0
,
6
0
,
8
0
,
1
0
0
}
Set o
f
C
C
R
(
C
C
R
)
=
{0
.
1
,
0
.
5
,
1
.
0
,
5
.
0
,
1
0
.
0
}
Set o
f
A
lp
h
a
(
α
)
=
{0
.
5
,
1
.
0
,
2
.
0
}
Set o
f
Ou
tDeg
r
ee
(
Od
eg
)
=
{
1
,
2
,
3
,
4
,
5
}
Set o
f
B
eta
(
β
)
=
{
0
.
2
5
,
0
.
5
,
0
.
7
5
,
1
.
0
}
Nu
m
b
er
o
f
An
t
s
(
K)
= {
m
in
(
(
av
g
(
Od
e
g
)
×
|
V
|
,
1
0
0
)
}
Nu
m
b
er
o
f
I
ter
atio
n
s
=
{
1
0
0
}
No
o
f
P
r
o
ce
s
s
o
r
s
=
{
3
}
3
.
2
.
Co
m
pa
ra
t
iv
e
M
et
r
ics
a
.
Sp
ee
du
p
:
T
h
e
r
atio
b
et
w
ee
n
th
e
s
eq
u
e
n
tial
ti
m
e
a
n
d
th
e
p
ar
allel
ex
ec
u
tio
n
ti
m
e
o
f
a
p
r
o
ce
s
s
is
d
ef
i
n
ed
as
th
e
s
p
ee
d
u
p
.
T
h
e
s
eq
u
e
n
tial
t
i
m
e
is
ca
lcu
la
ted
b
y
ad
d
i
n
g
,
s
eq
u
en
tiall
y
,
th
e
co
m
p
u
tat
io
n
al
co
s
t
o
f
ea
ch
task
i
n
t
h
e
g
r
ap
h
.
T
h
i
s
i
s
d
o
n
e
f
o
r
ea
ch
p
r
o
ce
s
s
o
r
an
d
th
en
t
h
e
s
m
alles
t
v
al
u
e
i
s
u
s
ed
.
T
h
e
p
ar
allel
ex
ec
u
t
io
n
ti
m
e
is
th
e
co
m
p
l
etio
n
ti
m
e
o
f
t
h
e
g
r
ap
h
,
w
h
i
ch
is
also
r
ef
er
r
ed
to
as
th
e
Ma
k
esp
an
o
r
Sch
ed
u
led
L
e
n
g
t
h
(
S
L
)
.
T
h
er
ef
o
r
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4752
I
n
d
o
n
esia
n
J
E
lec
E
n
g
&
C
o
m
p
Sc
i,
Vo
l.
10
,
No
.
1
,
A
p
r
il 2
0
1
8
:
3
2
0
–
3
2
9
326
SL
n
S
p
e
e
d
u
p
V
n
k
i
P
p
i
k
)}
(
{
m
i
n
,
(
1
2
)
w
h
er
e
)
(
,
k
i
n
d
en
o
tes th
e
co
m
p
u
ta
tio
n
al
co
s
t o
f
ta
s
k
n
i
o
n
p
r
o
ce
s
s
o
r
p
k
.
b.
Schedu
le
L
e
ng
t
h
Ra
t
io
:
T
h
e
Sch
ed
u
le
L
e
n
g
th
(
S
L
)
is
th
e
m
ai
n
p
er
f
o
r
m
an
ce
m
ea
s
u
r
e
o
f
a
s
ch
ed
u
li
n
g
alg
o
r
ith
m
.
I
n
o
u
r
e
x
p
er
i
m
e
n
t,
a
lar
g
e
s
et
o
f
ta
s
k
g
r
ap
h
s
w
i
t
h
v
ar
y
in
g
p
r
o
p
er
ties
is
u
s
ed
an
d
th
er
e
f
o
r
e
it
b
ec
o
m
e
s
n
ec
ess
ar
y
to
n
o
r
m
a
l
ize
th
e
s
c
h
ed
u
le
le
n
g
t
h
to
t
h
e
lo
w
er
b
o
u
n
d
.
T
h
is
is
ca
lle
d
th
e
Sch
ed
u
le
L
e
n
g
t
h
R
a
tio
(
SLR).
T
h
e
SLR
is
d
ef
in
ed
as
f
o
llo
w
s
:
M
I
N
i
k
C
r
i
P
n
k
i
P
p
n
SL
S
L
R
)}
(
{
m
i
n
,
(
1
3
)
T
h
e
d
en
o
m
in
ato
r
is
th
e
s
u
m
m
atio
n
o
f
t
h
e
m
in
i
m
u
m
co
m
p
u
tatio
n
co
s
t
s
o
f
t
h
e
ta
s
k
s
o
n
th
e
C
r
iP
MI
N
(
m
in
i
m
u
m
C
r
it
ical
P
ath
)
.
T
h
e
C
r
iP
MIN
i
s
d
er
iv
ed
b
y
f
ir
s
t
s
et
tin
g
ea
ch
ta
s
k
(
n
i
)
to
its
m
i
n
i
m
u
m
co
m
p
u
tat
io
n
al
co
s
t a
n
d
ca
lcu
lati
n
g
th
e
le
n
g
t
h
o
f
th
e
C
r
it
ical
P
ath
(
|
C
P
|
)
u
s
in
g
t
h
e
s
e
v
al
u
es.
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
4
.
1
.
P
re
li
m
ina
ry
Ana
ly
s
is
o
f
O
ur
P
ro
po
s
ed
Wo
r
k
AC
O
-
b
ased
al
g
o
r
ith
m
s
ca
n
o
b
tain
s
h
o
r
ter
s
c
h
ed
u
le
s
w
h
e
n
th
e
y
(
i)
i
n
co
r
p
o
r
ate
f
u
n
ctio
n
alit
y
t
h
at
en
s
u
r
es
p
r
o
ce
s
s
o
r
id
le
tim
e
is
k
ep
t
to
a
m
i
n
i
m
u
m
a
n
d
(
ii)
a
llo
w
an
ts
to
r
an
d
o
m
l
y
s
elec
t
s
ch
ed
u
le
s
-
th
er
eb
y
m
i
m
ic
k
in
g
t
h
eir
n
at
u
r
al
en
v
ir
o
n
m
e
n
t.
AC
O
-
b
ased
alg
o
r
ith
m
s
f
o
u
n
d
in
t
h
e
liter
at
u
r
e,
g
e
n
er
all
y
,
ap
p
l
y
a
lo
ca
l
o
p
tim
izatio
n
s
tr
ate
g
y
a
f
ter
g
en
er
atin
g
a
s
o
l
u
tio
n
.
T
h
e
id
ea
b
eh
i
n
d
t
h
is
s
tr
ate
g
y
i
s
n
o
r
m
al
l
y
to
m
a
k
e
ad
j
u
s
t
m
e
n
ts
,
w
h
er
e
f
ea
s
ib
le,
to
i
m
p
r
o
v
e
th
e
s
o
l
u
tio
n
o
b
tai
n
ed
.
On
e
s
u
c
h
s
tr
ate
g
y
is
to
ef
f
ec
tiv
el
y
u
t
iliz
e
id
le
p
r
o
ce
s
s
o
r
tim
e
[
2
1
]
,
[
2
2
]
,
[
2
6
]
,
th
u
s
,
r
ed
u
ci
n
g
t
h
e
o
v
er
all
s
ch
ed
u
le
le
n
g
t
h
.
Gi
v
en
t
h
is
b
as
is
,
w
e
d
esi
g
n
ed
o
u
r
alg
o
r
ith
m
s
u
ch
t
h
at,
as
ea
ch
an
t
co
n
s
tr
u
cts
a
s
o
lu
tio
n
,
w
h
en
a
task
is
s
elec
ted
,
th
e
id
en
ti
f
ied
p
r
o
ce
s
s
o
r
is
s
ea
r
ch
ed
f
o
r
p
o
s
s
ib
le
id
le
s
lo
t
s
w
h
er
e
t
h
e
tas
k
i
s
in
s
er
ted
,
s
o
th
at
it
ca
n
ac
h
ie
v
e
t
h
e
ea
r
li
est
p
o
s
s
ib
le
f
in
i
s
h
ti
m
e.
W
h
ile
o
u
r
u
til
izatio
n
o
f
id
le
s
lo
ts
is
co
n
s
is
te
n
t
w
i
th
t
h
e
liter
at
u
r
e;
w
ith
o
u
r
ap
p
r
o
a
ch
,
th
e
u
s
e
o
f
id
l
e
p
r
o
ce
s
s
o
r
s
lo
ts
is
d
eter
m
i
n
ed
as th
e
s
c
h
ed
u
le
s
ar
e
b
u
ilt,
n
o
t a
f
ter
.
W
e
also
ex
p
er
im
e
n
ted
in
th
e
f
ir
s
t
iter
atio
n
,
w
ith
t
h
e
an
t
s
s
elec
ti
n
g
tas
k
s
f
r
o
m
th
e
r
ea
d
y
li
s
t,
an
d
p
r
o
ce
s
s
o
r
in
a
r
an
d
o
m
m
a
n
n
er
.
Fro
m
T
ab
le
2
,
it
is
n
o
ti
ce
ab
le
th
at
s
h
o
r
ter
s
c
h
ed
u
les
w
er
e
a
n
d
ca
n
b
e
p
r
o
d
u
ce
d
w
h
en
t
h
i
s
ap
p
r
o
ac
h
is
i
m
p
le
m
e
n
ted
.
T
ab
le
2
.
Ma
k
esp
an
s
A
ttai
n
ed
b
y
O
u
r
A
l
g
o
r
ith
m
W
h
e
n
R
a
n
d
o
m
n
e
s
s
o
f
1
st
I
ter
atio
n
is
v
ar
ie
d
G
r
a
p
h
P
u
b
l
i
s
h
e
d
M
a
k
e
sp
a
n
M
a
k
e
sp
a
n
A
t
t
a
i
n
e
d
B
y
R
a
c
s
1
st
I
t
e
r
a
t
i
o
n
,
N
o
t
R
a
n
d
o
m
1
st
I
t
e
r
a
t
i
o
n
,
R
a
n
d
o
m
D
A
G
1
[
8
]
8
0
79
73
D
A
G
2
[
2
2
]
31
29
27
D
A
G
3
[
3
]
1
3
5
1
3
5
1
3
5
W
e
also
ex
p
er
im
e
n
ted
w
it
h
d
elib
er
ate
ev
ap
o
r
atio
n
o
f
p
h
er
o
m
o
n
e
s
o
as
to
m
iti
g
ate
s
ta
g
n
at
io
n
o
r
escap
e
lo
ca
l
o
p
ti
m
a
.
T
h
e
i
m
p
ac
t
w
a
s
n
o
t
as
s
i
g
n
i
f
ican
t
a
s
ex
p
ec
ted
.
W
e
p
o
s
t
u
late
th
a
t
th
e
v
a
lu
e
u
s
ed
to
g
en
er
ate
ev
ap
o
r
atio
n
h
ad
m
i
n
i
m
al
i
m
p
ac
t
b
ec
a
u
s
e
o
f
th
e
ti
m
i
n
g
o
f
i
n
v
o
ca
tio
n
a
n
d
t
h
e
a
m
o
u
n
t.
Ho
w
ev
er
,
b
ec
au
s
e
o
f
th
e
r
an
d
o
m
n
es
s
o
f
th
is
ac
tiv
it
y
,
w
h
en
i
n
v
o
ca
tio
n
o
cc
u
r
r
ed
d
u
r
in
g
th
e
ea
r
l
y
it
er
atio
n
s
w
h
er
e
th
e
p
h
er
o
m
o
n
e
co
n
ce
n
tr
atio
n
w
a
s
n
o
t
h
ig
h
,
n
e
w
er
o
p
p
o
r
tu
n
it
ies
w
er
e
p
r
o
v
id
ed
.
W
e
an
ticip
ate
th
at
a
m
o
r
e
i
m
p
ac
t
f
u
l
a
n
d
u
s
e
f
u
l
ap
p
r
o
ac
h
w
o
u
ld
b
e
to
,
at
th
e
b
eg
in
n
in
g
o
f
ea
ch
iter
atio
n
,
allo
w
a
r
an
d
o
m
n
u
m
b
er
o
f
an
t
s
to
r
an
d
o
m
l
y
cr
ea
te
s
o
l
u
tio
n
s
.
T
h
ese
n
e
w
s
c
h
ed
u
le
s
w
o
u
ld
b
e
in
co
r
p
o
r
ated
if
th
e
y
ar
e
w
o
r
t
h
y
.
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
t
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
(
r
A
C
S)
w
a
s
f
u
r
th
er
e
v
alu
a
ted
b
y
co
m
p
ar
is
o
n
w
it
h
its
p
r
o
g
en
ito
r
,
th
e
AC
S a
lg
o
r
it
h
m
[
2
9
]
,
an
d
th
e
A
C
O
-
T
MS
al
g
o
r
ith
m
[
3
0
]
.
Fo
r
th
is
co
m
p
ar
i
s
o
n
,
r
an
d
o
m
d
ir
ec
ted
ac
y
clic
g
r
ap
h
s
(
D
A
G
s
)
o
f
v
ar
y
in
g
attr
ib
u
tes
w
er
e
g
e
n
er
ated
an
d
th
en
e
x
ec
u
ted
b
y
th
e
al
g
o
r
ith
m
s
.
4
.2
.
Co
m
pa
ri
s
o
n
o
f
P
ro
po
s
ed
Wo
r
k
w
it
h Selec
t
ed
Alg
o
rit
h
m
s
T
h
e
r
A
C
S,
AC
S
a
n
d
A
C
O
-
T
MS
alg
o
r
it
h
m
s
w
er
e
f
ir
s
t
co
m
p
ar
ed
b
ased
o
n
t
h
e
av
er
a
g
e
m
ak
e
s
p
an
attain
ed
w
it
h
t
h
e
v
ar
y
i
n
g
s
h
ap
e
p
ar
am
eter
s
.
Fo
r
o
u
r
f
ir
s
t
e
x
p
er
i
m
en
t,
D
A
Gs
o
f
v
ar
y
i
n
g
d
e
g
r
ee
s
o
f
p
ar
allelis
m
w
er
e
g
e
n
er
ated
.
Fro
m
th
e
r
es
u
lts
i
n
Fi
g
.
3
,
it
w
as
f
o
u
n
d
th
a
t r
AC
S
o
u
tp
er
f
o
r
m
ed
th
e
o
th
e
r
t
w
o
a
lg
o
r
it
h
m
s
f
o
r
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s
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r
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h
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o
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h
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8
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ce
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AC
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8
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ce
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O
-
T
MS,
an
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as 5
2
p
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ce
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t b
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a
n
th
e
AC
S.
T
h
e
n
ex
t
e
x
p
er
i
m
e
n
t
e
x
a
m
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th
e
v
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n
o
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th
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er
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g
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SLR
o
f
th
e
a
lg
o
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it
h
m
s
as
th
e
n
u
m
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er
o
f
n
o
d
es
o
f
th
e
D
A
Gs
w
as
i
n
cr
ea
s
ed
.
Fig
.
4
s
h
o
w
s
t
h
at
as
th
e
n
u
m
b
er
o
f
n
o
d
es
in
cr
ea
s
e
s
,
t
h
e
d
i
f
f
er
e
n
ce
o
f
t
h
e
av
er
ag
e
S
L
R
v
alu
e
s
w
h
e
n
co
m
p
ar
ed
to
o
u
r
p
r
o
p
o
s
ed
alg
o
r
ith
m
a
n
d
th
at
o
f
t
h
e
AC
O
-
T
MS
s
h
o
w
s
a
s
tead
y
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s
e.
T
h
is
is
in
d
icati
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e
o
f
b
etter
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er
f
o
r
m
an
ce
f
r
o
m
o
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r
p
r
o
p
o
s
ed
alg
o
r
ith
m
f
o
r
lar
g
e
ap
p
licatio
n
s
w
it
h
m
o
r
e
ta
s
k
s
w
h
en
co
m
p
ar
ed
to
s
m
al
ler
ap
p
licatio
n
s
.
r
A
C
S
is
b
etter
th
an
AC
O
-
T
MS
b
y
6
p
e
r
ce
n
t
an
d
t
h
e
A
C
S
b
y
2
4
p
er
ce
n
t.
Fig
.
5
illu
s
tr
ates
t
h
e
b
eh
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io
r
o
f
th
e
alg
o
r
it
h
m
s
,
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r
o
m
o
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r
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i
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n
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ich
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e
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ated
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e
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ee
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u
p
as
th
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D
AG
s
ize
w
as
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n
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ea
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ed
.
Ou
r
p
r
o
p
o
s
ed
alg
o
r
ith
m
ex
p
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ie
n
ce
d
a
s
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n
cr
ea
s
e
in
th
e
a
v
er
ag
e
s
p
ee
d
u
p
,
o
u
tp
er
f
o
r
m
i
n
g
b
o
th
th
e
AC
S
an
d
t
h
e
AC
O
-
T
MS
alg
o
r
it
h
m
s
.
T
h
e
AC
S
ex
p
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ien
ce
d
m
i
n
i
m
al
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n
cr
ea
s
e
i
n
th
e
s
p
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u
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th
r
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g
h
o
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t
t
h
i
s
ex
p
er
i
m
en
t
.
T
h
e
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e
s
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u
p
ex
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d
b
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h
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C
O
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s
s
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h
o
w
e
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er
,
n
o
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as
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r
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n
o
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ce
d
as
r
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C
S.
F
u
r
th
er
,
as
th
e
n
u
m
b
er
o
f
n
o
d
es
o
f
th
e
D
A
G
w
as
in
cr
ea
s
ed
f
r
o
m
8
0
to
1
0
0
,
o
u
r
p
r
o
p
o
s
ed
alg
o
r
ith
m
y
ield
ed
th
e
m
o
s
t
p
r
o
m
i
n
en
t
o
u
tp
er
f
o
r
m
an
ce
o
f
t
h
e
o
th
er
t
w
o
al
g
o
r
ith
m
s
.
O
v
er
all,
o
u
r
p
r
o
p
o
s
ed
w
as
b
etter
th
a
n
A
C
S
an
d
A
C
O
-
T
MS
b
y
2
5
an
d
7
.
5
p
er
ce
n
t
r
esp
ec
tiv
el
y
.
A
lar
g
er
s
p
ee
d
u
p
v
alu
e
is
i
n
d
icativ
e
o
f
a
s
m
al
ler
ex
ec
u
tio
n
ti
m
e
i
n
a
p
ar
allel
en
v
ir
o
n
m
e
n
t.
Ou
r
re
s
u
lt
s
s
u
g
g
est
t
h
at,
g
e
n
er
all
y
,
o
u
r
p
ar
allel
ex
ec
u
tio
n
ti
m
es
w
er
e
co
n
s
is
te
n
tl
y
s
m
aller
th
an
t
h
e
s
eq
u
e
n
tia
l
ex
ec
u
t
io
n
ti
m
es,
e
v
en
a
s
th
e
n
u
m
b
er
o
f
n
o
d
es in
cr
ea
s
ed
.
Fig
u
r
e
3
.
R
esu
lts
f
o
r
Av
er
ag
e
Ma
k
esp
a
n
f
o
r
Var
ied
DA
G
St
r
u
ctu
r
e
Fig
u
r
e
4
.
R
esu
lts
f
o
r
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329
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5
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Ra
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in
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Distri
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Pro
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2
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P
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S
h
iraz
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a
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d
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M
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A
Ne
w
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p
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Du
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Distrib
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in
Pa
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Pro
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1
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In
ter
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1
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7
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s,
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3
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8
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A
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9
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9
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1
0
(
8
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1
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(
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2
0
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0
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B
a
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a
lo
re
,
In
d
ia:
IEE
E.
[2
2
]
Ch
u
n
,
L
.
,
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ti
ma
l
M
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lt
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-
Res
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u
rc
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tra
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Imp
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a
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tri
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p
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ter S
c
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0
1
4
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1
2
(4
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p
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2
8
9
8
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0
4
.
[2
3
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A
b
d
-
A
ll
a
h
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M
.
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A
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S
a
id
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a
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d
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A
li
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ti
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o
f
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t
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in
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a
za
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s
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th
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m
o
re
se
n
siti
v
e
p
o
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in
win
d
f
a
rm
s
u
sin
g
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0
1
6
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5
(2
):
p
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1
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.
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4
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Zh
a
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a
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in
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p
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d
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Jo
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rn
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tri
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1
5
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1
4
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1
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5
]
Ja
is
w
a
l,
U.
a
n
d
S
.
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g
g
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r
wa
l,
An
t
Co
lo
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ti
miza
ti
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n
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n
tern
a
ti
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Jo
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f
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c
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f
ic
&
En
g
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rin
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Re
se
a
rc
h
,
2
0
1
1
.
2
(
7
):
p
.
1
-
7.
[2
6
]
V
a
ss
il
iad
is,
V
.
a
n
d
G
.
Do
u
n
ias
,
Na
tu
re
–
I
n
sp
ire
d
I
n
telli
g
e
n
c
e
:
A
Rev
iew
Of
S
e
lec
ted
M
e
th
o
d
s
A
n
d
Ap
p
li
c
a
ti
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s.
In
tern
a
ti
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a
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Jo
u
rn
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A
rti
f
icia
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In
telli
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c
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T
o
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ls,
2
0
0
9
.
1
8
(0
4
):
p
.
4
8
7
-
5
1
6
.
[2
7
]
Ba
n
k
,
M
.
,
U.
H
o
n
ig
,
a
n
d
W
.
S
c
h
if
fm
a
n
n
.
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ACO
-
b
a
se
d
Ap
p
ro
a
c
h
f
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c
h
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d
u
li
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g
T
a
sk
Gr
a
p
h
s
w
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Co
mm
u
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ica
ti
o
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C
o
sts
.
in
2
0
0
5
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
Pa
r
a
ll
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l
Pro
c
e
ss
in
g
(
ICPP
'
05)
.
2
0
0
5
.
P
o
lan
d
:
IEE
E
.
[2
8
]
Do
rig
o
,
M
.
,
V.
M
a
n
iez
z
o
,
a
n
d
A.
Co
lo
rn
i,
An
t
S
y
ste
m:
Op
ti
miza
t
io
n
b
y
a
Co
l
o
n
y
Of
Co
o
p
e
ra
ti
n
g
Ag
e
n
ts.
IEE
E
T
ra
n
sa
c
ti
o
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s o
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S
y
ste
m
s,
M
a
n
,
a
n
d
Cy
b
e
rn
e
ti
c
s,
P
a
rt
B
(Cy
b
e
rn
e
ti
c
s),
1
9
9
6
.
2
6
(1
):
p
.
2
9
-
4
1
.
[2
9
]
Do
rig
o
,
M
.
a
n
d
L
.
M
.
G
a
m
b
a
rd
e
ll
a
,
An
t
Co
l
o
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y
S
y
ste
m:
A
Co
o
p
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ra
ti
v
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L
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a
rn
in
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Ap
p
ro
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c
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v
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ma
n
Pro
b
lem
.
IEE
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T
ra
n
sa
c
ti
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n
s O
n
Ev
o
l
u
ti
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a
ry
Co
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p
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tatio
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,
1
9
9
7
.
1
(
1
):
p
.
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3
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6
.
[3
0
]
Ch
ian
g
,
C.
-
W
.
,
e
t
a
l.
An
t
Co
l
o
n
y
Op
ti
misa
ti
o
n
fo
r
T
a
sk
M
a
tch
i
n
g
a
n
d
S
c
h
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d
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li
n
g
.
i
n
IEE
E
Pro
c
e
e
d
in
g
s
-
Co
m
p
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ter
s
a
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d
Dig
i
ta
l
T
e
c
h
n
i
q
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e
s
.
2
0
0
6
.
In
s
ti
tu
te
o
f
En
g
in
e
e
rin
g
a
n
d
T
e
c
h
n
o
l
o
g
y
.
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