I
A
E
S
I
n
t
e
r
n
at
io
n
al
Jou
r
n
al
of
A
r
t
if
ic
ia
l
I
n
t
e
ll
ig
e
n
c
e
(
I
J
-
AI
)
V
ol
.
11
, N
o.
1
,
M
a
r
c
h
2022
, pp.
13
~
22
I
S
S
N
:
2252
-
8938
,
D
O
I
:
10.11591/
ij
a
i.
v
11
.i
1
.pp
13
-
22
13
Jou
r
n
al
h
om
e
page
:
ht
tp
:
//
ij
ai
.
ia
e
s
c
or
e
.c
om
Im
p
r
ove
d
d
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e
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on
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gor
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t
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r
ave
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i
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e
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p
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ob
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H
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s
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e
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F
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ad
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lm
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i
1
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as
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put
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r
s
i
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a
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a
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i
a
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D
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of
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put
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ha
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t
A
l
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a
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t
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ol
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ge
, B
a
s
r
a
h
, I
r
a
q
A
r
t
ic
le
I
n
f
o
A
B
S
T
R
A
C
T
A
r
ti
c
le
h
is
to
r
y
:
R
e
c
e
iv
e
d
F
e
b 4
, 2021
R
e
vi
s
e
d
O
c
t
14
, 2021
A
c
c
e
pt
e
d
O
c
t
22
,
2021
The
primary
goal
of
traveling
salesman
problem
(TSP)
is
for
a
sales
man
to
visit
many
cities
and
return
to
the
starting
city
via
a
sequence
of
po
tential
shortest
paths.
Subsequently,
conventional
algorithms
are
inadequ
ate
for
large
-
scale
problems;
thus,
met
aheuristi
c
algorit
hms
have
been
propo
sed.
A
recent
metaheuristic
algorithm
that
has
been
implemented
to
solve
TSP
is
the
plant
propagation
algorithm
(PPA),
which
belongs
to
the
rose
fa
mily.
In
this
research,
this
existing
PPA
is
modified
to
solve
TSP.
Alth
ough
PPA
is
claimed
to
be
successful
,
it
suffers
from
th
e
slow
convergence
pr
oblem,
which
significantly
impedes
its
applicability
for
getting
good
so
lution.
Therefore,
the
proposed
partial
-
partitioned
greedy
algorithm
(PPGA)
offers
crossover
and
three
muta
tion
operations
(flip,
swap,
and
slide),
which
allow
local
and
global
search
and
seem
to
be
wise
methods
to
help
P
PA
in
s
olving
the
TSP.
The
PPGA
performance
is
evaluated
on
10
separate
d
atasets
available
in
the
literatu
re
and
compared
with
the
original
PP
A.
In
te
rms
of
distance,
the
computational
results
demonstrate
that
the
PPGA
outpe
rforms
the
original
PPA
in
nine
datasets
which
assures
that
it
is
90%
bett
er
than
PPA.
PPGA
produces
good
solutions
when
compared
with
other
algo
rithms
in the litera
ture, whe
re the average executi
on time red
uces by 10.7
3%.
K
e
y
w
o
r
d
s
:
G
e
ne
ti
c
a
lg
or
it
hm
M
e
ta
he
ur
is
ti
c
O
pt
im
iz
a
ti
on
P
la
nt
i
nt
e
ll
ig
e
nc
e
This is an
open
acce
ss artic
le unde
r the
CC BY
-
SA
license.
C
or
r
e
s
pon
di
n
g A
u
th
or
:
H
us
s
e
in
F
oua
d A
lm
a
z
in
i
S
c
hool
of
C
om
put
in
g
,
U
ni
ve
r
s
it
i
U
ta
r
a
M
a
la
ys
ia
S
in
to
k, K
e
da
h, M
a
la
ys
i
a
E
m
a
il
:
h.a
lm
a
z
ni
22@
gm
a
il
.c
om
1.
I
N
T
R
O
D
U
C
T
I
O
N
C
om
bi
na
to
r
ia
l
opt
im
iz
a
ti
on
pr
obl
e
m
s
(
C
O
P
s
)
a
r
e
a
s
ubs
e
t
of
m
a
th
e
m
a
ti
c
a
l
opt
im
iz
a
ti
on
pr
obl
e
m
s
th
a
t
a
r
e
us
e
d
in
di
f
f
e
r
e
nt
f
ie
ld
s
,
r
e
ga
r
dl
e
s
s
of
w
he
th
e
r
th
e
s
tr
uc
tu
r
e
is
c
om
pl
e
x
or
s
im
pl
e
.
V
a
r
io
us
f
unc
ti
ona
l
pr
obl
e
m
s
,
s
uc
h
a
s
th
e
tr
a
ve
li
ng
s
a
le
s
m
a
n
pr
obl
e
m
(
T
S
P
)
,
th
e
a
s
s
e
m
bl
y
li
ne
ba
la
nc
in
g
pr
obl
e
m
,
th
e
s
hor
te
s
t
pa
th
tr
e
e
,
a
nd
th
e
m
in
im
um
pe
r
io
d
tr
e
e
,
c
a
n
b
e
c
la
s
s
if
ie
d
a
s
C
O
P
s
.
T
S
P
is
c
om
m
onl
y
us
e
d
to
a
s
s
e
s
s
th
e
e
f
f
ic
ie
nc
y
of
r
e
c
e
nt
ly
de
s
ig
ne
d
a
ppr
oa
c
he
s
to
C
O
P
s
a
nd
of
th
o
s
e
r
e
le
va
nt
to
m
a
ny
s
ig
ni
f
ic
a
nt
f
ie
ld
s
,
s
uc
h
a
s
e
ngi
ne
e
r
in
g, l
ogi
s
ti
c
s
, a
nd t
r
a
ns
por
t.
T
S
P
i
s
a
n N
P
-
ha
r
d pr
obl
e
m
f
ol
lo
w
in
g a
H
a
m
il
to
ni
a
n c
yc
le
w
it
h m
in
im
a
l
e
xpe
ns
e
[
1]
,
[
2]
.
I
n
th
e
T
S
P
pr
in
c
ip
le
,
th
e
ve
ndor
be
gi
n
s
f
r
om
one
c
it
y,
vi
s
it
s
a
ll
ot
he
r
c
it
ie
s
pr
e
c
i
s
e
ly
onc
e
upon
a
ti
m
e
,
a
nd
r
e
tu
r
ns
to
th
e
b
e
gi
nni
ng
c
it
y
s
e
e
ki
ng
to
ge
t
a
c
lo
s
e
d
to
ur
w
it
h
lo
w
e
s
t
e
xpe
n
s
e
.
T
he
to
ur
e
xpe
ns
e
de
pe
nd
s
di
r
e
c
tl
y
on
th
e
to
ur
le
ngt
h
[
3]
,
[
4]
.
M
a
ny
r
e
s
e
a
r
c
he
r
s
ha
v
e
s
ugge
s
te
d
s
ol
vi
ng
T
S
P
,
w
it
h
it
s
s
im
pl
e
de
s
c
r
ip
ti
on
a
nd
ve
r
y
c
om
pl
ic
a
te
d
s
ol
ut
io
n.
I
ni
ti
a
ll
y,
e
xa
c
t
a
nd
a
ppr
oxi
m
a
te
(
he
ur
is
ti
c
or
m
e
ta
he
ur
is
ti
c
)
a
ppr
oa
c
he
s
w
e
r
e
de
v
e
lo
pe
d
to
r
e
s
ol
ve
T
S
P
[
5]
,
[
6]
.
E
xa
c
t
m
e
th
ods
c
a
n
s
ol
ve
s
m
a
ll
T
S
P
s
opt
im
a
ll
y.
B
y
c
ont
r
a
s
t,
he
ur
is
ti
c
m
e
th
ods
a
r
e
pr
e
f
e
r
a
bl
e
f
or
la
r
ge
T
S
P
s
.
M
or
e
ov
e
r
,
c
e
r
ta
in
gr
e
e
dy,
pr
in
c
ip
le
-
ba
s
e
d
a
lg
or
it
hm
s
m
a
y
be
us
e
d
to
s
ol
ve
T
S
P
.
H
ow
e
ve
r
,
c
onve
n
ti
ona
l
a
ppr
oa
c
he
s
le
a
d
to
e
xpone
nt
ia
l
ti
m
e
or
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
-
8938
I
nt
J
A
r
ti
f
I
nt
e
ll
,
V
ol
.
11
, N
o.
1
,
M
a
r
c
h 20
22
:
13
-
22
14
uns
a
ti
s
f
a
c
to
r
y
qua
li
ty
.
T
o
be
a
t
th
e
s
e
s
hor
tc
om
in
gs
,
m
a
ny
m
e
ta
he
ur
is
ti
c
a
lg
or
it
hm
s
in
th
e
li
te
r
a
tu
r
e
ha
ve
be
e
n
de
ve
lo
pe
d
f
or
T
S
P
due
to
th
e
im
por
ta
nc
e
of
a
c
c
om
pl
is
hi
ng
i
m
pr
ove
d
s
ol
ut
io
ns
in
r
e
a
li
s
ti
c
c
om
put
in
g
ti
m
e
[
7]
.
M
e
ta
-
he
ur
is
ti
c
a
lg
or
it
hm
s
c
a
n
be
c
la
s
s
if
ie
d
in
to
two
m
a
jo
r
gr
oups
;
s
in
gl
e
-
ba
s
e
d
s
ol
ut
io
n
a
nd
popula
ti
on
-
ba
s
e
d
s
ol
ut
io
n
[
6]
,
[
8
]
,
[
9
]
.
T
he
a
bi
li
ty
o
f
m
e
ta
-
he
ur
is
ti
c
a
lg
or
it
hm
s
to
a
ddr
e
s
s
opt
im
iz
a
ti
on
pr
obl
e
m
s
,
s
uc
h
a
s
T
S
P
,
r
e
li
e
s
on
two
e
le
m
e
nt
s
:
e
xpl
oi
ta
ti
o
n
a
nd
e
xpl
or
a
ti
on.
E
xpl
or
a
ti
on
r
e
f
e
r
s
to
th
e
r
e
s
e
a
r
c
h
w
it
hi
n
th
e
s
e
a
r
c
h
s
pa
c
e
of
unvi
s
it
e
d
r
e
gi
ons
,
w
he
r
e
a
s
e
xpl
oi
ta
ti
on
r
e
f
e
r
s
to
th
e
s
e
a
r
c
h
in
th
e
e
xi
s
ti
ng
pr
obl
e
m
s
pa
c
e
r
e
gi
ons
f
or
good
s
ol
ut
io
ns
[
10]
–
[
12]
.
S
in
gl
e
-
ba
s
e
d
a
lg
or
it
hm
s
,
in
c
lu
di
ng
va
r
ia
bl
e
ne
ig
hbor
hood
s
e
a
r
c
h
[
13]
,
s
im
ul
a
te
d
a
nne
a
li
ng
[
14]
,
a
nd
gui
de
d
lo
c
a
l
s
e
a
r
c
h
[
15]
,
a
im
to
im
pr
ove
a
s
in
gl
e
c
a
ndi
da
t
e
s
ol
ut
io
n
.
B
y c
ont
r
a
s
t,
popula
ti
on
-
ba
s
e
d
a
lg
or
it
hm
s
m
a
in
ta
in
a
nd
e
nh
a
nc
e
c
a
ndi
da
te
s
ol
ut
io
ns
,
of
te
n
us
in
g
popula
ti
on
f
e
a
tu
r
e
s
to
c
onduc
t
di
r
e
c
t
s
e
a
r
c
h;
s
uc
h
a
lg
or
it
hm
s
in
c
lu
de
bi
oge
ogr
a
phy
-
ba
s
e
d
opt
im
iz
a
ti
on
[
16]
,
gr
e
y
w
ol
f
opt
im
iz
e
r
[1
7]
,
pa
r
ti
c
le
s
w
a
r
m
opt
im
iz
a
ti
on
(
P
S
O
)
[
18]
,
e
m
pe
r
or
pe
ngui
n
c
ol
ony
[
19]
,
ge
ne
ti
c
a
lg
or
it
hm
(
G
A
)
[
20
]
,
a
nt
c
ol
ony
op
ti
m
iz
a
ti
on
(
A
C
O
)
[
21]
,
bl
a
c
k
hol
e
(
B
H
)
a
lg
or
it
hm
[
22]
,
a
nd
dr
a
gonf
ly
a
lg
or
it
hm
(
D
A
)
[
23]
.
I
n
r
e
c
e
nt
ye
a
r
s
,
s
tu
di
e
s
on
pl
a
nt
s
ha
ve
de
m
on
s
tr
a
t
e
d
th
a
t
pl
a
nt
s
di
s
pl
a
y
in
te
ll
ig
e
nt
be
ha
vi
or
.
C
ons
e
que
nt
ly
,
pl
a
nt
s
a
r
e
be
li
e
ve
d
to
ha
ve
a
ne
r
vous
s
ys
te
m
[
24]
.
E
xa
m
pl
e
s
of
pl
a
nt
in
te
ll
ig
e
nc
e
a
lg
or
it
hm
s
in
c
lu
de
th
e
s
a
pl
in
g
gr
ow
in
g
up
a
lg
or
it
hm
[
25]
,
r
oot
e
d
tr
e
e
opt
im
iz
a
ti
on
[
26]
,
r
unne
r
r
oot
a
lg
or
it
hm
[
27
]
, a
nd s
tr
a
w
be
r
r
y a
lg
or
it
hm
a
s
pl
a
nt
pr
opa
ga
ti
on a
lg
or
it
hm
(
P
P
A
)
[
28]
.
P
P
A
w
a
s
in
it
ia
ll
y
s
ugge
s
te
d
by
[
28]
to
s
ol
ve
num
e
r
ic
a
l
pr
obl
e
m
s
;
i
t
e
m
ul
a
te
s
th
e
s
ur
vi
va
l
te
c
hni
que
a
dopt
e
d
by
pl
a
nt
s
,
in
w
hi
c
h
th
e
y
s
ur
vi
ve
by
c
ol
oni
z
in
g
ne
w
a
r
e
a
s
w
it
h
good
gr
ow
in
g
c
ondi
ti
ons
.
T
he
s
tr
a
w
be
r
r
y
pl
a
nt
ha
s
a
s
ur
vi
va
l
of
s
us
ta
in
a
bi
li
ty
a
nd
gr
ow
th
th
a
t
s
e
nd
s
hor
t
r
unne
r
s
to
e
xpl
oi
t
th
e
que
s
t
f
or
good
s
ol
ut
io
n
s
in
e
xi
s
ti
ng
pr
obl
e
m
s
pa
c
e
r
e
gi
ons
a
nd
s
e
nd
lo
ng
r
unne
r
s
in
th
e
s
e
a
r
c
h
s
pa
c
e
to
e
xpl
or
e
unvi
s
it
e
d
r
e
gi
ons
.
I
n
[
29]
,
s
tu
di
e
d
P
P
A
to
s
ol
ve
T
S
P
a
nd
s
how
e
d
th
a
t
P
P
A
c
a
n
pr
oduc
e
b
e
tt
e
r
s
ol
ut
io
ns
th
a
n
ot
he
r
a
lg
or
it
hm
s
.
H
ow
e
ve
r
,
a
ppl
yi
ng
a
de
te
r
m
in
is
ti
c
lo
c
a
l
s
e
a
r
c
h
ba
s
e
d
on
2
-
opt
a
nd
k
-
opt
ta
ke
s
e
xpone
nt
ia
l
ti
m
e
to
f
in
d
a
n
opt
im
a
l
s
ol
ut
io
n;
m
or
e
ove
r
,
w
he
n
th
is
o
c
c
ur
s
s
lo
w
s
dow
n
it
s
c
onv
e
r
ge
nc
e
s
pe
e
d,
s
im
pl
y
be
c
a
us
e
th
e
r
e
m
a
y
be
a
de
f
ic
ie
nc
y
of
di
ve
r
s
it
y
in
c
e
r
ta
in
s
ol
ut
io
ns
w
hi
c
h
le
a
ds
not
to
th
r
us
t
th
e
a
lg
or
it
h
m
to
w
a
r
ds
opt
i
m
a
l
r
e
gi
ons
.
C
ons
e
que
nt
ly
,
to
e
ns
ur
e
be
tt
e
r
c
onve
r
ge
nc
e
,
a
nd
m
a
ke
th
e
a
lg
or
it
hm
ha
ve
s
ol
ut
io
n
di
ve
r
s
it
y
in
bot
h
lo
c
a
l
a
nd
gl
oba
l
s
e
a
r
c
h.
T
hi
s
pr
e
s
e
nt
s
tu
dy
im
pl
e
m
e
nt
s
a
c
r
os
s
ove
r
ope
r
a
ti
on
a
nd
th
r
e
e
m
ut
a
ti
on
ope
r
a
ti
ons
(
f
li
p,
s
w
a
p,
a
nd
s
li
de
)
in
P
P
A
a
nd
th
e
p
r
opos
e
d
te
r
m
e
d
a
s
p
a
r
ti
a
l
-
pa
r
ti
ti
one
d
gr
e
e
dy
a
lg
or
it
hm
(
P
P
G
A
)
.
T
he
m
a
in
c
ont
r
ib
ut
io
n
of
a
s
c
ie
nt
if
ic
s
tu
dy
is
to
im
pr
ove
P
P
A
f
or
s
ol
vi
ng
T
S
P
us
in
g
T
S
P
L
I
B
a
nd
pr
oduc
e
a
pr
om
is
in
g
v
a
r
ia
nt
of
P
P
A
.
T
he
pr
opos
e
d
a
lg
or
it
hm
P
P
G
A
is
e
va
lu
a
te
d
us
in
g
10
T
S
P
da
ta
s
e
ts
(
w
it
h
di
f
f
e
r
e
nt
s
iz
e
s
a
nd
c
om
pl
e
xi
ti
e
s
)
s
e
le
c
te
d
f
r
om
tr
a
ve
li
ng
s
a
le
s
m
a
n
pr
obl
e
m
li
br
a
r
y
(
T
S
P
L
I
B
)
.
T
he
pr
opos
e
d P
P
G
A
i
s
a
ls
o c
om
pa
r
e
d w
it
h
f
iv
e
m
e
ta
he
ur
is
ti
c
a
lg
or
it
hm
s
:
A
C
O
, P
S
O
,
G
A
, B
H
, a
nd D
A
.
T
he
m
a
in
a
dva
nt
a
ge
of
P
P
G
A
i
s
t
he
a
bi
li
ty
t
o f
in
d a
n i
de
a
l
or
ne
a
r
-
i
de
a
l
s
ol
ut
io
n i
n a
s
hor
t
ti
m
e
.
T
hi
s
pa
pe
r
is
s
tr
uc
tu
r
e
d
be
in
g
a
s
:
s
e
c
ti
on
2
e
xpl
a
in
s
th
e
m
a
th
e
m
a
ti
c
s
of
T
S
P
.
S
e
c
ti
on
3
pr
ovi
de
s
th
e
li
te
r
a
tu
r
e
r
e
vi
e
w
.
A
f
te
r
w
a
r
d,
s
e
c
ti
on
4
di
s
c
us
s
e
d
th
e
pr
opos
e
d
P
P
G
A
m
e
th
ods
.
S
e
c
ti
on
5
a
nd
6
e
xpl
or
e
s
th
e
e
xpe
r
i
m
e
nt
a
l
r
e
s
ul
ts
,
pe
r
f
or
m
a
nc
e
e
va
lu
a
ti
on,
a
nd
be
nc
hm
a
r
k
da
ta
s
e
ts
us
e
d
in
th
is
s
tu
dy
a
r
e
pr
e
s
e
nt
e
d.
L
a
s
tl
y, s
e
c
ti
on 7 the
c
onc
lu
s
io
ns
a
nd r
e
c
om
m
e
nd
a
ti
ons
f
or
pot
e
nt
ia
l
f
ut
ur
e
r
e
s
e
a
r
c
h a
r
e
gi
ve
n.
2.
T
R
A
V
E
L
I
N
G
S
A
L
E
S
M
A
N
P
R
O
B
L
E
M
T
he
im
por
ta
nc
e
of
T
S
P
is
a
tt
r
ib
ut
e
d
to
th
e
de
ta
il
e
d
s
tu
di
e
s
a
nd
hi
gh
gui
de
li
ne
s
of
c
om
put
e
r
s
c
ie
nt
is
ts
f
or
it
to
be
in
c
lu
d
e
d
in
th
e
a
s
s
e
s
s
m
e
nt
of
m
ode
r
n
op
ti
m
iz
a
ti
on
a
lg
or
it
hm
s
.
T
hi
s
pr
obl
e
m
ha
s
be
e
n
s
how
n
to
be
a
n
N
P
-
ha
r
d
pr
obl
e
m
.
I
t
c
a
n
be
de
f
in
e
d
be
in
g
a
s
:
A
n
a
ge
nt
m
us
t
vi
s
it
N
node
s
e
x
a
c
tl
y
onc
e
a
nd
r
e
tu
r
n
a
t
th
e
s
ta
r
ti
ng
node
a
t
th
e
lo
w
e
s
t
e
xpe
ns
e
,
i.
e
.,
lo
w
e
s
t
ti
m
e
of
vi
s
it
a
ti
on
or
th
e
s
hor
te
s
t
di
s
ta
nc
e
.
A
c
os
t
m
a
tr
ix
=
[
]
is
e
xpl
or
e
d
to
obt
a
in
a
pe
r
m
ut
a
ti
on
∶
{
0
,
…
,
−
1
}
→
{
0
,
…
,
−
1
}
,
w
he
r
e
c
ij
s
how
s
th
e
e
xpe
n
s
e
of
vi
s
it
in
g
node
(
j)
f
r
om
node
(
i)
.
T
he
a
im
i
s
to
r
e
d
uc
e
a
n
obj
e
c
ti
ve
f
unc
ti
on
r
e
pr
e
s
e
nt
e
d
by
(
,
)
a
s
s
how
n
in
(
1)
:
(
,
)
=
∑
(
(
)
,
(
+
1
)
)
+
(
(
)
,
(
1
)
)
−
1
=
0
(
1)
w
he
r
e
(
)
s
how
s
th
e
ℎ
node
in
pe
r
m
ut
a
ti
on
,
d
is
th
e
di
s
ta
nc
e
be
twe
e
n
node
s
a
nd
c
ij
=
c
ji
∀
i,
j
a
nd
th
e
pos
it
io
n of
c
it
y (
i)
c
a
n be
ve
r
if
ie
d by uti
li
z
in
g t
he
va
lu
e
s
of
t
he
x
-
a
xe
s
, a
nd y
-
a
xe
s
, i
.
e
.,
x
i
a
nd
y
i
s
e
que
nt
ia
ll
y.
3.
L
I
T
E
R
A
T
U
R
E
R
E
V
I
E
W
V
a
r
io
us
a
lg
or
it
hm
s
,
in
c
lu
di
ng
s
in
g
le
a
nd
hyb
r
id
a
lg
o
r
it
hm
s
,
f
or
T
S
P
ha
ve
be
e
n
de
ve
lo
pe
d.
I
n
[
30
]
pr
opos
e
d
a
hybr
id
a
ppr
oa
c
h
us
in
g
P
S
O
to
im
pr
ove
A
C
O
pe
r
f
or
m
a
nc
e
pa
r
a
m
e
te
r
s
.
I
n
a
ddi
ti
on,
a
3
-
opt
lo
c
a
l
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
A
r
ti
f
I
nt
e
ll
I
S
S
N
:
2252
-
8938
I
m
pr
ov
e
d di
s
c
r
e
te
pl
ant
pr
opagati
on algor
it
hm
f
o
r
s
ol
v
in
g
th
e
…
(
H
us
s
e
in
F
ouad A
lmaz
in
i)
15
s
e
a
r
c
h
w
a
s
e
ndow
e
d
to
th
e
pr
opos
e
d
a
ppr
oa
c
h
to
e
nh
a
nc
e
lo
c
a
l
s
e
a
r
c
h.
H
ow
e
ve
r
,
th
e
pr
opos
e
d
a
lg
or
it
hm
ha
s
m
a
ny
ope
r
a
ti
ons
th
a
t
c
ons
um
e
a
ddi
ti
ona
l
ti
m
e
in
im
pr
ovi
ng
t
he
s
a
m
e
s
e
a
r
c
h
r
e
gi
ons
to
de
te
r
m
in
e
th
e
be
s
t
im
pr
ove
m
e
nt
.
I
n
[
31]
s
ol
ve
d
th
e
is
s
ue
of
uns
ta
bl
e
na
tu
r
e
in
s
t
a
nc
e
pr
obl
e
m
by
pr
ovi
di
ng
A
C
O
w
it
h
a
lo
c
a
l
s
e
a
r
c
h
ope
r
a
to
r
. T
hi
s
ope
r
a
to
r
it
e
r
a
ti
ve
ly
c
hoo
s
e
s
th
e
b
e
s
t
s
ol
ut
io
n
f
ound
by
th
e
a
lg
or
it
hm
a
nd
th
e
n c
on
ti
nue
s
to
r
e
m
ove
or
in
s
e
r
t
c
it
ie
s
to
im
pr
ove
th
e
s
ol
ut
io
n
qua
li
ty
.
N
o
ne
th
e
le
s
s
,
us
in
g
m
ul
ti
-
ope
r
a
to
r
in
lo
c
a
l
s
e
a
r
c
h
m
a
y
r
a
di
c
a
ll
y
in
c
r
e
a
s
e
th
e
c
om
put
a
ti
on
ti
m
e
or
r
e
duc
e
th
e
ir
pe
r
f
or
m
a
nc
e
.
G
A
ha
s
be
e
n
im
pl
e
m
e
nt
e
d
by
s
e
ve
r
a
l
r
e
s
e
a
r
c
he
r
s
f
or
T
S
P
.
I
n
[
32]
pr
opos
e
d
th
e
us
e
of
G
A
to
r
e
s
ol
ve
th
e
c
ha
ll
e
ngi
ng
la
r
ge
-
s
c
a
le
c
ol
or
e
d
ba
la
nc
e
d
T
S
P
.
ne
ve
r
th
e
le
s
s
,
th
e
pr
opos
e
d
n
e
xt
ge
ne
r
a
ti
on
a
c
c
e
s
s
(
N
G
A
)
a
lg
or
it
hm
s
houl
d
de
m
ons
tr
a
te
good
pe
r
f
or
m
a
nc
e
i
n t
e
r
m
s
of
s
ol
vi
ng s
pe
e
d or
s
ol
ut
io
n qua
li
ty
.
I
n a
c
c
or
da
nc
e
w
it
h
[
33]
s
tu
di
e
d a
hybr
id
m
e
ta
he
ur
is
ti
c
a
lg
or
it
h
m
s
a
ddr
e
s
s
T
S
P
ba
s
e
d on
s
im
m
ul
a
te
d
a
nne
a
li
ng
(
SA
)
a
nd
th
e
s
ym
bi
ot
ic
or
ga
ni
s
m
s
s
e
a
r
c
h
. T
he
pos
s
ib
le
c
ha
ll
e
nge
of
th
e
pr
opos
e
d
a
lg
or
it
hm
c
a
n
be
f
ound
to
a
f
e
w
c
ons
id
e
r
a
ti
ons
,
th
e
pr
opos
e
d
a
lg
or
it
hm
in
c
lu
de
s
th
e
us
e
of
s
e
ve
r
a
l
pa
r
a
m
e
t
e
r
s
.
A
ddi
ti
ona
ll
y,
in
c
r
e
a
s
in
g
th
e
pr
obl
e
m
c
om
pl
e
xi
ty
,
th
e
c
onf
ig
ur
a
ti
on
of
th
e
a
l
gor
it
hm
is
li
nke
d
to
it
.
I
n
a
not
he
r
r
e
la
te
d
w
or
k
[
34]
s
tu
di
e
d
on
im
pr
ovi
ng
th
e
pe
r
f
or
m
a
nc
e
of
th
e
S
A
by
us
in
g
a
gr
e
e
dy
s
e
a
r
c
h
to
de
a
l
pr
ope
r
ly
w
it
h
la
r
ge
-
s
c
a
le
T
S
P
.
H
ow
e
ve
r
,
th
e
pr
opos
e
d
a
lg
or
it
hm
s
tu
c
k
in
lo
c
a
l
opt
im
a
.
T
hi
s
is
be
c
a
us
e
th
e
S
A
ut
il
iz
e
s
a
gr
e
e
dy
a
c
c
e
pt
a
nc
e
c
r
it
e
r
io
n
th
a
t
onl
y
ta
ke
s
a
n
opt
im
iz
e
d
s
ol
ut
io
n
a
nd
e
xc
lu
de
s
th
e
w
or
s
t
s
ol
ut
io
n.
T
h
e
pr
oba
bi
li
s
ti
c
T
S
P
w
a
s
s
ol
ve
d
in
m
ul
ti
pl
e
tr
ia
ls
in
[
35]
th
r
ough
a
n
a
da
pt
iv
e
m
ul
ti
s
w
a
r
m
P
S
O
.
I
n
th
e
s
ugge
s
te
d
a
da
pt
iv
e
P
S
O
,
r
a
ndom
va
lu
e
s
a
r
e
a
ll
oc
a
te
d
in
th
e
in
it
ia
l
s
ta
ge
of
th
e
s
e
a
r
c
h.
N
e
xt
,
th
e
s
e
pa
r
a
m
e
te
r
s
a
r
e
c
onf
ig
ur
e
d
dyna
m
ic
a
ll
y
a
t
th
e
s
a
m
e
ti
m
e
a
s
th
e
obj
e
c
ti
ve
f
unc
ti
on
o
f
th
e
pr
obl
e
m
is
opt
im
iz
e
d.
N
one
th
e
le
s
s
,
th
e
s
e
a
r
c
h
pr
oc
e
s
s
la
c
ks
f
e
e
dba
c
k
in
f
or
m
a
ti
on
a
nd
le
a
r
ni
ng
due
to
ha
vi
ng
le
s
s
va
lu
e
s
of
pa
r
a
m
e
te
r
s
to
opt
im
iz
e
.
I
n
[
36]
s
tr
e
ngt
he
ne
d
P
S
O
to
s
ol
ve
th
e
im
pr
e
c
i
s
e
c
o
s
t
m
a
tr
ix
T
S
P
.
T
he
P
S
O
m
odi
f
ic
a
ti
ons
c
ons
is
t
of
th
e
a
dopt
io
n
of
th
e
s
w
a
p s
e
r
ie
s
, t
he
s
w
a
p pr
oc
e
s
s
, a
nd t
h
e
gui
de
li
ne
s
f
or
va
r
io
us
s
pe
e
d upda
t
e
s
. N
one
th
e
l
e
s
s
,
s
e
ve
r
a
l
m
e
th
ods
ha
ve
be
e
n
u
s
e
d
in
th
e
pr
opo
s
e
d
a
lg
or
it
hm
w
hi
c
h
a
f
f
e
c
ts
to
ta
k
e
a
ddi
ti
ona
l
ti
m
e
to
ge
t
th
e
be
s
t
im
pr
ove
m
e
nt
.
I
n
[
37]
pr
opos
e
d
a
hybr
id
b
e
twe
e
n
f
ir
e
f
ly
a
lg
or
it
hm
(
F
A
)
a
nd
G
A
;
he
r
e
,
th
e
di
s
ta
nc
e
of
th
e
F
A
i
s
r
e
de
f
in
e
d
by
pr
e
s
e
nt
in
g
two
s
w
a
p
m
e
th
ods
to
p
r
e
ve
nt
dr
oppi
ng
in
to
lo
c
a
l
opt
im
a
.
T
he
c
r
e
a
te
d
popula
ti
on
w
hi
c
h
ha
s
poor
s
ol
ut
io
ns
t
ha
t
c
oul
d l
e
a
d t
o l
ong
-
te
r
m
c
onve
r
ge
nc
e
t
o a
n i
de
a
l
s
ol
ut
io
n.
A
c
c
or
di
ng
to
[
38]
in
ve
s
ti
ga
te
d
th
e
B
H
a
lg
or
it
hm
to
s
ol
ve
T
S
P
.
T
he
im
pl
e
m
e
nt
a
ti
on
of
th
e
B
H
a
lg
or
it
hm
w
a
s
a
s
s
e
s
s
e
d
on
10
da
ta
s
e
t
s
a
nd
th
e
out
c
om
e
s
in
c
o
m
pa
r
is
on
w
it
h
ot
he
r
opt
im
iz
a
ti
on
te
c
hni
que
s
.
T
he
c
om
put
a
ti
ona
l
r
e
s
ul
ts
s
ho
w
e
d
th
a
t
th
e
B
H
a
lg
or
it
hm
c
a
n
pr
ovi
de
s
ol
ut
io
ns
be
tt
e
r
th
a
n
A
C
O
,
G
A
,
a
nd
P
S
O
.
H
ow
e
ve
r
,
T
he
B
H
a
lg
or
it
hm
s
ti
ll
la
c
k
s
th
e
c
a
pa
bi
li
ty
to
pe
r
f
or
m
hi
gh
e
xpl
or
a
ti
on
dur
in
g
th
e
upda
te
pr
oc
e
s
s
.
D
ue
to
a
ne
w
s
ol
ut
io
n
is
pr
oduc
e
d
r
a
ndoml
y
w
he
n
th
e
pr
e
vi
ou
s
s
ol
ut
io
n
is
not
im
pr
ove
d.
F
ur
th
e
r
m
or
e
,
a
s
im
il
a
r
s
tu
dy
w
a
s
c
onduc
te
d
in
[
39]
to
in
ve
s
ti
ga
te
th
e
D
A
on
s
ol
vi
ng
T
S
P
.
P
P
A
ha
s
be
e
n
in
ve
s
ti
ga
te
d
to
w
or
k
on
di
s
c
r
e
te
pr
obl
e
m
s
,
s
pe
c
if
ic
a
ll
y
on
T
S
P
[
29]
.
T
he
r
e
s
e
a
r
c
h
c
onc
e
r
ns
th
e
us
a
ge
of
th
e
id
e
a
of
l
ong a
nd s
hor
t
r
unne
r
s
i
n
m
a
xi
m
um
gr
a
phs
w
hi
le
l
ooki
n
g f
or
H
a
m
il
to
ni
a
n c
yc
le
s
. T
he
pe
r
f
or
m
a
nc
e
of
th
e
P
P
A
a
lg
or
it
hm
w
a
s
te
s
te
d
on
a
tr
a
di
ti
ona
l
da
ta
s
e
t
a
nd
c
o
m
pa
r
e
d
w
it
h
th
a
t
of
P
S
O
S
A
,
G
A
,
a
nd
F
A
.
E
xpe
r
im
e
nt
a
l
r
e
s
ul
ts
w
e
r
e
in
c
lu
de
d;
how
e
ve
r
,
th
e
pe
r
f
or
m
a
n
c
e
of
th
e
a
lg
or
it
hm
in
s
ol
vi
ng
T
S
P
m
us
t
be
f
ur
th
e
r
in
ve
s
ti
ga
te
d
a
nd
c
om
pa
r
e
d
w
it
h
th
a
t
of
ot
he
r
opt
im
iz
a
ti
on
m
e
th
ods
.
B
e
s
id
e
s
,
th
e
P
P
A
a
lg
or
it
hm
s
uf
f
e
r
s
f
r
om
s
lo
w
s
dow
n
it
s
c
onve
r
ge
nc
e
s
pe
e
d,
s
i
m
pl
y
be
c
a
us
e
th
e
r
e
m
a
y
be
a
de
f
ic
ie
nc
y
of
di
ve
r
s
it
y
in
c
e
r
ta
in
s
ol
ut
io
ns
w
hi
c
h l
e
a
d
s
not
t
o t
hr
us
t
th
e
a
lg
or
it
hm
t
ow
a
r
ds
opt
im
a
l
r
e
gi
ons
.
4.
P
R
O
P
O
S
E
D
P
A
R
T
I
A
L
-
P
A
R
T
I
T
I
O
N
E
D
G
R
E
E
D
Y
A
L
G
O
R
I
T
H
M
F
O
R
T
R
A
V
E
L
I
N
G
S
A
L
E
S
M
A
N
P
R
O
B
L
E
M
P
P
G
A
r
a
ndoml
y
be
gi
ns
w
it
h
th
e
in
it
ia
l
popula
ti
on
of
p
la
nt
s
/t
our
s
/s
ol
ut
io
ns
a
nd
it
e
r
a
ti
ve
ly
im
pr
ovi
s
e
s
s
ol
ut
io
ns
f
or
a
gi
ve
n
pr
obl
e
m
in
s
ta
nc
e
.
I
n
e
a
c
h
it
e
r
a
ti
on,
P
P
G
A
im
pr
ovi
s
e
s
s
ol
ut
io
ns
by
us
in
g
s
hor
t
a
nd l
ong r
unne
r
s
. T
he
P
P
G
A
a
lg
or
it
hm
pr
oc
e
e
ds
a
s
:
4.1.
I
n
it
ia
l
p
op
u
la
t
io
n
T
he
in
it
ia
l
popula
ti
on
i
s
a
c
ol
le
c
ti
on
of
a
n
or
de
r
e
d
li
s
t
of
pl
a
nt
s
w
he
r
e
e
ve
r
y
pl
a
nt
r
e
pr
e
s
e
nt
s
a
s
e
que
nc
e
of
c
it
ie
s
.
is
to
ur
i,
i=
1,
.
.
.,
N
P
,
im
pl
yi
ng
th
a
t
N
P
i
s
t
he
pl
a
nt
popula
ti
on
s
iz
e
.
I
n
a
c
c
or
da
nc
e
w
it
h
th
e
E
uc
li
de
a
n
di
s
ta
nc
e
,
to
ur
le
ngt
hs
a
r
e
c
a
lc
ul
a
te
d.
E
a
c
h
c
it
y
of
pl
a
nt
is
a
s
s
ig
ne
d
a
la
b
e
l
of
c
it
y
s
uc
h
th
a
t
no
c
it
y
c
a
n
be
s
e
e
n
twi
c
e
in
th
e
s
a
m
e
pl
a
nt
.
T
S
P
to
u
r
r
e
pr
e
s
e
nt
a
ti
on
pr
im
a
r
il
y
ha
s
two
s
tr
a
te
gi
e
s
:
a
dj
a
c
e
nc
y
a
nd
pa
th
.
I
n
th
is
s
tu
dy,
pa
th
r
e
pr
e
s
e
nt
a
ti
on
is
c
hos
e
n
f
or
a
to
ur
.
A
s
s
how
n
in
F
ig
ur
e
1,
le
t
{
A
,
B
,
C
,
D
,
E
}
be
th
e
l
a
be
ls
of
c
it
ie
s
w
he
r
e
A
i
s
t
he
s
t
a
r
ti
ng point
.
F
ig
ur
e
1. P
la
nt
/t
our
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
-
8938
I
nt
J
A
r
ti
f
I
nt
e
ll
,
V
ol
.
11
, N
o.
1
,
M
a
r
c
h 20
22
:
13
-
22
16
4.2.
S
h
or
t
r
u
n
n
e
r
s
(
e
xp
lo
it
at
io
n
t
as
k
)
A
pr
e
-
de
te
r
m
in
e
d t
our
s
e
t
is
t
a
ke
n f
r
o
m
t
he
one
s
t
ha
t
ha
d s
hor
t
-
le
ngt
h t
our
s
a
f
te
r
s
or
ti
ng t
he
to
ur
s
by
t
he
ir
to
ur
le
ngt
hs
;
f
r
om
th
e
s
e
to
ur
s
,
s
hor
t
r
unne
r
s
a
r
e
s
e
nt
,
i.
e
.,
ne
w
lo
c
a
l
to
ur
s
a
r
e
pr
oduc
e
d
f
r
om
th
e
m
.
C
r
os
s
ove
r
is
th
e
s
ynt
he
s
is
of
th
e
two
to
u
r
s
to
c
r
e
a
te
ne
w
to
ur
s
th
a
t
a
r
e
c
opi
e
d
in
to
th
e
ne
w
to
ur
s
.
T
he
c
r
os
s
ove
r
ope
r
a
ti
on,
w
hi
c
h
ut
il
iz
e
s
th
e
c
r
os
s
ove
r
s
im
pl
e
s
t
c
a
s
e
,
r
a
ndoml
y
c
hoos
e
s
two
to
ur
s
to
c
r
os
s
ove
r
,
r
a
ndoml
y pi
c
ks
a
c
r
os
s
ov
e
r
poi
nt
on t
he
ba
s
is
of
(
2)
, a
nd t
he
n c
ha
nge
s
a
ll
c
it
ie
s
a
f
te
r
t
ha
t
poi
nt
.
.
.
.
=
r
.
(
.
.
.
−
2
)
+
1
(
2)
w
he
r
e
C
P
s
how
s
t
he
c
r
os
s
ov
e
r
poi
nt
, r
∈
[
0, 1]
i
s
a
r
a
ndoml
y s
e
le
c
te
d i
nde
x, a
nd L
i
s
t
he
s
iz
e
of
pl
a
nt
s
.
4.3.
L
on
g r
u
n
n
e
r
s
(
e
xp
lo
r
at
io
n
t
as
k
)
L
ong r
unne
r
s
a
r
e
i
m
pl
e
m
e
nt
e
d by us
in
g
th
r
e
e
m
ut
a
ti
on ope
r
a
ti
ons
(
f
li
p, s
w
a
p, a
nd s
li
de
)
. T
o e
xpl
a
i
n
th
e
f
li
p,
s
w
a
p,
a
nd
s
li
de
ope
r
a
ti
ons
,
A
,
B
,
C
,
D
a
nd
E
a
r
e
c
o
ns
id
e
r
e
d
c
it
ie
s
in
th
e
to
ur
vi
s
it
e
d
in
s
e
que
nc
e
{
A
→B
→C
→D
→E
}
. T
he
ope
r
a
ti
on s
tr
uc
tu
r
e
s
pr
oduc
e
d
a
r
e
pr
e
s
e
nt
e
d a
s
:
−
F
li
p:
O
r
de
r
s
t
he
c
it
ie
s
vi
c
e
ve
r
s
a
f
r
om
t
he
la
s
t
c
it
y t
o t
he
f
i
r
s
t
c
i
ty
;
th
e
ne
w
s
e
que
nc
e
i
s
{
A
→ E
→ D →
C
→ B
}
.
−
S
w
a
p:
S
w
a
ps
two
c
it
ie
s
in
th
e
to
ur
,
w
he
r
e
B
a
nd
E
a
r
e
e
xc
ha
n
ge
d
th
e
ne
w
s
e
que
n
c
e
is
{
A
→E
→
C
→
D
→ B
}
.
−
S
li
de
:
S
li
de
s
two
c
it
ie
s
(
B
a
nd
C
)
a
f
te
r
a
ll
th
e
ot
he
r
c
it
ie
s
’
pos
i
ti
ons
;
th
e
ne
w
s
e
que
nc
e
is
{
A
→
D
→
E
→ B
→ C
}
.
P
P
G
A
s
ta
r
te
d
w
it
h
a
good
popula
ti
on
of
to
ur
s
(
pl
a
nt
s
)
.
T
h
e
in
it
ia
l
popula
ti
on
di
ve
r
s
it
y
is
s
uppos
e
d
to
be
c
r
e
a
te
d
by
r
a
ndom
m
e
th
od
s
ut
il
iz
e
d
to
c
r
e
a
te
to
ur
s
.
T
h
e
r
e
f
or
e
,
s
hor
t
r
unne
r
s
c
onduc
t
th
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I
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2252
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8938
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il
a
bl
e
in
th
e
li
te
r
a
tu
r
e
:
i.
g.,
A
C
O
,
P
S
O
,
G
A
,
a
nd
B
H
by
[
38]
a
nd
D
A
pr
opos
e
d
by
[
39]
.
T
he
c
om
put
a
ti
ona
l
r
e
s
ul
t
s
a
r
e
pr
e
s
e
nt
e
d
in
T
a
bl
e
3
.
T
he
be
s
t,
w
or
s
t,
a
ve
r
a
ge
,
s
ta
nda
r
d
de
vi
a
ti
on (
S
td
)
, a
nd t
im
e
(
in
s
e
c
onds
)
a
r
e
s
ta
te
d f
or
e
a
c
h a
lg
or
it
hm
i
n T
a
bl
e
3
.
T
a
bl
e
3
il
lu
s
tr
a
te
s
da
ta
s
how
in
g
th
a
t
P
P
G
A
obt
a
in
s
th
e
be
s
t
r
e
s
ul
ts
in
s
ix
da
ta
s
e
ts
out
of
10
da
ta
s
e
ts
,
w
hi
c
h
m
e
a
ns
60%
be
tt
e
r
th
a
n
A
C
O
.
P
P
G
A
out
pe
r
f
or
m
s
P
S
O
,
G
A
,
a
nd
D
A
in
a
ll
10
da
t
a
s
e
t
s
.
P
P
G
A
a
ls
o
a
c
hi
e
ve
s
be
tt
e
r
out
c
om
e
s
i
n 5 da
ta
s
e
t
s
a
nd e
qua
l
r
e
s
ul
ts
i
n one
da
ta
s
e
t
th
a
n B
H
. S
m
a
ll
va
lu
e
s
de
m
ons
tr
a
te
t
he
be
s
t
s
ol
ut
io
ns
obt
a
in
e
d
a
nd
vi
c
e
ve
r
s
a
.
I
n
a
ddi
ti
on,
f
or
e
a
c
h
a
lg
or
it
hm
,
th
e
S
td
on
va
r
io
us
r
uns
is
gi
ve
n
t
o
de
m
ons
tr
a
te
a
lg
or
it
hm
e
f
f
ic
ie
nc
y
a
nd
s
ta
bi
li
ty
.
A
de
s
c
r
ip
ti
on
of
th
e
a
ve
r
a
ge
c
om
pa
r
is
on
is
s
how
n
in
th
e
lo
w
e
r
pa
r
t
of
th
e
ta
bl
e
.
A
lo
ng
w
it
h
th
e
r
e
s
ul
ts
gi
ve
n
in
T
a
bl
e
3
,
th
e
a
ve
r
a
ge
to
ur
c
os
ts
in
c
ol
um
n
f
iv
e
f
or
a
ll
th
e
da
ta
s
e
ts
pr
ove
t
ha
t
P
P
G
A
i
s
be
tt
e
r
t
ha
n A
C
O
, P
S
O
,
G
A
, B
H
, a
nd D
A
. B
a
s
e
d on the
r
e
s
ul
t
s
i
n T
a
bl
e
3, t
he
pr
opos
e
d
P
P
G
A
a
lg
or
it
hm
s
upe
r
io
r
i
ty
ot
he
r
a
lg
or
it
hm
s
in
s
om
e
da
ta
a
nd
r
iv
a
l
in
ot
he
r
da
ta
th
is
is
due
to
th
e
im
pr
ove
m
e
nt
pr
oc
e
s
s
a
c
hi
e
v
e
d
in
P
P
G
A
by
th
e
c
r
os
s
ov
e
r
a
n
d
th
r
e
e
m
ut
a
ti
on
op
e
r
a
ti
ons
(
f
li
p,
s
w
a
p,
a
nd
s
li
de
)
.
W
he
r
e
c
r
os
s
ove
r
a
nd
th
r
e
e
m
ut
a
ti
on
ope
r
a
ti
ons
(
f
li
p,
s
w
a
p,
a
nd
s
li
de
)
h
a
ve
a
r
e
s
pons
ib
il
it
y
in
th
e
ba
la
nc
e
be
twe
e
n e
xpl
oi
ta
ti
on a
nd e
xpl
or
a
ti
on. T
he
a
ve
r
a
ge
t
our
c
os
t
f
or
P
P
G
A
i
s
6477.39
f
or
t
he
s
e
le
c
te
d t
e
n
pr
obl
e
m
s
.
T
he
a
c
c
om
pl
is
he
d
a
ve
r
a
g
e
to
ur
c
os
ts
f
or
A
C
O
,
P
S
O
,
G
A
,
B
H
,
a
nd
D
A
a
r
e
7089.73,
8307.81
,
7661.78,
6546.42,
a
nd
6994.93,
r
e
s
pe
c
ti
ve
ly
.
M
or
e
ove
r
,
th
e
s
ta
nda
r
d
s
ol
ut
io
n
de
vi
a
ti
on
a
c
hi
e
v
e
d
by
th
e
P
P
G
A
a
lg
or
it
hm
is
s
li
ght
ly
w
or
s
e
th
a
n
D
A
,
but
be
tt
e
r
th
a
n
A
C
O
,
P
S
O
,
G
A
,
a
nd
B
H
.
T
hi
s
r
e
s
ul
t
im
pl
ie
s
th
a
t
in
s
e
e
ki
ng opti
m
a
l
s
ol
ut
io
ns
, t
he
P
P
G
A
a
lg
o
r
it
hm
i
s
m
o
r
e
e
f
f
ic
i
e
nt
a
nd
r
obus
t,
w
he
r
e
a
s
ot
he
r
a
lg
or
it
hm
s
s
uc
h
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
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2252
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I
m
pr
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d di
s
c
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te
pl
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pr
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on algor
it
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(
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F
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19
a
s
A
C
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P
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,
a
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B
H
m
a
y
be
s
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c
k
in
lo
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F
in
a
ll
y,
th
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p
r
opos
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d
P
P
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a
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on of
P
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ve
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r
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S
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m
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22
A
C
O
75.39
75.84
75.48
0.19
84.27
PSO
75.91
77.18
76.21
0.55
61.87
GA
75.77
76.44
75.98
1.23
63.39
BH
75.30
75.93
75.68
0.34
50.44
DA
76.82
80.93
77.83
1.16
21.00
P
P
G
A
75.30
76.58
75.92
0.56
4.86
ba
ys
29
A
C
O
9239.19
11014.44
9823.20
722.41
88.25
PSO
9120.33
9498.17
9195.90
168.97
88.82
GA
9751.42
10513.91
10015.23
319.87
57.11
BH
9396.47
9507.17
9463.25
60.95
52.10
DA
9387.03
9611.78
9480.29
64.96
22.00
P
P
G
A
9105.87
9764.46
9311.17
287.96
6.44
ba
yg29
A
C
O
9447.49
11033.54
9882.21
675.83
99.95
PSO
9329.25
11332.72
9947.02
799.40
75.29
GA
9579.12
10411.19
9771.95
127.11
56.16
BH
9375.44
9375.44
9375.44
0.00
45.87
DA
9464.41
9704.98
9547.75
64.75
22.00
P
P
G
A
9120.33
9568.70
9318.19
178.09
2.57
a
t
t
48
A
C
O
35230.90
46204.24
39436.18
4874.29
133.45
PSO
36996.44
61421.99
47018.41
9685.89
84.73
GA
35312.51
50671.45
43620.63
2004.00
57.35
BH
34200.86
35528.51
34473.84
589.80
43.21
DA
37225.85
38683.21
37759.73
425.69
23.00
P
P
G
A
33961.11
34581.00
34585.88
495.81
9.33
e
i
l
51
A
C
O
454.38
469.05
461.01
6.29
59.19
PSO
469.15
737.52
574.80
107.23
57.25
GA
448.83
462.11
453.47
9.41
59.63
BH
437.89
526.89
458.92
38.63
44.39
DA
471.56
491.65
475.16
4.51
23.00
P
P
G
A
444.03
458.42
450.39
5.20
9.91
be
r
l
i
n52
A
C
O
7757.02
10541.12
8522.90
1152.2
65.07
PSO
9218.46
14279.43
11089.52
2067.93
68.64
GA
8779.75
9565.37
9288.44
1301.21
52.73
BH
8188.07
9356.74
8455.83
508.98
43.40
DA
9400.75
9610.15
9486.70
72.54
23.00
P
P
G
A
7748.63
8359.85
8190.14
261.48
10.00
s
t
70
A
C
O
711.65
855.20
757.75
59.60
94.56
PSO
1030.84
1756.12
1321.81
269.27
55.28
GA
1112.30
1242.20
1158.84
52.17
55.09
BH
723.26
1081.10
797.57
125.22
45.33
DA
797.47
887.08
839.01
24.28
29.00
P
P
G
A
714.36
804.27
770.25
34.71
13.14
e
i
l
76
A
C
O
574.24
665.99
594.14
40.21
61.74
PSO
804.26
1195.90
975.63
152.40
56.76
GA
619.22
679.78
652.05
122.09
46.69
BH
566.24
925.84
659.10
152.17
46.54
DA
624.92
674.48
644.89
13.03
30.00
P
P
G
A
586.47
632.15
604.68
17.33
14.35
gr
96
A
C
O
555.75
639.91
580.54
33.93
84.38
PSO
1095.11
1728.82
1378.86
247.50
56.21
GA
737.96
748.35
742.42
4.32
63.24
BH
546.83
1197.87
807.24
258.81
43.58
DA
671.00
836.00
734.05
47.26
40.00
P
P
G
A
634.36
721.80
670.88
34.65
17.92
e
i
l
101
A
C
O
725.09
868.20
763.92
59.96
89.63
PSO
1158.70
1973.81
1499.99
319.74
62.09
GA
828.88
854.43
838.83
9.96
55.18
BH
720.38
1249.86
897.38
210.14
45.83
DA
812.80
997.60
898.52
47.90
36.00
P
P
G
A
774.68
835.36
796.48
27.11
18.85
A
ve
r
a
ge
A
C
O
6477.11
8236.75
7089.73
762.49
86.04
PSO
6929.84
10400.17
8307.81
1381.88
66.69
GA
6724.57
8522.52
7661.78
395.13
56.65
BH
6423.07
6882.53
6546.42
194.50
46.06
DA
6893.26
7157.78
6994.93
76.60
26.9
P
P
G
A
6316.51
6580.25
6477.39
134.29
10.73
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
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I
nt
J
A
r
ti
f
I
nt
e
ll
,
V
ol
.
11
, N
o.
1
,
M
a
r
c
h 20
22
:
13
-
22
20
7.
C
O
N
C
L
U
S
I
O
N
F
or
s
e
ve
r
a
l
de
c
a
de
s
,
th
e
c
r
e
a
ti
on
of
in
te
ll
ig
e
nt
be
ha
vi
or
in
pl
a
nt
s
to
s
ol
ve
c
om
pl
e
x
pr
obl
e
m
s
ha
s
be
e
n
a
n
im
por
ta
nt
r
e
s
e
a
r
c
h
a
r
e
a
.
I
n
th
is
s
tu
dy,
di
s
c
r
e
te
P
P
A
is
i
m
pr
ove
d
to
s
ol
ve
C
O
P
s
,
pa
r
ti
c
ul
a
r
ly
th
e
T
S
P
.
T
he
a
lg
or
it
hm
is
e
va
lu
a
te
d
on
te
n
be
nc
hm
a
r
k
da
ta
s
e
ts
a
nd
c
o
m
pa
r
e
d
w
it
h
f
iv
e
c
om
m
on
a
lg
or
it
hm
s
in
th
e
li
te
r
a
tu
r
e
to
de
te
r
m
in
e
th
e
e
f
f
ic
a
c
y
of
th
e
pr
opos
e
d
P
P
G
A
a
lg
or
it
hm
f
o
r
s
ol
vi
ng
T
S
P
.
T
he
e
xpe
r
im
e
nt
a
l
r
e
s
ul
ts
in
di
c
a
te
th
a
t,
r
e
la
ti
ve
to
A
C
O
,
P
S
O
,
G
A
,
B
H
,
a
nd
D
A
,
th
e
P
P
G
A
a
lg
o
r
it
hm
c
a
n
y
ie
ld
hi
gh
-
qua
li
t
y
s
ol
ut
io
ns
.
M
or
e
ove
r
,
th
e
e
xpe
r
im
e
nt
a
l
r
e
s
ul
ts
de
m
ons
tr
a
te
th
a
t
P
P
G
A
c
ons
id
e
r
a
bl
y
out
pe
r
f
o
r
m
s
ot
he
r
a
lg
or
it
hm
s
in
te
r
m
s
o
f
a
ve
r
a
ge
to
ur
c
os
t
a
nd
e
xe
c
ut
io
n
ti
m
e
.
F
ur
th
e
r
r
e
s
e
a
r
c
h
c
onc
e
r
ns
e
xt
e
ndi
ng
P
P
G
A
t
o
s
ol
ve
ot
he
r
C
O
P
s
s
u
c
h
a
s
,
th
e
f
a
c
il
it
y
la
yout
pr
ob
le
m
,
th
e
qua
d
r
a
ti
c
a
s
s
ig
nm
e
nt
pr
obl
e
m
,
a
nd
ve
hi
c
le
r
out
in
g
pr
obl
e
m
s
.
R
E
F
E
R
E
N
C
E
S
[
1]
T
.
S
a
ha
i
,
“
D
yna
m
i
c
a
l
s
y
s
t
e
m
s
t
he
or
y
a
nd
a
l
gor
i
t
hm
s
f
or
N
P
-
ha
r
d
pr
obl
e
m
s
,”
S
t
udi
e
s
i
n
Sy
s
t
e
m
s
,
D
e
c
i
s
i
on
and
C
ont
r
ol
,
vol
.
304,
pp. 183
–
206, 2020, doi
:
10.1007/
978
-
3
-
030
-
51264
-
4_8.
[
2]
S
.
M
or
t
a
da
a
nd
Y
.
Y
us
of
,
“
A
n
e
i
ghbour
hood
s
e
a
r
c
h
f
or
a
r
t
i
f
i
c
i
a
l
be
e
c
ol
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t
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kyol
a
nd
B
.
A
l
a
t
a
s
,
“
P
l
a
nt
i
nt
e
l
l
i
ge
nc
e
b
a
s
e
d
m
e
t
a
h
e
ur
i
s
t
i
c
opt
i
m
i
z
a
t
i
on
a
l
gor
i
t
hm
s
,”
A
r
t
i
f
i
c
i
al
I
nt
e
l
l
i
ge
nc
e
R
e
v
i
e
w
,
vol
.
47,
no. 4, pp. 417
–
462, 2017, doi
:
10.1007/
s
10462
-
016
-
9486
-
6.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
A
r
ti
f
I
nt
e
ll
I
S
S
N
:
2252
-
8938
I
m
pr
ov
e
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s
c
r
e
te
pl
ant
pr
opagati
on algor
it
hm
f
o
r
s
ol
v
in
g
th
e
…
(
H
us
s
e
in
F
ouad A
lmaz
in
i)
21
[
25]
A
. K
a
r
c
i
, “
T
he
or
y of
s
a
pl
i
ngs
gr
ow
i
ng up a
l
gor
i
t
hm
,”
i
n
L
e
c
t
ur
e
N
ot
e
s
i
n C
om
put
e
r
Sc
i
e
nc
e
(
i
nc
l
udi
ng s
ubs
e
r
i
e
s
L
e
c
t
ur
e
N
ot
e
s
i
n
A
r
t
i
f
i
c
i
al
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nt
e
l
l
i
ge
nc
e
and
L
e
c
t
ur
e
N
ot
e
s
i
n
B
i
oi
nf
or
m
at
i
c
s
)
,
2007,
vol
.
4431
L
N
C
S
,
no.
P
A
R
T
1,
pp.
450
–
460,
doi
:
10.1007/
978
-
3
-
540
-
71618
-
1_50.
[
26]
Y
.
L
a
bbi
,
D
.
B
e
n
A
t
t
ous
,
H
.
A
.
G
a
bba
r
,
B
.
M
a
hda
d,
a
nd
A
.
Z
i
da
n,
“
A
ne
w
r
oot
e
d
t
r
e
e
opt
i
m
i
z
a
t
i
on
a
l
gor
i
t
hm
f
or
e
c
onom
i
c
di
s
pa
t
c
h
w
i
t
h
va
l
ve
-
poi
nt
e
f
f
e
c
t
,”
I
nt
e
r
nat
i
onal
J
our
nal
of
E
l
e
c
t
r
i
c
al
P
ow
e
r
and
E
ne
r
gy
Sy
s
t
e
m
s
,
vol
.
79,
pp.
298
–
31
1,
2016,
doi
:
10.1016/
j
.i
j
e
pe
s
.2016.01.028.
[
27]
F
.
M
e
r
r
i
kh
-
B
a
ya
t
,
“
T
he
r
unne
r
-
r
oot
a
l
go
r
i
t
hm
:
a
m
e
t
a
he
ur
i
s
t
i
c
f
or
s
ol
vi
ng
uni
m
oda
l
a
nd
m
ul
t
i
m
oda
l
opt
i
m
i
z
a
t
i
on
pr
obl
e
m
s
i
ns
pi
r
e
d
by
r
unne
r
s
a
nd
r
oot
s
of
pl
a
nt
s
i
n
n
a
t
ur
e
,”
A
ppl
i
e
d
Sof
t
C
o
m
pu
t
i
ng
J
our
nal
,
vol
.
33,
pp.
292
–
303,
2015,
doi
:
10.1016/
j
.a
s
oc
.2015.04.048.
[
28]
A
.
S
a
l
hi
a
nd
E
.
S
.
F
r
a
ga
,
“
N
a
t
ur
e
-
i
ns
pi
r
e
d
opt
i
m
i
s
a
t
i
on
a
ppr
oa
c
he
s
a
nd
t
he
n
e
w
pl
a
nt
pr
opa
ga
t
i
on
a
l
gor
i
t
hm
,”
i
n
I
nt
e
r
nat
i
onal
C
onf
e
r
e
nc
e
on N
um
e
r
i
c
al
A
nal
y
s
i
s
and O
pt
i
m
i
z
at
i
on (
I
C
e
M
A
T
H
)
,
2011.
[
29]
B
.
S
e
l
a
m
oğl
u
a
nd
A
.
S
a
l
hi
,
“
T
he
pl
a
nt
pr
opa
ga
t
i
on
a
l
gor
i
t
h
m
f
or
di
s
c
r
e
t
e
opt
i
m
i
s
a
t
i
on:
T
he
c
a
s
e
of
t
he
t
r
a
ve
l
l
i
ng
s
a
l
e
s
m
a
n
pr
obl
e
m
,”
i
n
St
udi
e
s
i
n C
om
put
at
i
onal
I
nt
e
l
l
i
ge
nc
e
, vol
. 637, S
pr
i
nge
r
, 2016, p
p. 43
–
61.
[
30]
M
. M
a
hi
, Ö
.
K
. B
a
yk
a
n, a
nd H
.
K
oda
z
, “
A
ne
w
hybr
i
d m
e
t
hod ba
s
e
d on
pa
r
t
i
c
l
e
s
w
a
r
m
opt
i
m
i
z
a
t
i
on, a
nt
c
ol
ony opt
i
m
i
z
a
t
i
on
a
n
d
3
-
opt
a
l
gor
i
t
hm
s
f
or
t
r
a
ve
l
i
ng
s
a
l
e
s
m
a
n
pr
obl
e
m
,”
A
ppl
i
e
d
Sof
t
C
om
put
i
ng
J
our
nal
,
vol
.
30,
pp.
484
–
490,
2015,
doi
:
10.1016/
j
.a
s
oc
.2015.01.068.
[
31]
M
.
M
a
vr
ovouni
ot
i
s
,
F
.
M
.
M
ul
l
e
r
,
a
nd
S
.
Y
a
ng,
“
A
nt
c
ol
ony
opt
i
m
i
z
a
t
i
on
w
i
t
h
l
oc
a
l
s
e
a
r
c
h
f
or
dyna
m
i
c
t
r
a
ve
l
i
ng
s
a
l
e
s
m
a
n
pr
obl
e
m
s
,”
I
E
E
E
T
r
ans
ac
t
i
ons
on C
y
be
r
ne
t
i
c
s
, vol
. 47, no. 7, pp. 1743
–
1756, 2017, doi
:
10.1109/
T
C
Y
B
.2016.2556742.
[
32]
X
. D
ong a
nd Y
.
C
a
i
, “
A
nov
e
l
ge
ne
t
i
c
a
l
gor
i
t
hm
f
or
l
a
r
ge
s
c
a
l
e
c
ol
or
e
d ba
l
a
nc
e
d t
r
a
ve
l
i
ng s
a
l
e
s
m
a
n
pr
obl
e
m
,”
F
ut
ur
e
G
e
ne
r
at
i
on
C
om
put
e
r
Sy
s
t
e
m
s
, vol
. 95, pp. 727
–
742, 2019, doi
:
10.1016/
j
.f
ut
ur
e
.2018.12.065.
[
33]
A
.
E
.
S
.
E
z
ugw
u,
A
.
O
.
A
de
w
um
i
,
a
nd
M
.
E
.
F
r
î
nc
u,
“
S
i
m
ul
a
t
e
d
a
nne
a
l
i
n
g
ba
s
e
d
s
ym
bi
ot
i
c
or
ga
ni
s
m
s
s
e
a
r
c
h
opt
i
m
i
z
a
t
i
on
a
l
gor
i
t
hm
f
or
t
r
a
ve
l
i
ng
s
a
l
e
s
m
a
n
pr
obl
e
m
,”
E
x
pe
r
t
Sy
s
t
e
m
s
w
i
t
h
A
p
pl
i
c
at
i
ons
,
vol
.
77,
pp.
189
–
210,
2017,
doi
:
10.1016/
j
.e
s
w
a
.2017.01.053.
[
34]
X
.
W
u
a
nd
D
.
G
a
o,
“
A
s
t
udy
on
gr
e
e
dy
s
e
a
r
c
h
t
o
i
m
pr
ove
s
i
m
ul
a
t
e
d
a
nne
a
l
i
ng
f
or
l
a
r
ge
-
s
c
a
l
e
t
r
a
ve
l
i
ng
s
a
l
e
s
m
a
n
pr
obl
e
m
,”
i
n
L
e
c
t
ur
e
N
ot
e
s
i
n
C
om
put
e
r
Sc
i
e
nc
e
(
i
nc
l
udi
ng
s
ubs
e
r
i
e
s
L
e
c
t
ur
e
N
ot
e
s
i
n
A
r
t
i
f
i
c
i
al
I
nt
e
l
l
i
ge
nc
e
and
L
e
c
t
ur
e
N
ot
e
s
i
n
B
i
oi
nf
or
m
at
i
c
s
)
, 2017, vol
. 10386 L
N
C
S
, pp. 250
–
257, doi
:
10.1007/
978
-
3
-
319
-
61833
-
3_26.
[
35]
Y
.
M
a
r
i
na
ki
s
,
M
.
M
a
r
i
na
ki
,
a
nd
A
.
M
i
gda
l
a
s
,
“
A
da
pt
i
ve
t
unni
ng
of
a
l
l
pa
r
a
m
e
t
e
r
s
i
n
a
m
ul
t
i
-
s
w
a
r
m
pa
r
t
i
c
l
e
s
w
a
r
m
opt
i
m
i
z
a
t
i
on
a
l
gor
i
t
hm
:
A
n
a
ppl
i
c
a
t
i
on
t
o
t
he
pr
oba
bi
l
i
s
t
i
c
t
r
a
ve
l
i
ng
s
a
l
e
s
m
a
n
pr
obl
e
m
,”
Sp
r
i
nge
r
P
r
oc
e
e
di
ngs
i
n
M
at
he
m
at
i
c
s
and
St
at
i
s
t
i
c
s
,
vol
. 130, pp. 187
–
207, 2015, doi
:
10.1007/
978
-
3
-
319
-
18567
-
5_10.
[
36]
I
.
K
ha
n,
S
.
P
a
l
,
a
nd
M
.
K
.
M
a
i
t
i
,
“
A
m
odi
f
i
e
d
pa
r
t
i
c
l
e
s
w
a
r
m
op
t
i
m
i
z
a
t
i
on
a
l
g
or
i
t
hm
f
o
r
s
ol
vi
ng
t
r
a
ve
l
i
ng
s
a
l
e
s
m
a
n
pr
obl
e
m
w
i
t
h
i
m
pr
e
c
i
s
e
c
os
t
m
a
t
r
i
x,”
i
n
P
r
oc
e
e
di
ngs
of
t
he
4t
h I
E
E
E
I
nt
e
r
nat
i
onal
C
onf
e
r
e
nc
e
on
R
e
c
e
nt
A
dv
anc
e
s
i
n
I
nf
or
m
at
i
on
T
e
c
hnol
ogy
,
R
A
I
T
2018
, 2018, pp. 1
–
8, do
i
:
10.1109/
R
A
I
T
.2018.8389060.
[
37]
L
.
T
e
ng
a
nd
H
.
L
i
,
“
M
odi
f
i
e
d
di
s
c
r
e
t
e
f
i
r
e
f
l
y
a
l
gor
i
t
hm
c
om
bi
ni
ng
ge
n
e
t
i
c
a
l
gor
i
t
hm
f
or
t
r
a
ve
l
i
ng
s
a
l
e
s
m
a
n
pr
obl
e
m
,
”
T
E
L
K
O
M
N
I
K
A
(
T
e
l
e
c
om
m
uni
c
at
i
on
C
om
put
i
ng
E
l
e
c
t
r
oni
c
s
and
C
ont
r
ol
)
,
vol
.
16,
no.
1,
pp.
424
–
431,
2018,
doi
:
10.12928/
T
E
L
K
O
M
N
I
K
A
.V
16I
1.4752.
[
38]
A
.
H
a
t
a
m
l
ou,
“
S
ol
vi
ng
t
r
a
ve
l
l
i
ng
s
a
l
e
s
m
a
n
pr
obl
e
m
us
i
ng
bl
a
c
k
hol
e
a
l
gor
i
t
hm
,”
Sof
t
C
om
put
i
ng
,
vol
.
22,
no.
24,
pp.
8167
–
8175,
2018, doi
:
10.1007/
s
00500
-
017
-
2760
-
y.
[
39]
A
.
I
.
H
a
m
m
our
i
,
E
.
T
.
A
.
S
a
m
r
a
,
M
.
A
.
A
l
-
B
e
t
a
r
,
R
.
M
.
K
h
a
l
i
l
,
Z
.
A
l
a
s
m
e
r
,
a
nd
M
.
K
a
na
n,
“
A
dr
a
gonf
l
y
a
l
gor
i
t
hm
f
or
s
ol
vi
ng
t
r
a
ve
l
i
ng
s
a
l
e
s
m
a
n
pr
obl
e
m
,”
i
n
P
r
o
c
e
e
di
ngs
-
8t
h
I
E
E
E
I
nt
e
r
nat
i
onal
C
onf
e
r
e
nc
e
on
C
ont
r
ol
S
y
s
t
e
m
,
C
om
put
i
ng
an
d
E
ngi
ne
e
r
i
ng, I
C
C
SC
E
2018
, 2019, pp. 136
–
141, doi
:
10.1109/
I
C
C
S
C
E
.2018.8684963.
B
I
O
G
R
A
P
H
I
E
S
O
F
A
U
T
H
O
R
S
Hussein
Fouad
Almazini
is
a
Ph.D
student
at
School
of
Comp
uting,
Sintok,
Universiti
Utara
Malaysia,
Kedah,
Malaysia.
He
holds
a
master’s
degree
in
information
technology
in
the
area
(Artificia
l
Intelligenc
e).
He
works
in
a
artificia
l
intelligence
,
evoluti
onary
computat
ion,
meta
-
heuristic
algorithms
and
swarm
i
ntelligence.
He
is
also
interested
in
mining
scientific
datasets
in
domains
such
as
IoT,
healthca
re,
cyber
security,
social
network,
business,
demographic,
sustainability,
and
intelligen
ce
analysis.
He
can
be
contacted
at email
:
h.almazni22@
gmail.com
.
Salah
Mortada
is
a
Ph.D
student
at
School
of
Computing,
Sint
ok,
Universiti
Utara
Malaysia,
Kedah,
Malaysia.
He
holds
a
master’s
degree
in
inf
ormation
technology
in
the
area
(Usability
and
User
Experience).
His
current
r
esearch
int
erests
include
artificial
intelligence
,
evolutionar
y
computation,
meta
-
heuristic
algorithms,
s
warm
intelligence,
and
their
applications
in
the
design
and
optimization
of
intelligent
tran
sportation
management
such as VRPs.
He can be contacted at email:
sms099@
yahoo.com
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
-
8938
I
nt
J
A
r
ti
f
I
nt
e
ll
,
V
ol
.
11
, N
o.
1
,
M
a
r
c
h 20
22
:
13
-
22
22
Hassan
Fouad
Almazini
is
a
Ph.D
.
student
at
School
of
Comp
uting,
Sintok,
Universiti
Utara
Malaysia,
Kedah,
Malaysia.
He
holds
a
master’s
degree
in
information
technology
in
the
area
(Artificia
l
Intelligenc
e).
Hassan
resear
ch
and
developmen
t
experie
nce
includes
over
8
years
in
the
academia
and
Industry.
He
works
in
a
artificial
intelligence,
evoluti
onary
computat
ion,
meta
-
heuristic
algorit
hms
and
swarm
i
ntelli
gence.
He
is
also
interested
in
mining
scientific
datasets
in
domains
such
as
IoT,
healthca
re,
cyber
security,
social
network,
business,
demographic,
sustainability,
and
intelligen
ce
analysis.
He
can
be
contacted
at email
:
abba@
ahsgs.uum.edu.my
.
Dr.
Hayder
Naser
Khraibet
Al
-
Behadili
has
a
Ph.D.
degree
i
n
Information
Technology
specialization
in
artificial
intelligence.
His
research
is
mainly
focused
o
n
development
of
artificial
intelligence
and
data
mining
techniques
base
d
on
swarm
intelligence
algorit
hms.
He can be contacted at email
:
hayderkhraibet@sa
-
uc.edu.iq
.
Jawad
Kadum
Hussein
is
a
master
student
in
In
formation
System specialization
in
data
mining.
His
research
is
mainly
focused
on
improvement
th
e
data
mining
based
on
artificial
intell
igence,
evoluti
onary
computat
ion,
meta
-
heuristic
algorithms,
and
swarm
intelligence
.
He can be
contacted
at email
:
Jawadalkena
ni@
sa
-
us.edu.iq.
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