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IS
S
N
:
2252
-
8792
Int
J
A
ppl
P
o
w
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r
E
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g
,
V
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10
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1
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M
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2021
:
21
–
25
22
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a
s
:
H
a
m
i
l
t
o
n
c
y
c
l
e
a
l
go
ri
t
hm
a
s
f
o
l
l
o
w
s
:
Commence
Step 1:
node
v
1 chosen as initial point,.
Step 2:
is chosen and
is picked with least weight
linking
, then the
is obtained.
S
t
e
p
3
:
when
i
+1<
n
,
s
u
b
s
e
q
u
e
n
t
l
y
i
+
1
i
s
u
s
e
d
t
o
s
u
b
s
t
i
t
u
t
e
i
,
a
n
d
r
e
v
i
s
i
t
t
o
S
t
e
p
2
;
condition
not
occurred
,
then
revisit
to
the
final
Hamiltonian
cycle
then
go
back to
Step 4
.
Step 4:
(
)
;
(
)
(
)
(
)
(
)
(
)
Then
(
{
}
)
{
}
End if
End for
Step 5:
C
is substituted by
C
1, and revisit
Step 4
.
Step 6:
compute the extent of the Hamiltonian cycle
C
.
End for
i
In
t
h
e
p
r
o
po
s
e
d
a
m
pl
i
f
i
e
d
b
r
a
i
n
s
t
o
rm
o
pt
i
m
i
z
a
t
i
o
n
(A
B
S
O
)
a
l
go
ri
t
hm
H
a
m
i
l
t
o
ni
a
n
c
y
c
l
e
w
i
l
l
i
m
p
r
o
v
e
t
h
e
e
xp
l
o
r
e
a
b
i
l
i
t
i
e
s
a
nd
a
l
s
o
s
t
a
y
a
w
a
y
f
r
o
m
l
o
c
a
l
o
pt
i
m
a
l
s
o
l
ut
i
on
.
Commence
Step 1: “
n”
potential solutions are arbitrarily engendered
Step 2: “
n”
individuals are clustered into “
m”
clusters
Step 3: “
n”
individuals will be appraised
S
t
e
p
4
:
I
n
e
v
e
r
y
c
l
u
s
t
e
r
r
a
n
k
t
h
e
i
n
d
i
v
i
d
u
a
l
s
t
h
e
n
t
h
e
m
o
s
t
e
x
c
e
l
l
e
n
t
i
n
d
i
v
i
d
u
a
l
’
s
a
r
e
recorded
as
cluster
center
S
t
e
p
5
:
Between
0
and
1
arbitrarily
a
value
will
be
engendered;
If the value is smaller than a probability; then
i
.
a
c
l
u
s
t
e
r
c
e
n
t
e
r
h
a
s
b
e
e
n
A
r
b
i
t
r
a
r
i
l
y
c
h
o
s
e
n
;
i
i
.
T
o
s
w
a
p
t
h
e
c
e
r
t
a
i
n
c
l
u
s
t
e
r
c
e
n
t
e
r
arbitrarily engender an individual
(2)
∑
|
|
(3)
(4)
(10)
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
A
ppl
P
o
w
e
r
E
n
g
IS
S
N
:
2252
-
8792
A
m
pl
i
f
i
e
d
and
quan
t
um
bas
e
d
br
ai
n
s
t
or
m
op
t
i
m
i
z
a
t
i
o
n
a
l
go
r
i
t
h
m
s
f
or
r
e
al
pow
e
r
…
(
Kanagas
abai
L
e
ni
n
)
23
Step 6:
new
-
fangled individuals are engendered
Calculate the Hamiltonian cycle C and its extent L
t
by Hamilton algorithm
{
Commence
Step 1:
node
v
1 chosen as initial p
oint,
S
t
e
p
2
:
i
s
c
h
o
s
e
n
a
n
d
i
s
p
i
c
k
e
d
w
i
t
h
l
e
a
s
t
w
e
i
g
h
t
l
i
n
k
i
n
g
,
t
h
e
n
t
h
e
is obtained.
Step 3:
when
i
+1<
n
, subsequently
i
+1 is used to substitute
i
, and revisit to
Step 2
Step 4: for
all
i
and
j
in cycle
C
, if 1<
i
+1<
j
<
n
,
then
(
)
(
)
(
)
(
)
(
)
(
)
Then
(
{
}
)
{
}
End if
End for
Step 5:
C
is substituted by
C
1, and revisit
Step 4
.
Step 6:
compute the extent of the Hamiltonian cycle
C
.
End for “
i”
}
When t>1 then calculate value of the
by
End if
Execute decision optimization procedure
{
Commence
or
Arbitrarily engender
n
r
individuals;
End if
End
}
Calculate the population according to the recently modernized positions;
t = t+1.
S
t
e
p
7
:
w
h
e
n
“
n”
new
-
fangled
individuals
are
engen
dered,
then
go
to
S
t
e
p
8
;
o
r
e
l
s
e
g
o
t
o
Step 6
.
Step 8:
end conditions met ; or else go to
Step 2
.
End
4.
Q
U
A
N
TU
M
B
A
S
ED
BR
A
I
N
S
TO
R
M
O
P
TI
M
I
ZA
TI
O
N
A
LG
O
R
I
T
H
M
In
B
S
O
a
l
go
ri
t
hm
po
pul
a
t
i
o
n
i
s
i
n
d
i
c
a
t
e
d
a
s
s
w
a
rm
m
o
r
e
o
v
e
r
e
ve
r
y
i
n
di
v
i
du
a
l
i
s
de
s
c
ri
b
e
d
a
s
a
n
i
de
a
.
O
r
i
gi
na
l
l
y
,
e
ve
r
y
i
de
a
i
s
a
r
b
i
t
r
a
ri
l
y
i
n
i
t
i
a
l
i
z
e
d
i
n
s
i
de
t
he
e
xpl
o
r
a
t
i
o
n
s
p
a
c
e
.
S
ub
s
e
que
n
t
l
y
m
o
s
t
e
xc
e
l
l
e
n
t
o
n
e
i
n
e
v
e
r
y
c
l
us
t
e
r
i
s
s
e
l
e
c
t
e
d
a
s
t
h
e
c
l
us
t
e
r
c
e
nt
r
e
.
S
po
ra
di
c
a
l
l
y
,
a
n
a
r
b
i
t
ra
r
i
l
y
c
h
o
s
e
n
c
e
n
t
r
e
i
s
s
w
a
ppe
d
b
y
a
r
e
c
e
n
t
l
y
e
n
ge
n
de
r
e
d
i
de
a
,
by
t
ha
t
t
h
e
s
w
a
rm
ha
s
b
e
e
n
ke
pt
a
w
a
y
f
r
o
m
t
h
e
l
o
c
a
l
o
pt
i
m
um
.
(
)
(11)
(12)
i
s
a
f
a
c
t
o
r
us
e
d
i
n
t
h
e
e
v
o
l
ut
i
o
n
p
r
o
c
e
s
s
a
n
d
c
a
n
b
e
a
r
t
i
c
u
l
a
t
e
d
a
s
,
(
)
(
⁄
)
(13)
Q
ua
n
t
u
m
s
t
a
t
e
o
f
a
n
i
de
a
i
s
i
l
l
us
t
ra
t
e
d
by
a
w
a
v
e
f
un
c
t
i
o
n
(
⃗
)
a
s
a
n
a
l
t
e
rna
t
i
v
e
of
t
h
e
po
s
i
t
i
o
n
m
o
de
rn
i
z
e
d
o
n
l
y
i
n
B
ra
i
n
s
t
o
r
m
o
pt
i
m
i
z
a
t
i
o
n
a
l
go
ri
t
hm
.
By
us
i
n
g
S
c
hr
ö
di
n
ge
r
e
qua
t
i
o
n
p
r
o
b
a
b
i
l
i
t
y
de
n
s
i
t
y
f
un
c
t
i
o
n
o
f
t
h
e
po
s
i
t
i
o
n
i
s
i
de
nt
i
f
i
e
d
s
uc
h
t
ha
t
e
a
c
h
i
de
a
i
s
l
o
c
a
t
e
d.
M
o
nt
e
Ca
rl
o
s
i
m
u
l
a
t
i
o
n
m
e
t
h
o
d
i
s
us
e
d,
t
o
m
e
a
s
ur
e
t
h
e
po
s
i
t
i
o
n
f
o
r
e
a
c
h
i
de
a
f
r
o
m
t
h
e
qua
nt
u
m
s
t
a
t
e
t
o
t
h
e
t
ra
di
t
i
o
n
a
l
o
n
e
.
{
(
⁄
)
(
⁄
)
(
)
(
⁄
)
(
⁄
)
(
)
(1
4
)
(
)
(
15
)
|
|
(16)
(17)
∑
⁄
(18)
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2252
-
8792
Int
J
A
ppl
P
o
w
e
r
E
n
g
,
V
o
l
.
10
,
N
o
.
1
,
M
a
r
c
h
2021
:
21
–
25
24
Step a: Initialize the parameters.
Step b: Arbitrarily produce “
n”
ideas Step c: By
k
-
means
algorithm cluster “
n”
ideas.
Step d: With a predetermined probability modernize the centre of a capriciously chosen
cluster.
Step e: Individual generation created.
Step f: Quantum mechanism is exploited based on the chosen idea
Step g: Crossover operator i
s implemented
Step h: evaluate the new
-
fangled idea with the older one,
Step i: If “
n”
ideas have been engender, then go to Step 9. Or else go to Step 5.
Step j: Stop whether the present number of iterations
N
c
attain the
N
c
max
. or else, go to
5.
S
I
M
U
LA
T
I
O
N
S
TU
D
Y
P
r
o
po
s
e
d
A
B
S
o
pt
i
m
i
z
a
t
i
o
n
a
l
go
r
i
t
hm
a
n
d
Q
B
S
o
pt
i
m
i
z
a
t
i
o
n
a
l
go
r
i
t
h
m
h
a
s
b
e
e
n
t
e
s
t
e
d,
i
n
I
E
E
E
57
B
us
s
y
s
t
e
m
[18]
.
T
a
b
l
e
1
s
h
o
w
s
t
h
e
c
o
m
pa
r
i
s
o
n
r
e
s
ul
t
s
.
T
a
b
l
e
1
.
S
i
m
u
l
a
t
i
o
n
r
e
s
ul
t
s
o
f
IE
E
E
-
57
s
y
s
t
e
m
Co
n
t
r
o
l
v
a
ri
a
b
l
e
s
Ba
s
e
c
a
s
e
M
P
S
O
[1
9
]
P
S
O
[1
9
]
CG
A
[1
9
]
A
G
A
[1
9
]
A
B
S
Q
BS
1
1
.
0
4
0
1
.
0
9
3
1
.
0
8
3
0
.
9
6
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1
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1
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9
1
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1
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N
R
*
N
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*
1
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36
1
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N
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