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Evaluation Warning : The document was created with Spire.PDF for Python.
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Generation of the initial population
Repeat
For
each employed bee
Generate new solution Vi using (1) and compute the fitness value fit
End
Compute the probability values Pi by using (2)
For
each onlooker bee
S
e
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value
End
If an abandoned solution exist for the scout Then generate new solution by using (3)
Save the best solution
Until the requirements are met
Algorithm 1: The ABC algorithm pseudo
-
code
2.
2
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o
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dge
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a
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a
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f
o
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l
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s
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k
i
j
i
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(
1
)
*
(6)
w
h
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r
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i
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h
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nt
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k
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f
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nt
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e
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n
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our
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0
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O
t
he
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w
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n
t
k.
T
h
e
ps
e
udo
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c
o
d
e
of
t
h
e
A
CO
pr
o
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e
dur
e
c
a
n
b
e
pr
e
s
e
nt
e
d
a
s
f
o
l
l
ow
s
:
Random initialization of the pheromone value
Do
For
each iteration
For
each ant
For
each variable
Compute of the probability P using (4)
Determine the Pmax
Deduce the value of Vi
End
Compute objective function
End
Deduce the best objective function and update pheromone values using (6) and
(7)
End
Report the best solution
End
Algorithm 2: Pseudo
-
code of the ACO algorithm
2.
3
.
D
i
ffe
r
e
n
t
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al
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v
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m
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i
f
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pp
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d
by
R
.
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t
o
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a
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.
P
r
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e
i
n
1995
[11
],
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(9)
Evaluation Warning : The document was created with Spire.PDF for Python.
In
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d
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G
i
j
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G1
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f
f
(
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f
(
)
UU
X
X
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O
t
h
e
r
w
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s
e
X
(10)
w
h
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r
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f
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e
f
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s
s
f
un
c
t
i
o
n.
T
h
e
D
E
a
l
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ri
t
hm
h
a
s
ps
e
udo
-
c
o
d
e
a
s
f
o
l
l
ow
s
:
Generate the initial population of individuals NP
Do
For
each individual jϵ [1, NP],
Select r1, r2, r3 from the range [1, NP] randomly.
For
each parameter i
Generate the mutant vector using the equation (8)
Generate a new vector with equation (9)
End
Replace
with
or
by using the equation (10)
End
Until the termination condition is achieved
Algorithm 3
.
Pseudo
-
code of the DE algorithm
3.
EX
A
M
P
LE
A
P
P
LI
C
A
TI
O
N
:
S
Q
U
A
R
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S
P
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A
L
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D
U
C
TO
R
3.
1
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.
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9.
[
15]
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.
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.
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-
2
35,
2
018
.
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17]
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.
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s
s
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l
.
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,
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-
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,
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6.
[
18]
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.
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r
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ou
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l
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l
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m
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z
at
i
on
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v
o
l
.
3
9,
no
.
3
,
pp.
4
59
-
471
,
2007
.
[
19]
D
.
K
a
r
a
bo
g
a
,
"
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n
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s
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005
.
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20]
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.
L
.
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ng
,
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.
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.
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.
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.
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uo
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s
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l
.
6,
no
.
3
,
pp.
37
5
-
383,
2
015
.
[
21]
M
.
D
o
r
i
g
o
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.
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ni
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o
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.
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d
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c
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ne
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,
v
o
l
.
26
,
no
.
1,
pp
.
29
-
41
,
1996
.
[
22]
S
.
H
a
r
i
k
i
s
ho
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e
,
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.
S
um
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l
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ha
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ndo
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an
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ou
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nal
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ng
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J
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S)
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v
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l
.
1
6,
no
.
3,
p
p.
13
71
-
1378
,
201
9.
[
23]
M
.
A
.
A
bd.
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a
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a
n,
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.
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s
m
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i
l
,
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.
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i
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E
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S)
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v
o
l
.
15,
no
.
1
,
pp.
3
73
-
381
,
2019
.
[
24]
C
.
P
.
Y
ue
,
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.
R
y
u,
J
.
L
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u,
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.
H
.
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.
S
.
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o
,
C
A
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S
A
,
19
96
,
p
p.
15
5
-
158
.
[
25]
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.
P
.
D
u
r
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,
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.
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.
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.
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s
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o
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n
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l
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c
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o
,
p
p
.
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7
8
-
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2
0
1
0
.
[
26]
V
.
D
ur
e
v
,
E
.
G
a
d
j
e
v
a
,
M
.
H
r
i
s
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o
v
,
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a
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m
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r
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t
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nt
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n
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nduc
t
o
r
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o
de
l
,
"
P
r
oc
e
e
di
ngs
o
f
t
he
17
t
h
I
n
t
e
r
na
t
i
o
nal
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on
f
e
r
e
nc
e
M
i
x
e
d
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e
s
i
gn
o
f
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n
t
e
gr
at
e
d
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i
r
c
ui
t
s
a
nd
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y
s
t
e
m
s
-
M
I
X
D
E
S
201
0
,
W
a
r
s
a
w
,
pp
.
4
20
-
424
,
2010
.
[
27]
K
.
O
ka
da
,
H
.
,
H
o
s
hi
no
,
H
.
O
no
de
r
a
,
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o
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l
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a
nd
o
pt
i
m
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.
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.
0
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3751
2)
,
V
a
nc
o
uv
e
r
,
B
C
,
p
p.
V
-
V
,
200
4
.
[
28]
M
o
m
e
nt
um
,
A
D
S
2002
,
“
A
g
i
l
e
nt
T
e
c
hno
l
o
g
i
e
s
,
”
E
E
s
of
d
i
v
i
s
i
on
,
S
a
nt
a
R
o
s
a
,
C
A
,
2006
.
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