I
nte
rna
t
io
na
l J
o
urna
l o
f
E
lect
rica
l a
nd
Co
m
pu
t
er
E
ng
ineering
(
I
J
E
CE
)
Vo
l.
1
6
,
No
.
2
,
A
p
r
il
20
2
6
,
p
p
.
883
~
894
I
SS
N:
2088
-
8
7
0
8
,
DOI
: 1
0
.
1
1
5
9
1
/ijece.
v
1
6
i
2
.
pp
8
8
3
-
8
9
4
883
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
ec
e.
ia
esco
r
e.
co
m
Elitist gene
tic
a
lg
o
rithm impro
v
ed
with
pa
re
nting
fit
ness
pa
ra
meter
O
uis
s
M
us
t
a
p
ha
,
E
t
t
a
o
ufik
Abdela
ziz,
M
a
rz
a
k
Abdela
zi
z
F
a
c
u
l
t
y
o
f
S
c
i
e
n
c
e
o
f
B
e
n
M
si
k
,
H
a
ss
a
n
I
I
U
n
i
v
e
r
s
i
t
y
C
a
s
a
b
l
a
n
c
a
,
C
a
s
a
b
l
a
n
c
a
,
M
o
r
o
c
c
o
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Ma
r
2
2
,
2
0
2
5
R
ev
is
ed
Dec
1
4
,
2
0
2
5
Acc
ep
ted
J
an
1
6
,
2
0
2
6
In
g
e
n
e
ti
c
a
l
g
o
ri
th
m
s,
t
h
e
se
lec
ti
o
n
o
f
i
n
d
i
v
id
u
a
ls
th
a
t
wi
ll
b
e
p
a
r
t
o
f
f
u
tu
re
g
e
n
e
ra
ti
o
n
s
is
a
c
rit
ica
l
p
r
o
c
e
ss
o
f
th
e
a
l
g
o
r
it
h
m
.
Va
rio
u
s
stra
teg
ie
s
e
x
ist
t
o
se
lec
t
th
e
se
in
d
iv
i
d
u
a
ls:
t
h
e
g
e
n
e
ra
l
a
p
p
r
o
a
c
h
a
n
d
th
e
e
li
ti
st
a
p
p
r
o
a
c
h
.
Th
e
g
e
n
e
ra
l
a
p
p
ro
a
c
h
i
n
v
o
lv
e
s
re
p
lac
in
g
t
h
e
wh
o
le
c
u
rre
n
t
p
o
p
u
latio
n
with
t
h
e
o
ffsp
ri
n
g
g
e
n
e
ra
ted
so
fa
r.
T
h
e
e
li
ti
st
a
p
p
r
o
a
c
h
in
tro
d
u
c
e
s
a
c
o
m
p
e
ti
ti
v
e
e
lem
e
n
t
in
wh
ic
h
b
o
t
h
p
a
re
n
ts
a
n
d
o
ffs
p
rin
g
c
o
m
p
e
te
fo
r
s
u
rv
i
v
a
l,
a
n
d
o
n
l
y
fit
i
n
d
i
v
id
u
a
ls
wil
l
b
e
p
a
rt
o
f
th
e
n
e
x
t
g
e
n
e
ra
ti
o
n
.
Wh
il
e
se
lec
ti
n
g
fi
t
in
d
i
v
id
u
a
ls
h
e
l
p
s
th
e
a
l
g
o
r
it
h
m
t
o
p
r
o
d
u
c
e
b
e
tt
e
r
re
su
lt
s,
th
e
e
li
t
i
sm
h
a
s
a
m
a
jo
r
d
ra
wb
a
c
k
:
th
e
p
re
m
a
tu
re
c
o
n
v
e
r
g
e
n
c
e
,
wh
ich
c
a
n
li
m
it
t
h
e
a
lg
o
rit
h
m
'
s
o
v
e
ra
ll
p
e
rf
o
rm
a
n
c
e
.
In
th
is
a
rti
c
le,
we
c
o
m
p
a
re
d
a
ty
p
ica
l
e
li
ti
st
g
e
n
e
ti
c
a
lg
o
rit
h
m
a
n
d
a
n
e
li
ti
st
a
lg
o
rit
h
m
imp
ro
v
e
d
with
th
e
p
a
re
n
t
i
n
g
fit
n
e
ss
p
a
ra
m
e
ter
in
re
so
lv
in
g
t
h
e
v
e
h
i
c
le
ro
u
ti
n
g
p
r
o
b
lem
wit
h
d
ro
n
e
s
(VRPD).
Th
e
p
a
re
n
ti
n
g
fit
n
e
ss
p
a
ra
m
e
te
r
h
e
lp
s
p
re
se
rv
in
g
d
iv
e
rsity
b
y
re
tain
in
g
p
a
re
n
ts
with
h
i
g
h
o
ffsp
ri
n
g
p
o
ten
ti
a
l
d
e
sp
it
e
o
f
th
e
ir
p
e
rso
n
a
l
fi
t
n
e
ss
.
Th
e
fin
d
i
n
g
s
fro
m
t
h
e
stu
d
y
d
e
m
o
n
st
ra
tes
th
a
t
in
te
g
ra
ti
n
g
t
h
e
p
a
re
n
t
i
n
g
f
it
n
e
ss
p
a
ra
m
e
ter
lea
d
to
b
e
tt
e
r
re
su
lt
s
i
n
c
o
m
p
a
riso
n
wit
h
a
t
y
p
ica
l
e
li
ti
st
g
e
n
e
ti
c
a
lg
o
rit
h
m
,
wit
h
re
lativ
e
im
p
ro
v
e
m
e
n
t
v
a
ry
i
n
g
fro
m
1
.
0
6
%
t
o
1
0
.
3
4
%
a
c
c
o
rd
in
g
to
th
e
d
a
tas
e
t’s
siz
e
.
K
ey
w
o
r
d
s
:
E
liti
s
t g
en
etic
alg
o
r
ith
m
Ma
ch
in
e
lear
n
in
g
Par
en
tin
g
f
itn
ess
Pre
m
atu
r
e
co
n
v
er
g
e
n
ce
Veh
icle
r
o
u
tin
g
p
r
o
b
lem
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Ou
is
s
Mu
s
tap
h
a
Dep
ar
tm
en
t o
f
Ma
th
an
d
I
n
f
o
r
m
atic,
Facu
lty
o
f
Scien
ce
o
f
B
en
Msik
,
Hass
an
I
I
Un
iv
er
s
ity
C
asab
lan
ca
C
o
m
m
an
d
an
t D
r
is
s
Al
Har
ti R
o
ad
,
C
asab
lan
ca
2
0
6
7
0
,
Mo
r
o
cc
o
E
m
ail: m
u
s
tap
h
a.
o
u
is
s
-
etu
@
etu
.
u
n
iv
h
2
c.
m
a
1.
I
NT
RO
D
UCT
I
O
N
Gen
etic
alg
o
r
ith
m
s
(
GAs)
b
elo
n
g
to
p
o
p
u
latio
n
-
b
ased
m
eta
h
eu
r
is
tics
,
an
d
wer
e
in
tr
o
d
u
c
ed
f
o
r
th
e
f
ir
s
t
tim
e
in
1
9
7
5
b
y
Ho
llan
d
[
1
]
.
T
h
eir
n
atu
r
e
m
ak
es
th
e
m
a
s
p
ec
ialized
f
o
r
m
o
f
r
an
d
o
m
h
e
u
r
is
tic
s
ea
r
ch
(
R
HS)
[
2
]
.
Gen
etic
alg
o
r
ith
m
s
ar
e
u
s
ed
to
r
eso
lv
e
co
m
p
lex
an
d
tim
e
-
co
n
s
u
m
i
n
g
p
r
o
b
le
m
s
.
Sin
ce
g
en
etic
alg
o
r
ith
m
s
u
s
e
a
s
et
o
f
in
d
iv
id
u
als,
th
e
alg
o
r
ith
m
co
n
tin
u
es
ev
o
lv
in
g
th
ese
s
o
lu
tio
n
s
u
s
in
g
th
e
s
elec
tio
n
m
ec
h
an
is
m
s
an
d
g
en
etic
o
p
e
r
atio
n
s
s
u
ch
as
cr
o
s
s
o
v
er
an
d
m
u
tatio
n
.
T
h
e
ca
n
o
n
ical
v
er
s
io
n
o
f
g
e
n
etic
alg
o
r
ith
m
s
,
o
f
ten
r
ef
er
r
e
d
to
a
s
th
e
s
im
p
le
g
en
etic
alg
o
r
ith
m
(
SGA)
was
d
etailed
in
th
e
wo
r
k
o
f
[
2
]
an
d
[
3
]
.
Gen
etic
alg
o
r
ith
m
s
h
av
e
th
e
in
ter
esti
n
g
ca
p
ac
ity
to
f
in
d
g
o
o
d
s
o
lu
tio
n
s
to
co
m
p
le
x
p
r
o
b
lem
s
.
Gen
etic
alg
o
r
ith
m
s
ar
e
wid
ely
u
s
ed
in
th
e
liter
atu
r
e,
an
d
th
ey
a
r
e
co
n
s
tr
u
cted
f
r
o
m
v
a
r
io
u
s
co
m
p
o
n
e
n
ts
s
u
ch
as
ch
r
o
m
o
s
o
m
e
en
co
d
i
n
g
,
f
itn
es
s
f
u
n
ctio
n
s
,
p
ar
en
t
s
elec
tio
n
m
ec
h
an
is
m
s
,
g
en
etic
o
p
er
at
o
r
s
(
cr
o
s
s
o
v
er
an
d
m
u
tatio
n
)
,
a
n
d
th
e
e
v
o
lu
tio
n
s
tr
ateg
ies,
th
ese
co
m
p
o
n
en
ts
ar
e
d
etailed
as f
o
llo
ws:
−
Po
p
u
latio
n
o
f
s
o
l
u
tio
n
s
:
Gen
e
tic
alg
o
r
ith
m
s
a
r
e
p
o
p
u
latio
n
-
b
ased
m
etah
eu
r
is
tics
,
th
at
is
,
t
h
ey
m
a
n
ip
u
late
a
s
et
o
f
ch
r
o
m
o
s
o
m
es,
also
ca
lled
s
o
lu
tio
n
s
.
T
h
e
r
e
p
r
esen
tatio
n
o
f
t
h
e
ch
r
o
m
o
s
o
m
e
d
ep
en
d
s
o
n
th
e
co
n
s
id
er
ed
p
r
o
b
lem
.
C
h
r
o
m
o
s
o
m
es
ca
n
b
e
b
in
ar
y
en
co
d
ed
,
r
ea
l
en
co
d
ed
,
o
r
e
v
en
a
m
ix
o
f
th
ese
en
co
d
in
g
ty
p
es.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
2
,
Ap
r
il
20
2
6
:
8
8
3
-
894
884
−
Fit
n
ess
f
u
n
ctio
n
:
T
h
e
f
itn
ess
f
u
n
ctio
n
is
th
e
m
o
s
t
cr
itica
l
p
ar
t
o
f
t
h
e
alg
o
r
ith
m
,
also
k
n
o
wn
as
th
e
o
b
jectiv
e
f
u
n
ctio
n
.
T
h
e
v
alu
e
o
f
th
is
f
u
n
ctio
n
d
ef
i
n
es
t
h
e
q
u
ality
o
f
th
e
s
o
lu
tio
n
t
h
at
th
e
g
en
etic
alg
o
r
ith
m
s
tr
y
to
o
p
tim
ize.
I
ts
im
p
lem
en
tatio
n
v
a
r
ies f
r
o
m
o
n
e
p
r
o
b
lem
to
a
n
o
th
er
.
−
Par
en
t
s
elec
tio
n
:
T
h
is
p
r
o
ce
s
s
is
r
esp
o
n
s
ib
le
o
f
s
elec
t
in
g
s
o
lu
tio
n
s
th
at
will
p
r
o
d
u
ce
n
ew
s
o
lu
tio
n
s
u
s
in
g
g
en
etic
o
p
er
at
o
r
s
.
T
h
e
p
r
o
ce
s
s
s
elec
ts
two
p
ar
en
ts
f
r
o
m
th
e
p
o
p
u
latio
n
.
−
C
r
o
s
s
o
v
er
:
T
h
e
cr
o
s
s
o
v
er
o
p
e
r
atio
n
m
ix
es
th
e
g
en
etic
m
ate
r
ial
o
f
th
e
s
elec
ted
p
ar
en
ts
in
o
r
d
er
to
c
r
ea
te
o
f
f
s
p
r
in
g
.
−
Mu
tatio
n
:
T
h
e
m
u
tatio
n
o
p
e
r
atio
n
allo
ws
th
e
alg
o
r
ith
m
to
en
h
an
ce
th
e
q
u
ality
o
f
a
n
o
f
f
s
p
r
in
g
,
b
y
ch
an
g
in
g
its
g
en
es’
v
alu
e,
f
r
o
m
0
to
1
,
f
o
r
ex
am
p
le,
in
a
b
in
ar
y
en
co
d
ed
ch
r
o
m
o
s
o
m
e
,
o
r
b
y
f
lip
p
in
g
g
en
es in
a
s
tr
in
g
e
n
co
d
e
d
ch
r
o
m
o
s
o
m
e.
−
E
v
o
lu
tio
n
s
ch
em
e:
T
h
e
e
v
o
lu
t
io
n
s
ch
em
e
is
th
e
p
h
ase
in
wh
ich
th
e
g
en
etic
alg
o
r
ith
m
s
elec
t
s
s
o
lu
tio
n
s
th
a
t
will
b
e
p
ar
t
o
f
th
e
n
ex
t
p
o
p
u
l
atio
n
.
T
h
is
p
h
ase
is
an
im
p
o
r
t
an
t
p
ar
t
o
f
th
e
alg
o
r
ith
m
.
E
x
is
tin
g
ap
p
r
o
ac
h
es
f
all
in
to
two
s
tr
ateg
ies:
i)
g
en
er
al,
an
d
ii)
elitis
t.
T
h
e
g
en
er
a
l
ap
p
r
o
ac
h
is
th
e
s
tr
aig
h
tf
o
r
war
d
ap
p
r
o
ac
h
in
wh
ich
th
e
wh
o
le
p
o
p
u
latio
n
is
r
ep
lace
d
b
y
th
e
o
f
f
s
p
r
in
g
g
en
er
ated
s
o
f
ar
.
I
n
th
e
e
liti
s
t
s
tr
ateg
y
,
n
in
d
iv
id
u
als
ar
e
s
elec
ted
f
r
o
m
t
h
e
cu
r
r
en
t
p
o
p
u
latio
n
(
n
<
N)
,
wh
er
e
N
is
th
e
s
ize
o
f
th
e
p
o
p
u
latio
n
.
T
h
ese
in
d
iv
id
u
als
h
av
e
th
e
b
est
f
itn
ess
v
alu
e.
T
h
e
r
em
ain
in
g
in
d
iv
id
u
als
(
N
−
n
)
ar
e
b
ein
g
s
elec
ted
f
r
o
m
th
e
p
ar
en
ts
an
d
o
f
f
s
p
r
in
g
,
s
in
ce
th
ey
co
m
p
ete
f
o
r
s
u
r
v
iv
al.
W
e
m
ay
f
i
n
d
in
th
e
liter
atu
r
e
v
ar
ian
ts
o
f
th
ese
s
tr
ateg
ies;
h
o
wev
er
,
th
ey
b
elo
n
g
eith
er
to
th
e
g
e
n
er
al
ap
p
r
o
a
ch
o
r
to
th
e
elitis
t o
n
e
Un
f
o
r
tu
n
atel
y
,
g
en
etic
alg
o
r
it
h
m
s
,
as
o
th
er
m
etah
eu
r
is
tics
,
ca
n
p
r
em
atu
r
ely
co
n
v
er
g
e
an
d
lo
s
e
alleles
in
th
e
r
u
n
.
Pre
m
at
u
r
e
co
n
v
er
g
en
ce
is
a
m
ajo
r
p
r
o
b
lem
th
at
ev
er
y
m
etah
eu
r
is
tic
s
u
f
f
er
s
f
r
o
m
,
n
o
ex
ce
p
tio
n
f
o
r
g
en
etic
alg
o
r
ith
m
s
.
W
ith
th
is
d
r
awb
ac
k
o
f
th
e
g
en
etic
alg
o
r
ith
m
,
r
esear
ch
er
s
tr
y
t
o
av
o
id
p
r
em
atu
r
e
co
n
v
er
g
en
ce
u
s
in
g
s
ev
er
al
ap
p
r
o
ac
h
es.
T
h
e
p
r
em
atu
r
e
co
n
v
er
g
e
n
ce
ch
allen
g
e
h
as
b
ee
n
ad
d
r
ess
ed
th
r
o
u
g
h
d
iv
e
r
s
e
ap
p
r
o
ac
h
es
in
th
e
liter
atu
r
e.
Var
n
am
k
h
asti
an
d
L
ee
[
4
]
tac
k
le
th
e
p
r
em
atu
r
e
co
n
v
er
g
en
ce
p
r
o
b
lem
b
y
d
iv
i
d
in
g
th
e
p
o
p
u
latio
n
in
to
a
g
r
o
u
p
o
f
m
ale
c
h
r
o
m
o
s
o
m
es
an
d
a
n
o
th
e
r
g
r
o
u
p
o
f
f
e
m
ale
ch
r
o
m
o
s
o
m
es.
I
n
th
e
m
a
tin
g
p
h
ase,
a
f
em
ale
is
s
elec
ted
b
y
a
to
u
r
n
am
en
t
s
elec
tio
n
,
wh
ile
a
m
ale
is
s
elec
ted
b
ased
o
f
h
a
m
m
in
g
d
is
tan
ce
(
HD)
.
I
n
th
e
s
am
e
g
o
al,
a
n
o
th
er
tech
n
iq
u
e,
wh
ic
h
co
n
s
is
t
o
n
u
s
in
g
ch
ao
s
t
h
eo
r
y
in
s
tead
o
f
r
a
n
d
o
m
n
ess
is
u
s
ed
in
t
h
e
wo
r
k
o
f
[
5
]
.
E
ac
h
tim
e
a
r
an
d
o
m
n
u
m
b
er
is
n
ee
d
ed
b
y
th
e
g
en
etic
a
lg
o
r
ith
m
,
a
l
o
g
is
tic
m
ap
,
o
r
te
n
t
m
ap
ar
e
u
s
ed
to
g
en
er
ate
ch
ao
tic
v
ar
ia
b
les.
I
n
th
e
r
esear
ch
o
f
[
6
]
,
th
e
g
en
etic
alg
o
r
ith
m
d
y
n
a
m
ically
ch
an
g
es
th
e
g
en
etic
o
p
er
atio
n
s
d
u
r
in
g
th
e
ex
ec
u
tio
n
to
d
ec
r
ea
s
e
th
e
p
r
o
b
ab
ilit
y
o
f
p
r
em
at
u
r
e
c
o
n
v
er
g
en
ce
.
T
h
e
alg
o
r
ith
m
ch
an
g
es
th
e
cr
o
s
s
o
v
er
r
ate
an
d
m
u
tatio
n
r
ate
d
u
r
i
n
g
th
e
ex
ec
u
tio
n
.
I
n
th
e
p
ap
er
o
f
[
7
]
,
au
th
o
r
s
p
r
esen
t
a
r
an
k
-
b
ased
s
elec
tio
n
o
p
er
ato
r
,
th
at
aim
to
av
o
id
p
r
em
atu
r
e
co
n
v
e
r
g
en
ce
b
y
ap
p
ly
in
g
a
b
alan
ce
b
et
wee
n
d
iv
er
s
ity
an
d
s
elec
tio
n
p
r
ess
u
r
e.
I
n
d
iv
id
u
al
s
ar
e
p
r
io
r
itized
ac
co
r
d
in
g
to
th
eir
f
itn
ess
s
tatu
s
u
s
in
g
wei
g
h
ts
,
an
d
class
if
ied
in
to
th
r
ee
f
it
ca
teg
o
r
ies;
lo
west,
av
er
ag
e
an
d
b
est
o
n
es.
T
h
e
s
elec
tio
n
weig
h
ts
ar
e
f
u
r
th
e
r
em
p
lo
y
e
d
with
in
ea
ch
class
en
s
u
r
in
g
p
o
p
u
lati
o
n
d
iv
er
s
ity
,
an
d
h
i
g
h
er
wei
g
h
ts
ar
e
o
f
f
er
ed
to
th
e
m
o
s
t
f
it
in
d
iv
id
u
als
to
m
ain
tain
s
elec
tio
n
p
r
ess
u
r
e.
Sev
er
al
wo
r
k
s
[
8
]
–
[
1
0
]
u
s
ed
a
d
is
tr
ib
u
tio
n
m
ec
h
an
is
m
o
f
g
en
etic
alg
o
r
ith
m
m
o
d
el.
T
h
e
id
ea
is
to
s
p
lit
th
e
p
o
p
u
latio
n
in
to
i
n
d
ep
e
n
d
en
t
s
u
b
-
p
o
p
u
latio
n
s
.
T
h
ese
s
u
b
p
o
p
u
latio
n
s
m
ay
h
av
e
d
if
f
er
en
t
g
e
n
etic
co
n
f
ig
u
r
atio
n
s
.
E
x
ch
an
g
in
g
in
d
iv
id
u
als
is
p
o
s
s
ib
le
b
etwe
en
s
u
b
-
p
o
p
u
latio
n
s
u
s
in
g
th
e
m
ig
r
atio
n
m
ec
h
an
is
m
.
W
ith
t
h
is
ap
p
r
o
ac
h
,
s
u
b
-
p
o
p
u
latio
n
s
ev
o
lv
e
in
d
if
f
er
en
t
p
ath
,
wh
ic
h
m
ak
es
th
e
g
en
etic
alg
o
r
ith
m
e
x
p
lo
r
e
wid
e
ar
ea
s
.
Hy
b
r
id
izatio
n
o
f
g
en
etic
alg
o
r
ith
m
is
u
s
ed
in
th
e
wo
r
k
o
f
[
1
1
]
an
d
[
1
2
]
.
T
h
ese
wo
r
k
s
u
s
e
o
t
h
er
alg
o
r
ith
m
s
to
h
an
d
le
th
e
m
u
tatio
n
o
p
er
atio
n
.
I
n
ter
v
en
tio
n
o
n
b
o
th
c
r
o
s
s
o
v
er
an
d
m
u
tatio
n
i
s
ap
p
lied
in
t
h
e
wo
r
k
o
f
[
1
3
]
–
[
1
5
]
,
o
n
m
u
tatio
n
o
n
ly
in
th
e
wo
r
k
o
f
[
1
6
]
,
an
d
o
n
cr
o
s
s
o
v
er
o
n
l
y
in
[
1
7
]
.
Hy
b
r
id
izatio
n
ca
n
also
b
e
p
er
f
o
r
m
e
d
with
o
th
er
m
etah
e
u
r
is
tics
[
1
8
]
,
[
1
9
]
.
Nico
ar
ă
[
2
0
]
in
tr
o
d
u
ce
d
two
d
if
f
er
en
t
a
p
p
r
o
ac
h
es
to
alle
v
iate
th
e
p
r
e
m
atu
r
e
c
o
n
v
e
r
g
en
ce
b
y
ap
p
ly
in
g
d
if
f
er
e
n
t
g
en
etic
o
p
er
ato
r
s
d
y
n
am
ically
,
an
d
b
y
r
e
-
in
itializin
g
a
p
o
r
tio
n
o
f
t
h
e
p
o
p
u
lati
o
n
in
th
e
r
u
n
.
I
n
t
h
e
wo
r
k
o
f
[
2
1
]
,
au
th
o
r
s
u
s
e
a
s
ec
o
n
d
alg
o
r
ith
m
ca
lled
ex
ten
d
ed
-
Neld
er
-
Me
a
d
(
E
NM
)
to
e
n
h
an
ce
th
e
b
est
f
o
u
n
d
s
o
lu
tio
n
s
p
r
o
d
u
ce
d
b
y
t
h
e
g
en
etic
alg
o
r
ith
m
.
An
o
t
h
er
ap
p
r
o
ac
h
is
u
s
ed
in
th
e
a
r
ticle
o
f
[
2
2
]
,
wh
ich
co
n
s
is
ts
o
f
in
s
er
tin
g
r
an
d
o
m
g
en
es
in
th
e
n
ewly
cr
ea
ted
o
f
f
s
p
r
in
g
.
I
n
th
e
ar
ticle
o
f
[
2
3
]
,
a
g
en
etic
alg
o
r
ith
m
was
p
r
o
p
o
s
ed
th
at
u
s
ed
ch
r
o
m
o
s
o
m
es
im
p
lem
en
ted
i
n
f
o
u
r
lay
er
s
,
ea
ch
o
n
e
r
esp
o
n
s
i
b
le
f
o
r
e
n
co
d
i
n
g
ce
r
tain
r
eq
u
ir
em
en
ts
;
h
en
ce
,
th
e
m
u
tatio
n
an
d
c
r
o
s
s
o
v
er
o
p
er
atio
n
s
ar
e
p
e
r
f
o
r
m
ed
o
n
ea
c
h
lay
er
s
ep
ar
ately
,
lea
d
in
g
to
a
d
iv
er
s
ity
in
th
e
o
f
f
s
p
r
in
g
i
n
d
iv
id
u
als
wh
ile
av
o
id
in
g
u
n
d
esira
b
le
g
e
n
es.
T
h
e
alg
o
r
ith
m
c
o
m
b
in
es
th
e
r
an
d
o
m
l
y
s
elec
ted
d
o
m
in
an
t
in
d
iv
id
u
als
u
s
in
g
a
r
o
u
lette
wh
ee
l
s
elec
tio
n
p
r
o
c
ess
.
T
h
ese
in
d
iv
id
u
als
will
b
e
k
ep
t
in
th
e
f
u
tu
r
e
g
en
er
atio
n
.
A
s
u
m
m
ar
y
o
f
t
h
e
s
e
wo
r
k
s
is
p
r
o
v
id
e
d
in
T
ab
le
1
.
W
h
ile
ex
is
tin
g
r
esear
ch
f
o
cu
s
es
o
n
s
elec
tio
n
tech
n
iq
u
es,
o
p
er
ato
r
m
o
d
if
icatio
n
s
,
o
r
h
y
b
r
id
izatio
n
,
th
is
ar
ticle
in
v
esti
g
ates
th
e
im
p
ac
t
o
f
in
teg
r
atin
g
a
p
a
r
en
t
in
g
f
itn
ess
p
ar
am
eter
[
2
4
]
in
t
o
an
elitis
t
g
en
etic
alg
o
r
ith
m
to
m
itig
ate
p
r
em
atu
r
e
co
n
v
er
g
e
n
ce
with
o
u
t
ex
ter
n
al
alg
o
r
ith
m
s
,
in
o
p
tim
izin
g
th
e
v
eh
icle
r
o
u
tin
g
p
r
o
b
lem
(
VR
P)
.
T
h
e
m
ajo
r
s
tr
en
g
th
o
f
th
e
p
a
r
en
tin
g
f
itn
ess
is
th
at
it
ca
n
b
e
in
teg
r
ated
in
ex
is
tin
g
g
en
etic
alg
o
r
ith
m
s
with
m
in
im
u
m
ef
f
o
r
ts
,
an
d
with
o
u
t
ch
an
g
in
g
t
h
e
alg
o
r
ith
m
’
s
co
r
e.
T
h
e
im
p
li
ca
tio
n
s
o
f
th
is
wo
r
k
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
E
liti
s
t g
en
etic
a
lg
o
r
ith
m
imp
r
o
ve
d
w
ith
p
a
r
en
tin
g
fitn
ess
p
a
r
a
mete
r
(
Ou
is
s
Mu
s
ta
p
h
a
)
885
ex
ten
d
to
r
ea
l
-
wo
r
l
d
ap
p
licatio
n
s
s
u
ch
as
n
etwo
r
k
d
esig
n
an
d
r
eso
u
r
ce
allo
ca
tio
n
am
o
n
g
o
th
er
s
.
Un
lik
e
h
y
b
r
id
izatio
n
m
eth
o
d
s
(
e.
g
.
,
[
1
1
]
)
,
i
n
teg
r
atin
g
th
e
p
a
r
en
tin
g
f
itn
ess
p
ar
am
eter
d
o
es
n
o
t
n
ee
d
to
u
s
e
ex
ter
n
al
alg
o
r
ith
m
s
to
tack
le
p
r
em
atu
r
e
co
n
v
er
g
en
ce
.
T
h
e
r
em
ain
d
er
o
f
t
h
is
p
ap
er
is
s
tr
u
ctu
r
ed
as
f
o
llo
ws:
s
ec
tio
n
2
d
etails
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
.
Sectio
n
3
d
escr
ib
es
th
e
ex
p
er
im
en
ts
.
Sectio
n
4
p
r
esen
ts
an
d
d
is
cu
s
s
es
th
e
r
esu
lts
,
an
d
s
ec
tio
n
5
co
n
clu
d
es
with
f
u
tu
r
e
r
esear
c
h
d
ir
ec
tio
n
s
.
T
ab
le
1
.
Su
m
m
a
r
y
o
f
liter
atu
r
e
o
n
p
r
em
atu
r
e
c
o
n
v
e
r
g
en
ce
a
v
o
id
an
ce
i
n
g
as
Wo
rk
P
re
m
a
tu
re
c
o
n
v
e
rg
e
n
c
e
a
v
o
i
d
a
n
c
e
m
e
c
h
a
n
ism
[4
]
P
o
p
u
latio
n
d
iv
isio
n
b
y
se
x
[5
]
Ch
a
o
s th
e
o
ry
f
o
r
ra
n
d
o
m
n
e
ss
re
p
l
a
c
e
m
e
n
t
[6
]
Dy
n
a
m
ic ad
ju
stm
e
n
t
o
f
c
ro
ss
o
v
e
r
/mu
tatio
n
ra
tes
[7
]
Ra
n
k
-
b
a
se
d
se
lec
ti
o
n
with
we
ig
h
t
e
d
fit
n
e
ss
c
las
se
s
[8
]
–
[
1
0
]
P
a
ra
ll
e
l
su
b
p
o
p
u
lati
o
n
s wit
h
m
ig
r
a
ti
o
n
[1
1
],
[1
2
],
[
1
8
],
[1
9
],
[
2
1
]
Hy
b
ri
d
iza
ti
o
n
with
o
t
h
e
r
a
lg
o
rit
h
m
s
[1
3
]
–
[1
5
]
M
o
d
if
ied
c
ro
ss
o
v
e
r
a
n
d
m
u
tati
o
n
o
p
e
ra
ti
o
n
s
[1
6
],
[2
2
]
M
u
tatio
n
a
d
a
p
tatio
n
s
[1
7
]
Cro
ss
o
v
e
r
a
d
a
p
tatio
n
s
[2
0
]
Dy
n
a
m
ic g
e
n
e
ti
c
o
p
e
ra
to
r
a
p
p
li
c
a
ti
o
n
[2
3
]
Cu
sto
m
c
h
r
o
m
o
so
m
e
e
n
c
o
d
in
g
2.
E
L
I
T
I
S
T
G
E
N
E
T
I
C
AL
G
O
RIT
H
M
WI
T
H
P
ARE
NT
I
N
G
F
I
T
NE
SS
2
.
1
.
P
a
re
nting
f
it
nes
s
:
co
ncept
a
nd
m
ec
ha
nis
m
T
h
e
g
e
n
etic
alg
o
r
ith
m
im
p
r
o
v
ed
with
p
ar
en
tin
g
f
itn
ess
p
ar
am
eter
(
eGA
wPF)
[
2
4
]
is
an
elitis
t
alg
o
r
ith
m
th
at
im
p
lem
en
ts
th
e
p
ar
e
n
tin
g
f
itn
ess
p
ar
am
eter
to
tack
le
p
r
em
atu
r
e
co
n
v
er
g
en
ce
,
in
o
r
d
e
r
to
o
b
tain
b
etter
f
in
al
r
esu
lts
.
T
h
e
v
alu
e
o
f
th
e
p
ar
en
tin
g
f
itn
ess
q
u
an
tifie
s
th
e
ca
p
ac
ity
o
f
a
p
ar
en
t
to
p
r
o
d
u
ce
,
f
r
o
m
m
atin
g
,
f
it
o
f
f
s
p
r
in
g
.
Sin
ce
th
e
g
en
etic
alg
o
r
ith
m
d
ea
ls
with
ch
r
o
m
o
s
o
m
es
co
m
p
o
s
ed
b
y
g
en
es
co
n
s
id
er
ed
as
b
u
ild
in
g
b
lo
ck
s
[
3
]
ca
n
,
b
y
c
o
m
b
in
in
g
t
h
em
,
p
r
o
d
u
ce
b
etter
o
f
f
s
p
r
in
g
.
T
h
e
in
teg
r
atio
n
o
f
th
e
p
a
r
en
t
in
g
f
itn
ess
p
ar
am
eter
s
h
o
u
l
d
b
e
d
o
n
e
with
m
o
d
er
ate
ef
f
o
r
t,
s
in
ce
it
r
eq
u
ir
es th
e
f
o
llo
win
g
:
−
Ad
d
in
g
th
e
u
p
d
ati
n
g
f
u
n
ctio
n
in
th
e
lo
o
p
;
−
Ad
d
in
g
th
r
ee
n
ew
g
e
n
es in
th
e
ch
r
o
m
o
s
o
m
e.
On
e
ca
n
u
s
e
ex
t
er
n
al
ar
r
ay
s
f
o
r
th
e
s
am
e
g
o
al;
−
Ad
d
in
g
th
e
s
elec
tio
n
m
ec
h
an
i
s
m
o
f
th
e
b
est p
a
r
en
ts
in
th
e
e
v
o
lu
tio
n
p
h
ase.
T
h
e
Fig
u
r
e
1
illu
s
tr
ates
an
ex
a
m
p
le
o
f
a
cr
o
s
s
o
v
er
o
p
er
atio
n
o
n
av
e
r
ag
e
f
it
p
ar
en
ts
,
t
h
at
will
p
r
o
d
u
ce
o
f
f
s
p
r
in
g
with
a
co
m
b
in
atio
n
o
f
th
e
p
ar
en
t
’
s
b
u
ild
in
g
b
l
o
ck
s
.
T
h
e
g
en
es B
1
,
B
2
,
B
3
,
an
d
B
4
ar
e
co
n
s
id
er
ed
in
th
is
ex
am
p
le
a
p
o
r
tio
n
o
f
th
e
b
est
f
in
al
s
o
lu
tio
n
.
W
ith
th
is
p
h
ilo
s
o
p
h
y
,
th
e
b
est
s
o
lu
tio
n
s
ar
e
b
ein
g
co
n
s
tr
u
cted
,
b
y
co
m
b
in
in
g
b
u
i
ld
in
g
b
lo
c
k
s
wh
ich
ar
e
s
m
all
p
o
r
tio
n
s
with
h
ig
h
p
o
te
n
tial.
I
n
a
g
e
n
etic
alg
o
r
ith
m
im
p
r
o
v
ed
with
th
e
p
ar
e
n
tin
g
f
itn
ess
p
ar
am
eter
,
in
d
iv
id
u
als
with
h
ig
h
p
ar
en
tin
g
f
itn
ess
ar
e
b
ein
g
k
ep
t
th
r
o
u
g
h
g
en
e
r
atio
n
s
,
ev
en
if
th
eir
f
itn
ess
(
p
er
s
o
n
al
f
itn
ess
)
m
ay
b
e
wea
k
.
Sin
ce
th
e
alg
o
r
ith
m
u
s
es
elitis
m
to
ch
o
o
s
e
in
d
iv
id
u
als
th
at
will
s
u
r
v
iv
e
th
r
o
u
g
h
g
en
er
atio
n
s
,
it
is
co
n
s
id
er
ed
an
elitis
t g
en
etic
alg
o
r
ith
m
.
Fig
u
r
e
1
.
An
ex
am
p
le
o
f
a
c
r
o
s
s
o
v
er
o
p
er
atio
n
o
n
a
v
er
ag
e
f
i
t p
ar
en
ts
2
.
2
.
Alg
o
rit
hm
re
presenta
t
i
o
n
T
h
e
g
en
etic
alg
o
r
ith
m
im
p
r
o
v
ed
with
p
ar
en
tin
g
f
itn
ess
p
ar
a
m
eter
(
eGA
wPF)
[
2
4
]
illu
s
tr
ated
b
y
th
e
Alg
o
r
ith
m
1
ex
ten
d
s
th
e
s
im
p
le
g
en
etic
alg
o
r
ith
m
[
2
]
,
[
3
]
b
y
in
teg
r
atin
g
th
e
p
a
r
en
tin
g
f
it
n
ess
p
ar
am
eter
an
d
th
e
p
ar
en
tin
g
f
itn
ess
ca
lcu
latio
n
f
u
n
ctio
n
.
T
h
e
Fig
u
r
e
2
illu
s
tr
ates
th
e
f
lo
w
o
f
th
e
alg
o
r
it
h
m
.
T
h
e
in
te
g
r
atio
n
o
f
th
e
p
a
r
en
tin
g
f
itn
ess
p
ar
a
m
eter
d
o
es
n
o
t
p
er
tu
r
b
th
e
g
en
etic
alg
o
r
ith
m
’
co
r
e
,
h
en
ce
it
ca
n
b
e
ea
s
ily
im
p
lem
en
ted
in
e
x
is
tin
g
alg
o
r
i
th
m
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
2
,
Ap
r
il
20
2
6
:
8
8
3
-
894
886
Alg
o
r
ith
m
1
.
p
s
eu
d
o
-
co
d
e
o
f
a
g
en
etic
alg
o
r
ith
m
im
p
r
o
v
ed
with
p
ar
en
tin
g
f
itn
ess
p
ar
am
et
er
1:
define crossover rate: χ;
2:
define mutation rate: µ;
3:
Generate initial population P (t = 0);
4:
Initialize pf(i)
0
← −1
∀
i
∈
P
5:
while
t # maximal generation number loop
do
6:
Select parents P
1
(t) and P
2
(t) from population;
7:
Generate a random number rnd
χ
in ]0,1[;
8:
if
χ > rnd
χ
then
9:
Execute crossover operation χ on the selected parents;
10:
for all
child
∈
offspring
do
11:
for all
gene
∈
child's genes
do
12:
Generate a random number rnd
µ
in ]0,1[;
13:
if
µ > rnd
µ
then
14:
Execute mutation operation µ on gene;
15:
end if
16:
end for
17:
end for
18:
end if
19:
for all
individual
o
in the offspring population
do
20:
update parent's parenting fitness of
o
21:
end for
22:
Prepare the next population;
23:
end while
Fig
u
r
e
2
.
Flo
w
o
f
a
g
e
n
etic
alg
o
r
ith
m
im
p
r
o
v
ed
with
th
e
p
ar
en
tin
g
f
itn
ess
p
ar
am
eter
2
.
3
.
E
v
o
lutio
n pha
s
e
a
nd
f
it
nes
s
u
pd
a
t
e
2
.
3
.
1
.
E
v
o
lutio
n pha
s
e
T
h
e
Alg
o
r
ith
m
2
illu
s
tr
ates
h
o
w
th
e
n
ex
t
p
o
p
u
latio
n
is
b
ei
n
g
p
r
o
ce
s
s
ed
.
A
p
er
ce
n
ta
g
e
o
f
th
e
b
est
p
ar
en
ts
is
b
ein
g
s
et
in
th
e
b
eg
in
n
in
g
o
f
th
e
alg
o
r
ith
m
,
d
en
o
t
ed
as
r
.
Nex
t,
in
th
e
e
v
o
lu
tio
n
p
h
ase,
p
a
r
en
ts
an
d
o
f
f
s
p
r
in
g
ar
e
m
e
r
g
ed
in
to
o
n
e
p
o
p
u
latio
n
d
e
n
o
ted
P
µλ
.
T
h
e
p
o
p
u
latio
n
P
µλ
is
s
o
r
ted
ac
co
r
d
in
g
to
t
h
e
f
itn
ess
f
u
n
ctio
n
o
f
its
in
d
iv
id
u
als.
An
o
th
er
s
o
r
tin
g
is
ex
ec
u
ted
o
n
th
e
p
ar
en
ts
µ
,
th
is
tim
e
in
a
d
escen
d
in
g
wa
y
ac
co
r
d
in
g
to
th
e
p
ar
en
tin
g
f
itn
ess
p
ar
am
eter
pf
.
A
p
o
r
tio
n
o
f
th
e
b
est
p
ar
en
ts
µ
c
eq
u
al
to
r
×
µ
is
s
elec
ted
to
b
e
p
ar
t
o
f
th
e
n
ex
t
p
o
p
u
latio
n
.
T
h
e
r
em
ain
i
n
g
p
lace
s
o
f
th
e
n
e
x
t
p
o
p
u
latio
n
ar
e
b
ein
g
co
m
p
o
s
ed
with
th
e
b
est
in
d
iv
id
u
als o
f
th
e
p
o
p
u
latio
n
P
µλ
,
wh
ich
is
co
m
p
o
s
ed
o
f
in
d
iv
id
u
als in
th
e
s
et
P
µλ
-
µ
c
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
E
liti
s
t g
en
etic
a
lg
o
r
ith
m
imp
r
o
ve
d
w
ith
p
a
r
en
tin
g
fitn
ess
p
a
r
a
mete
r
(
Ou
is
s
Mu
s
ta
p
h
a
)
887
Alg
o
r
ith
m
2
.
Pre
p
ar
atio
n
o
f
t
h
e
n
ex
t p
o
p
u
latio
n
.
1:
r ← percentage of best parents;
2:
P
µλ
← µ+λ;
3:
sorting P
µλ
by fitness function
f
4:
sorting
µ
by parenting fitness
pf
5:
µ
c
←
r
×
µ
6:
P
n
← []
7:
P
n
← µ
c
first parents from
µ
8:
P
n
← P
n
+(P
µλ
-
µ
c
)
9:
P ← P
n
2
.
3
.
2
.
P
a
re
nting
f
it
nes
s
up
da
t
e
T
h
e
p
ar
en
tin
g
f
itn
ess
o
f
p
ar
e
n
ts
is
u
p
d
ated
af
ter
th
e
cr
ea
ti
o
n
o
f
th
e
wh
o
le
o
f
f
s
p
r
in
g
in
th
e
cu
r
r
en
t
lo
o
p
.
Fo
r
ea
ch
o
f
f
s
p
r
in
g
,
th
e
p
ar
en
tin
g
f
itn
ess
p
ar
am
ete
r
o
f
its
b
o
t
h
p
a
r
en
ts
in
g
e
n
e
r
atio
n
t
is
u
p
d
ated
ac
co
r
d
in
g
to
(
1
)
:
(
)
=
(
)
−
1
+
(
)
(
1
)
wh
ile
th
e
v
alu
e
o
f
(
)
is
ca
lcu
late
d
b
y
(
2
)
.
(
)
=
−
(
)
(
2
)
wh
er
e
d
ef
in
es
th
e
m
ea
n
o
f
t
h
e
wh
o
le
o
f
f
s
p
r
in
g
’
s
f
itn
ess
in
th
e
cu
r
r
en
t
l
o
o
p
,
an
d
(
)
d
ef
in
es
th
e
f
itn
ess
f
u
n
ctio
n
o
f
th
e
in
d
iv
id
u
al
i
(
t
h
e
o
f
f
s
p
r
in
g
o
f
th
e
cu
r
r
en
t
s
el
ec
ted
p
ar
e
n
t
to
u
p
d
ate
its
p
ar
e
n
tin
g
f
itn
ess
)
i
n
th
e
cu
r
r
en
t lo
o
p
t
.
T
h
e
m
ea
n
v
alu
e
is
ca
lcu
lated
ac
co
r
d
in
g
to
(
3
)
.
=
∑
(
)
×
2
(
3
)
wh
er
e
N
r
ep
r
esen
ts
th
e
p
o
p
u
latio
n
s
ize.
T
h
e
p
ar
e
n
tin
g
f
it
n
ess
o
f
th
e
p
ar
e
n
ts
in
th
e
cu
r
r
en
t
p
o
p
u
latio
n
is
u
p
d
ated
as f
o
llo
ws:
Step
1
: T
h
e
p
a
r
en
tin
g
f
itn
ess
is
in
itialized
af
ter
th
e
g
en
er
atio
n
o
f
th
e
f
ir
s
t p
o
p
u
latio
n
with
t
h
e
d
ef
au
lt
v
alu
e
-
1.
Step
2:
T
h
e
g
e
n
etic
alg
o
r
ith
m
ca
lcu
lates
th
e
f
itn
ess
f
u
n
c
tio
n
o
f
th
e
p
r
o
d
u
ce
d
o
f
f
s
p
r
in
g
f
r
o
m
th
e
m
atin
g
p
r
o
ce
s
s
o
f
th
e
two
s
elec
ted
p
ar
en
ts
,
u
s
in
g
t
h
e
cr
o
s
s
o
v
e
r
o
p
er
ato
r
.
E
ac
h
o
f
f
s
p
r
i
n
g
h
as
two
ad
d
e
d
p
ar
am
eter
s
: th
e
in
d
e
x
es o
f
its
p
ar
en
ts
,
wh
ich
will b
e
u
s
ed
to
u
p
d
ate
th
e
i
n
d
iv
id
u
als with
th
ese
in
d
ex
es.
Step
3:
T
h
e
p
ar
en
tin
g
f
itn
ess
is
u
p
d
ated
at
th
e
e
n
d
o
f
th
e
o
p
er
atio
n
s
o
f
m
atin
g
,
c
r
o
s
s
o
v
er
,
an
d
m
u
tatio
n
,
an
d
b
ef
o
r
e
t
h
e
ev
o
l
u
tio
n
o
p
er
atio
n
.
Step
4:
T
h
e
f
itn
ess
f
u
n
ctio
n
o
f
ea
ch
o
f
f
s
p
r
in
g
is
co
m
p
ar
e
d
t
o
th
e
m
ea
n
o
f
th
e
n
ewly
cr
ea
ted
o
f
f
s
p
r
i
n
g
.
T
h
e
d
if
f
er
en
ce
b
etwe
en
an
d
th
e
o
f
f
s
p
r
in
g
’
s
f
itn
ess
is
d
en
o
ted
(
)
.
I
n
th
is
f
o
r
m
u
latio
n
,
a
v
alu
e
i
s
co
n
s
id
er
ed
,
wh
ich
is
eq
u
al
to
th
e
s
u
m
o
f
th
e
f
itn
ess
v
alu
es
o
f
th
e
o
f
f
s
p
r
in
g
p
o
p
u
latio
n
d
iv
id
ed
b
y
N×
2
.
Sin
ce
th
e
o
f
f
s
p
r
in
g
p
o
p
u
latio
n
is
2
tim
es
b
ig
g
er
t
h
an
th
e
s
ize
o
f
th
e
p
o
p
u
lati
o
n
.
Fo
r
ea
ch
o
f
f
s
p
r
in
g
,
th
e
p
a
r
en
tin
g
f
itn
ess
o
f
its
p
ar
en
ts
is
u
p
d
ate
d
u
s
in
g
(
1
)
.
2
.
4
.
Chro
m
o
s
o
m
e
r
epre
s
ent
a
t
io
n
T
h
e
Fig
u
r
e
3
illu
s
tr
ates
a
r
e
p
r
esen
tatio
n
o
f
t
h
e
ch
r
o
m
o
s
o
m
e
s
’
s
tr
u
ctu
r
e
u
s
ed
in
th
e
g
en
etic
alg
o
r
ith
m
im
p
r
o
v
e
d
with
p
ar
en
tin
g
f
itn
e
s
s
p
ar
am
eter
.
T
h
e
f
g
en
e
d
ef
in
es
th
e
f
itn
ess
f
u
n
ctio
n
o
f
th
e
c
h
r
o
m
o
s
o
m
e
,
wh
er
e
th
e
pf
d
e
f
in
es
th
e
p
ar
en
tin
g
f
it
n
ess
.
T
h
e
v
alu
e
id
x
1
an
d
id
x
2
a
r
e
u
s
ed
to
s
to
r
e
th
e
i
n
d
ex
es o
f
th
e
ch
r
o
m
o
s
o
m
e’
s
p
ar
en
ts
,
in
o
r
d
er
t
o
u
p
d
ate
th
ei
r
p
ar
en
tin
g
f
itn
ess
v
alu
e
in
t
h
e
co
r
r
esp
o
n
d
in
g
p
h
ase.
f
pf
id
x
1
id
x
2
Fig
u
r
e
3
.
C
h
r
o
m
o
s
o
m
e
in
te
g
r
a
tin
g
th
e
p
ar
e
n
tin
g
f
itn
ess
p
ar
am
eter
T
h
e
Fig
u
r
e
4
illu
s
tr
ates
an
ex
am
p
le
o
f
th
e
r
ep
r
esen
tatio
n
o
f
p
ar
en
ts
at
th
e
en
d
o
f
a
lo
o
p
.
Fo
r
ea
ch
p
ar
en
t’
s
p
a
r
en
tin
g
f
itn
ess
p
ar
am
eter
,
a
n
ew
v
al
u
e
is
ass
ig
n
ed
to
it.
Fig
u
r
e
5
r
ep
r
esen
ts
an
e
x
am
p
le
o
f
a
n
in
d
iv
id
u
al
th
at
h
as
a
g
o
o
d
f
itn
ess
f
u
n
ctio
n
,
b
u
t
a
wea
k
p
ar
e
n
tin
g
f
itn
ess
v
alu
e.
On
th
e
co
n
tr
ar
y
,
th
e
Fig
u
r
e
6
r
ep
r
esen
ts
a
g
o
o
d
p
a
r
en
t
(
ac
c
o
r
d
in
g
to
its
p
ar
en
tin
g
f
it
n
ess
)
,
b
u
t
with
a
wea
k
er
f
itn
ess
f
u
n
ctio
n
.
Sin
ce
we
ar
e
d
ea
lin
g
with
a
m
in
im
izin
g
p
r
o
b
lem
,
th
e
b
est
in
d
iv
id
u
als
a
r
e
th
o
s
e
with
a
lo
w
f
itn
ess
v
alu
e.
T
h
e
Alg
o
r
ith
m
3
s
h
o
ws th
e
p
ar
en
tin
g
f
itn
ess
u
p
d
atin
g
p
h
ase.
Evaluation Warning : The document was created with Spire.PDF for Python.
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I
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C
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,
Vo
l.
1
6
,
No
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2
,
Ap
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2
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6
2
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20
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17
19
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...
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9
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18
1
9
2
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Fig
u
r
e
4
.
E
x
am
p
le
o
f
r
e
p
r
esen
tatio
n
o
f
p
a
r
en
ts
in
th
e
e
n
d
o
f
a
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o
p
12
17
19
10
...
14
9
3
18
1
9
2
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60
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1
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1
Fig
u
r
e
5
.
E
x
am
p
le
o
f
r
e
p
r
esen
tatio
n
o
f
an
in
d
iv
id
u
al
with
g
o
o
d
f
itn
ess
an
d
wea
k
p
ar
en
ti
n
g
f
itn
ess
6
14
8
20
...
10
18
4
1
2
0
3
24
-
1
-
1
Fig
u
r
e
6
.
E
x
am
p
le
o
f
r
e
p
r
esen
tatio
n
o
f
an
in
d
iv
id
u
al
with
w
ea
k
f
itn
ess
an
d
g
o
o
d
p
ar
en
tin
g
f
itn
ess
Alg
o
r
ith
m
3
.
Par
en
tin
g
f
itn
ess
u
p
d
atin
g
p
h
ase
1:
Initialize
pf (i)
0
← −1,
∀
i
∈
P
2:
for each
offspring o
∈
O
do
3:
Calculate d(t)
im
via Eq. 2
4:
Update
pf (i)
t
←
pf (i)
t
-
1
+
d(t)
im
5:
end for
6:
Preparation of the next population;
3.
E
XP
E
R
I
M
E
N
T
S
I
n
o
r
d
er
to
co
m
p
r
eh
e
n
s
iv
ely
ev
alu
ate
th
e
ef
f
icien
c
y
o
f
o
u
r
alg
o
r
ith
m
im
p
r
o
v
ed
with
th
e
p
ar
en
tin
g
f
itn
ess
,
we
h
av
e
s
elec
ted
a
ch
allen
g
in
g
o
p
tim
izatio
n
p
r
o
b
le
m
to
s
er
v
e
as
o
u
r
test
in
g
g
r
o
u
n
d
.
Sp
ec
if
ically
,
we
h
av
e
o
p
ted
to
wo
r
k
o
n
th
e
VR
P,
wi
th
a
p
ar
ticu
lar
f
o
cu
s
o
n
th
e
v
eh
icle
r
o
u
tin
g
p
r
o
b
lem
with
d
r
o
n
es
(
VR
PD)
v
ar
ian
t.
VR
PD
is
an
ex
ten
s
io
n
o
f
th
e
well
-
k
n
o
w
n
c
ap
ac
itat
ed
v
eh
icle
r
o
u
tin
g
p
r
o
b
lem
(
C
VR
P),
wh
ich
was
in
tr
o
d
u
ce
d
f
o
r
th
e
f
ir
s
t
tim
e
in
th
e
wo
r
k
o
f
[
2
5
]
.
On
e
p
ar
ti
cu
lar
asp
ec
t
th
at
s
ets
V
R
P
ap
ar
t
is
th
e
f
ac
t
th
at
allele
lo
s
s
is
n
o
t
a
c
o
n
ce
r
n
,
as th
e
p
r
o
b
lem
f
o
r
m
u
latio
n
e
n
s
u
r
es
th
at
all
n
o
d
es
ar
e
in
clu
d
e
d
i
n
th
e
c
h
r
o
m
o
s
o
m
e
en
co
d
in
g
.
I
n
th
is
ty
p
e
o
f
o
p
ti
m
izatio
n
p
r
o
b
lem
,
th
e
p
r
im
ar
y
ch
allen
g
e
lies
in
th
e
ten
d
en
cy
to
g
et
s
tu
ck
in
lo
ca
l
o
p
tim
a.
T
h
e
p
o
p
u
latio
n
co
m
p
o
s
ed
o
f
N
in
d
iv
id
u
als
is
r
an
d
o
m
ly
g
en
er
ated
at
th
e
b
eg
in
n
in
g
o
f
th
e
alg
o
r
ith
m
.
E
ac
h
in
d
iv
id
u
al
is
co
m
p
o
s
ed
o
f
l
g
en
es,
wh
er
e
l
r
ep
r
esen
ts
th
e
n
u
m
b
er
o
f
n
o
d
es
in
th
e
d
ataset.
An
in
d
iv
id
u
al
(
o
r
s
o
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tio
n
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r
ep
r
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ts
th
e
to
t
al
s
et
o
f
n
o
d
es c
lu
s
ter
ed
t
o
th
e
d
ep
ar
tu
r
e
n
o
d
e
N
0
,
th
at
a
d
r
o
n
e
s
h
o
u
ld
v
is
it.
T
h
e
T
ab
le
2
in
d
icate
s
th
e
s
elec
ted
g
en
etic
p
ar
a
m
eter
s
f
o
r
b
o
th
eGA
wPF
an
d
eGA
.
B
o
th
alg
o
r
ith
m
s
s
h
ar
e
co
m
m
o
n
p
ar
a
m
eter
s
,
s
u
ch
as
th
e
n
u
m
b
er
o
f
g
en
er
atio
n
s
an
d
th
e
p
o
p
u
latio
n
s
ize.
T
h
e
g
en
etic
alg
o
r
ith
m
s
(
eGA
an
d
eGA
wPF)
wer
e
im
p
lem
en
ted
u
s
in
g
th
e
Py
th
o
n
lan
g
u
ag
e
,
an
d
ex
ec
u
ted
o
n
an
I
n
tel
®
i3
m
ac
h
in
e,
with
a
d
u
al
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co
r
e
2
.
2
0
GHz
,
a
n
d
4
Go
R
AM
.
Als
o
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b
o
th
alg
o
r
ith
m
s
wer
e
ex
ec
u
te
d
u
n
d
er
th
e
s
am
e
s
to
ch
asti
c
co
n
d
itio
n
s
,
th
at
is
,
n
o
r
an
d
o
m
s
ee
d
was u
s
ed
in
th
e
ex
p
e
r
im
e
n
ts
.
T
ab
le
2
.
Selecte
d
g
e
n
etic
p
ar
a
m
eter
s
f
o
r
b
o
th
eGA
wPF an
d
eGA
P
a
r
a
me
t
e
r
V
a
l
u
e
P
o
p
u
l
a
t
i
o
n
s
i
z
e
N
×
2
(
N
i
s
t
h
e
s
i
z
e
o
f
t
h
e
d
a
t
a
s
e
t
)
N
u
m
b
e
r
o
f
l
o
o
p
s
N
×
2
P
a
r
e
n
t
s
e
l
e
c
t
i
o
n
2
-
T
o
u
r
n
a
m
e
n
t
C
r
o
s
s
o
v
e
r
o
p
e
r
a
t
i
o
n
O
r
d
e
r
c
r
o
s
s
o
v
e
r
o
p
e
r
a
t
o
r
C
r
o
s
s
o
v
e
r
r
a
t
e
0
.
7
5
M
u
t
a
t
i
o
n
o
p
e
r
a
t
i
o
n
S
w
a
p
m
u
t
a
t
i
o
n
M
u
t
a
t
i
o
n
r
a
t
e
0
.
0
2
3
.
1
.
M
a
t
hema
t
ica
l f
o
rm
ula
t
i
o
n o
f
t
he
VRP
D
I
n
th
e
VR
PD,
th
e
o
b
jectiv
e
f
u
n
ctio
n
is
to
m
in
im
ize
th
e
m
ax
im
u
m
d
is
tan
ce
o
f
all
r
o
u
tes
p
er
f
o
r
m
e
d
b
y
th
e
d
r
o
n
e.
T
h
e
VR
PD
m
at
h
em
atica
l
f
o
r
m
u
latio
n
is
ad
ap
ted
f
r
o
m
th
e
well
-
k
n
o
wn
f
ly
in
g
s
id
ek
ick
tr
av
elin
g
s
alesm
an
p
r
o
b
lem
(
FS
T
SP
)
[
2
6
]
.
W
e
co
n
s
id
er
th
e
f
o
llo
win
g
n
o
tatio
n
s
an
d
c
o
n
s
tr
ain
ts
[
2
4
]
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
E
liti
s
t g
en
etic
a
lg
o
r
ith
m
imp
r
o
ve
d
w
ith
p
a
r
en
tin
g
fitn
ess
p
a
r
a
mete
r
(
Ou
is
s
Mu
s
ta
p
h
a
)
889
−
T
h
e
s
et
o
f
n
o
d
es
N
(
N
= 1
,
.
.
.
,
n
)
;
−
T
h
e
d
ep
a
r
tu
r
e
an
d
f
in
al
a
r
r
iv
al
n
o
d
e
N
0
;
−
T
h
e
s
et
o
f
n
o
d
es
N
+
to
v
is
it;
−
Dis
tan
ce
L
i,
j
b
etwe
en
i
an
d
j
;
−
Set
R
d
ef
in
in
g
all
r
o
u
tes p
er
f
o
r
m
ed
b
y
a
d
r
o
n
e;
−
Ma
x
im
u
m
f
lig
h
t r
an
g
e
mf
d
o
f
t
h
e
d
r
o
n
e
d
.
T
h
e
o
b
jectiv
e
f
u
n
ctio
n
is
f
o
r
m
u
lated
as:
∑
=
1
(
4
)
T
h
e
co
n
s
tr
ain
t 5
en
s
u
r
e
th
at
t
h
e
r
o
u
te
R
i
d
o
n
o
t e
x
ce
e
d
th
e
m
ax
im
u
m
f
lig
h
t d
is
tan
ce
o
f
t
h
e
d
r
o
n
e
d
:
≤
(
5
)
I
n
th
ese
ex
p
e
r
im
en
ts
,
n
o
c
o
n
s
tr
ain
t
is
co
n
s
id
er
e
d
f
o
r
th
e
m
ax
im
u
m
d
r
o
n
e
l
o
ad
.
W
e
co
n
s
id
er
th
e
m
ain
d
e
p
o
t
as
a
tak
e
-
o
f
f
n
o
d
e
an
d
th
e
lan
d
in
g
n
o
d
e.
C
o
n
s
tr
ain
t
6
en
s
u
r
es
th
at
th
e
d
r
o
n
e
tak
es
o
f
f
f
r
o
m
th
e
ce
n
tr
al
m
ain
d
ep
o
t e
x
ac
tly
o
n
ce
,
wh
ile
th
e
co
n
s
tr
ain
t 7
r
e
q
u
ir
es th
e
d
r
o
n
e
to
r
etu
r
n
to
th
e
m
ain
d
e
p
o
t e
x
ac
tly
o
n
ce
.
∑
0
∈
=
1
(
6
)
∑
0
∈
=
1
(
7
)
T
h
e
co
n
s
tr
ain
t 8
en
s
u
r
es th
at
a
n
o
d
e
is
v
is
ited
ex
ac
tly
o
n
ce
.
∑
,
∈
+
∑
,
∈
=
1
≠
(
8
)
3
.
2
.
F
i
t
nes
s
f
un
ct
io
n
T
o
co
m
p
ar
e
t
h
e
ef
f
ec
tiv
en
ess
o
f
o
u
r
a
p
p
r
o
ac
h
ag
ain
s
t
a
ty
p
ical
elitis
t
g
en
etic
alg
o
r
ith
m
(
eGA
)
,
we
im
p
lem
en
ted
th
e
ex
ac
t sam
e
f
itn
ess
f
u
n
ctio
n
,
f
o
r
th
e
r
ea
s
o
n
t
h
at
a
f
itn
ess
f
u
n
ctio
n
im
p
lem
en
tatio
n
is
a
cr
itica
l
p
ar
t
o
f
th
e
g
e
n
etic
alg
o
r
ith
m
,
an
d
a
wr
o
n
g
im
p
lem
en
tatio
n
m
ay
lead
to
wr
o
n
g
ca
lcu
latio
n
s
eith
er
in
a
p
o
s
itiv
e
way
o
r
a
n
e
g
ativ
e
o
n
e.
T
h
e
f
itn
ess
f
u
n
ctio
n
c
alcu
latio
n
f
o
r
th
e
VR
PD
is
d
ef
in
ed
in
th
e
A
lg
o
r
ith
m
4
,
wh
ic
h
co
r
r
esp
o
n
d
s
to
th
e
d
e
co
m
p
o
s
itio
n
o
f
t
h
e
b
ig
t
o
u
r
d
ef
in
ed
b
y
t
h
e
ch
r
o
m
o
s
o
m
e,
i
n
to
f
ea
s
ib
le
r
o
u
tes.
Alg
o
r
ith
m
4
.
VR
PD Su
b
-
to
u
r
s
co
n
s
tr
u
ctio
n
1:
Initialization of the Maximum Route Length
mrl ←
0;
2:
mf
d
←
Maximum flight distance of the drone d;
3:
mrl
←
distance(depot, chromosome(0));
4:
for all
gene i, gene i+1
∈
chromosome
do
5:
md
i
,i+1
←
distance(i,i+1);
6:
if
mrl
+
md
i,i+1
>
mf
d
then
create new route
(return to the depot, and from depot to the
position defined in the gene I + 1;
7:
else
8
:
mrl
← mrl
+
md
i,i+1
;
9
:
end if
10
:
end for
11
:
mrl
← mrl
+
distance(chromosome(L), depot)
; // L: chromosome length.
3
.
3
.
Da
t
a
s
et
des
cr
iptio
n
T
o
test
th
e
alg
o
r
ith
m
,
we
u
s
ed
m
u
ltip
le
d
atasets
d
o
w
n
lo
a
d
ed
f
r
o
m
th
e
in
s
tan
ce
s
p
r
esen
ted
in
th
e
wo
r
k
o
f
[
2
7
]
.
E
ac
h
in
s
tan
ce
f
ile
is
lab
elled
N.
M.
T
,
wh
er
e
is
th
e
n
u
m
b
er
o
f
cu
s
to
m
er
s
,
is
th
e
g
r
id
’
s
d
im
en
s
io
n
,
an
d
is
th
e
s
ce
n
ar
i
o
’
s
g
en
er
ic
n
am
e
.
T
h
e
f
ir
s
t
lin
e
in
ea
ch
in
s
tan
ce
f
ile
in
d
ica
tes
th
e
n
u
m
b
er
o
f
cu
s
to
m
er
s
.
E
ac
h
lin
e
f
r
o
m
th
e
s
ec
o
n
d
lin
e
co
n
tain
s
co
o
r
d
in
ates
,
an
d
d
e
m
an
d
o
f
th
e
c
u
s
to
m
er
.
An
o
th
er
f
ile
co
n
tain
in
g
i
n
f
o
r
m
atio
n
a
b
o
u
t th
e
co
o
r
d
in
ates o
f
th
e
d
e
p
o
t,
an
d
i
n
f
o
r
m
atio
n
ab
o
u
t th
e
u
s
ed
d
r
o
n
e,
is
u
s
ed
.
3
.
4
.
Ro
ute
co
ns
t
ruct
io
n f
un
ct
io
n
I
n
th
e
v
eh
icle
r
o
u
tin
g
p
r
o
b
lem
o
p
tim
izatio
n
,
th
e
m
ain
g
o
al
is
to
c
o
n
s
tr
u
ct
r
o
u
tes
th
at
r
esp
e
ct
d
ef
in
ed
co
n
s
tr
ain
ts
an
d
o
b
jectiv
es.
T
h
e
f
itn
ess
o
f
ea
ch
ch
r
o
m
o
s
o
m
e
in
th
e
lo
o
p
t
is
ca
lcu
lated
with
(
9
)
.
(
)
=
∑
=
1
(
9
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
2
,
Ap
r
il
20
2
6
:
8
8
3
-
894
890
I
n
th
e
VR
P,
ch
r
o
m
o
s
o
m
es d
ef
in
e
th
e
s
eq
u
en
ce
o
f
n
o
d
es v
is
ited
b
y
th
e
v
eh
icle.
T
h
e
alg
o
r
ith
m
4
r
ep
r
esen
ts
th
e
p
s
eu
d
o
-
co
d
e
o
f
th
e
d
ec
o
m
p
o
s
itio
n
o
f
th
e
b
ig
to
u
r
in
to
s
u
b
-
to
u
r
s
.
T
h
e
d
is
tan
ce
f
u
n
ctio
n
is
a
f
u
n
ctio
n
th
at
r
etu
r
n
s
th
e
d
is
tan
ce
b
etwe
en
t
h
e
n
o
d
e
i
an
d
th
e
n
o
d
e
i +
1
.
T
h
e
d
is
tan
ce
is
ca
lcu
lated
b
y
(
10
)
.
(
,
)
=
√
∑
(
−
)
2
=
1
(
1
0
)
A
g
ap
v
alu
e
b
etwe
en
th
e
b
est o
f
eGA
wPF f
o
r
ea
ch
p
er
ce
n
ta
g
e
an
d
t
h
e
b
est o
f
eGA
is
d
ef
i
n
ed
b
y
(
1
1
)
:
Ga
p
1
= (
B
ega
− B
pf
)
/ B
pf
(
1
1
)
wh
ile
th
e
g
ap
v
alu
e
b
etwe
en
t
h
e
o
v
er
all
b
est o
f
eGA
wPF an
d
th
e
b
est o
f
eGA
is
d
ef
in
ed
b
y
(
1
2
)
:
Ga
p
2
= (
B
ega
− B
*
pf
)
/B
*
pf
(
1
2
)
wh
er
e
B
ega
is
t
h
e
b
est
-
k
n
o
wn
s
o
lu
tio
n
(
B
KS)
o
f
th
e
eGA
an
d
B
pf
is
th
e
b
est
-
k
n
o
wn
s
o
l
u
tio
n
o
f
t
h
e
elitis
t
g
en
etic
alg
o
r
ith
m
with
p
a
r
en
t
in
g
f
itn
ess
f
o
r
a
p
ar
ticu
lar
p
a
r
en
tin
g
f
itn
ess
p
er
ce
n
tag
e
,
an
d
B
*
pf
is
th
e
o
v
er
all
b
est o
f
eGA
wPF.
3
.
5
.
Cro
s
s
o
v
er
T
h
e
cr
o
s
s
o
v
er
co
n
tr
o
ls
th
e
d
iv
er
s
if
icatio
n
m
ec
h
an
is
m
.
W
e
co
n
s
id
er
th
e
o
r
d
er
cr
o
s
s
o
v
er
o
p
er
ato
r
(
OX)
[
2
8
]
,
[
2
9
]
.
Alg
o
r
ith
m
5
p
r
esen
ts
th
e
Or
d
er
cr
o
s
s
o
v
er
o
p
er
ato
r
s
tep
s
.
T
h
e
o
r
d
er
cr
o
s
s
o
v
er
o
p
er
ates
as
f
o
llo
ws:
−
T
wo
p
ar
en
ts
P
1
(
t)
a
n
d
P
2
(
t)
ar
e
s
elec
ted
f
r
o
m
th
e
p
o
p
u
latio
n
ac
co
r
d
in
g
to
a
d
ef
in
ed
s
tr
ateg
y
.
−
C
r
o
s
s
o
v
er
p
o
in
ts
crp
1
an
d
crp
2
ar
e
ch
o
s
en
r
an
d
o
m
ly
in
th
e
i
n
ter
v
al
[
2
,
L
-
1
]
,
wh
er
e
is
th
e
len
g
th
o
f
th
e
ch
r
o
m
o
s
o
m
e,
an
d
crp
1
>
crp
2
.
−
Gen
es o
f
th
e
p
a
r
en
ts
ar
e
s
wap
p
ed
to
cr
ea
te
n
ew
o
f
f
s
p
r
in
g
O
1
(
t)
an
d
O
2
(
t)
o
n
t
h
e
cr
o
s
s
o
v
er
p
o
in
ts
.
−
T
h
e
r
ed
u
n
d
a
n
t g
en
es o
f
th
e
o
f
f
s
p
r
in
g
ar
e
r
em
o
v
ed
,
a
n
d
th
e
g
ap
s
ar
e
f
illed
with
th
e
r
e
m
ain
i
n
g
v
alu
es.
Alg
o
r
ith
m
5
.
Or
d
er
c
r
o
s
s
o
v
er
(
OX)
o
p
er
ato
r
p
s
eu
d
o
co
d
e
1:
Select parents
P
1
(t)
and
P
2
(t)
from population;
2:
Select crossover points
crp
1
and
crp
2
;
3:
Swap Genes of
P
1
(t)
and
P
2
(t)
between
crp
1
and
crp
2
;
4:
Remove redundant genes from the offspring
O
1
(t)
and
O
2
(t)
;
5:
for all
offspring
O
do
6:
Fill empty genes with remaining values;
7:
end for
3
.
6
.
M
uta
t
io
n
T
h
e
n
atu
r
al
m
u
tatio
n
o
p
er
ato
r
f
o
r
th
e
v
eh
icle
r
o
u
tin
g
p
r
o
b
lem
,
as
well
a
s
s
im
i
lar
co
m
b
in
ato
r
ial
o
p
tim
izatio
n
p
r
o
b
lem
s
,
is
th
e
s
wap
m
u
tatio
n
(
SM)
o
p
er
at
o
r
.
I
n
th
e
co
n
te
x
t
o
f
s
wap
m
u
tatio
n
,
th
e
g
e
n
etic
alg
o
r
ith
m
s
elec
ts
two
p
o
s
itio
n
s
r
n
d
1
an
d
r
n
d
2
(
wh
er
e
r
n
d
1
#
r
n
d
2
)
at
r
an
d
o
m
o
n
th
e
ch
r
o
m
o
s
o
m
e,
an
d
in
ter
ch
an
g
es th
eir
v
alu
es.
T
h
e
alg
o
r
ith
m
6
r
ep
r
esen
ts
th
e
s
wa
p
m
u
tatio
n
o
p
er
atio
n
.
Alg
o
r
ith
m
6
.
Swap
m
u
tatio
n
(
SM)
o
p
er
ato
r
p
s
eu
d
o
c
o
d
e
1:
Generate a random numbers
rnd
1
in [1, n];
2:
Generate a random numbers
rnd
2
in [
rnd
1
, n];
3:
tmp
←
individual_i[
rnd
1
];
4:
individual_i[
rnd
1
]
←
individual_i[
rnd
2
];
5:
individual_i[
rnd
2
]
← tmp
;
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
4
.
1
.
Sens
it
iv
it
y
a
na
ly
s
is
I
n
o
r
d
er
t
o
s
tu
d
y
th
e
v
ar
iatio
n
im
p
ac
t
o
f
th
e
p
a
r
en
tin
g
f
itn
ess
in
itializatio
n
b
etwe
en
lo
o
p
s
,
th
e
g
en
etic
alg
o
r
ith
m
im
p
r
o
v
ed
with
p
ar
en
tin
g
f
itn
ess
p
ar
a
m
eter
was
ex
ec
u
ted
in
two
v
er
s
io
n
s
:
i
)
with
r
ein
itializatio
n
o
f
t
h
e
p
ar
e
n
tin
g
f
itn
ess
o
f
p
ar
e
n
ts
,
an
d
ii
)
with
o
u
t
r
ein
itializatio
n
.
I
n
th
e
f
ir
s
t
s
et,
w
e
r
ein
itialize
th
e
p
ar
en
tin
g
f
itn
ess
o
f
th
e
p
ar
en
ts
at
ea
ch
ite
r
atio
n
,
wh
ile
in
th
e
s
ec
o
n
d
s
et,
th
e
v
alu
e
o
f
th
e
p
ar
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r
em
ain
s
a
f
ter
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l
o
o
p
.
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o
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th
e
p
ar
e
n
tin
g
f
itn
ess
r
ate
is
s
et
to
2
%,
1
0
%,
an
d
5
0
%
o
f
th
e
b
est
p
ar
en
ts
.
T
h
e
r
em
ain
in
g
i
n
d
iv
id
u
als
ar
e
th
e
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est
o
f
th
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in
ed
o
f
f
s
p
r
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d
in
d
i
v
id
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o
f
th
e
cu
r
r
en
t
p
o
p
u
latio
n
.
E
x
ec
u
tin
g
th
e
alg
o
r
ith
m
with
d
if
f
er
e
n
t
p
ar
e
n
tin
g
f
itn
ess
p
er
ce
n
tag
es
o
f
f
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s
a
p
er
s
p
ec
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e
o
n
th
e
im
p
ac
t o
f
d
i
f
f
er
en
t
p
er
ce
n
ta
g
e
s
o
n
th
e
alg
o
r
ith
m
’
s
p
er
f
o
r
m
a
n
ce
an
d
its
f
in
al
r
esu
lt.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
E
liti
s
t g
en
etic
a
lg
o
r
ith
m
imp
r
o
ve
d
w
ith
p
a
r
en
tin
g
fitn
ess
p
a
r
a
mete
r
(
Ou
is
s
Mu
s
ta
p
h
a
)
891
4
.
2
.
Resul
t
s
Fo
r
th
e
e
x
p
er
im
en
ts
o
n
th
e
e
GAwPF
with
o
u
t
r
ein
itializatio
n
o
f
p
ar
e
n
tin
g
f
itn
ess
,
T
ab
les
3
,
4
,
an
d
5
r
ep
r
esen
t
th
e
co
r
r
esp
o
n
d
in
g
r
e
s
u
lts
f
o
r
s
m
all,
m
ed
iu
m
,
a
n
d
l
ar
g
e
in
s
tan
ce
s
,
r
esp
ec
tiv
ely
.
T
h
e
r
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lts
o
b
tain
ed
f
r
o
m
o
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r
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ch
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f
o
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th
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ex
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wPF
with
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o
f
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f
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in
T
ab
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6
,
7
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d
8
f
o
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s
m
all,
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ed
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m
,
a
n
d
lar
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e
in
s
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,
r
esp
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.
T
a
b
l
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3
.
C
o
m
p
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t
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ti
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a
l
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s
m
a
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s
t
a
n
c
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,
wi
t
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t
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n
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t
ia
l
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za
t
i
o
n
e
G
A
E
G
A
w
P
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(
5
0
%
)
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A
w
P
F
(
1
0
%
)
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G
A
w
P
F
(
2
%
)
B*
pf
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n
s
t
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a
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,
w
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(
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F
(
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(
2
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T
a
b
l
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5
.
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p
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t
a
ti
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n
a
l
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l
a
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e
i
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s
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a
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,
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t
h
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t
h
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n
it
i
al
i
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a
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(
5
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%)
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(
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T
a
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6
.
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o
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G
A
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A
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5
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%
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1
0
%
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w
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F
2
%
B*
pf
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A
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n
st
a
n
c
e
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e
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T
a
b
l
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.
C
o
m
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a
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m
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d
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,
w
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A
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%
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o
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u
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l
a
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e
i
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s
t
a
n
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es
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t
h
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wP
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wi
t
h
r
e
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it
i
al
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z
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ti
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n
e
G
A
EG
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5
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w
P
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1
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w
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F
2
%
B*
pf
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n
st
a
n
c
e
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st
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st
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5
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J E
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Vo
l.
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6
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No
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E
x
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c
u
t
i
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n
a
n
a
l
y
s
is
T
h
e
g
en
etic
alg
o
r
ith
m
u
s
es f
o
u
r
f
u
n
ctio
n
s
: p
ar
e
n
ts
’
s
elec
tio
n
,
cr
o
s
s
o
v
er
,
an
d
m
u
tatio
n
,
ea
ch
o
f
th
ese
f
u
n
ctio
n
s
h
a
v
e
a
c
o
m
p
lex
it
y
o
f
O(
n
)
.
Ho
wev
e
r
,
th
e
g
en
eti
c
alg
o
r
ith
m
r
u
n
s
n
iter
atio
n
s
;
h
en
ce
,
t
h
e
o
v
er
all
co
m
p
lex
ity
is
O(
n
2
)
.
T
h
e
co
m
p
lex
ity
o
f
th
e
p
ar
en
tin
g
f
itn
ess
f
u
n
ctio
n
is
O(
n
)
,
s
in
ce
it
u
s
es
n
iter
atio
n
s
wh
ile
u
p
d
atin
g
th
e
p
ar
e
n
ts
’
p
ar
e
n
tin
g
f
itn
ess
.
4
.
4
.
Rela
t
iv
e
im
pro
v
e
m
ent
L
et
N,
E
b
e
t
h
e
m
ea
n
v
alu
e
o
f
r
esu
lts
f
o
u
n
d
b
y
eGA
an
d
th
e
b
est
r
esu
lts
o
f
eGA
wPF
f
o
r
s
m
all,
m
ed
iu
m
,
an
d
lar
g
e
in
s
tan
ce
s
.
T
h
e
u
s
ed
eq
u
atio
n
to
ca
lcu
l
ate
th
e
r
elativ
e
im
p
r
o
v
e
m
en
t
is
d
ef
in
ed
b
y
(
14
)
,
wh
ile
T
ab
les
9
an
d
1
0
r
e
p
r
ese
n
t th
e
r
esu
lts
o
f
th
e
ca
lc
u
latio
n
.
∆
=
¯
−
¯
¯
×
100
(
1
4
)
T
a
b
l
e
9
.
R
el
a
t
i
v
e
i
m
p
r
o
v
e
m
e
n
t
w
i
t
h
r
e
i
n
it
i
a
li
z
a
ti
o
n
o
f
p
a
r
e
n
t
in
g
f
i
t
n
e
s
s
e
G
A
EG
A
w
P
F
S
mal
l
i
n
st
a
n
c
e
s
M
e
a
n
4
0
.
6
3
6
.
4
M
e
d
i
a
n
31
29
R
e
l
a
t
i
v
e
i
mp
r
o
v
e
m
e
n
t
(
%)
1
0
.
3
4
M
e
d
i
u
m
i
n
st
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n
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e
s
M
e
a
n
9
0
8
.
4
8
9
6
.
4
M
e
d
i
a
n
9
3
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4
R
e
l
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t
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v
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mp
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e
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t
(
%)
1
.
3
2
La
r
g
e
i
n
s
t
a
n
c
e
s
M
e
a
n
4
9
8
9
4
9
3
6
.
2
M
e
d
i
a
n
4
4
5
6
4
5
2
1
R
e
l
a
t
i
v
e
i
mp
r
o
v
e
m
e
n
t
(
%)
1
.
0
6
T
a
b
l
e
1
0
.
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e
la
t
i
v
e
i
m
p
r
o
v
e
m
e
n
t
w
i
t
h
o
u
t
r
e
i
n
i
t
i
al
i
z
at
i
o
n
o
f
p
a
r
e
n
t
i
n
g
f
i
t
n
e
s
s
e
G
A
EG
A
w
P
F
S
mal
l
i
n
st
a
n
c
e
s
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e
a
n
4
0
.
6
3
9
.
4
M
e
d
i
a
n
31
27
R
e
l
a
t
i
v
e
i
mp
r
o
v
e
m
e
n
t
(
%)
2
.
9
6
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e
d
i
u
m
i
n
st
a
n
c
e
s
M
e
a
n
9
0
8
,
4
8
9
6
.
6
M
e
d
i
a
n
9
3
4
9
5
9
R
e
l
a
t
i
v
e
i
mp
r
o
v
e
m
e
n
t
(
%)
1
.
3
La
r
g
e
i
n
s
t
a
n
c
e
s
M
e
a
n
4
9
8
9
4
8
8
8
.
4
M
e
d
i
a
n
4
4
5
6
4
5
4
5
R
e
l
a
t
i
v
e
i
mp
r
o
v
e
m
e
n
t
(
%)
2
.
0
2
4
.
5
.
D
i
s
cus
s
i
o
n
T
h
e
eGA
wPF s
h
o
ws s
ig
n
if
ican
t p
er
f
o
r
m
an
ce
in
co
m
p
a
r
is
o
n
with
a
s
tan
d
ar
d
eGA
.
T
h
e
eG
AwPF
wa
s
ex
ec
u
ted
in
two
v
er
s
io
n
:
o
n
e
with
o
u
t
r
ein
itializatio
n
o
f
th
e
p
ar
en
tin
g
f
itn
ess
v
alu
e
o
f
p
ar
en
ts
,
an
d
a
n
o
th
er
with
r
ein
itializatio
n
.
Fo
r
th
e
f
i
r
s
t e
x
ec
u
tio
n
,
th
e
o
v
er
all
g
a
p
i
n
p
er
f
o
r
m
an
ce
,
f
o
r
th
e
u
s
ed
d
a
tasets
,
r
an
g
es f
r
o
m
0
.
1
1
1
to
0
.
1
9
2
,
0
.
0
0
6
to
0
.
0
4
2
,
0
.
0
0
3
to
0
.
0
7
3
,
f
o
r
s
m
all,
m
e
d
iu
m
an
d
lar
g
e
i
n
s
tan
ce
s
,
r
esp
ec
tiv
ely
.
T
h
e
latte
r
s
h
o
ws
an
o
v
er
all
p
er
f
o
r
m
an
ce
g
ap
s
,
th
at
v
ar
ied
f
r
o
m
0
.
0
3
4
to
0
.
4
0
9
,
0
.
0
0
6
to
0
.
0
9
7
,
a
n
d
0
.
0
1
5
to
0
.
0
3
6
f
o
r
s
m
all,
m
ed
iu
m
a
n
d
lar
g
e
in
s
tan
ce
s
,
r
esp
ec
tiv
ely
.
Ho
wev
er
,
in
s
o
m
e
ca
s
es,
th
e
eGA
o
u
tp
er
f
o
r
m
s
t
h
e
eGA
wPF,
h
o
wev
er
,
ev
e
n
in
th
ese
ca
s
es
(
ex
ce
p
t
f
o
r
th
e
d
atas
et
2
0
.
1
0
.
4
in
t
h
e
f
ir
s
t
s
et
o
f
e
x
p
er
im
en
ts
)
,
th
e
g
a
p
d
o
es
n
o
t
e
x
ce
ed
th
e
p
er
f
o
r
m
an
ce
r
an
g
es
o
b
s
er
v
e
d
wh
e
n
eGA
wPF
o
u
tp
er
f
o
r
m
s
eGA
.
Als
o
,
th
e
n
o
n
-
r
ein
itializatio
n
o
f
th
e
p
ar
e
n
tin
g
f
itn
ess
ca
n
p
r
o
d
u
ce
m
o
r
e
f
it
in
d
iv
i
d
u
als.
T
h
e
ex
p
e
r
im
en
ts
co
n
d
u
cted
d
em
o
n
s
tr
ates
th
at
t
h
e
p
a
r
en
tin
g
f
itn
ess
p
ar
a
m
eter
e
n
h
an
ce
s
t
h
e
p
er
f
o
r
m
a
n
ce
o
f
t
h
e
g
e
n
etic
alg
o
r
ith
m
.
Un
lik
e
o
th
er
tec
h
n
iq
u
es
as
h
y
b
r
id
iza
tio
n
,
th
at
m
ay
n
ee
d
s
ig
n
if
ica
n
t
u
p
d
ates
in
t
h
e
g
en
etic
alg
o
r
ith
m
’
s
co
r
e,
t
h
e
p
ar
en
tin
g
f
itn
ess
p
ar
am
eter
c
an
b
e
ea
s
ily
in
teg
r
ate
d
in
to
e
x
is
tin
g
GA
f
r
am
ewo
r
k
s
in
a
n
o
n
-
d
is
tu
r
b
in
g
wa
y
with
m
in
im
u
m
ef
f
o
r
t
an
d
r
ed
u
ce
d
ch
an
g
es,
s
in
ce
it
o
n
ly
r
eq
u
ir
es
ad
d
in
g
th
e
u
p
d
atin
g
f
u
n
ctio
n
an
d
ad
a
p
tin
g
th
e
ev
o
lu
tio
n
p
h
ase.
5.
CO
NCLU
SI
O
N
AND
F
U
T
U
RE
DIR
E
C
T
I
O
N
S
I
n
th
is
ar
ticle,
we
in
v
esti
g
ated
th
e
im
p
ac
t
o
f
in
teg
r
atin
g
th
e
p
ar
en
tin
g
f
itn
ess
p
ar
am
eter
in
t
o
an
elitis
t
g
en
etic
alg
o
r
ith
m
to
m
itig
at
e
p
r
em
atu
r
e
co
n
v
er
g
e
n
ce
in
th
e
co
n
tex
t
o
f
o
p
tim
izin
g
t
h
e
v
eh
icle
r
o
u
tin
g
p
r
o
b
lem
.
Ou
r
ex
p
e
r
im
en
ts
r
e
v
ea
led
a
r
elativ
e
im
p
r
o
v
em
e
n
t o
f
1
.
0
6
to
1
0
.
3
4
%
d
e
p
en
d
in
g
o
n
th
e
d
ataset’
s
s
ize
an
d
th
e
p
ar
e
n
tin
g
f
itn
ess
r
ein
itializatio
n
ap
p
r
o
ac
h
.
T
h
ese
ex
p
er
im
en
ts
v
alid
ate
th
at
p
r
es
er
v
in
g
h
i
g
h
-
q
u
ality
Evaluation Warning : The document was created with Spire.PDF for Python.