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A
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.
1
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I
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tr
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I
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i
nf
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1]
.
I
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D
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hm
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s
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m
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3
].
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as
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I
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6
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T
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14
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.
3,
S
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2016
:
10
35
–
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g
m
at
es
an
d
pr
od
uc
i
ng
o
f
f
s
pr
i
ng
,
u
nder
s
uc
h
nat
ur
al
r
ul
es
and
l
a
w
s
,
t
h
e n
at
ur
a
l
w
or
l
d
gr
adu
al
l
y
de
v
e
l
o
ps
an
d e
nr
i
c
hes
.
N
i
c
h
e t
ec
hno
l
og
y
dec
om
pos
es
t
he
gene
t
i
c
i
n
di
v
i
dua
l
s
of
eac
h
gener
at
i
on
i
n
t
o
s
ev
er
al
k
i
nds
,
s
el
ec
t
s
c
er
t
ai
n
i
n
di
v
i
du
al
s
w
i
t
h
b
i
g
ger
f
i
t
nes
s
f
r
o
m
eac
h
k
i
nd as
t
h
e
ex
c
el
l
e
nt
r
epr
es
ent
at
i
v
es
t
o f
or
m
a popul
a
t
i
o
n and pr
oduc
es
a ne
w
popu
l
at
i
o
n
w
i
t
h
i
n
t
he
pop
ul
at
i
o
n a
nd am
ong
di
f
f
er
ent
p
opu
l
a
t
i
o
ns
t
hr
o
ugh
c
r
os
s
ov
er
an
d
m
ut
at
i
on
[
5]
.
T
hi
s
paper
f
i
r
s
t
l
y
ana
l
y
z
es
t
he c
har
ac
t
er
i
s
t
i
c
s
of
s
uc
h oper
at
i
ons
as
c
r
os
s
ov
er
,
m
ut
at
i
o
n
and s
e
l
ec
t
i
on
of
D
E
al
gor
i
t
hm
.
T
hen,
i
t
i
nt
r
od
uc
es
ni
c
he t
ec
h
no
l
og
y
i
nt
o
D
E
al
go
r
i
t
hm
,
per
f
or
m
s
s
t
r
uc
t
ur
al
des
i
gn of
ni
c
he
di
f
f
er
ent
i
al
a
l
gor
i
t
hm
,
us
es
adapt
i
v
e pr
oba
bi
l
i
t
y
s
t
r
at
eg
y
i
n t
he
c
r
os
s
ov
er
an
d m
ut
at
i
o
n of
D
E
a
l
g
or
i
t
hm
,
ens
ur
es
ac
c
el
er
at
e
d
e
v
ol
ut
i
onar
y
opt
i
m
i
z
at
i
on
of
t
he
ent
i
r
e
pop
ul
at
i
on i
n t
h
e ear
l
y
e
v
ol
ut
i
on p
has
e a
nd a
v
o
i
ds
dam
age on t
he
pop
ul
at
i
on opt
i
m
i
z
at
i
o
n
i
n t
he pos
t
e
v
o
l
ut
i
on s
o as
t
o
m
ai
nt
a
i
n t
he p
opu
l
at
i
o
n di
v
er
s
i
t
y
,
r
et
ai
ns
c
er
t
ai
n d
i
s
t
anc
e bet
w
een
t
he i
nd
i
v
i
d
ua
l
s
,
c
r
eat
e a
n
i
c
he e
v
ol
ut
i
onar
y
e
nv
i
r
onm
ent
a
nd
i
m
pr
ov
e t
h
e c
on
v
er
genc
e s
p
eed
and
t
he
gl
oba
l
s
ear
c
h
per
f
or
m
anc
e
of
D
E
al
g
or
i
t
hm
.
T
he
f
i
nal
ex
p
er
i
m
ent
r
es
ul
t
pr
ov
es
t
hat
t
he
m
et
hod of
t
hi
s
p
ap
er
has
s
t
abl
e c
on
v
er
g
enc
e
per
f
or
m
a
nc
e an
d h
i
g
her
c
om
put
at
i
o
n ef
f
i
c
i
enc
y
i
n
so
l
v
i
ng
c
om
pl
i
c
at
ed
opt
i
m
i
z
at
i
o
n pr
o
bl
em
s
.
2.
O
p
er
at
i
o
n
s
o
f D
i
ffe
r
e
n
ti
a
l
E
v
o
l
u
ti
o
n
A
l
g
o
r
i
th
m
A
s
s
um
e t
hat
t
he c
ur
r
ent
e
v
ol
ut
i
o
n gen
er
at
i
on
i
s
t
,
t
he p
opu
l
at
i
on s
i
z
e
i
s
NP
,
t
he s
pac
e
di
m
ens
i
on i
s
D
,
t
h
e c
ur
r
ent
popu
l
at
i
o
n i
s
{
}
12
()
,
,
,
tt
t
NP
X
t
x
x
x
=
L
and
(
)
12
,
,,
t
t
t
t
i
i
i
iD
x
x
x
x
=
L
is
t
h
e
th
i
i
nd
i
v
i
d
ua
l
of
t
he
po
pul
at
i
o
n.
P
er
f
or
m
t
he f
ol
l
o
w
i
n
g t
h
r
ee op
er
at
i
ons
o
n e
ac
h i
n
di
v
i
d
ua
l
t
i
x
su
cce
ssi
v
e
l
y
.
(
1)
Mut
at
i
o
n
D
E
a
l
gor
i
t
hm
adds
t
h
e
w
e
i
ght
ed
di
f
f
er
enc
e v
ec
t
or
b
et
w
ee
n t
h
e t
w
o m
e
m
ber
s
of
t
he
popu
l
at
i
o
n t
o t
he
t
hi
r
d m
em
ber
t
o pr
oduc
e
n
e
w
par
a
m
et
er
v
ec
t
or
a
nd
t
hi
s
op
er
at
i
o
n
i
s
c
al
l
e
d
m
ut
at
i
on.
E
v
er
y
i
nd
i
v
i
d
ua
l
t
i
x
w
i
l
l
pr
o
duc
e t
he m
ut
at
i
on
i
n
di
v
i
d
ua
l
12
(,
,
,
)
t
tt
t
i
i
i
iD
v
vv
v
=
L
ac
c
or
di
ng
t
o
t
he f
or
m
ul
a bel
o
w
[6
]
.
1
23
(
)
1,
2
,
,
tt
t
t
ij
r
j
r
j
r
j
v
x
x
x
j
D
λ
=
+−
=
L
(
1)
I
n t
h
i
s
f
or
m
ul
a,
1
11
1
12
(
,
,,
)
t
tt
t
r
r
r
rD
x
xx
x
=
L
,
2
22
2
12
(
,
,,
)
t
tt
t
r
r
r
rD
x
xx
x
=
L
and
3
3
3
3
12
(
,
,,
)
t
tt
t
r
r
r
rD
x
xx
x
=
L
ar
e t
hr
ee
i
nd
i
v
i
dua
l
s
r
and
o
m
l
y
s
el
ec
t
ed f
r
om
t
he pop
ul
at
i
o
n an
d
12
3
rr
r
i
≠
≠
≠
,
λ
is
a
s
c
a
lin
g
f
ac
t
or
w
i
t
h a r
ang
e of
[
0,
2
]
.
(
2)
C
r
os
s
ov
er
D
E
a
l
gor
i
t
hm
m
i
x
es
t
he par
am
et
er
of
t
he
m
ut
at
i
on
v
ec
t
or
a
nd t
h
e pr
ed
ef
i
ne
d
t
ar
get
par
am
et
er
and pr
oduc
es
t
h
e t
es
t
v
ec
t
or
ac
c
or
di
n
g t
o c
er
t
ai
n r
u
l
es
,
k
now
n as
c
r
os
s
ov
er
.
T
he t
es
t
in
d
iv
id
u
a
l
12
(,
,
,
)
t
t
t
t
i
i
i
iD
u
uu
u
=
L
c
an
be
pr
oduc
e
d
ac
c
or
di
n
g
t
o
t
h
e
m
ut
at
i
o
n
i
nd
i
v
i
dua
l
t
i
v
and
t
he
par
ent
i
n
di
v
i
dua
l
t
i
x
and
i
f
o
r
i
f
a
n
d
t
ij
j
t
ij
t
ij
j
v
r
and
C
R
j
r
and
u
x
r
and
C
R
j
r
and
≤=
=
>
≠
(
2)
I
n
t
h
i
s
f
or
m
ul
a,
r
and
i
s
a
r
and
o
m
nu
m
ber
w
i
t
hi
n
t
h
e
s
c
op
e
of
[
0
,
1]
,
CR
i
s
a
c
o
ns
t
ant
w
it
h
in
[
0
,
1]
,
w
h
i
c
h i
s
c
a
l
l
e
d c
r
os
s
ov
er
f
ac
t
or
an
d
j
r
and
i
s
a r
an
do
m
i
nt
eger
w
i
t
hi
n
[
1,
]
D
[
7]
.
(
3)
S
el
ec
t
i
on
I
f
t
he c
os
t
f
unc
t
i
on
of
t
he
t
es
t
v
ec
t
or
i
s
l
o
w
er
t
ha
n t
hat
of
t
h
e t
ar
g
et
v
ec
t
or
,
t
h
e t
es
t
v
ec
t
or
w
i
l
l
r
e
pl
ac
e
t
he
t
a
r
get
v
ec
t
or
i
n
t
he
n
ex
t
g
ener
at
i
o
n.
T
he
f
i
nal
oper
at
i
o
n
i
s
c
al
l
ed
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NI
K
A
I
S
S
N
:
1
693
-
6
930
A
n I
mpr
ov
ed
A
dapt
i
v
e N
i
c
h
e
D
if
f
e
r
e
n
t
ia
l E
v
o
lu
t
io
n
A
lg
o
r
it
h
m
(
H
u
i
W
ang
)
1037
s
el
ec
t
i
on,
w
h
i
c
h i
s
t
o s
el
ec
t
t
he i
n
di
v
i
dua
l
w
i
t
h
t
he b
es
t
f
i
t
nes
s
f
r
o
m
t
he par
ent
i
n
di
v
i
dua
l
t
i
x
and
t
he t
es
t
i
n
di
v
i
dua
l
t
i
u
as
t
he
i
n
di
v
i
d
ua
l
1
t
i
x
+
of
t
he nex
t
gen
er
a
t
i
on
[
8]
.
1
i
f
()
()
ot
he
r
w
i
s
e
t
tt
i
ii
t
i
t
i
x
fit
x
fit
u
x
u
+
<
=
(
3)
I
n t
h
i
s
f
or
m
ul
a
(
3)
,
()
fit
⋅
i
s
t
he f
i
t
nes
s
f
unc
t
i
on.
F
ig
ur
e
1 i
s
t
he s
c
hem
at
i
c
f
or
D
E
a
l
g
or
i
t
hm
t
o per
f
or
m
opt
i
m
i
z
at
i
o
n s
ear
c
h o
n m
ul
t
i
-
peak
f
unc
t
i
on.
(
a)
(
b)
(c
)
F
i
gur
e 1.
O
pt
i
m
i
z
at
i
on s
e
ar
c
h of
di
f
f
er
ent
i
al
e
v
ol
ut
i
on
a
l
gor
i
t
hm
on m
ul
t
i
-
peak
f
unc
t
i
on
3.
D
e
si
g
n
o
f
A
d
a
p
ti
v
e
N
i
c
h
e
D
i
ffe
r
e
n
ti
a
l
E
v
o
l
u
ti
o
n
A
l
g
o
r
i
th
m
T
he bas
i
c
i
dea
of
ada
pt
i
v
e
ni
c
he
di
f
f
er
ent
i
al
ev
ol
ut
i
on
al
g
or
i
t
hm
i
s
t
o
adj
us
t
t
he
f
i
t
nes
s
of
eac
h
i
n
di
v
i
dua
l
f
r
o
m
t
he popu
l
at
i
on
b
y
r
ef
l
ec
t
i
ng
t
h
e s
i
m
i
l
ar
i
t
i
es
of
t
hes
e
i
ndi
v
i
d
ual
s
,
b
as
ed on
w
hi
c
h t
he a
l
gor
i
t
hm
c
an per
f
or
m
s
el
ec
t
i
on o
per
at
i
on an
d r
ea
l
i
z
e t
he e
v
o
l
u
t
i
on
oper
a
t
i
on
env
i
r
onm
ent
of
n
i
c
he.
T
he r
adi
us
of
t
he
ni
c
h
e i
s
of
gr
e
at
i
m
por
t
anc
e.
I
f
i
t
i
s
t
oo
s
m
al
l
,
t
her
e m
a
y
be t
oo m
an
y
ni
c
hes
w
h
i
l
e i
f
i
t
i
s
t
oo bi
g
,
m
an
y
s
m
al
l
ni
c
hes
c
an be s
een as
one n
i
c
he an
d i
t
w
i
l
l
af
f
ec
t
t
he
ev
ol
ut
i
on
pr
oc
es
s
of
t
he
ni
c
he
[9
]
.
T
he
H
a
m
m
i
ng
di
s
t
anc
e
of
an
y
t
w
o
i
nd
i
v
i
d
ual
s
i
X
and
j
X
i
n
a t
h
e po
pu
l
at
i
on
i
s
s
ho
w
n
as
:
(
)
2
1
(
1
,
2...,
1
,
1
,
...,
)
M
ij
i
j
ik
jk
k
d
X
X
x
x
i
MN
j
i
MN
=
=
−
=
−
=
+−
=
+
+
∑
(
4)
i
X
and
j
X
ar
e t
he
th
i
and
th
j
i
n
di
v
i
d
ual
s
r
es
pec
t
i
v
el
y
a
nd
N
i
s
t
he num
ber
of
t
he
in
i
t
ia
l p
o
p
u
la
t
io
n
s
.
U
s
ual
l
y
,
a f
unc
t
i
on
w
hi
c
h
i
n
di
c
at
es
t
h
e r
el
at
i
ons
h
i
p de
g
r
ee of
di
s
t
anc
e of
t
w
o i
nd
i
v
i
dua
l
s
i
n t
he p
opu
l
at
i
o
n i
s
c
a
l
l
ed s
har
i
n
g f
unc
t
i
o
n a
nd
i
t
i
s
m
ar
k
ed as
(,
)
Pi
j
.
(,
)
1
(,
)
/
P
i
j
d
i
j
p
=
−
(
5)
I
n t
h
i
s
f
or
m
ul
a,
ij
d
i
s
t
he r
e
l
at
i
ons
hi
p of
t
he
di
s
t
a
nc
e be
t
w
een
i
nd
i
v
i
d
ua
l
i
and i
nd
i
v
i
d
u
al
j
.
S
har
i
ng
de
gr
ee
i
s
a m
eas
ur
em
ent
t
o m
eas
ur
e t
he
de
gr
ee
of
s
har
i
n
g
of
a
c
er
t
ai
n
i
nd
i
v
i
d
ual
i
n t
he p
opu
l
at
i
o
n and i
t
i
s
def
i
n
ed as
t
he s
um
of
t
he s
har
i
ng f
unc
t
i
ons
of
t
hi
s
i
nd
i
v
i
dua
l
and
ot
her
i
n
di
v
i
dua
l
s
of
t
he
popu
l
at
i
o
n.
I
t
i
s
dem
ons
t
r
at
ed as
f
ol
l
o
w
s
w
i
t
h
i
S
.
1
(
)
,
1
,
2
,
...,
N
i
ij
j
S
Sd
i
N
=
=
=
∑
(
6)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
:
1
6
9
3
-
6
930
T
E
L
KO
M
NI
K
A
V
o
l.
14
,
N
o
.
3,
S
ept
em
ber
2016
:
10
35
–
1
041
1038
I
n t
h
i
s
f
or
m
ul
a,
N
i
s
t
he
pop
ul
at
i
o
n s
i
z
e.
A
s
s
um
e
t
hat
t
he
f
i
t
nes
s
of
t
he
i
ndi
v
i
du
al
i
is
i
F
and
t
h
e
p
opu
l
at
i
on
s
i
z
e
i
s
N
,
t
hen
t
he
pr
oba
bi
l
i
t
y
i
P
f
or
i
ndi
v
i
du
al
i
t
o
be s
e
l
ec
t
ed
i
s
:
1
/
(
)
(
1,
2
,
,
)
N
ii
i
i
PF
F
i
N
=
=
=
∑
L
(
7)
Start
End
Initialize the population
,
the algorithm parameters
,
clarify the
decoding and encoding schemes
Evaluate every individual of the current population
s
Whether the convergence criterion is
met or not
?
Obtain the initial population and determine the number of samples
Perform the adaptive operations of
crossover
Perform the
adaptive
operations
of
mutation
Output the optimization
result
Perform niche elimination operation on the new population formed
by N g
roups
Y
N
...
...
Use selection and give higher probability to the individual with higher
performance
,
select M different individuals and form the individual set
to the mating pool
F
i
gur
e
2
.
F
l
o
w
c
h
ar
t
of
opt
i
m
i
z
at
i
on
op
er
at
i
ons
of
ad
a
pt
i
v
e
ni
c
he
di
f
f
er
ent
i
al
ev
ol
ut
i
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n
a
l
gor
i
t
hm
T
he
s
t
eps
of
adapt
i
v
e n
i
c
he
di
f
f
er
ent
i
a
l
e
v
o
l
ut
i
on
al
g
or
i
t
hm
ar
e c
l
ar
i
f
i
ed as
f
ol
l
o
w
s
:
(
1)
S
et
t
h
e e
v
o
l
u
t
i
o
n
gen
e
r
at
i
on
c
ou
nt
er
1
t
＝
,
r
an
dom
l
y
pr
oduc
e
N
in
i
t
ia
l in
d
i
v
i
d
u
a
ls
and f
or
m
t
he i
ni
t
i
a
l
p
opu
l
a
t
i
on
(
)
Pt
,
i
n
i
t
i
al
i
z
e t
he c
r
os
s
ov
er
pr
ob
abi
l
i
t
y
c
P
and
t
he
m
u
t
at
i
o
n
pr
oba
bi
l
i
t
y
m
P
.
(
2)
O
bt
ai
n
t
he
f
i
t
nes
s
of
ea
c
h
i
nd
i
v
i
du
al
(
)
(
12
)
i
Ft
i
N
…
＝
，
，
，
and
m
ai
nt
a
i
n
t
he
i
n
di
v
i
du
al
ma
x
X
w
i
t
h
t
he
m
ax
i
m
u
m
f
i
t
nes
s
.
(
3)
A
dj
us
t
c
P
and
m
P
ac
c
or
di
n
g t
o F
or
m
ul
as
(
4)
-
(6
).
R
and
om
l
y
s
el
ec
t
t
w
o
i
ndi
v
i
dua
l
s
f
r
o
m
t
he p
ar
ent
po
p
ul
at
i
o
n
of
eac
h n
i
c
he.
R
et
ai
n
t
he
in
d
iv
id
u
a
ls
w
it
h
b
ig
f
it
n
e
s
s
,
i
n
or
der
t
o
ens
ur
e
t
he
c
r
o
s
s
ov
er
qua
l
i
t
y
,
t
he
c
r
os
s
ov
er
pr
obab
i
l
i
t
y
i
s
pr
oduc
e
d i
n t
h
e ad
apt
i
v
e
w
a
y
and
t
he
ad
apt
i
v
e c
r
o
s
s
ov
er
pr
ob
ab
i
l
i
t
y
i
s
d
et
er
m
i
ned b
y
t
he
f
ol
l
o
w
i
ng f
or
m
ul
a.
1
ma
x
ma
x
1
1
(
)/
(
)
(
0
,
1]
ca
ca
c
ca
ff
k
ff
ff
P
k
ff
k
≥
−−
=
∈
<
(
8)
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NI
K
A
I
S
S
N
:
1
693
-
6
930
A
n I
mpr
ov
ed
A
dapt
i
v
e N
i
c
h
e
D
if
f
e
r
e
n
t
ia
l E
v
o
lu
t
io
n
A
lg
o
r
it
h
m
(
H
u
i
W
ang
)
1039
I
n t
h
i
s
f
or
m
ul
a,
ma
x
f
and
a
f
ar
e
t
he m
ax
i
m
u
m
f
i
t
nes
s
and t
he a
v
er
a
ge f
i
t
n
es
s
of
t
he
par
ent
ge
ner
at
i
on r
es
pec
t
i
v
el
y
an
d
c
f
i
s
t
he
bi
gge
r
f
i
t
n
es
s
of
t
w
o
i
n
di
v
i
dua
l
s
t
o
be c
r
os
s
-
ov
er
ed.
N
on
-
un
i
f
or
m
m
ut
at
i
on o
per
at
i
o
n i
s
us
ed
and t
he m
ut
at
i
on pr
oba
bi
l
i
t
y
i
s
c
ont
r
o
l
l
ed
b
y
t
h
e
ev
o
l
ut
i
o
n d
egr
ee
i
n or
d
er
t
o
guar
a
nt
e
e t
he m
ut
at
i
on
qu
al
i
t
y
.
T
he ad
apt
i
v
e m
ut
at
i
o
n pr
ob
ab
i
l
i
t
y
i
s
det
er
m
i
ned b
y
t
he f
o
r
m
ul
a bel
o
w
.
2
ma
x
ma
x
2
2
(
)/
(
)
(
0
,
1]
m
a
m
a
m
m
a
ff
k
ff
ff
P
k
ff
k
≥
−−
=
∈
<
(
9)
I
n t
h
i
s
f
or
m
ul
a,
ma
x
f
and
a
f
ar
e
t
he m
ax
i
m
u
m
f
i
t
nes
s
and t
he a
v
er
a
ge f
i
t
n
es
s
of
t
he
par
ent
po
pul
at
i
on r
es
p
ec
t
i
v
el
y
an
d
m
f
i
s
t
he f
i
t
nes
s
of
t
he
i
nd
i
v
i
d
ua
l
t
o
be m
ut
at
ed
.
(
4)
S
el
ec
t
i
on
o
per
at
i
o
n.
U
s
e
s
el
ec
t
i
on
an
d
gi
v
e
h
i
gh
er
pr
obab
i
l
i
t
y
t
o
t
he
i
nd
i
v
i
du
a
l
w
i
t
h
hi
g
her
per
f
or
m
anc
e,
s
el
ec
t
M
di
f
f
er
ent
i
ndi
v
i
du
al
s
ac
c
or
di
n
g t
o F
or
m
ul
a (
7)
and f
or
m
t
he
i
nd
i
v
i
d
ual
s
et
t
o
t
he
m
at
i
ng
poo
l
an
d o
bt
a
i
n t
he
ne
w
po
pul
at
i
on.
(
5)
C
on
v
er
g
enc
e
c
r
i
t
er
i
o
n
j
udgm
ent
.
I
f
t
he
c
on
v
er
g
en
c
e
c
r
i
t
er
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o
n
i
s
no
t
m
et
,
upd
at
e
t
he
c
ount
er
1
tt
=+
an
d
r
et
a
i
n
t
he
be
s
t
i
nd
i
v
i
d
ua
l
d
i
r
ec
t
l
y
i
nt
o
t
h
e
nex
t
gen
er
at
i
on,
obt
ai
n
t
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f
i
t
nes
s
()
i
fit
t
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h i
ndi
v
i
d
ual
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r
et
ai
n
t
he c
ur
r
ent
opt
i
m
al
i
nd
i
v
i
dua
l
ma
x
()
X
t
and t
ur
n t
o S
t
ep 3,
ot
her
w
i
s
e,
o
ut
p
ut
t
h
e o
pt
i
m
al
l
a
y
out
r
es
ul
t.
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as
ed
on
t
he
ab
ov
e a
na
l
y
s
i
s
,
F
i
g
ur
e
2
i
s
t
he f
l
o
w
c
har
t
of
t
he
opt
i
m
i
z
at
i
on o
per
at
i
ons
of
adap
t
i
v
e ni
c
he
di
f
f
er
ent
i
al
e
v
o
l
ut
i
on al
gor
i
t
hm
.
4
.
E
x
p
e
r
i
m
e
n
t S
i
m
u
l
a
ti
o
n
a
n
d
A
n
al
ysi
s
4.
1
.
T
est
F
u
n
c
ti
o
n
I
n or
der
t
o
t
es
t
t
he per
f
or
m
anc
es
of
A
NDE
s
uc
h
as
t
he
ab
i
l
i
t
y
t
o ov
er
c
om
e
pr
e
m
at
ur
e
c
onv
er
g
enc
e
an
d t
h
e g
l
ob
al
o
pt
i
m
i
z
a
t
i
o
n c
ap
ab
i
l
i
t
y
,
f
our
f
unc
t
i
o
ns
s
ho
w
e
d b
y
F
or
m
ul
a
(
10)
t
o
F
or
m
ul
a (
13)
ha
v
e
be
en
s
el
ec
t
ed
as
t
he
t
es
t
f
unc
t
i
ons
.
A
m
ong t
h
em
,
1
f
i
s
a
s
i
ngl
e
-
pe
ak
f
unc
t
i
on w
hi
l
e
24
ff
−
ar
e m
ul
t
i
-
pe
ak
f
unc
t
i
ons
.
S
ee
t
he
i
r
r
es
p
ec
t
i
v
e c
har
ac
t
er
i
s
t
i
c
s
i
n
T
abl
e
1.
(
)
2
1
11
ni
j
ij
fx
x
=
=
=
∑∑
(
10
)
(
)
[
)
4
2
1
0,
1
n
i
i
f
x
i
x
r
andom
=
=
+
∑
(
11)
(
)
2
3
11
1
1
20
e
xp
0.2
e
xp
c
os
2
20
nn
ii
i
i
fx
x
x
e
n
n
π
=
=
=
−
−
−
++
∑∑
(
12)
(
)
(
)
2
4
1
10
c
os
2
10
n
i
i
i
fx
x
x
π
=
=
−+
∑
(
13)
T
abl
e 1.
C
har
ac
t
er
i
s
t
i
c
s
of
t
es
t
f
unc
t
i
ons
F
unc
t
i
on
V
ar
i
abl
e r
ange
V
ar
i
abl
e l
engt
h
G
l
obal
opt
i
m
al
s
ol
ut
i
on
1
f
[
-
100,
100]
n
8
0
2
f
[
-
1.
28,
1.
28
]
n
10
0
3
f
[
-
32,
32]
n
10
0
4
f
[
-
5.
12,
5
.
12]
n
12
0
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
:
1
6
9
3
-
6
930
T
E
L
KO
M
NI
K
A
V
o
l.
14
,
N
o
.
3,
S
ept
em
ber
2016
:
10
35
–
1
041
1040
1
f
i
s
a
c
o
nt
i
nuo
us
s
i
n
gl
e
-
pea
k
f
unc
t
i
on.
S
ur
r
ou
nd
i
ng
t
he
v
a
l
l
e
y
i
s
t
he
r
e
l
at
i
v
el
y
s
m
oot
h
s
ur
f
ac
e and i
t
i
s
m
ai
nl
y
us
e
d
t
o t
es
t
t
he
op
t
i
m
i
z
at
i
on
ac
c
ur
ac
y
of
t
he
al
g
or
i
t
hm
.
2
f
has
m
an
y
un
ev
enl
y
di
s
t
r
i
but
e
d pe
ak
s
,
w
hi
c
h
ha
v
e
di
f
f
er
ent
l
en
gt
hs
.
I
t
has
s
e
v
er
a
l
l
oc
al
m
ax
i
m
u
m
and
m
i
ni
m
um
and a hug
e os
c
i
l
l
a
t
i
o
n.
3
f
has
a
m
ul
t
i
-
peak
and
m
ul
t
i
-
v
a
l
l
e
y
s
ur
f
ac
e and
i
t
h
as
one
an
d o
nl
y
o
ne
opt
i
m
al
ex
t
r
em
u
m
.
B
es
i
des
,
i
t
h
as
t
he s
pa
t
i
a
l
di
s
t
r
i
but
i
on
of
di
f
f
er
ent
hei
ght
s
and
pe
ak
s
and i
t
i
s
us
u
al
l
y
us
ed
t
o
m
eas
ur
e
t
he
per
f
or
m
anc
e
of
t
he
s
ear
c
h
a
l
gor
i
t
hm
i
n
pr
oc
es
s
i
ng
t
h
e
op
t
i
m
i
z
at
i
on
pr
obl
em
s
w
i
t
h m
an
y
noi
s
es
.
4
f
has
a
s
t
r
o
ng
os
c
i
l
l
at
i
on
as
w
el
l
as
m
an
y
t
r
a
ps
.
D
u
e
t
o
t
he
os
c
i
l
l
at
i
o
n
an
d
t
h
e
m
an
y
l
oc
al
o
pt
i
m
al
poi
nt
s
s
ur
r
oun
di
n
g t
he gl
oba
l
opt
i
m
al
poi
n
t
,
i
t
c
an t
r
i
c
k
and
m
i
s
gui
de t
he pop
ul
at
i
on
s
ear
c
h i
nt
o l
oc
al
opt
i
m
a
l
po
i
nt
s
a
nd
i
t
i
s
qui
t
e d
ec
ept
i
v
e t
o t
he
al
g
or
i
t
hm
.
(
a)
T
es
t
f
unc
t
i
on
1
(
b)
T
es
t
f
unc
t
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on
2
(
c
)
T
es
t
f
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t
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on 3
(
d)
T
es
t
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t
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F
i
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3.
T
hr
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di
m
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s
ur
f
ac
es
of
f
our
t
es
t
f
unc
t
i
ons
F
r
o
m
t
he
abo
v
e
an
al
y
s
i
s
,
i
t
c
an
be
s
een
t
h
at
t
h
e
f
our
f
unc
t
i
ons
of
14
f
f
−
ar
e
gener
a
l
l
y
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epr
es
ent
a
t
i
v
e
and
t
he
y
c
a
n be
us
ed t
o t
es
t
t
he
opt
i
m
i
z
at
i
on
per
f
or
m
anc
e of
t
he a
l
gor
i
t
hm
.
4
.
2
.
C
o
m
p
a
r
i
s
o
n
o
f g
l
o
b
a
l
o
p
ti
m
i
z
a
ti
o
n
p
e
r
fo
r
m
a
n
c
e
T
abl
e 2
i
s
t
he
s
t
at
i
s
t
i
c
c
o
m
par
i
s
on of
t
h
e g
l
ob
al
opt
i
m
i
z
at
i
on p
er
f
or
m
anc
e af
t
er
r
epeat
i
n
g
30
t
i
m
es
on
ev
er
y
t
es
t
f
unc
t
i
on
w
i
t
h
A
N
D
E
and
B
D
E
w
h
en
t
he
m
ax
i
m
um
i
t
er
at
i
on
i
s
500.
,,
be
s
t
w
or
s
t
m
e
an
and
st
d
ar
e
t
he
op
t
i
m
al
s
ol
ut
i
on,
t
he
w
or
s
t
s
ol
ut
i
on,
t
he
m
ean
v
al
ue
a
n
d
t
he m
ean s
quar
e er
r
or
.
T
abl
e 2
i
s
t
he s
t
at
i
s
t
i
c
c
o
m
par
i
s
on of
t
he gl
ob
al
opt
i
m
i
z
at
i
on
per
f
or
m
anc
e
.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
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NI
K
A
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S
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:
1
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dapt
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T
abl
e 2.
S
t
a
t
i
s
t
i
c
c
om
par
i
s
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t
he
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oba
l
o
pt
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m
i
z
a
t
i
o
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or
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F
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t
i
on
A
l
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e
s
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s
t
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ean
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DE
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9515
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6.
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2
f
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2
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I
t
c
an be s
een f
r
o
m
t
he
dat
a i
n T
abl
e 2 t
h
at
A
N
D
E
has
t
he b
es
t
opt
i
m
i
z
at
i
on
per
f
or
m
anc
e
w
h
i
l
e
BD
E
ha
s
t
he
w
or
s
t
and
t
ha
t
A
N
D
E
c
an
j
u
m
p
out
of
t
he
l
oc
al
opt
i
m
um
m
or
e
ef
f
ec
t
i
v
el
y
,
r
ed
uc
e t
h
e pr
e
m
at
ur
e c
onv
er
ge
nc
e a
nd s
ho
w
s
t
r
on
g o
pt
i
m
i
z
at
i
o
n per
f
or
m
anc
e.
As
f
or
1
f
,
A
N
D
E
has
s
i
m
i
l
ar
per
f
or
m
anc
e
w
i
t
h B
D
E
,
how
ev
e
r
,
BD
E
has
dr
opp
ed
i
nt
o
t
he d
eep
pi
t
s
ur
r
o
und
i
ng
t
h
e gl
oba
l
o
pt
i
m
u
m
i
n 30 ex
p
er
i
m
ent
s
.
T
her
ef
or
e,
c
o
m
p
ar
ed
w
i
t
h
BD
E
,
A
N
D
E
has
bet
t
er
per
f
or
m
a
nc
e t
o
ov
er
c
om
e l
oc
al
o
pt
i
m
i
z
at
i
on.
F
or
2
f
and
3
f
,
t
he
av
er
age
i
t
er
at
i
o
ns
of
A
N
D
E
ar
e
b
i
g
ger
t
han
t
hos
e
of
BD
E
bec
aus
e
2
f
an
d
3
f
ha
v
e
pl
ent
y
of
l
oc
a
l
o
pt
i
m
al
po
i
nt
s
an
d
A
N
D
E
c
a
n j
um
p out
of
t
he
l
oc
a
l
opt
i
m
i
z
at
i
on,
l
ea
di
n
g t
o t
he
i
nc
r
eas
e
of
a
v
er
ag
e
i
t
er
at
i
o
ns
.
B
es
i
d
es
,
i
t
c
an
a
l
s
o b
e s
ee
n
i
n
t
he
e
x
per
i
m
ent
t
hat
w
hen t
he c
y
c
l
i
c
i
t
er
at
i
ons
i
nc
r
eas
e,
A
N
D
E
c
an h
av
e
m
or
e gl
ob
al
o
pt
i
m
al
s
ol
ut
i
ons
b
ut
BD
E
bar
el
y
c
h
ang
es
.
5.
C
o
n
c
l
u
s
i
o
n
B
as
ed
on
t
he
s
h
or
t
c
om
i
ngs
and
f
l
a
w
s
of
D
E
a
l
go
r
i
t
hm
i
n
t
heor
y
a
nd
app
l
i
c
at
i
on
t
ec
hno
l
og
y
,
t
hi
s
pap
er
has
i
nt
r
oduc
e
d n
i
c
he
and
s
har
i
n
g de
gr
ee
i
n t
he
opt
i
m
i
z
at
i
o
n c
om
put
at
i
o
n.
B
es
i
d
es
,
i
n t
h
e e
v
o
l
ut
i
on
pr
oc
es
s
,
i
t
h
as
l
i
m
i
t
ed t
he
i
nc
r
eas
e of
ot
her
i
n
di
v
i
dua
l
s
b
y
a
dj
us
t
i
ng
t
he
f
i
t
nes
s
of
eac
h i
ndi
v
i
du
al
and c
r
eat
e
d n
i
c
he e
v
o
l
ut
i
o
n en
v
i
r
o
nm
ent
.
I
n t
he m
ean
w
h
i
l
e,
i
t
h
as
us
ed c
r
os
s
ov
er
and
m
ut
at
i
on
oper
at
or
s
,
w
h
i
c
h ar
e
good
f
or
t
he d
i
v
er
s
i
t
y
of
t
he p
opu
l
at
i
o
n
ev
o
l
ut
i
o
n,
an
d
i
m
pr
ov
ed
t
h
e
s
ear
c
h
al
gor
i
t
h
m
of
t
he
al
g
or
i
t
hm
.
T
he
ex
per
i
m
ent
s
ho
w
s
t
hat
t
h
e
al
g
or
i
t
hm
pr
opos
ed
b
y
t
hi
s
pa
per
ef
f
ec
t
i
v
e
l
y
m
ai
nt
ai
ns
pop
ul
at
i
on d
i
v
er
s
i
t
y
,
h
as
f
as
t
er
c
onv
er
g
enc
e
r
at
e,
j
um
ps
out
f
r
o
m
t
he
l
oc
al
opt
i
m
u
m
,
al
l
ev
i
at
es
pr
em
at
ur
i
t
y
an
d
s
ho
w
s
s
t
r
onger
opt
i
m
i
z
at
i
o
n p
er
f
or
m
anc
e
.
R
ef
er
en
ces
[1
]
Li
ng
j
uan
H
o
u,
Z
h
i
j
i
ang
H
ou
.
A
nov
el
di
s
c
r
et
e
d
i
f
f
er
e
nt
i
al
ev
ol
ut
i
o
n
al
g
or
i
t
hm
.
T
E
L
KO
M
N
I
KA
I
ndon
es
i
an J
our
nal
of
E
l
ec
t
r
i
c
al
E
ng
i
ne
er
i
ng
.
20
13;
11(
4)
:
1
883
-
18
88
.
[2
]
D
ex
uan Z
ou,
J
i
anhu
a
W
u
,
L
i
qun G
ao,
S
t
ev
en Li
.
A
M
od
i
f
i
ed D
i
f
f
er
ent
i
al
E
v
ol
ut
i
on
A
l
gor
i
t
h
m
f
or
U
nc
on
s
t
r
ai
ned
O
pt
i
m
i
z
at
i
o
n P
r
obl
e
m
s
.
N
eur
o
c
om
put
i
ng
.
201
3
;
120(
23)
:
469
-
481.
[3
]
C
am
i
l
a
S
i
l
v
a
de
M
agal
h
ães
,
D
i
ogo
M
ar
i
nho
A
l
m
ei
d
a,
H
e
l
i
o
J
os
é
C
or
r
ea
B
ar
bo
s
a,
Laur
e
nt
E
m
m
a
nuel
D
ar
denn
e.
A
D
y
nam
i
c
N
i
c
hi
ng G
enet
i
c
A
l
gor
i
t
hm
S
t
r
at
e
gy
f
or
D
oc
k
i
ng H
i
g
hl
y
F
l
ex
i
bl
e Li
g
and
s
.
I
nf
or
m
at
i
on S
c
i
en
c
e
s
.
20
14
;
2
89(
24)
:
206
-
224.
[4
]
Li
nda
S
l
i
m
an
i
,
T
ar
ek
B
ou
k
t
i
r
,
A
l
ger
i
a.
O
pt
i
m
al
P
ow
er
F
l
ow
S
ol
ut
i
on
o
f
t
h
e
A
l
g
er
i
a
n
E
l
e
c
t
r
i
c
al
N
e
t
w
or
k
us
i
n
g D
i
f
f
er
ent
i
al
E
v
ol
ut
i
on A
l
gor
i
t
h
m
.
T
E
LK
O
M
N
I
K
A
I
ndones
i
a
n J
ou
r
nal
o
f
E
l
ec
t
r
i
c
al
E
ngi
ne
er
i
n
g
.
2012;
10(
2)
:
1
99
-
210
.
[5
]
M
os
t
af
a Z
Al
i
,
N
o
o
r H
A
w
ad.
A
N
ov
el
C
l
as
s
o
f
N
i
c
h
e H
y
br
i
d C
ul
t
ur
a
l
A
l
go
r
i
t
h
m
s
f
or
C
ont
i
nu
ou
s
E
ngi
ne
er
i
n
g O
pt
i
m
i
z
at
i
on
.
I
nf
o
r
m
at
i
on S
c
i
en
c
e
s
.
2
014
;
267(
2
0)
:
158
-
190
.
[6
]
M
oham
m
ad H
M
or
adi
,
M
oham
m
a
d A
bedi
ni
,
S
M
R
ez
a
T
ous
i
,
S
Ma
hdi
H
os
s
ei
n
i
an.
O
pt
i
m
al
S
i
t
i
n
g and
S
i
z
i
ng
of
R
enew
abl
e
E
ner
gy
S
our
c
e
s
an
d
C
har
gi
ng
S
t
at
i
o
ns
S
i
m
ul
t
a
neo
us
l
y
B
a
s
ed
on
D
i
f
f
er
en
t
i
a
l
E
v
ol
ut
i
on
A
l
g
or
i
t
h
m
.
I
nt
er
n
at
i
o
nal
J
our
nal
of
E
l
ec
t
r
i
c
a
l
P
ow
e
r
&
E
ner
g
y
S
y
s
t
em
s
.
20
15
;
73
(
12)
:
1
015
-
1024.
[7
]
M
ar
t
i
n K
ot
y
r
ba,
E
v
a
V
ol
na,
P
et
r
B
uj
o
k
.
U
nc
onv
ent
i
ona
l
M
o
del
l
i
ng of
C
o
m
pl
ex
S
y
s
t
em
v
i
a C
el
l
u
l
ar
A
ut
om
at
a a
nd D
i
f
f
er
e
nt
i
a
l
E
v
ol
ut
i
on
.
S
w
ar
m
and E
v
o
l
ut
i
onar
y
C
om
put
at
i
on
.
2
015
;
25(
12)
:
52
-
62.
[8
]
C
ar
l
os
S
eg
ur
a,
C
ar
l
o
s
A
C
oel
l
o C
oel
l
o,
A
l
f
r
edo G
H
er
nánd
e
z
-
D
í
az
.
I
m
pr
ov
i
ng T
he
V
ec
t
or
G
ener
at
i
on
S
t
r
at
egy
of
D
i
f
f
er
en
t
i
a
l
E
v
ol
ut
i
on f
or
Lar
ge
-
S
c
a
l
e O
pt
i
m
i
z
at
i
on
.
I
n
f
or
m
at
i
on S
c
i
en
c
es
.
20
15
;
32
3(
1)
:
106
-
12
9.
[9
]
J
av
i
er
E
V
i
t
e
l
a,
O
c
t
av
i
o
C
as
t
a
ños
.
A
S
eq
uent
i
al
N
i
c
hi
n
g
M
em
et
i
c
A
l
gor
i
t
hm
f
or
C
ont
i
nuo
u
s
M
ul
t
i
m
o
dal
F
unc
t
i
on O
p
t
i
m
i
z
at
i
o
n
.
Ap
p
l
i
e
d
M
at
hem
at
i
c
s
a
nd C
om
pu
t
at
i
o
n
.
201
2
;
2
18(
1
7)
:
82
42
-
8
259.
Evaluation Warning : The document was created with Spire.PDF for Python.