I
A
E
S
I
n
t
e
r
n
at
io
n
al
Jou
r
n
al
of
A
r
t
if
ic
ia
l
I
n
t
e
ll
ig
e
n
c
e
(
I
J
-
A
I
)
V
ol
.
10
, N
o.
1
,
M
a
r
c
h
2021
, pp.
166
~
174
I
S
S
N
:
2252
-
8938
,
D
O
I
:
10.11591/
ij
a
i.
v
10
.i
1
.pp
166
-
174
166
Jou
r
n
al
h
om
e
page
:
ht
tp
:
//
ij
ai
.
ia
e
s
c
or
e
.c
om
E
st
i
m
at
i
n
g o
n
e
-
d
i
od
e
-
PV
m
od
e
l
u
s
i
n
g au
t
on
om
o
u
s gr
ou
p
s
p
ar
t
i
c
l
e
swar
m
op
t
i
m
i
z
at
i
on
M
oh
a
m
m
ad
A
lS
h
ab
i
1
, C
h
aou
k
i
G
h
e
n
ai
2
, M
aam
ar
B
e
t
t
aye
b
3
, F
ah
ad
F
ar
a
z
A
h
m
ad
4
1
Mechanical a
nd Nuclear E
ngineering Dep
artment, Univer
sity of Sharjah, Shar
jah,
United Arab Emirates
2
Sustaina
ble an
d Rene
wable
Ener
gy Engi
neer
ing De
partme
nt, Univ
ersity
of Sha
rjah,
Sharja
h,
United Arab Emirates
2,4
Sustaina
ble En
ergy
Devel
opment
Resea
rch G
r
oup, Research Institute for Science
s and Engineering, University of
Sharja
h, Shar
jah,
United Arab Emirates
3
Electrical Engineering Department, University of Sharjah, Sharjah,
United Arab Emirates
3
Centre o
f Exce
llence
in Intellig
ent Engin
eering
systems (CE
IES), King
Abdulaziz Uni
versity, J
eddah, Saudi
Arabia
A
r
t
ic
le
I
n
f
o
A
B
S
T
R
A
C
T
A
r
ti
c
le
h
is
to
r
y
:
R
e
c
e
iv
e
d
M
a
y
2
0
, 20
20
R
e
vi
s
e
d
J
a
n
11
, 20
21
A
c
c
e
pt
e
d
F
e
b
3
, 20
2
1
In
this
paper,
the
on
e
-
diode
model
of
a
photovoltaic
PV
solar
cell
(P
VSC)
is
estimat
ed
for
an
experiment
al
characterist
ic
cu
rves
data
by
using
a
r
ecently
proposed
version
of
the
particle
swarm
optimiza
tion
(PSO)
algorithm,
which
is
known
as
the
autonom
ous
groups
particles
swarm
optim
ization
(PS
OAG).
This
meta
-
heuristic
algorithm
is
used
to
identify
the
model
of
the
PVSC.
The
PSOAG
divides
the
particles
into
groups
and
then,
uses
different
funct
ions
to
tune
the
social
and
cognitive
parameters
of
these
groups
.
By
usin
g
these
groups, the performance of
the PSO is improved
in terms of converge
nce rate
and
escaping
the
local
minima/maxima.
Six
versions
of
PSOAG
alg
orithms
were
developed
in
this
work.
Therefore,
nine
versions
of
PSOAG,
in
cluding
these
six
algorith
ms
and
three
newly
developed
PSOAG
reported
previously,
will
be
used
in
this
research
to
cover
more
social’s
behaviors.
Th
e
res
ults
are
compared
to
the
original
PSO
and
other
versions
of
PSO
like
conve
ntional
and
asymmetr
ic tim
e
-
varying accelera
ted coeffi
c
ient PSOs,
and the im
proved
PSO.
The
result
shows
that
the
proposed
methods
improve
the
performance
by
up
to
14%
in
terms
of
root
mean
squared
error
and
maximum
a
bsolute
error,
and
by
up
to
20%
in
term
of
convergence
rate,
when
thes
e
were
compared t
o the b
est resul
ts obt
ained from
the ot
her algori
thms.
K
e
y
w
o
r
d
s
:
A
ut
onomous
gr
oups
C
ogni
ti
ve
c
oe
f
f
ic
ie
nt
O
ne
-
di
ode
m
ode
l
P
a
r
ti
c
le
s
s
w
a
r
m
opt
im
iz
a
ti
on
S
oc
ia
l
c
oe
f
f
ic
ie
nt
S
ol
a
r
P
V
T
im
e
-
va
r
yi
ng a
c
c
e
le
r
a
te
d
c
oe
f
f
ic
ie
nt
This is an
open
acce
ss artic
le unde
r the
CC BY
-
SA
license.
C
or
r
e
s
pon
di
n
g A
u
th
or
:
M
oha
m
m
a
d A
lS
ha
bi
M
e
c
ha
ni
c
a
l
a
nd N
uc
le
a
r
E
ngi
ne
e
r
in
g D
e
pa
r
tm
e
nt
U
ni
ve
r
s
it
y of
S
ha
r
ja
h
S
ha
r
ja
h,
U
ni
te
d A
r
a
b E
m
ir
a
te
s
E
m
a
il
:
m
a
ls
ha
bi
@
S
ha
r
ja
h.a
c
.a
e
1.
I
N
T
R
O
D
U
C
T
I
O
N
D
e
s
pi
te
of
unc
e
r
ta
in
ty
in
e
nvi
r
onm
e
nt
a
l
c
ondi
ti
ons
,
s
ol
a
r
e
ne
r
g
y
is
ge
tt
in
g
m
or
e
a
nd
m
or
e
a
tt
e
nt
io
n
f
r
om
r
e
s
e
a
r
c
he
r
s
due
to
it
s
c
h
a
r
a
c
te
r
is
ti
c
s
of
be
in
g
e
c
onomi
c
a
l,
lo
w
m
a
in
te
na
nc
e
c
os
t
a
nd
lo
ng
-
li
f
e
s
pa
n.
T
h
e
a
va
il
a
bi
li
ty
of
s
ol
a
r
ir
r
a
di
a
nc
e
a
nd
di
r
e
c
t
c
o
nve
r
s
io
n
of
s
ol
a
r
e
ne
r
gy
in
to
e
le
c
tr
ic
it
y
a
r
e
a
ls
o
th
e
ot
he
r
f
a
c
to
r
s
,
w
hi
c
h
m
a
ke
phot
ovol
ta
ic
s
ys
te
m
s
m
or
e
de
s
ir
a
bl
e
th
a
n
ot
he
r
a
lt
e
r
na
ti
ve
s
our
c
e
s
[
1]
.
H
ow
e
ve
r
,
th
e
e
f
f
ic
ie
nc
y
of
P
V
s
ys
te
m
s
is
di
r
e
c
tl
y
a
f
f
e
c
te
d
by
phys
ic
a
l
c
ha
nge
s
in
t
he
e
nvi
r
onm
e
nt
s
uc
h
a
s
s
ol
a
r
ir
r
a
di
a
nc
e
a
nd
te
m
pe
r
a
tu
r
e
[
2]
.
F
or
r
e
li
a
bl
e
de
s
ig
n
a
nd
e
xpl
oi
ta
ti
on
of
m
a
xi
m
um
e
ne
r
gy
a
nd
e
ne
r
gy s
e
c
ur
it
y
of
P
V
s
ys
t
e
m
s
,
it
is
c
r
it
ic
a
l
to
de
vi
s
e
a
c
om
pr
e
he
ns
iv
e
a
nd
a
c
c
ur
a
te
m
a
th
e
m
a
ti
c
a
l
m
ode
l
to
pr
e
di
c
t
th
e
be
ha
vi
or
of
P
V
s
ol
a
r
c
e
ll
(
P
V
S
C
)
m
odul
e
unde
r
a
ll
e
nvi
r
onm
e
nt
a
l
c
ondi
ti
ons
[
3]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
A
r
ti
f
I
nt
e
ll
I
S
S
N
:
2252
-
8938
E
s
ti
m
at
in
g one
-
di
ode
-
P
V
m
ode
l
us
in
g autonomous
gr
oups
par
t
ic
le
s
w
ar
m
…
(
M
ohamm
ad A
lS
habi
)
167
S
e
ve
r
a
l
m
a
th
e
m
a
ti
c
a
l
m
ode
ls
ba
s
e
d
on
e
le
c
tr
ic
a
l
e
qui
va
le
nt
c
ir
c
ui
ts
a
r
e
r
e
por
te
d
in
th
e
li
te
r
a
tu
r
e
s
uc
h
a
s
one
-
di
ode
m
ode
l
[4
-
5]
,
two
-
di
ode
m
ode
l
[
6]
,
m
ul
ti
-
di
o
de
m
ode
l
[
7]
,
-
M
ode
l,
a
nd
m
ode
l
[4
-
7]
.
T
he
one
-
di
ode
m
od
e
l
is
m
o
s
t
w
id
e
ly
u
s
e
d
a
nd
c
it
e
d
a
s
it
pr
ovi
de
s
good
tr
a
de
-
of
f
be
twe
e
n
a
c
c
ur
a
c
y
a
nd
c
om
pl
e
xi
ty
[
8]
.
T
he
one
-
di
ode
m
ode
l
is
gov
e
r
ne
d
by
f
iv
e
pa
r
a
m
e
te
r
s
s
ta
te
d
a
s
r
e
v
e
r
s
e
s
a
tu
r
a
ti
on
(
)
,
a
nd
phot
o
-
c
ur
r
e
nt
s
(
ℎ
)
,
di
ode
id
e
a
li
ty
f
a
c
to
r
(
)
,
a
nd
s
e
r
ie
s
(
)
a
nd
s
hunt
(
ℎ
)
r
e
s
is
ta
nc
e
s
.
T
he
two
-
di
ode
m
ode
l
pr
ovi
de
s
m
or
e
a
c
c
u
r
a
c
y
but
a
ls
o
in
c
r
e
a
s
e
s
th
e
c
om
pl
e
xi
ty
of
m
ode
l
a
nd
is
gove
r
ne
d
by
s
e
ve
n
pa
r
a
m
e
te
r
s
[
6]
.
T
he
e
s
ti
m
a
ti
on
of
c
h
a
r
a
c
te
r
is
ti
c
pa
r
a
m
e
te
r
s
c
onc
is
e
w
it
h
r
e
a
l
da
ta
i
s
th
e
m
a
in
c
on
c
e
r
n
in
m
a
th
e
m
a
ti
c
a
l
m
ode
li
ng
of
P
V
S
C
.
U
nknown
pa
r
a
m
e
te
r
s
c
a
n
be
e
xt
r
a
c
te
d
m
a
in
ly
by
two
m
e
th
odol
ogi
e
s
c
la
s
s
if
ie
d a
s
a
na
ly
ti
c
a
l
a
nd
num
e
r
ic
a
l
a
ppr
oa
c
h
e
s
.
I
n
th
e
a
na
ly
ti
c
a
l
a
ppr
oa
c
h,
th
e
in
f
or
m
a
ti
on
pr
ovi
de
d
by
th
e
m
a
nuf
a
c
tu
r
e
r
or
I
-
V
c
ur
ve
da
ta
is
us
e
d
to
de
te
r
m
in
e
th
e
unkno
w
n
pa
r
a
m
e
te
r
s
[
9]
.
T
he
m
a
nuf
a
c
tu
r
e
r
us
u
a
ll
y
pr
ovi
de
s
th
e
da
ta
onl
y
a
t
s
ta
nd
a
r
d
te
s
ti
ng
c
ondi
ti
ons
(
S
T
C
)
w
hi
c
h
m
a
de
th
is
a
ppr
oa
c
h
in
a
ppr
opr
ia
te
to
be
us
e
d
f
or
c
ha
ngi
ng
ir
r
a
di
a
nc
e
a
nd
te
m
pe
r
a
tu
r
e
c
ondi
ti
ons
.
I
n
a
d
di
ti
on,
th
e
s
im
pl
if
yi
ng
a
s
s
um
pt
io
ns
c
on
s
id
e
r
e
d
dur
in
g
th
e
f
or
m
ul
a
ti
on
of
a
na
ly
ti
c
a
l
m
ode
ls
le
a
d
to
c
om
pr
om
is
in
g
th
e
a
c
c
ur
a
c
y
[
10]
.
I
n
or
de
r
to
ove
r
c
om
e
th
e
di
s
a
dva
nt
a
ge
s
of
a
na
ly
ti
c
a
l
m
e
th
ods
,
s
e
v
e
r
a
l
non
-
li
ne
a
r
C
ur
ve
f
it
ti
ng
te
c
hni
que
s
a
r
e
r
e
por
te
d
a
nd
c
a
te
gor
iz
e
d
a
s
num
e
r
ic
a
l
m
e
th
ods
[
11]
.
N
um
e
r
ic
a
l
m
e
th
ods
a
r
e
f
ur
th
e
r
di
vi
de
d
in
c
onve
nt
io
na
l
or
it
e
r
a
ti
ve
m
e
th
ods
a
nd
m
e
ta
he
ur
is
ti
c
m
e
th
ods
.
N
e
w
to
n
R
a
phs
on
[
12
]
a
nd
L
e
ve
nbe
r
g
M
a
r
qua
r
dt
a
lg
or
it
hm
s
a
r
e
e
xa
m
pl
e
s
of
c
onve
nt
io
na
l
it
e
r
a
ti
ve
m
e
th
ods
[
13
-
14]
.
I
n
s
pi
te
of
th
e
e
f
f
ic
ie
nc
y
of
c
onve
nt
io
na
l
te
c
hni
que
s
,
th
e
y
c
onve
r
ge
pr
e
m
a
tu
r
e
ly
a
r
ound
lo
c
a
l
m
in
im
a
a
nd
r
e
qu
ir
e
c
ont
in
ui
ty
a
nd
di
f
f
e
r
e
nt
ia
bi
li
ty
of
th
e
f
unc
ti
ons
.
I
n a
ddi
ti
on, t
he
e
f
f
ic
ie
nc
y of
c
onve
nt
io
na
l
it
e
r
a
ti
ve
m
e
th
ods
de
pe
nds
upon ini
ti
a
l
pos
it
io
ns
[
15]
.
A
w
id
e
va
r
ie
ty
of
m
e
ta
he
ur
is
ti
c
a
lg
or
it
hm
s
is
pr
e
s
e
nt
e
d
in
th
e
li
te
r
a
tu
r
e
to
s
ol
ve
non
-
li
ne
a
r
it
y
opt
im
iz
a
ti
on
pr
obl
e
m
s
.
T
h
e
s
e
opt
im
iz
a
ti
on
te
c
hni
que
s
in
c
l
ude
ge
ne
ti
c
a
lg
or
it
hm
[
15]
,
pa
r
ti
c
le
s
w
a
r
m
opt
im
iz
a
ti
on
(
P
S
O
)
[
16]
,
hybr
id
pa
r
ti
c
le
s
w
a
r
m
opt
im
iz
a
ti
on
[
17]
,
ha
r
m
ony
s
e
a
r
c
h
[
18]
,
di
f
f
e
r
e
nt
ia
l
e
vol
ut
io
n,
a
da
pt
iv
e
di
f
f
e
r
e
nt
ia
l
e
vol
ut
io
n
[
19]
,
c
a
t
s
w
a
r
m
op
ti
m
iz
a
ti
on
a
lg
or
it
hm
[
20]
,
ba
c
te
r
ia
l
f
or
a
gi
ng
opt
im
iz
a
ti
on
[
21]
,
bi
oge
ogr
a
phy
-
ba
s
e
d
opt
im
iz
a
ti
on
[
22]
,
f
lo
w
e
r
pol
li
na
ti
on
a
lg
or
it
hm
[
23]
,
a
r
ti
f
ic
ia
l
be
e
c
ol
ony a
lg
or
it
hm
[
24]
.
M
e
ta
he
ur
is
ti
c
a
lg
or
it
hm
s
a
r
e
a
bl
e
to
id
e
nt
if
y
th
e
pa
r
a
m
e
te
r
s
of
a
non
-
li
ne
a
r
m
ode
l
in
va
r
yi
ng
e
nvi
r
onm
e
nt
a
l
c
ondi
ti
o
ns
.
P
S
O
is
a
w
id
e
ly
a
dopt
e
d
opt
im
iz
a
ti
on
a
lg
or
it
hm
due
to
it
s
s
im
pl
ic
it
y
a
nd
in
e
xpe
ns
iv
e
ne
s
s
in
te
r
m
of
c
om
put
a
ti
ona
l
c
os
t
[
25]
.
O
n
th
e
ot
he
r
ha
nd,
it
e
xpr
e
s
s
e
s
th
e
di
s
a
dva
nt
a
g
e
of
c
onve
r
gi
ng
to
lo
c
a
l
m
in
im
a
/m
a
xi
m
a
a
nd
s
lo
w
c
onve
r
ge
nc
e
r
a
t
e
(
C
R
)
r
e
s
ul
ti
ng
in
lo
w
qua
li
ty
e
s
ti
m
a
ti
on
of
pa
r
a
m
e
te
r
s
[
26]
.
T
o
a
ll
e
vi
a
te
th
e
s
e
is
s
ue
s
,
m
a
ny
im
pr
ove
d
ve
r
s
io
ns
ha
ve
be
e
n
pr
e
s
e
nt
e
d
in
c
lu
di
ng
ti
m
e
va
r
yi
ng
a
c
c
e
le
r
a
te
d
c
oe
f
f
ic
ie
nt
P
S
O
(
P
S
O
T
A
C
)
,
a
s
ym
m
e
tr
ic
a
l
ti
m
e
va
r
yi
ng
a
c
c
e
le
r
a
te
d
c
oe
f
f
ic
ie
nt
pa
r
ti
c
le
s
w
a
r
m
(
P
S
O
M
)
a
nd
a
ut
onomous
gr
oup
pa
r
ti
c
le
s
w
a
r
m
opt
i
m
iz
a
ti
on
(
P
S
O
A
G
)
[
27
-
31]
.
I
n
P
S
O
T
A
C
,
th
e
m
odi
f
ic
a
ti
on
in
pos
it
iv
e
a
c
c
e
le
r
a
ti
on c
ons
ta
nt
s
a
r
e
in
tr
oduc
e
d
d
ur
in
g
th
e
opt
im
iz
a
ti
on
to
ove
r
c
om
e
pr
e
m
a
tu
r
e
c
onve
r
ge
nc
e
[
27]
.
T
he
z
e
r
o
ve
lo
c
it
y
pa
r
ti
c
le
s
a
r
e
r
e
in
it
ia
li
z
in
g
w
it
h
r
a
ndom
ve
lo
c
it
y
to
ove
r
c
om
e
pr
e
m
a
tu
r
e
c
onve
r
ge
nc
e
[
28]
.
I
n
[
29]
,
th
e
a
ut
hor
a
dopt
e
d
a
n
a
dj
us
tm
e
nt
s
tr
a
te
gy
of
a
s
ym
m
e
tr
ic
a
l
ti
m
e
de
pe
nde
nt
a
c
c
e
le
r
a
ti
on
c
oe
f
f
ic
ie
nt
s
to
e
li
m
in
a
te
th
e
lo
c
a
l
m
in
im
a
pr
obl
e
m
(
P
S
O
M
)
.
T
he
im
pr
ove
d
ve
r
s
io
n
of
P
S
O
M
is
out
li
ne
d
in
[
30]
.
A
n
a
ut
onomous
gr
oup
pa
r
t
ic
le
s
w
a
r
m
opt
im
iz
a
ti
on
(
P
S
O
A
G
)
ha
s
be
e
n
de
ve
lo
pe
d
c
ons
id
e
r
in
g
th
e
di
ve
r
s
it
y
in
bi
r
d
f
lo
c
ki
ng
or
in
s
e
c
t
s
w
a
r
m
in
g
[
31]
.
T
he
m
a
th
e
m
a
ti
c
a
l
m
ode
li
ng
of
a
ut
onomous
gr
oups
w
a
s
pr
e
s
e
nt
e
d,
a
nd
r
e
s
ul
ts
ha
d
s
how
n
good
pe
r
f
or
m
a
nc
e
in
te
r
m
of
a
voi
di
ng
lo
c
a
l
m
in
im
a
/m
a
xi
m
a
a
nd
c
onve
r
ge
nc
e
s
pe
e
d.
A
ut
onomou
s
gr
oups
a
r
e
e
m
pl
oye
d
in
s
uc
h
a
w
a
y
to
gi
ve
in
de
pe
nde
nc
e
t
o di
ve
r
s
e
p
a
r
ti
c
le
s
i
n or
de
r
t
o e
nh
a
nc
e
t
h
e
pe
r
f
or
m
a
nc
e
[
31]
.
I
n
th
is
pa
pe
r
,
f
or
th
e
f
ir
s
t
ti
m
e
,
a
r
e
c
e
nt
ly
de
ve
lo
pe
d
a
ut
onomous
gr
oup
pa
r
ti
c
le
s
w
a
r
m
opt
im
iz
a
ti
on
(
P
S
O
A
G
)
[
31]
is
e
m
pl
oye
d
to
de
te
r
m
in
e
th
e
f
iv
e
pa
r
a
m
e
te
r
s
of
one
di
ode
m
ode
l.
T
he
pa
r
ti
c
le
s
a
r
e
di
vi
de
d
in
to
gr
oups
w
it
h
tu
ne
d
s
oc
ia
l
a
nd
c
ogni
ti
ve
pa
r
a
m
e
te
r
s
.
I
n
th
is
s
tu
dy,
s
ix
ne
w
ve
r
s
io
ns
of
P
S
O
A
G
(
P
S
O
A
G
4
…
P
S
O
A
G
9)
a
r
e
de
ve
lo
pe
d
a
lo
ng
w
it
h
th
r
e
e
v
e
r
s
io
ns
pr
e
s
e
nt
e
d
in
[
31]
a
r
e
s
tu
di
e
d.
A
br
ie
f
c
om
pa
r
is
on
of
th
e
pr
opos
e
d
m
e
th
ods
w
it
h
c
onve
nt
io
na
l
P
S
O
,
P
S
O
T
A
C
[
2
7
-
28]
,
P
S
O
M
[
29]
a
nd
it
s
im
p
r
ove
d
ve
r
s
io
n
(
P
S
O
I
)
[
30
]
is
a
ls
o
in
c
lu
de
d. T
he
pa
pe
r
or
ga
ni
z
a
ti
on
is
:
s
e
c
ti
on
2
pr
ovi
de
s
th
e
r
e
s
e
a
r
c
h
m
e
th
odol
ogy,
a
nd
th
e
pr
opos
e
d
a
lg
or
it
hm
is
pr
opo
s
e
d
in
s
e
c
ti
on
3.
R
e
s
ul
ts
a
nd
di
s
c
us
s
io
n
a
r
e
pr
e
s
e
nt
e
d
in
s
e
c
ti
on
4.
I
n
th
e
e
nd,
th
e
s
tu
dy i
s
c
onc
lu
de
d i
n
s
e
c
ti
on 5. T
h
e
c
ont
r
ib
ut
io
ns
of
t
hi
s
w
or
k c
a
n be
s
um
m
a
r
iz
e
d a
s
:
-
D
e
ve
lo
pi
ng s
ix
ne
w
ve
r
s
io
n
s
of
t
he
P
S
O
A
G
t
o c
ove
r
m
or
e
s
oc
ia
l
be
ha
vi
our
s
.
-
A
ppl
yi
ng
a
ll
ve
r
s
io
ns
of
P
S
O
A
G
;
th
e
ne
w
de
ve
lo
pe
d
m
e
th
ods
i
n
th
is
w
or
k,
a
nd
th
e
pr
e
vi
ous
ly
de
ve
lo
pe
d
m
e
th
ods
i
n
[
31]
, t
o
f
in
d t
he
pa
r
a
m
e
te
r
s
of
a
one
di
ode
P
V
m
ode
l
(
O
D
M
)
f
r
om
e
xpe
r
im
e
nt
a
l
da
ta
.
-
U
s
e
s
ta
ti
s
ti
c
a
l
to
ol
s
to
e
xa
m
in
e
th
e
m
e
th
ods
in
te
r
m
s
o
f
how
m
a
ny
ti
m
e
s
th
e
m
e
th
od
r
e
a
c
he
d
th
e
ta
r
ge
ts
(
T
R
T
)
,
m
a
x
-
min
-
m
e
a
n
of
c
onduc
te
d
it
e
r
a
ti
ons
(
M
M
M
)
,
r
oo
t
m
e
a
n
s
qua
r
e
d
e
r
r
or
(
R
M
S
E
)
,
C
R
,
a
nd
m
a
xi
m
um
a
bs
ol
ut
e
e
r
r
or
(
M
A
E
)
i
n t
he
r
e
s
ul
ts
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
-
8938
I
nt
J
A
r
ti
f
I
nt
e
ll
,
V
ol
.
10
, N
o.
1
,
M
a
r
c
h
20
2
1
:
166
–
174
168
2.
R
E
S
E
A
R
C
H
M
E
T
H
O
D
S
e
ve
r
a
l
r
e
pr
e
s
e
nt
a
ti
ons
w
e
r
e
pr
opos
e
d
to
de
s
c
r
ib
e
th
e
P
V
S
C
.
O
ne
of
th
e
w
id
e
ly
us
e
d
m
ode
l
is
th
e
S
D
M
r
e
pr
e
s
e
nt
e
d i
n F
ig
ur
e
1 a
nd i
s
gi
ve
n i
n
[4
-
5]
. T
he
m
ode
l
r
e
pr
e
s
e
nt
s
t
he
P
V
S
C
by
(
1)
.
=
ℎ
−
(
(
+
)
−
1
)
−
+
ℎ
(
1)
F
ig
ur
e
1
.
O
ne
-
di
ode
m
ode
l
[4
-
5]
W
he
r
e
is
th
e
e
le
c
tr
on
c
ha
r
ge
,
is
th
e
b
ol
tz
m
a
nn’
s
c
on
s
ta
nt
,
is
th
e
te
m
pe
r
a
tu
r
e
in
K
e
lv
in
,
a
nd
is
th
e
vol
ta
ge
of
th
e
P
V
S
C
in
(
)
.
T
he
pa
r
a
m
e
te
r
s
:
ℎ
,
,
,
ℎ
a
nd
a
r
e
unknown
a
nd
a
r
e
n
e
e
de
d
to
b
e
obt
a
in
e
d
ba
s
e
d
on
th
e
c
ur
ve
of
I
-
V
c
ha
r
a
c
te
r
is
ti
c
s
.
O
nc
e
th
e
s
e
pa
r
a
m
e
te
r
s
a
r
e
id
e
nt
if
ie
d,
th
e
e
nt
ir
e
c
e
ll
pe
r
f
or
m
a
nc
e
c
oul
d
be
pr
e
di
c
te
d,
a
nd
th
e
m
a
xi
m
um
pow
e
r
c
oul
d
be
a
c
hi
e
ve
d.
T
he
r
e
f
or
e
,
s
e
ve
r
a
l
w
or
ks
h
a
ve
be
e
n
c
onduc
te
d
to
f
in
d
th
e
s
e
pa
r
a
m
e
te
r
s
a
s
in
[
25
-
32]
.
B
y
r
e
a
r
r
a
ngi
ng
(
1)
,
th
e
obj
e
c
ti
ve
f
unc
ti
on
c
a
n
be
obt
a
in
e
d a
s
[4
-
5]
:
=
√
1
∑
(
−
ℎ
+
(
(
+
)
−
1
)
+
+
ℎ
)
2
=
1
(
2)
W
he
r
e
is
th
e
num
be
r
of
da
ta
a
va
il
a
bl
e
.
T
he
s
ubs
c
r
ip
t
is
a
c
ount
e
r
.
T
he
a
im
is
to
m
in
im
iz
e
s
o
th
a
t
th
e
e
xa
c
t
f
iv
e
pa
r
a
m
e
te
r
s
a
r
e
obt
a
in
e
d
w
h
e
n
=
0
.
F
our
w
e
ll
kn
ow
n
ve
r
s
io
ns
of
P
S
O
a
lg
or
it
hm
s
;
P
S
O
,
P
S
O
A
G
1,
…,
P
S
O
A
G
3,
a
nd
s
ix
ne
w
a
lg
or
it
hm
s
;
P
S
O
A
G
4,
…
,
P
S
O
A
G
9,
a
r
e
us
e
d
in
th
is
w
or
k
to
s
ol
ve
th
e
P
V
S
C
pr
obl
e
m
.
2
.1. I
n
t
r
od
u
c
t
io
n
t
o
P
S
O
P
a
r
ti
c
le
s
w
a
r
m
opt
im
iz
a
ti
on
is
one
of
th
e
m
os
t
f
a
m
ous
m
e
ta
he
ur
is
ti
c
opt
im
iz
a
ti
on
te
c
hni
que
s
.
I
t
s
ta
r
ts
w
it
h
c
hoo
s
in
g
c
a
ndi
da
t
e
s
to
b
e
a
s
ol
ut
io
n
s
e
t
f
or
th
e
pr
ob
le
m
,
r
e
f
e
r
r
e
d
to
a
s
pa
r
ti
c
le
s
,
a
nd
th
e
n
im
pr
ove
th
e
s
e
pa
r
ti
c
le
s
it
e
r
a
ti
ve
ly
to
e
nh
a
nc
e
th
e
pe
r
f
or
m
a
nc
e
.
T
he
pa
r
ti
c
le
s
m
ove
w
it
hi
n
a
s
pa
c
e
tr
yi
ng
to
f
in
d
th
e
s
ol
ut
io
n
in
th
e
ir
lo
c
a
ti
on;
,
or
th
e
b
e
s
t
lo
c
a
ti
on
of
th
e
ne
ig
hbor
hood
w
it
h;
.
E
a
c
h
pa
r
ti
c
le
m
e
m
or
iz
e
s
it
s
pos
it
io
n,
a
nd
it
s
ve
lo
c
it
y,
w
hi
c
h
a
r
e
de
f
in
e
d
f
o
r
pa
r
ti
c
le
s
a
s
=
[
1
2
…
]
,
a
nd
=
[
1
2
…
]
,
r
e
s
pe
c
ti
ve
ly
. T
h
e
s
e
a
r
e
i
ni
ti
a
li
z
e
d r
a
ndoml
y.
T
he
n, t
he
y a
r
e
e
nh
a
nc
e
d us
in
g
[
27
-
31]
:
+
1
=
+
1
×
×
(
−
)
+
2
×
×
(
−
)
(
3)
+
1
=
+
+
1
(
4)
W
he
r
e
is
t
he
i
ne
r
ti
a
l
w
e
ig
ht
a
nd i
t
ha
s
a
va
lu
e
of
[
0.4,0.9]
,
1
a
nd
2
a
r
e
t
he
l
e
a
r
ni
ng c
oe
f
f
ic
ie
nt
of
th
e
in
di
vi
dua
l
a
nd
g
r
oup
be
s
t
s
ol
ut
io
ns
f
ound,
r
e
s
pe
c
ti
ve
ly
,
a
nd
is
a
r
a
ndom
num
be
r
in
[
0,1
]
.
T
he
s
e
c
oe
f
f
ic
ie
nt
s
;
,
1
a
nd
2
,
a
r
e
c
on
s
ta
nt
in
th
e
c
onve
nt
io
na
l
P
S
O
.
H
ow
e
ve
r
,
it
ha
s
be
e
n
f
ound
th
a
t
th
e
pe
r
f
or
m
a
nc
e
be
c
om
e
s
b
e
tt
e
r
w
he
n
th
e
y
a
r
e
ti
m
e
va
r
yi
ng
[
27
-
31]
,
th
is
is
th
e
e
s
s
e
nt
ia
l
m
ot
iv
a
ti
on
f
or
de
ve
lo
pi
ng t
he
ot
he
r
ve
r
s
io
ns
di
s
c
u
s
s
e
d i
n t
hi
s
pa
pe
r
.
2
.2.
P
r
op
os
e
d
al
gor
it
h
m
-
au
t
on
om
ou
s
gr
ou
p
s
P
S
O
I
n
[
31]
,
th
e
a
ut
hor
s
us
e
d
th
e
f
a
c
t
th
a
t
th
e
in
di
vi
dua
ls
a
r
e
not
qui
te
s
im
il
a
r
in
te
r
m
s
of
a
bi
li
ty
or
in
te
ll
ig
e
nc
e
a
lt
hough
th
e
y
do
th
e
ir
dut
ie
s
.
T
he
r
e
f
or
e
,
th
e
y
di
vi
d
e
th
e
s
w
a
r
m
in
to
f
our
gr
oups
,
a
nd
e
a
c
h
gr
oup
ha
s
di
f
f
e
r
e
nt
le
a
r
ni
ng
c
oe
f
f
ic
ie
nt
s
1
a
nd
2
;
s
e
ve
r
a
l
f
unc
ti
ons
a
r
e
us
e
d
s
uc
h
a
s
li
ne
a
r
,
pa
r
a
bol
ic
,
qua
dr
a
ti
c
,
e
xpone
nt
ia
l,
s
in
us
oi
da
l
a
nd
lo
ga
r
it
hm
ic
f
unc
ti
ons
.
T
h
e
s
e
gr
oup
s
a
r
e
c
a
ll
e
d
a
ut
onomous
gr
oup
s
(
A
G
)
,
a
nd
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
A
r
ti
f
I
nt
e
ll
I
S
S
N
:
2252
-
8938
E
s
ti
m
at
in
g one
-
di
ode
-
P
V
m
ode
l
us
in
g autonomous
gr
oups
par
t
ic
le
s
w
ar
m
…
(
M
ohamm
ad A
lS
habi
)
169
m
e
th
od
th
e
y
r
e
pr
e
s
e
nt
i
s
c
a
ll
e
d
P
S
O
A
G
.
F
ig
ur
e
2
s
how
s
th
e
ps
e
udo
-
c
ode
f
or
P
S
O
A
G
.
T
a
bl
e
1
s
how
s
th
e
c
oe
f
f
ic
ie
nt
s
f
or
ni
ne
di
f
f
e
r
e
nt
ve
r
s
io
ns
of
P
S
O
A
G
r
e
f
e
r
r
e
d
to
P
S
O
A
G
1,
P
S
O
A
G
2,
…
P
S
O
A
G
9,
w
he
r
e
th
e
f
ir
s
t
th
r
e
e
a
r
e
de
r
iv
e
d i
n
[
31]
a
nd t
he
r
e
s
t
a
r
e
pr
opos
e
d f
or
t
he
f
i
r
s
t
ti
m
e
i
n t
hi
s
pa
pe
r
.
F
ig
ur
e
2
.
P
s
e
udo
-
c
ode
f
or
P
S
O
A
G
T
a
bl
e
1
.
L
e
a
r
ni
ng c
oe
f
f
ic
ie
nt
s
f
or
t
he
P
S
O
A
G
1, P
S
O
A
G
2 … P
S
O
A
G
9
L
e
a
r
ni
ng C
oe
f
f
i
c
i
e
nt
P
S
O
A
G
#
G
r
oup
1
2
1
[
31]
1
−
2
.
05
+
2
.
55
+
1
.
25
2
−
2
.
05
+
2
.
55
2
3
+
0
.
5
3
−
2
3
+
2
.
5
+
1
.
25
4
−
2
3
+
2
.
5
2
3
+
0
.
5
2
[
31]
1
2
.
5
−
1
0
.
5
+
1
2
−
2
3
+
2
.
5
2
3
+
0
.
5
3
0
.
5
+
2
−
16
2
2
.
2
−
2
−
16
2
4
2
.
5
+
2
2
−
4
0
.
5
−
2
2
+
4
3
[
31]
1
−
2
1
/
3
+
1
.
95
2
1
/
3
+
0
.
05
2
−
2
3
+
2
.
5
2
3
+
0
.
5
3
−
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/
3
+
1
.
95
2
3
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5
4
−
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3
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2
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5
2
1
/
3
+
0
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4
1
−
2
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05
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2
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55
2
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−
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+
4
2
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2
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05
+
2
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55
2
.
2
−
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3
−
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3
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+
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5
2
6
+
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.
5
w
he
r
e
=
/
,
t
is
t
he
i
te
r
a
ti
on numbe
r
c
om
pa
r
e
d t
o t
he
t
ot
a
l
it
e
r
a
ti
ons
T
1
=
2
l
o
g
(
)
l
o
g
(
)
,
1
=
2
.
5
c
o
s
(
2
)
−
16
2
2
=
0
.
5
+
10
s
in
(
/
2
)
−
16
2
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
-
8938
I
nt
J
A
r
ti
f
I
nt
e
ll
,
V
ol
.
10
, N
o.
1
,
M
a
r
c
h
20
2
1
:
166
–
174
170
3.
R
E
S
U
L
T
S
A
N
D
D
I
S
C
U
S
S
I
O
N
S
T
o
e
nr
ic
h
th
e
c
om
pa
r
is
on,
th
e
r
e
s
ul
t
s
of
th
r
e
e
w
e
ll
-
known
ve
r
s
io
ns
of
th
e
ti
m
e
-
va
r
yi
ng
a
c
c
e
l
e
r
a
te
d
c
oe
f
f
ic
ie
nt
P
S
O
w
e
r
e
in
c
lu
de
d;
P
S
O
T
A
C
in
[
27]
,
P
S
O
M
in
[
29]
,
a
nd
P
S
O
I
in
[
30]
.
T
he
s
e
a
lg
or
it
hm
s
a
nd
th
e
a
lg
or
it
hm
s
m
e
nt
io
ne
d
in
s
e
c
ti
on
3
w
e
r
e
te
s
te
d
u
s
in
g
th
e
I
-
V
da
ta
r
e
por
te
d
in
[
31
-
32]
f
or
57
m
m
di
a
m
e
te
r
c
om
m
e
r
c
ia
l
s
il
ic
on
s
ol
a
r
c
e
ll
(
R
.T
.
C
F
r
a
nc
e
)
unde
r
a
n
ir
r
a
di
a
ti
on
of
1000
W
/m
2
a
nd
a
te
m
pe
r
a
tu
r
e
of
33
oC
.
T
he
im
pl
e
m
e
nt
a
ti
on
w
a
s
c
ondu
c
te
d
in
M
a
tl
a
b
e
nvi
r
onm
e
nt
.
T
he
s
i
m
ul
a
ti
on
w
a
s
c
onduc
te
d
1000
ti
m
e
s
,
e
a
c
h
ti
m
e
i
t
la
s
te
d f
or
1000
i
te
r
a
ti
ons
. T
he
s
im
ul
a
ti
on w
a
s
r
un f
or
20
, 50, 100, 500, 750 a
nd 1000
pa
r
ti
c
le
s
/Age
nt
s
.
A
c
om
pr
e
he
ns
iv
e
c
om
pa
r
is
on
i
s
m
a
d
e
in
te
r
m
s
of
pr
e
s
e
nt
R
M
S
E
,
M
A
E
of
th
e
f
in
a
l
it
e
r
a
ti
on,
th
e
C
R
to
r
e
a
c
h
R
M
S
E
of
1.25%
a
nd 2.5%
, a
nd
th
e
r
e
qui
r
e
d s
im
ul
a
ti
on
ti
m
e
. T
he
be
s
t
te
n r
e
s
ul
ts
a
r
r
a
nge
d i
n a
s
c
e
ndi
ng or
de
r
a
r
e
s
how
n i
n T
a
bl
e
2. F
ig
ur
e
3 s
how
s
t
he
pe
r
f
o
r
m
a
nc
e
of
a
ll
P
S
O
A
G
s
a
t
popula
ti
on
of
250 a
ge
nt
s
. T
he
C
R
i
s
s
how
n
in
F
ig
ur
e
4
f
or
a
ll
th
e
a
lg
or
it
hm
s
a
t
th
r
e
e
di
f
f
e
r
e
nt
a
ge
nt
s
’
num
be
r
;
20,
250
a
nd
1000
a
ge
nt
s
.
T
h
e
be
s
t
c
a
ndi
da
te
w
a
s
f
ound
to
be
P
S
O
A
G
8
a
s
it
ha
s
th
e
f
a
s
te
s
t
C
R
w
it
h
m
in
im
um
M
A
E
a
nd
one
of
th
e
m
in
im
um
R
M
S
E
. F
ig
ur
e
5 s
how
s
t
he
r
e
s
ul
ts
of
P
S
O
A
G
8 a
t
di
f
f
e
r
e
nt
pop
ul
a
ti
ons
;
20, 250 a
nd 1000 a
ge
n
ts
.
I
nc
r
e
a
s
in
g
th
e
a
ge
nt
/p
a
r
ti
c
le
num
be
r
im
pr
ove
s
th
e
pe
r
f
or
m
a
nc
e
a
s
e
xp
e
c
te
d
f
r
om
m
e
ta
he
ur
is
ti
c
te
c
hni
que
s
. T
hi
s
c
a
n be
dr
a
w
n f
r
om
c
om
pa
r
in
g t
he
pe
r
f
o
r
m
a
nc
e
s
a
t
20 a
ge
nt
s
t
o 1000 a
ge
nt
s
. T
h
e
R
M
S
E
a
nd
M
A
E
a
r
e
r
e
duc
e
d by 70
-
87
%
w
he
n t
he
popula
ti
on i
nc
r
e
a
s
e
d. T
he
s
a
m
e
w
a
s
obs
e
r
ve
d f
or
t
he
C
R
s
i
n F
ig
ur
e
4
a
nd T
a
bl
e
2, a
s
t
he
y w
e
r
e
r
e
duc
e
d by (
up t
o)
32%
a
nd 55
%
f
o
r
th
e
c
onve
r
ge
nc
e
t
o R
M
S
E
w
it
h va
lu
e
s
of
0.01
a
nd
0.02,
r
e
s
pe
c
ti
ve
ly
.
M
or
e
ove
r
,
th
e
s
ta
bi
li
ty
of
th
e
m
e
th
od
w
a
s
im
pr
ove
d
a
s
w
e
ll
.
B
a
s
e
d
on
F
ig
ur
e
5,
e
a
c
h
a
lg
or
it
hm
ga
ve
a
lm
os
t
th
e
s
a
m
e
r
e
s
ul
ts
w
he
n
it
w
a
s
r
e
pe
a
te
d
1
000
ti
m
e
s
w
it
h
popula
ti
on
o
f
1000
a
ge
nt
s
;
th
e
va
r
ia
ti
on
box
be
c
a
m
e
s
m
a
ll
e
r
in
F
ig
ur
e
5(
c
)
c
om
pa
r
e
d
t
o
F
ig
ur
e
5(
a
)
-
(
b)
.
O
n
th
e
ot
he
r
ha
nd,
th
e
c
om
put
a
ti
ona
l
ti
m
e
be
c
a
m
e
s
ig
ni
f
ic
a
nt
ly
la
r
ge
;
e
.g.
f
or
1000
a
ge
nt
s
,
th
e
r
e
qui
r
e
d
ti
m
e
w
a
s
a
lm
os
t
28
-
41
ti
m
e
s
t
he
r
e
qui
r
e
d t
im
e
f
or
20 a
ge
nt
s
a
nd 17
-
30 t
im
e
s
t
he
r
e
qui
r
e
d t
im
e
f
or
250 a
ge
nt
s
.
T
he
r
e
s
ul
ts
s
how
e
d
th
a
t
di
vi
di
ng
th
e
popula
ti
on
in
to
gr
o
ups
w
it
h
di
f
f
e
r
e
nt
s
o
c
ia
l
be
h
a
vi
or
s
im
pr
ove
d
th
e
pe
r
f
o
r
m
a
nc
e
.
A
c
c
or
di
ng
to
[
27,
29
-
36]
,
s
om
e
a
ppl
ic
a
ti
ons
r
e
qui
r
e
d
c
e
r
ta
in
s
ym
m
e
tr
ic
s
oc
ia
l
f
unc
ti
ons
,
w
hi
le
ot
he
r
s
r
e
qui
r
e
d
a
s
ym
m
e
tr
ic
s
oc
ia
l
f
unc
ti
ons
.
B
y
di
vi
di
ng
th
e
popula
ti
on
in
to
gr
oups
,
e
a
c
h
gr
oup c
oul
d be
a
s
s
ig
ne
d
to
a
di
f
f
e
r
e
nt
f
unc
ti
on. M
ix
in
g
th
e
s
e
f
unc
ti
ons
f
or
t
he
s
a
m
e
a
ppl
ic
a
ti
on i
m
pr
ove
d t
he
a
lg
or
it
hm
pe
r
f
or
m
a
nc
e
in
te
r
m
s
of
s
ta
bi
li
ty
,
C
R
,
R
M
S
E
,
a
nd
M
A
E
.
T
ha
t
w
a
s
b
e
c
a
u
s
e
th
e
a
ppl
ic
a
ti
on
c
oul
d
r
e
ly
on i
ts
pr
e
f
e
r
r
e
d f
unc
ti
on.
T
he
r
e
s
ul
ts
of
T
a
bl
e
2 s
ho
w
e
d t
ha
t
be
s
t
r
e
s
ul
ts
f
or
m
ode
li
ng t
he
da
ta
l
is
te
d i
n
[
31
-
32]
c
oul
d be
obt
a
in
e
d us
in
g
a
ut
onomous
gr
oups
w
it
h s
ym
m
e
tr
ic
a
nd a
s
ym
m
e
tr
ic
pow
e
r
f
unc
ti
ons
a
s
s
oc
i
a
l
le
a
r
ni
ng c
oe
f
f
ic
ie
nt
s
. T
hi
s
w
a
s
obs
e
r
ve
d
by
tr
a
c
ki
ng
th
e
be
s
t
p
e
r
f
or
m
a
nc
e
,
w
hi
c
h
w
a
s
a
c
hi
e
ve
d
by
P
S
O
A
G
3
a
nd
P
S
O
A
G
8.
T
he
s
e
two
m
e
th
ods
s
how
e
d
s
im
il
a
r
pe
r
f
or
m
a
nc
e
s
in
te
r
m
s
of
R
M
S
E
a
n
d
M
A
E
w
he
n
th
e
num
be
r
of
popula
ti
ons
w
a
s
hi
gh;
i.
e
.
a
bove
500
a
ge
nt
s
.
A
s
th
e
popula
ti
on’
s
s
iz
e
de
c
r
e
a
s
e
d,
P
S
O
A
G
8
be
c
a
m
e
be
tt
e
r
th
a
n
P
S
O
A
G
3,
w
he
r
e
th
e
R
M
S
E
a
nd
M
A
E
of
P
S
O
A
G
8
w
e
r
e
13.6%
a
nd
13.9%
s
m
a
ll
e
r
th
a
n
th
e
ir
c
or
r
e
s
ponding
va
lu
e
s
f
or
P
S
O
A
G
3,
r
e
s
pe
c
ti
ve
ly
.
O
n
th
e
ot
he
r
ha
nd,
P
S
O
A
G
8
ha
d
a
C
R
th
a
t
w
a
s
2
-
20%
f
a
s
te
r
th
a
n
P
S
O
A
G
3
in
a
ll
te
s
ts
e
xc
e
pt
f
or
t
he
te
s
t
w
it
h popula
ti
on s
iz
e
of
250, whe
r
e
i
t
w
a
s
s
lo
w
e
r
by up to 5.5%
.
T
he
r
e
f
or
e
,
if
c
om
put
a
ti
ona
l
ti
m
e
is
not
im
por
ta
nt
,
th
e
n
P
S
O
A
G
8
a
nd
P
S
O
A
G
3
w
it
h
1000 a
ge
nt
s
a
r
e
th
e
be
s
t
c
a
ndi
da
te
s
.
H
ow
e
ve
r
,
if
th
e
c
om
put
a
ti
ona
l
ti
m
e
is
im
p
or
ta
nt
a
s
w
e
ll
a
s
th
e
e
r
r
or
,
t
he
n
P
S
O
A
G
8
w
it
h
250
a
ge
nt
s
is
th
e
be
s
t
c
a
ndi
da
te
.
T
he
c
hoi
c
e
of
250
a
ge
nt
s
is
il
lu
s
tr
a
te
d
in
F
ig
ur
e
5.
W
it
hout
lo
s
in
g
ge
ne
r
a
li
ty
,
P
S
O
A
G
8
gi
ve
s
th
e
be
s
t
r
e
s
ul
ts
c
om
pa
r
e
d
to
ot
he
r
t
e
c
hni
que
s
;
e
.g.
F
ig
ur
e
3
s
how
s
th
e
s
upe
r
io
r
it
y
of
P
S
O
A
G
8 a
m
ong the
ot
he
r
s
f
o
r
250 a
ge
nt
s
. T
he
r
e
f
or
e
, i
t
w
a
s
s
e
le
c
te
d i
n t
hi
s
w
or
k.
T
a
bl
e
2
.
C
om
pa
r
is
on b
e
twe
e
n a
ll
P
S
O
ve
r
s
io
ns
i
n
a
s
c
e
ndi
ng or
de
r
(
onl
y t
he
f
ir
s
t
10)
R
M
S
E
I
N
F
I
N
A
L
S
O
L
M
A
E
I
N
F
I
N
A
L
S
O
L
C
O
N
V
<0.02
C
O
N
V
<0.01
A
ge
nt
M
e
a
n
A
ge
nt
M
e
a
n
A
ge
nt
M
e
a
n
A
ge
nt
M
e
a
n
P
S
O
A
G
3
1000
0.0132
P
S
O
A
G
8
1000
0.011
P
S
O
A
G
8
1000
406.3
P
S
O
A
G
8
1000
662.6
P
S
O
A
G
8
1000
0.0135
P
S
O
A
G
3
1000
0.011
P
S
O
A
G
8
750
453.8
P
S
O
A
G
8
750
705.6
P
S
O
A
G
8
750
0.0147
P
S
O
A
G
8
750
0.012
P
S
O
A
G
3
1000
487.8
PSO
1000
750.0
P
S
O
A
G
3
750
0.0147
P
S
O
A
G
3
750
0.012
P
S
O
A
G
7
1000
497.7
P
S
O
A
G
8
500
757.7
P
S
O
A
G
3
500
0.0163
P
S
O
A
G
3
500
0.014
P
S
O
A
G
2
1000
510.2
PSO
750
770.7
P
S
O
A
G
8
500
0.0169
P
S
O
A
G
8
500
0.014
P
S
O
T
A
C
1000
516.4
P
S
O
A
G
3
1000
776.6
P
S
O
A
G
2
1000
0.0174
P
S
O
A
G
2
1000
0.015
P
S
O
A
G
8
500
526.3
P
S
O
A
G
3
750
805.0
P
S
O
A
G
7
1000
0.0181
P
S
O
A
G
7
1000
0.015
P
S
O
A
G
3
750
537.8
P
S
O
T
A
C
1000
814.0
P
S
O
T
A
C
1000
0.0188
P
S
O
T
A
C
1000
0.016
P
S
O
A
G
7
750
546.1
P
S
O
A
G
2
1000
819.7
P
S
O
A
G
8
250
0.0200
P
S
O
A
G
8
250
0.017
P
S
O
T
A
C
750
548.1
P
S
O
A
G
8
250
823.4
P
S
O
A
G
7
750
0.0205
P
S
O
A
G
7
750
0.017
P
S
O
A
G
2
750
566.5
PSO
500
824.7
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
A
r
ti
f
I
nt
e
ll
I
S
S
N
:
2252
-
8938
E
s
ti
m
at
in
g one
-
di
ode
-
P
V
m
ode
l
us
in
g autonomous
gr
oups
par
t
ic
le
s
w
ar
m
…
(
M
ohamm
ad A
lS
habi
)
171
(
a
)
(
b)
(
c
)
(
d)
(
e
)
(f)
(
g)
(
h)
(
i)
(
j)
F
ig
ur
e
3
.
C
om
pa
r
is
on be
twe
e
n P
S
O
ve
r
s
io
ns
a
t
250
a
g
e
nt
s
, (
a
)
K
e
y F
ig
ur
e
t
o r
e
pr
e
s
e
nt
t
he
s
ta
ti
s
ti
c
a
l
a
na
ly
s
is
gr
a
phi
c
a
ll
y, (
b)
P
S
O
A
G
1, (
c
)
P
S
O
A
G
2,
(
d)
P
S
O
A
G
3, (
e
)
P
S
O
A
G
4, (
f
)
P
S
O
A
G
5, (
g
)
P
S
O
A
G
6, (
h)
PSO
A
G
7, (
i)
P
S
O
A
G
8, a
nd (
j
)
P
S
O
A
G
9
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
-
8938
I
nt
J
A
r
ti
f
I
nt
e
ll
,
V
ol
.
10
, N
o.
1
,
M
a
r
c
h
20
2
1
:
166
–
174
172
F
ig
ur
e
4
.
C
onve
r
ge
nc
e
r
a
te
of
a
ll
P
S
O
ve
r
s
io
ns
f
or
20, 250, a
nd 1000 Age
nt
s
(
a
)
(
b)
(
c
)
F
ig
ur
e
5
.
C
om
pa
r
is
on be
twe
e
n P
S
O
A
G
8 a
t
di
f
f
e
r
e
nt
a
ge
nt
s
’
numbe
r
, (
a
)
2
0, (
b)
250, a
nd (
c
)
1000 Age
nt
s
4.
C
O
N
C
L
U
S
I
O
N
I
n
th
is
pa
pe
r
,
s
e
ve
r
a
l
m
odi
f
ie
d
ve
r
s
io
ns
of
a
ut
onomous
gr
oupi
ng
P
S
O
w
e
r
e
p
r
opos
e
d.
T
he
s
e
ve
r
s
io
ns
w
e
r
e
in
s
pi
r
e
d
by
th
e
di
ve
r
s
it
y
of
in
te
ll
e
c
tu
a
l
a
bi
li
ty
f
or
in
di
vi
dua
ls
in
th
e
ir
c
ol
oni
e
s
.
T
o
e
va
lu
a
te
th
e
pe
r
f
or
m
a
nc
e
of
th
e
a
lg
or
it
hm
s
,
th
e
I
-
V
da
ta
w
a
s
u
s
e
d
.
T
h
e
r
e
s
ul
ts
w
e
r
e
c
om
pa
r
e
d
in
te
r
m
s
of
R
M
S
E
,
M
A
E
,
C
R
to
R
M
S
E
va
lu
e
s
of
0.02
a
nd
0.01,
a
nd
th
e
s
im
ul
a
ti
on
ti
m
e
.
F
or
be
tt
e
r
c
om
pa
r
is
ons
,
th
e
s
e
r
e
s
ul
ts
w
e
r
e
c
om
pa
r
e
d
to
ne
w
ly
de
ve
lo
pe
d
m
e
th
ods
;
i.
e
.
P
S
O
T
A
C
,
P
S
O
M
a
nd
P
S
O
I
.
T
he
r
e
s
ul
ts
s
how
e
d
th
a
t
P
S
O
A
G
8
w
a
s
t
he
be
s
t
c
a
ndi
da
te
a
s
it
ha
d
th
e
f
a
s
te
s
t
C
R
,
a
nd
one
of
th
e
m
in
im
um
R
M
S
E
a
nd
M
A
E
c
om
pa
r
e
d
to
ot
he
r
a
lg
or
it
hm
s
.
I
t
ga
ve
be
tt
e
r
pe
r
f
or
m
a
nc
e
in
t
e
r
m
s
of
R
M
S
E
a
nd
M
A
E
c
om
pa
r
e
d
to
th
e
a
ut
onomous
pa
r
ti
c
le
s
gr
oups
f
or
P
S
O
w
he
n
popula
ti
on
w
a
s
of
s
iz
e
500
or
le
s
s
.
T
he
s
e
va
lu
e
s
de
c
r
e
a
s
e
d
by
up
to
14%
.
M
or
e
ov
e
r
,
th
e
pr
opos
e
d
a
lg
or
it
hm
s
how
e
d
up
to
20%
f
a
s
te
r
C
R
c
om
pa
r
e
d
to
th
e
a
ut
onomous
p
a
r
ti
c
le
s
gr
oup
s
f
or
P
S
O
a
lg
or
it
hm
. M
or
e
f
unc
ti
ons
w
il
l
be
e
xpl
or
e
d i
n t
he
f
ut
ur
e
f
or
t
he
s
oc
ia
l
c
oe
f
f
ic
ie
nt
s
’
be
ha
vi
or
.
R
E
F
E
R
E
N
C
E
S
[1]
M.
Kermadi
and
E.
M.
Berkouk,
“Artificial
intelligence
-
based
ma
ximum
power
point
tracking
controllers
for
Photovolta
ic
systems:
Compara
tive
study,”
Renew.
Sustain.
En
ergy
Rev.
,
vol.
69,
pp.
369
-
386,
2
017
.
https://doi.org/10.1016/j.rser.2016.11.125.
[2]
R.
C.
M.
Gomes,
M.
A.
Vitorino,
M.
B.
de
Rossiter
Correa,
D.
A.
F
ernandes,
and
R.
Wang,
“Shuffled
Complex
Evolution
on
Photovoltaic
Paramet
er
Extraction:
A
Comparative
An
alysis,”
IEEE
Trans.
Sustain.
Energy
,
vol.
8,
no. 2, pp. 805
-
815, Apr. 2017.
DOI: 10.1109/TS
TE.2016.2620941
.
[3]
V. J. Chin,
Z.
Salam, and K.
Ishaque, “Cell mod
elling
and model para
meters estimatio
n techniques for phot
ovoltai
c
simulator
application:
A
review,”
Appl.
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,
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-
519,
2015
.
https://doi.org/10.1016/j.apenergy.2015.05.035.
[4]
R.
Abbassi,
A.
Abbassi,
M.
Jemli,
and
S.
Chebbi,
“Identification
of
unknown
parameters
of
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