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[
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[
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[
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T
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[
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8]
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12
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.
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[
13]
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15]
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[
18]
,
[
19
]
.
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20]
.
A
c
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22]
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23]
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[
22]
,
[
23]
.
T
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5)
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m
i
n
)
(
I
m
ax
−
I
c
u
r
r
en
t
I
m
ax
)
(
5)
w
h
e
r
e
t
h
e
n
u
m
e
r
i
c
v
a
l
ue
o
f
i
ne
r
t
i
a
ω
m
i
n
i
s
e
qua
l
t
o
0.
4
t
h
a
t
r
e
pr
e
s
e
n
t
s
m
a
ll
e
s
t
v
a
l
ue
a
n
d
t
h
e
v
a
l
ue
o
f
ω
m
a
x
i
s
e
qua
l
to
0
.
9
t
h
a
t
i
s
e
x
t
r
e
m
e
v
a
l
ue
o
f
i
n
e
r
t
i
a
we
i
gh
t
.
s
y
m
b
o
l
I
m
a
x
a
n
d
I
c
u
r
r
e
nt
a
r
e
m
a
xim
u
m
a
n
d
c
ur
r
e
n
t
n
u
m
be
r
o
f
i
t
e
r
a
t
i
o
n
c
o
r
r
e
s
po
n
d
i
n
g
l
y
.
P
r
e
s
e
n
t
e
d
a
n
un
de
t
e
r
m
i
ne
d
i
ne
r
t
i
a
we
i
g
h
t
v
a
l
ue
f
o
r
t
r
a
c
ki
n
g
c
ha
n
g
i
n
g
e
nvi
r
o
nm
e
n
t
s
[
24
]
,
[
25
]
.
T
h
e
f
o
l
l
o
w
i
n
g
e
qua
t
i
o
n
de
s
c
r
i
be
s
h
o
w
ω
f
l
uc
t
ua
t
e
s
r
a
n
doml
y
a
s
(
6)
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
do
n
e
s
i
a
n
J
E
l
e
c
E
n
g
&
C
o
m
p
S
c
i
I
S
S
N:
2
5
0
2
-
4
7
52
P
ar
ame
te
r
tuni
ng
f
or
e
nhanc
ing
pe
r
f
or
manc
e
o
f
a
v
ar
iant
of
par
ti
c
le
s
w
a
r
m
opti
miz
ati
on
…
(
A
s
hok
K
umar
)
1255
ω
=
0
.
5
+
r
2
(
6)
wh
e
r
e
t
h
e
s
ym
b
o
l
r
de
n
o
t
e
s
a
uni
f
o
r
m
ly
d
i
s
t
r
i
b
ut
e
d
r
a
n
do
m
n
u
m
be
r
b
e
t
we
e
n
0
a
n
d
1.
A
t
t
h
e
b
e
g
i
nn
i
ng
o
f
t
h
e
o
pt
i
m
i
z
a
t
i
o
n
pr
o
c
e
s
s
,
t
h
e
P
S
O
-
T
VA
C
m
e
t
h
o
d
a
i
m
s
t
o
i
m
pr
o
v
e
t
h
e
e
x
p
l
o
r
a
t
i
o
n
wor
l
dw
i
d
e
;
a
t
t
h
e
e
n
d
o
f
t
he
s
e
a
r
c
h
,
i
t
e
n
c
o
ur
a
ge
s
a
ll
pa
r
t
i
c
l
e
s
t
o
m
e
e
t
to
wa
r
ds
t
h
e
w
o
r
l
dw
i
de
o
p
t
i
m
u
m
.
T
h
e
f
o
ll
o
w
i
ng
e
qua
t
i
o
ns
de
t
e
r
m
i
ne
h
o
w
t
h
e
we
i
g
h
t
o
f
i
ne
r
t
i
a
,
t
h
e
c
o
e
f
f
i
c
i
e
n
t
o
f
c
o
gni
t
i
v
e
a
c
c
e
l
e
r
a
t
i
o
n
,
a
n
d
t
h
e
c
o
e
f
f
i
c
i
e
n
t
o
f
s
o
c
i
a
l
a
c
c
e
l
e
r
a
t
i
o
n
e
v
o
l
ve
i
n
t
hi
s
a
l
go
r
i
t
hm
[
26]
-
[
28]
:
c
1
=
c
1
m
i
n
+
(
c
1
m
a
x
−
c
1
m
i
n
)
(
I
m
ax
−
I
c
u
r
r
en
t
I
m
ax
)
(
7)
c
2
=
c
2
m
a
x
+
(
c
2
m
i
n
-
c
2
m
a
x
)
(
I
m
ax
-
I
c
u
r
r
en
t
I
m
ax
)
(
8)
ω
=
ω
m
i
n
+
(
ω
m
a
x
-
ω
m
i
n
)
(
I
m
ax
-
I
c
u
r
r
en
t
I
m
ax
)
(
9)
W
h
e
r
e
t
h
e
v
a
l
ue
o
f
c
1
m
i
n
i
s
e
qua
l
t
o
0.
5
t
h
a
t
i
s
mi
n
i
mu
m
v
a
l
ue
o
f
c
1
a
n
d
t
h
e
v
a
l
ue
o
f
c
1
m
a
x
i
s
e
qua
l
t
o
2
.
5
t
h
a
t
i
s
m
a
xim
u
m
v
a
l
ue
o
f
c
2
.
whi
l
e
t
h
e
v
a
l
e
o
f
c
2
m
i
n
i
s
e
qua
l
to
2.
5
t
h
a
t
i
s
m
i
nim
u
m
va
l
u
e
o
f
c
2
a
n
d
t
h
e
v
a
l
ue
o
f
c
2
m
a
x
is
2.
5
t
h
a
t
i
s
m
a
xim
u
m
v
a
l
ue
o
f
c
2
.
T
h
e
a
l
go
r
i
t
hm
's
pe
r
f
o
r
m
a
n
c
e
i
s
e
nh
a
n
c
e
d
by
c
h
a
n
g
i
ng
c
1
f
r
o
m
2.
5
to
0.
5
,
c
2
f
r
o
m
0.
5
to
2.
5
,
a
n
d
ω
f
r
o
m
0.
9
to
0
.
4
o
v
e
r
t
h
e
s
e
a
r
c
h
s
pa
c
e
.
T
h
e
wo
r
k
p
r
o
vi
d
e
s
a
m
o
r
e
c
o
m
p
l
e
t
e
kn
o
w
l
e
dge
o
f
P
S
O
b
e
h
a
vi
o
r
a
n
d
pe
r
f
o
r
m
a
n
c
e
u
n
de
r
a
va
r
i
e
t
y
o
f
e
nvi
r
o
nm
e
n
t
a
l
s
i
t
ua
t
i
o
n
s
.
T
h
e
s
ugge
s
t
e
d
t
e
c
h
ni
que
m
a
ke
s
t
h
e
f
o
l
l
o
w
i
ng
ke
y
c
o
n
t
r
i
b
ut
i
o
ns
:
De
t
e
r
m
i
ne
t
h
e
b
e
s
t
a
n
s
we
r
i
n
a
m
i
n
im
u
m
n
u
m
be
r
o
f
ge
ne
r
a
t
i
o
ns
.
Opt
i
mi
z
e
i
r
r
e
gu
l
a
r
pa
r
a
m
e
t
e
r
s
to
e
s
c
a
pe
f
r
o
m
l
o
c
a
l
o
p
t
i
m
a
.
As
s
e
s
s
d
i
ve
r
s
e
s
o
l
ut
i
o
n
t
h
r
o
ugh
P
r
o
pe
r
t
uni
n
g
o
f
r
a
n
do
m
pa
r
a
m
e
t
e
r
s
.
2.
M
E
T
HO
D
2.
1.
M
at
h
e
m
at
ical
an
al
ys
is
A
c
c
e
l
e
r
a
t
i
o
n
i
s
a
v
e
c
tor
te
r
m
t
h
a
t
i
n
d
i
c
a
tes
t
h
e
r
a
te
a
t
whi
c
h
a
s
ub
s
tan
c
e
c
h
a
n
ge
s
i
t
s
v
e
l
oc
i
t
y
a
n
d
gi
v
e
n
by
t
h
e
e
q
ua
t
i
o
n
a
=
(
v
−
u
)
/
t
,
w
h
e
r
e
di
s
p
l
a
c
e
m
e
n
t
i
n
n
t
h
s
e
c
o
n
d
i
s
g
i
v
e
n
by
t
h
e
e
qua
t
i
o
n
,
s
n
=
d
n
−
d
n
−
1
W
h
e
r
e
th
e
s
y
m
b
o
l
d
n
a
n
d
d
n
−
1
b
e
i
n
g
hi
s
di
s
p
l
a
c
e
m
e
n
t
p
o
s
i
t
i
o
n
o
f
p
a
r
t
i
c
l
e
a
t
n
a
n
d
n
-
1
th
s
e
c
o
n
d
r
e
s
p
e
c
t
i
v
e
l
y
.
P
a
r
t
i
c
l
e
a
c
c
e
l
e
r
a
t
i
o
n
b
a
s
e
d
P
S
O
(
P
A
-
P
S
O
)
i
n
tr
od
uc
e
s
t
h
e
f
o
l
l
o
wi
n
g
m
o
di
f
i
c
a
t
i
o
n
o
v
e
r
or
i
gi
n
a
l
P
S
O:
A
c
c
e
l
e
r
a
t
i
o
n
m
a
t
r
i
x
o
f
pa
r
t
i
c
l
e
s
a
r
e
c
a
l
c
u
l
a
t
e
d
a
s
f
o
l
l
o
ws
:
A.
I
ni
t
i
a
l
i
z
e
i
ni
t
i
a
l
ve
l
o
c
i
t
y
u
i
d
m
a
t
r
i
x
w
i
t
h
c
ur
r
e
n
t
v
e
lo
c
i
t
y
m
a
t
r
i
x
v
id
.
u
id
t
=
v
id
t
(
10)
B.
Ve
l
o
c
i
t
y
m
a
t
r
i
x
o
f
pa
r
t
i
c
l
e
s
a
r
e
upda
t
e
d
by
us
i
ng
th
e
v
e
l
o
c
i
t
y
e
qu
a
t
i
o
n
o
f
b
a
s
i
c
P
S
O
w
i
t
h
v
a
l
ue
o
f
c
1
, c
2
a
n
d
ω
i
s
a
d
j
us
t
i
n
g
a
c
c
o
r
di
n
g
t
o
P
S
O
-
T
VA
C
:
v
id
t
+
1
=
ω
.
v
id
t
+
c
1
.
r
1
.
(
P
id
−
x
id
t
)
+
c
2
.
r
2
.
(
P
gd
−
x
id
t
)
(
11)
C.
C
a
l
c
u
l
a
t
i
o
n
o
f
a
c
c
e
l
e
r
a
t
i
o
n
m
a
t
r
i
x
:
a
id
t
+
1
=
v
id
t
−
u
id
t
(
12)
Af
t
e
r
c
a
l
c
u
l
a
t
i
n
g
a
c
c
e
l
e
r
a
t
i
o
n
po
s
i
t
i
o
n
o
f
s
wa
r
m
i
s
c
a
l
c
u
l
a
t
e
d
by
us
i
ng
t
h
e
s
e
c
o
n
d
e
qua
t
i
o
n
o
f
m
o
t
i
o
n
a
s
f
o
l
l
o
ws
:
x
id
t
+
1
=
x
id
t
+
v
id
t
+
1
+
a
id
t
+
1
/
(
2
∗
(
t
+
1
)
)
(
13)
2.
2
.
P
r
op
os
e
d
P
A
-
P
S
O
al
go
r
it
h
m
A
ne
w
pa
r
a
m
e
t
e
r
a
c
c
e
l
e
r
a
t
i
o
n
to
pa
r
t
i
c
l
e
i
s
f
o
und
o
u
t
a
f
t
e
r
t
h
a
t
p
o
s
i
t
i
o
n
o
f
pa
r
t
i
c
l
e
i
s
upda
t
e
d
by
us
i
n
g
t
h
e
s
e
c
o
n
d
e
qua
t
i
o
n
o
f
m
o
t
i
o
n
.
Input:
P
opulation
size
(pop), dimension (dim), fitness function f(x) with its constraints
and maximum iteration
(I
max
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2
5
0
2
-
4
7
52
I
n
do
n
e
s
i
a
n
J
E
l
e
c
E
n
g
&
C
o
m
p
S
c
i
,
Vo
l
.
36
,
N
o
.
2
,
N
o
v
e
m
b
e
r
20
24
:
1
253
-
1
260
1256
Output:
Function f(x)'s optimal fitness value and the particle's location at which it
occurs
.
The proposed algorithm
PA
-
PSO
includes the steps listed below
:
1.
Create
a
position
matrix
x
id
of
order
pop
by
dim
and
initialize
it
with
random
number
s
within search space.
2.
Create
a
velocity
matrix
v
id
of
order
pop
by
dim
and
initialize
it
with
random
number
s
between 0 and 1.
3.
Calculate fitness vector f (
x
id
).
4.
Create vec
tor personal best
P
id
and initialize it with fitness vector.
5.
Set the parameters' initial values to
c
1
min
=
c
2
min
= 0.5 and
c
1
ma
x
=
c
2
ma
x
= 2.5 and
ω
min
=
0.4 and
ω
ma
x
= 0.9.
6.
For
iteration
t = 1 to I
max
7.
Configure the al
gorithm's parameters as follows (7)
-
(9
)
8.
For id = 1 to pop.
9.
Find Personal best
P
id
and Global best
P
gd
If
f (
x
id
)
<
P
id
P
id
=
x
id
10.
Find
Global
best
P
gd
If
f (
x
id
)
<
P
gd
P
gd
=
x
id
11.
Initialize initial velocity of
particle
as (10)
12.
Utilize the velocity vector equation to update the particle's
velocity
as (11)
13.
Calculate Acc
eleration of particle
as (12)
14.
Update the position of particle
by the position vector
as (13)
15.
Repeat
7
-
12 s
tep
s
(id becomes equal to pop).
16.
Repeat
6
-
14
step (t becomes equal to I
max
).
17.
Obtain global best position
.
3.
RE
S
UL
T
AN
D
DI
S
CU
S
S
I
ON
T
h
e
pr
o
p
o
s
e
d
P
A
-
P
S
O
m
e
t
h
o
d
i
s
c
o
m
pa
r
e
d
to
t
h
e
pr
i
o
r
P
S
O
-
T
VA
C
a
l
go
r
i
t
hm
u
s
i
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[
1]
G
. D
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nt
z
ig
,
L
in
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ar
pr
ogr
am
m
in
g and e
x
te
n
s
io
ns
. R
A
N
D
C
o
r
por
a
ti
o
n, 2018.
[
2]
I
. R
e
c
he
nb
e
r
g, “
E
vo
lu
ti
o
ns
s
tr
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te
gi
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s
i
n c
o
mpu
ta
ti
o
na
l
in
te
ll
ig
e
nc
e
,”
F
r
om
m
ann H boog, Stutt
gar
t
, 1994.
[
3]
A
.
K
uma
r
,
B
.
K
uma
r
,
a
nd
B
.
D
.,
“
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:
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s
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ir
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o
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r
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J
our
nal
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C
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put
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r
A
ppl
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at
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ns
, v
o
l.
135, n
o
. 5, pp. 24
–
30,
F
e
b. 201
6, do
i:
10.5120/i
jc
a
2016908406.
[
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D
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put
e
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e
ngi
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r
in
g de
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Evaluation Warning : The document was created with Spire.PDF for Python.
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i
a
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J
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r
m
opti
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…
(
A
s
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K
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)
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a
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G
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e
e
di
ng
p
o
pul
a
ti
o
ns
of
c
o
mput
e
r
pr
o
g
r
a
ms
to
s
o
l
ve
pr
o
bl
e
ms
in
a
r
ti
f
i
c
ia
l
in
t
e
ll
ig
e
n
c
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,”
in
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P
r
oc
e
e
di
ngs
of
th
e
2nd
I
nt
e
r
nat
io
nal
I
E
E
E
C
onf
e
r
e
nc
e
on
T
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H
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ge
n
e
ti
c
a
lg
o
r
it
hms
,”
C
onne
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ls
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“
I
nt
e
ll
ig
e
nt
d
e
c
is
i
on
ma
ki
ng
th
r
o
ugh
a
s
im
ul
a
ti
o
n
of
e
vo
lu
ti
o
n.,”
B
e
hav
io
r
al
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c
ie
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e
,
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J
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ti
o
n
in
na
tu
r
a
l
a
nd
a
r
t
i
f
i
c
ia
l
s
y
s
t
e
ms
,”
A
nn
A
r
bor
:
T
he
U
ni
v
e
r
s
it
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M
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,
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M
a
ni
e
z
z
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,
“
D
is
tr
ib
ut
e
d
o
pt
i
mi
z
a
ti
o
n
b
y
a
nt
c
o
l
o
ni
e
s
,”
I
n
P
r
oc
e
e
di
ngs
o
f
th
e
f
i
r
s
t
E
ur
o
pe
an
c
onf
e
r
e
nc
e
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ti
f
ic
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A
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S
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l
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s
w
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m
o
pt
im
i
z
a
ti
o
n,”
in
T
he
I
ndus
tr
ia
l
E
le
c
tr
oni
c
s
H
andbook
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F
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Se
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J
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y
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ti
c
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s
w
a
r
m:
S
oc
ia
l
a
da
pt
a
ti
o
n
of
kn
o
w
l
e
dge
,”
in
P
r
oc
e
e
di
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of
th
e
I
E
E
E
C
onf
e
r
e
n
c
e
on
E
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ut
io
nar
y
C
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R
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“
N
e
w
o
pt
im
i
z
e
r
us
in
g
pa
r
ti
c
l
e
s
w
a
r
m
th
e
or
y
,”
in
P
r
oc
e
e
di
ngs
of
th
e
I
nt
e
r
nat
io
nal
Sy
m
pos
iu
m
on
M
ic
r
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ac
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Y
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M
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d
i
f
i
e
d
pa
r
ti
c
l
e
s
w
a
r
m
o
pt
im
i
z
e
r
,”
in
P
r
oc
e
e
di
ngs
of
th
e
I
E
E
E
C
onf
e
r
e
n
c
e
on
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ut
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nar
y
C
om
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Y
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E
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r
ha
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mpi
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i
c
a
l
s
tu
d
y
of
pa
r
ti
c
l
e
s
w
a
r
m
o
p
ti
mi
z
a
ti
o
n,”
in
P
r
oc
e
e
di
ngs
of
th
e
1999
C
ongr
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s
s
on
E
v
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ut
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G
r
und
y
,
“
P
a
r
ti
c
l
e
s
w
a
r
m
o
p
ti
mi
z
a
ti
o
n
w
it
h
mut
a
ti
o
n,”
in
2003
C
ongr
e
s
s
on
E
v
ol
ut
io
nar
y
C
om
put
at
io
n, C
E
C
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r
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B
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.
S
e
c
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s
t
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G
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B
.
L
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m
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n
t,
“
V
is
ua
li
z
in
g
pa
r
ti
c
l
e
s
w
a
r
m
opt
im
iz
a
ti
o
n
-
G
a
us
s
ia
n pa
r
ti
c
l
e
s
w
a
r
m
o
pt
im
iz
a
ti
o
n,”
i
n
2003
I
E
E
E
Sw
ar
m
I
nt
e
ll
ig
e
nc
e
Sy
m
pos
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m
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A
.
K
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,
B
.
D
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P
a
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r
o
,
a
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B
.
K
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S
in
gh,
“
P
a
r
a
m
e
te
r
tu
ni
ng
f
or
s
of
twa
r
e
e
f
f
or
t
e
s
ti
ma
ti
o
n
us
in
g
pa
r
ti
c
l
e
s
w
a
r
m
o
p
ti
mi
z
a
ti
o
n
a
lg
o
r
it
h
m,”
I
nt
e
r
nat
io
nal
J
our
nal
of
A
ppl
ie
d E
ngi
ne
e
r
in
g R
e
s
e
ar
c
h
, v
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l.
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[
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A
.
K
uma
r
,
B
.
K
.
S
in
gh,
a
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B
.
D
.
K
.
P
a
tr
o
,
“
H
y
br
id
a
lg
o
r
it
hm
ba
s
e
d
o
n
G
A
a
nd
P
S
O
w
it
h
im
pr
ove
c
o
n
ve
r
g
e
n
c
e
a
nd
di
v
e
r
s
it
y
,”
I
nt
e
r
nat
io
nal
J
our
nal
of
C
om
put
e
r
S
c
ie
nc
e
and I
n
f
or
m
at
io
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c
ur
it
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l.
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. 10, pp. 103
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19]
A
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uma
r
,
B
.
R
. A
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.
E
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.
H
.
K
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I
N
G
H
,
a
nd
B
. D
.
K
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P
a
tr
o
.,
“
D
iv
e
r
s
it
y
pr
e
s
e
r
v
in
g a
ut
o
im
pr
ove
d
-
P
S
O
f
o
r
s
ol
v
in
g
o
pt
im
iz
a
t
io
n
pr
o
bl
e
ms
,”
J
our
nal
of
M
ul
ti
pl
e
-
V
al
ue
d L
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c
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t
C
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R
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C
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E
be
r
ha
r
t
a
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Y
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S
hi
,
“
T
r
a
c
ki
ng
a
nd
o
pt
im
i
z
in
g
d
y
na
mi
c
s
y
s
t
e
ms
w
it
h
pa
r
ti
c
l
e
s
w
a
r
ms
,”
in
Pr
oc
e
e
di
ngs
of
th
e
I
E
E
E
C
onf
e
r
e
nc
e
on E
v
ol
ut
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y
C
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at
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n, I
C
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R
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C
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r
ha
r
t
a
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Y
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S
hi
,
“
P
a
r
ti
c
le
s
w
a
r
m
o
pt
im
i
z
a
ti
o
n:
D
e
v
e
lo
pm
e
nt
s
,
a
ppl
i
c
a
ti
o
ns
a
nd
r
e
s
o
ur
c
e
s
,”
in
P
r
oc
e
e
di
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of
th
e
I
E
E
E
C
onf
e
r
e
nc
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on E
v
ol
ut
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J
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L
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,
W
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X
u,
a
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J
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S
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“
Q
u
a
nt
um
-
be
ha
ve
d
pa
r
ti
c
l
e
s
w
a
r
m
o
pt
im
i
z
a
ti
o
n
w
it
h
mut
a
ti
o
n
o
pe
r
a
t
o
r
,”
in
P
r
oc
e
e
di
ngs
-
I
nt
e
r
nat
io
nal
C
on
f
e
r
e
n
c
e
on
T
ool
s
w
i
th
A
r
ti
f
i
c
ia
l
I
nt
e
ll
ig
e
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e
,
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C
T
A
I
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A
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C
ha
tt
e
r
j
e
e
a
nd
P
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S
ia
r
r
y
,
“
N
o
nl
in
e
a
r
in
e
r
ti
a
w
e
ig
ht
v
a
r
i
a
ti
o
n
f
or
d
y
na
mi
c
a
da
pt
a
ti
o
n
in
pa
r
ti
c
l
e
s
w
a
r
m
o
pt
im
i
z
a
ti
on,”
C
om
put
e
r
s
and
O
pe
r
at
io
ns
R
e
s
e
ar
c
h
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A
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le
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A
ppl
y
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h
e
pa
r
ti
c
l
e
s
w
a
r
m o
pt
i
mi
z
e
r
t
o
n
o
n
-
s
t
a
ti
o
na
r
y
e
n
v
ir
o
nm
e
nt
s
,”
A
ubur
n U
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e
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s
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A
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R
a
tn
a
w
e
e
r
a
,
S
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K
.
H
a
lg
a
mug
e
,
a
nd
H
.
C
.
W
a
ts
o
n,
“
S
e
l
f
-
o
r
ga
ni
z
in
g
hi
e
r
a
r
c
hi
c
a
l
pa
r
ti
c
le
s
w
a
r
m
o
pt
im
i
z
e
r
w
it
h
ti
m
e
-
v
a
r
yi
ng
a
c
c
e
l
e
r
a
ti
o
n
c
oe
f
f
i
c
i
e
nt
s
,”
I
E
E
E
T
r
ans
ac
ti
ons
on
E
v
ol
ut
io
nar
y
C
om
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T
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X
ia
ng,
X
.
L
ia
o
,
a
nd
K
.
w
o
W
o
ng,
“
A
n
im
pr
ov
e
d
pa
r
ti
c
l
e
s
w
a
r
m
o
pt
im
i
z
a
ti
o
n
a
lg
o
r
it
hm
c
o
mb
in
e
d
w
i
th
pi
e
c
e
w
is
e
li
ne
a
r
c
ha
o
ti
c
ma
p,”
A
ppl
ie
d M
at
he
m
at
ic
s
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A
.
I
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S
e
l
v
a
kuma
r
a
nd
K
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T
ha
nus
hk
o
di
,
“
A
ne
w
pa
r
ti
c
le
s
w
a
r
m
o
pt
im
i
z
a
ti
o
n
s
o
lu
ti
o
n
t
o
n
o
nc
o
n
ve
x
e
c
o
n
o
mi
c
di
s
pa
tc
h
pr
o
bl
e
ms
,”
I
E
E
E
T
r
ans
ac
ti
ons
on P
o
w
e
r
Sy
s
te
m
s
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l.
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. 1, pp. 42
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