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[
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Dif
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[
3
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[
5
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[
1
2
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P
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[
1
3
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1
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I
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m
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1
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T
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y
b
e
d
o
n
e
b
y
s
ele
ctin
g
t
h
e
co
m
b
i
n
atio
n
o
f
th
e
g
en
er
atio
n
u
n
its
th
a
t
s
atis
f
ies
a
ll
th
e
co
n
s
tr
ai
n
ts
o
f
t
h
e
p
o
w
er
s
y
s
te
m
a
n
d
th
e
g
en
e
r
atio
n
u
n
it
it
s
elf
a
n
d
th
e
s
e
co
m
b
in
at
io
n
s
0
-
1
th
a
t
r
ep
r
esen
ted
th
e
s
tat
u
s
o
f
ea
ch
g
en
er
ato
r
ON/OFF.
T
h
e
f
o
r
m
u
latio
n
o
f
co
s
t
f
u
n
ctio
n
f
o
r
th
e
UC
p
r
o
b
le
m
th
a
t
m
u
s
t
b
e
m
i
n
i
m
ized
b
y
t
h
e
s
u
m
o
f
t
h
e
s
tar
ti
n
g
co
s
t
o
f
t
h
e
g
en
er
ato
r
s
an
d
o
p
er
atio
n
al
co
s
t
f
o
r
ea
ch
u
n
it
o
v
er
a
s
p
ec
ef
ied
p
er
io
d
o
f
tim
e
a
n
d
it c
an
b
e
ex
p
r
ess
ed
b
y
th
e
f
o
ll
o
w
i
n
g
eq
u
atio
n
:
F
=
∑
∑
[
f
gk
(
P
gk
)
+
STC
gk
(
1
−
U
g
(
k
−
1
)
]
U
gk
N
g
=
1
T
k
=
1
(
1
)
w
h
er
e
f
gk
is
th
e
f
u
el
co
s
t
f
u
n
ctio
n
,
U
gk
is
th
e
s
tate
o
f
u
n
it
g
w
h
ic
h
c
an
b
e
0
o
r
1
at
th
e
h
o
u
r
k
,
N
i
s
th
e
n
u
m
b
er
o
f
g
e
n
er
atio
n
u
n
it
s
,
T
is
th
e
t
i
m
e
h
o
r
izo
n
,
g
is
t
h
e
i
n
d
ex
o
f
th
e
u
n
it,
k
is
t
h
e
i
n
d
ex
o
f
t
i
m
e,
P
gk
is
t
h
e
p
o
w
er
d
eliv
er
ed
f
r
o
m
t
h
e
u
n
it
g
at
th
e
h
o
u
r
k
a
n
d
STC
gk
is
th
e
s
tar
t
-
u
p
co
s
t
o
f
th
e
u
n
it
g
at
t
h
e
h
o
u
r
k
.
T
h
e
f
u
el
co
s
t
f
u
n
ctio
n
is
ca
lc
u
lated
as f
o
llo
w
s
f
gk
(
P
gk
)
=
c
g
(
P
gk
)
²
+
b
g
(
P
gk
)
+
a
g
(
2
)
w
h
er
e
c
g
,
b
g
,
a
g
ar
e
th
e
f
u
el
co
s
t c
o
ef
ici
en
ts
a
n
d
th
e
s
tar
t
-
u
p
ar
e
r
ep
r
es
en
ted
b
y
th
e
f
o
llo
w
i
n
g
eq
u
a
tio
n
:
STC
gk
=
{
HSC
g
if
M
DT
g
≤
T
g
o
f
f
≤
M
DT
g
+
C
SH
g
C
SC
g
if
T
g
o
f
f
>
M
DT
g
+
C
SH
g
(
3
)
w
h
er
e
(
HSC
g
,
C
SC
g
)
ar
e
th
e
h
o
t a
n
d
co
ld
s
ta
r
t
-
u
p
co
s
t
o
f
th
e
u
n
it
g
;
C
SH
g
is
th
e
co
ld
s
tar
t h
o
u
r
s
f
o
r
th
e
u
n
it
g
;
(
M
UT
g
,
M
DT
g
)
ar
e
th
e
m
i
n
i
m
u
m
u
p
an
d
d
o
w
n
ti
m
e
o
f
th
e
u
n
it
g
an
d
(
T
g
on
,
T
g
o
f
f
)
ar
e
th
e
ti
m
e
o
f
th
e
u
n
it
g
is
co
n
tin
u
o
u
s
l
y
ON
o
r
OFF
T
h
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
o
f
U
C
p
r
o
b
lem
i
s
r
ester
er
cted
b
y
s
o
m
e
co
n
s
tr
ai
n
ts
a
n
d
t
h
ese
co
n
s
tr
ain
ts
ar
e
th
e
s
y
s
te
m
co
n
s
tr
ain
ts
a
n
d
th
e
g
en
er
atio
n
u
n
it c
o
n
s
tr
ai
n
ts
[
1
]
.
1.
T
h
e
d
em
a
n
d
m
u
s
t b
e
s
u
p
p
lied
b
y
t
h
e
g
e
n
er
ato
r
s
at
ea
ch
h
o
u
r
.
∑
P
gk
N
g
=
1
U
gk
=
D
k
(
4
)
2.
T
h
e
co
n
s
tr
ain
t o
f
s
p
in
n
i
n
g
r
es
er
v
e
in
ca
s
e
o
f
in
cr
ea
s
e
t
h
e
d
e
m
an
d
o
r
lo
s
s
g
e
n
er
ato
r
u
n
it f
r
o
m
t
h
e
g
r
o
u
p
.
∑
P
g
m
ax
N
g
=
1
U
gk
≥
D
k
+
R
k
(
5
)
3.
T
h
e
g
en
er
ato
r
ca
n
p
r
o
d
u
ce
p
o
w
er
i
n
th
e
r
an
g
e
b
et
w
ee
n
th
e
m
ax
i
m
u
m
an
d
m
i
n
i
m
u
m
v
alu
es.
P
g
m
ax
≥
P
gk
≥
P
g
m
i
n
(
6
)
4.
T
h
e
g
en
er
atio
n
u
n
i
t
m
u
s
t b
e
o
p
er
ated
at
least f
o
r
a
ti
m
e
eq
u
a
ls
to
th
e
m
in
i
m
u
m
u
p
ti
m
e.
T
g
on
≥
M
UT
g
(
7
)
5.
T
h
e
g
en
er
atio
n
u
n
it
m
u
s
t
b
e
s
h
u
t
-
d
o
w
n
o
r
in
th
e
OFF
s
tat
e
at
least
f
o
r
a
tim
e
eq
u
als
t
o
th
e
m
in
i
m
u
m
d
o
w
n
t
i
m
e.
T
g
o
f
f
≥
M
DT
g
(
8
)
w
h
er
e
D
k
is
th
e
lo
ad
d
e
m
an
d
o
f
t
h
e
s
y
s
te
m
at
th
e
h
o
u
r
k
;
R
k
is
th
e
s
p
in
n
i
n
g
r
eser
v
e
o
f
t
h
e
s
y
s
te
m
at
th
e
h
o
u
r
k
an
d
(
P
g
m
ax
,
P
g
m
i
n
)
ar
e
th
e
m
ax
i
m
u
m
an
d
m
i
n
i
m
u
m
p
o
w
er
t
h
at
ca
n
b
e
s
u
p
p
lied
f
r
o
m
th
e
u
n
it g
.
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:
2
0
8
8
-
8708
Op
era
tio
n
co
s
t red
u
ctio
n
in
u
n
it c
o
mmitmen
t p
r
o
b
lem
u
s
in
g
imp
r
o
ve
d
q
u
a
n
tu
m
… (
A
li N
a
s
s
er Hu
s
s
a
in
)
1151
3.
P
ARTI
C
L
E
SWA
RM
O
P
T
I
M
I
Z
AT
I
O
N
A
G
O
RI
T
H
M
P
ar
ticle
S
w
ar
m
Op
ti
m
izatio
n
(
P
SO)
is
in
tr
o
d
u
ce
d
f
ir
s
tl
y
b
y
J
am
e
s
Ken
n
ed
y
an
d
R
u
s
s
ell
E
b
er
h
ar
t
in
1
9
9
5
[
2
1
]
.
P
SO
alg
o
r
ith
m
is
a
h
eu
r
i
s
tic
o
p
ti
m
iza
tio
n
m
et
h
o
d
b
ase
d
o
n
th
e
p
ar
allel
ex
p
er
ien
ce
o
f
th
e
in
d
i
v
id
u
a
ls
to
s
ea
r
ch
f
o
r
th
e
o
p
ti
m
u
m
s
o
lu
t
io
n
.
T
h
e
P
SO
p
ar
ticle
s
s
p
r
ea
d
in
a
s
ea
r
ch
s
p
ac
e
D
o
f
th
e
p
r
o
b
le
m
an
d
ea
c
h
o
f
t
h
e
m
h
as
a
p
o
s
itio
n
v
ec
to
r
an
d
s
p
ee
d
v
ec
to
r
[
2
1
]
.
I
n
th
is
a
lg
o
r
it
h
m
,
t
h
e
p
ar
ticles
ar
e
g
u
id
ed
u
s
in
g
th
e
p
er
s
o
n
a
l
ex
p
er
ien
ce
f
o
r
ea
ch
p
ar
ticl
e
w
h
ic
h
is
k
n
o
w
n
as
an
d
th
e
o
v
er
all
o
r
th
e
g
lo
b
al
e
x
p
er
ien
ce
a
m
o
n
g
all
p
ar
ticles
th
at
ter
m
ed
as
.
T
h
en
,
th
e
v
elo
cit
y
an
d
lo
ca
tio
n
o
f
ea
ch
p
ar
ticle
in
t
h
e
p
o
p
u
latio
n
a
r
e
m
o
d
if
ied
b
y
u
s
i
n
g
t
h
e
c
alcu
latio
n
o
f
th
e
cu
r
r
en
t
p
a
r
ticle
v
elo
cit
y
a
n
d
th
e
d
is
ta
n
ce
f
r
o
m
lo
ca
tio
n
a
n
d
lo
ca
tio
n
[
2
2
]
.
Fu
r
th
er
m
o
r
e,
th
e
e
x
p
er
ien
ce
ca
n
b
e
ac
ce
ler
ated
b
y
t
w
o
s
et
o
f
t
h
e
ac
ce
ler
atio
n
f
ac
to
r
s
,
(
1
,
2
)
ar
e
th
e
co
g
n
it
iv
e
a
n
d
aso
cial
ac
ce
ler
atio
n
co
n
s
t
an
t
f
ac
to
r
s
r
esp
ec
tiv
el
y
;
(
1
,
2
)
ar
e
t
w
o
r
an
d
o
m
n
u
m
b
er
s
g
en
er
ated
b
et
w
ee
n
[
0
,
1
]
.
T
h
e
m
o
v
e
m
e
n
t
is
a
ls
o
ca
n
b
e
co
n
tr
o
lled
b
y
m
u
lt
ip
l
y
i
n
g
it
b
y
in
er
tia
f
ac
to
r
th
at
lies
i
n
th
e
r
an
g
e
o
f
[
⍵
,
⍵
]
an
d
th
e
ty
p
ical
r
an
g
e
i
s
⍵
=
0
.
9
to
⍵
=
0
.
4
.
T
h
e
v
elo
cit
y
u
p
d
ate
is
d
escr
ib
ed
b
y
th
e
f
o
llo
w
i
n
g
eq
u
atio
n
:
+
1
=
⍵
+
1
1
(
−
)
+
2
2
(
−
)
(
9
)
w
h
er
e
m
i
s
th
e
c
u
r
r
en
t itr
atio
n
.
T
h
e
p
o
s
itio
n
o
f
t
h
e
p
ar
ticles
ca
n
b
e
u
p
d
ated
as f
o
llo
w
s
eq
u
atio
n
:
+
1
=
+
+
1
(
1
0
)
th
e
in
er
t
ia
f
ac
to
r
is
r
ep
r
esen
te
d
b
y
t
h
e
f
o
llo
w
i
n
g
eq
u
atio
n
:
⍵
=
⍵
−
(
⍵
−
⍵
)
⤫
(
1
1
)
w
h
er
e
(
⍵
,
⍵
)
ar
e
th
e
in
itial
an
d
f
in
al
w
ei
g
h
t
s
,
is
th
e
m
a
x
i
m
u
m
iter
atio
n
n
u
m
b
er
an
d
is
th
e
c
u
r
r
en
t
i
ter
atio
n
n
u
m
b
er
.
T
h
e
b
in
ar
y
v
er
s
io
n
o
f
t
h
e
P
S
O
(
B
P
SO)
h
as
b
ee
n
p
r
ese
n
ted
b
y
J
a
m
es
Ke
n
n
ed
y
an
d
R
u
s
s
ell
E
b
er
h
ar
t
to
b
e
u
s
e
d
in
d
is
cr
ete
s
p
ac
es
[
2
3
]
.
T
h
e
u
p
d
ate
p
r
o
ce
s
o
f
t
h
e
p
o
s
it
io
n
f
o
r
th
e
p
ar
ticles
ca
n
b
e
ac
h
iev
ed
b
y
u
s
i
n
g
a
n
e
w
v
a
r
iab
le
k
n
o
w
n
a
s
Si
g
m
o
id
L
i
m
i
tin
g
T
r
an
s
f
o
r
m
at
io
n
an
d
ca
n
b
e
w
r
itte
n
as
(
+
1
)
=
1
1
−
(
+
1
)
(
1
2
)
B
y
u
s
i
n
g
th
e
s
ig
m
o
id
f
u
n
ctio
n
,
th
e
p
o
s
itio
n
u
p
d
ate
o
f
t
h
e
p
ar
ticle
in
t
h
e
b
in
ar
y
v
er
s
io
n
o
f
a
P
SO a
lg
o
r
ith
m
is
d
o
n
e
as th
e
f
o
llo
w
i
n
g
eq
u
atio
n
+
1
=
{
1
if
<
(
+
1
)
0
ℎ
(
1
3
)
w
h
er
e
is
a
r
an
d
o
m
n
u
m
b
er
d
is
tr
ib
u
ted
u
n
i
f
o
r
m
l
y
b
et
w
ee
n
[
0
,
1
]
.
4.
H
YB
RIDI
Z
A
T
I
O
N
O
F
Q
U
ANTUM
CO
M
P
UT
I
NG
WI
T
H
B
P
SO
AL
G
O
R
I
T
H
M
T
h
e
q
u
an
tu
m
b
it
is
k
n
o
w
n
as
th
e
s
m
alle
s
t
u
n
it
o
f
i
n
f
o
r
m
atio
n
t
h
at
s
to
r
e
in
th
e
q
u
an
tu
m
co
m
p
u
ter
[
2
4
]
.
T
h
e
q
u
an
tu
m
b
it
ca
n
b
e
in
t
w
o
s
tate
s
,
th
e
f
ir
s
t
s
tate
i
s
0
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d
th
e
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ec
o
n
d
is
1
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T
h
ese
s
tates
m
a
y
b
e
w
r
itte
n
as
|
0
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d
|
1
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an
d
th
e
q
u
a
n
tu
m
b
it s
tate
ca
n
b
e
r
ep
r
o
d
u
ce
d
as f
o
llo
w
s
:
|
Ѱ
⟩
=
|
0
⟩
+
|
1
⟩
(
1
4
)
w
h
er
e
an
d
ar
e
tw
o
co
m
p
lex
n
u
m
b
er
s
th
at
id
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t
if
ies
th
e
p
r
o
b
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m
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l
itu
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e
o
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elativ
e
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n
d
itio
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s
.
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h
e
s
tate
o
f
t
h
e
q
u
a
n
t
u
m
b
it
ca
n
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e
n
o
r
m
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lized
to
u
n
it
y
to
g
u
ar
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n
tee
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at
|
|
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|
2
=
1
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a
n
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m
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av
e
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ee
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u
s
ed
to
c
h
an
g
e
th
e
s
tate
o
f
t
h
e
q
u
an
t
u
m
b
it
an
d
f
o
r
ex
a
m
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le
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h
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ate
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N
OT
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ate,
Had
a
m
ar
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ate
a
n
d
r
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tatio
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ate
[
2
5
]
.
T
h
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o
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el
QE
A
h
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s
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ee
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p
r
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p
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ed
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y
K
i
m
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n
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Ha
n
as
[
2
4
]
.
T
h
is
QE
A
is
in
s
p
ir
ed
f
r
o
m
t
h
e
q
u
a
n
t
u
m
-
co
m
p
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ti
n
g
co
n
ce
p
t
s
o
th
e
q
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a
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t
u
m
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it
h
as
b
ee
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d
es
ig
n
ed
to
g
et
t
h
e
b
in
ar
y
s
o
l
u
tio
n
s
.
T
h
e
q
u
an
t
u
m
b
it
is
d
ef
i
n
ed
b
y
p
air
o
f
n
u
m
b
er
s
w
h
ich
ar
e
α
a
n
d
β
an
d
th
e
q
u
a
n
t
u
m
b
it
ca
n
b
e
f
o
r
m
u
lated
a
s
a
s
tr
in
g
o
f
=
[
1
1
|
2
2
|
.
.
.
.
.
.
|
]
(
1
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
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I
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&
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m
p
E
n
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Vo
l.
10
,
No
.
2
,
A
p
r
il 2
0
2
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1
1
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-
1155
1152
w
h
er
e
|
|
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2
=
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d
j
=
1
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2
……n
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T
h
e
r
o
tatio
n
g
ate
ca
n
b
e
u
s
ed
as a
v
ar
ian
ce
f
ac
to
r
to
u
p
d
ate
th
e
in
d
i
v
id
u
al
o
f
th
e
q
u
an
t
u
m
b
it a
n
d
th
e
r
o
tatio
n
g
a
te
is
r
ep
r
esen
ted
b
y
t
h
e
f
o
llo
w
i
n
g
eq
u
atio
n
:
(
)
=
[
(
)
−
(
)
(
)
(
)
]
(
1
6
)
w
h
er
e
is
t
h
e
j
th
q
u
a
n
t
u
m
b
it
r
o
tatio
n
an
g
le
th
at
g
o
e
s
to
0
o
r
1
s
tate.
A
lo
o
k
u
p
tab
le
as
s
h
o
w
n
i
n
T
ab
le
1
is
u
s
ed
to
d
eter
m
i
n
e
th
e
v
al
u
e
o
f
an
d
ad
j
u
s
ted
as
1
=
0
,
2
=
0
,
3
=
0
.
01
,
4
=
0
,
5
=
−
0
.
01
,
6
=
0
,
7
=
0
,
8
=
0
an
d
B
is
t
h
e
b
est
s
o
l
u
tio
n
w
h
er
e
B
=
(
1
,
2
,
3
,
.
.
.
.
.
.
.
,
)
as
d
escr
ib
ed
in
r
ef
er
en
ce
[
2
4
]
.
T
ab
le
1
.
L
o
o
k
u
p
tab
le
to
d
eter
m
i
n
e
r
o
tatio
n
an
g
le
F
i
t
n
e
ss (X
)
≥
F
i
t
n
e
ss (
B
)
Δ
θ
j
0
0
F
a
l
s
e
1
0
0
T
r
u
e
2
0
1
F
a
l
s
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3
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r
u
e
4
1
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a
l
s
e
5
1
0
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r
u
e
6
1
1
F
a
l
s
e
7
1
1
T
r
u
e
8
A
n
e
w
B
P
SO
in
s
p
ir
ed
b
y
q
u
a
n
tu
m
co
m
p
u
ti
n
g
w
h
ic
h
is
k
n
o
w
n
a
s
Qu
a
n
t
u
m
B
in
ar
y
P
ar
tic
le
S
w
ar
m
Op
ti
m
izatio
n
(
QB
P
SO)
[
2
6
]
.
E
ac
h
ele
m
en
t
in
t
h
e
p
ar
ticle
h
as
a
s
tate
o
f
1
o
r
0
ac
co
r
d
in
g
t
o
th
e
p
r
o
b
ab
ilit
y
o
f
|
|
2
+
|
|
2
=
1
.
T
h
e
QB
P
SO
p
r
o
p
o
s
es
a
n
ew
w
a
y
to
u
p
d
ate
th
e
v
elo
cit
y
o
f
ea
c
h
p
ar
ticle
b
y
t
h
e
u
s
e
o
f
Qu
a
n
tu
m
C
o
m
p
u
ti
n
g
.
T
h
e
in
er
tia
f
ac
to
r
s
(
⍵
,
⍵
)
an
d
th
e
ac
ce
le
r
atio
n
f
ac
to
r
s
(
1
,
2
)
ar
e
o
m
itted
i
n
th
e
QB
P
SO
an
d
r
ep
lace
d
b
y
th
e
r
o
tatio
n
an
g
le.
T
h
e
u
p
d
ate
p
r
o
ce
s
s
o
f
th
e
p
o
s
itio
n
v
ec
t
o
r
ca
n
b
e
d
o
n
e
b
y
u
s
i
n
g
th
e
p
r
o
b
ab
ilit
y
|
|
2
th
at
h
as
b
ee
n
s
to
r
ed
in
t
h
e
i
th
q
u
a
n
tu
m
b
it
i
n
d
iv
id
u
al
(
)
.
T
h
er
ef
o
r
e,
th
e
j
th
ele
m
e
n
t o
f
t
h
e
i
th
p
ar
ticle
ta
k
e
s
a
v
al
u
e
o
f
1
o
r
0
as in
th
e
f
o
l
lo
w
i
n
g
eq
u
atio
n
[
2
6
]
:
+
1
=
{
1
if
<
|
|
2
0
ℎ
(
1
7
)
T
h
e
r
o
tatio
n
an
g
le
ca
n
b
e
d
e
ter
m
i
n
ed
b
y
u
s
in
g
th
e
cu
r
r
e
n
t
p
o
s
itio
n
an
d
th
e
g
lo
b
al
p
o
s
itio
n
o
f
th
e
s
w
ar
m
as i
n
t
h
e
f
o
llo
w
i
n
g
eq
u
atio
n
:
=
×
{
1
×
(
−
)
+
2
×
(
−
)
(
1
8
)
w
h
er
e
is
th
e
r
o
tatio
n
an
g
le
m
ag
n
it
u
d
e
an
d
(
1
,
2
)
ca
n
b
e
f
o
u
n
d
b
y
a
co
m
p
ar
is
o
n
a
m
o
n
g
t
h
e
f
it
n
es
s
o
f
th
e
c
u
r
r
en
t
p
o
s
itio
n
o
f
t
h
e
p
ar
ticle
i
,
th
e
f
it
n
es
s
o
f
th
e
b
est
p
o
s
itio
n
an
d
t
h
e
f
itn
e
s
s
o
f
th
e
g
lo
b
al
p
o
s
itio
n
r
esp
ec
tiv
el
y
as i
n
eq
u
atio
n
s
(
1
9
)
an
d
(
2
0
)
:
1
=
{
0
if
(
)
≥
(
)
1
ℎ
(
1
9
)
2
=
{
0
if
(
)
≥
(
)
1
ℎ
(
2
0
)
T
h
e
m
a
g
n
it
u
d
e
o
f
th
e
r
o
ta
tio
n
is
d
ec
r
ea
s
ed
m
o
n
o
to
n
o
u
s
l
y
f
r
o
m
a
m
a
x
i
m
u
m
v
al
u
e
to
a
m
i
n
i
m
u
m
v
al
u
e
alo
n
g
t
h
e
iter
atio
n
b
y
t
h
e
f
o
llo
w
i
n
g
eq
u
atio
n
:
=
−
−
×
(
2
1
)
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:
2
0
8
8
-
8708
Op
era
tio
n
co
s
t red
u
ctio
n
in
u
n
it c
o
mmitmen
t p
r
o
b
lem
u
s
in
g
imp
r
o
ve
d
q
u
a
n
tu
m
… (
A
li N
a
s
s
er Hu
s
s
a
in
)
1153
5.
I
M
P
RO
VE
D
Q
B
P
SO
AL
G
O
RIT
H
M
T
h
e
QB
P
SO
alg
o
r
ith
m
m
a
y
f
a
il
in
f
i
n
d
in
g
t
h
e
o
p
ti
m
u
m
v
al
u
e
o
f
t
h
e
s
o
l
u
tio
n
,
th
er
ef
o
r
;
an
i
m
p
r
o
v
e
m
en
t
is
m
ad
e
o
n
th
e
QB
P
SO
to
g
et
th
e
b
etter
s
o
lu
tio
n
.
T
h
e
i
m
p
r
o
v
e
m
e
n
t
o
n
QB
P
SO
is
to
s
ea
r
ch
f
o
r
th
e
f
i
tn
e
s
s
i
n
th
e
p
er
s
o
n
al
b
est
f
o
r
th
e
f
ir
s
t
h
al
f
o
f
t
h
e
iter
atio
n
s
a
n
d
af
ter
f
i
n
d
i
n
g
it
th
e
f
itn
e
s
s
i
n
th
e
g
lo
b
al
b
est
w
ill
b
e
s
ea
r
ch
ed
in
th
e
s
ec
o
n
d
h
al
f
o
f
th
e
iter
atio
n
s
.
T
h
is
i
m
p
r
o
v
e
m
en
t
ca
n
b
e
ex
p
r
ess
ed
as t
h
e
f
o
llo
w
i
n
g
eq
u
atio
n
s
:
1
=
{
0
if
≥
(
/
2
)
1
ℎ
(
2
2
)
2
=
{
1
if
≥
(
/
2
)
0
ℎ
(
2
3
)
an
d
th
e
r
o
tatio
n
a
n
g
le
i
s
u
p
d
at
ed
as in
(
1
8
,
2
1
)
6.
RE
SU
L
T
S
A
ND
AN
AL
Y
SI
S
T
h
e
s
i
m
u
latio
n
i
s
i
m
p
le
m
e
n
te
d
u
s
in
g
M
A
T
L
A
B
p
r
o
g
r
am
v
er
s
io
n
(
R
1
7
b
)
f
o
r
test
s
y
s
te
m
co
n
s
is
t
o
f
1
0
g
en
er
atio
n
u
n
it
s
o
v
er
a
ti
m
e
h
o
r
izo
n
o
f
2
4
h
o
u
r
s
[
2
6
]
.
T
h
e
v
alu
e
s
o
f
an
d
ar
e
ch
o
s
e
n
eq
u
al
to
0
.
05
an
d
0
.
1
r
esp
ec
tiv
el
y
.
T
h
e
n
u
m
b
er
o
f
p
o
p
u
latio
n
a
n
d
iter
atio
n
s
ar
e
5
0
an
d
2
6
r
esp
ec
tiv
el
y
.
T
ab
le
2
lis
ts
th
e
g
e
n
er
atio
n
o
f
ea
c
h
u
n
i
t.
T
h
e
to
tal
o
p
er
atio
n
co
s
t t
h
at
h
as b
ee
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o
b
tain
ed
b
y
th
e
I
QB
P
SO is 5
6
3
9
3
8
.
4
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w
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h
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el
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o
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th
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er
atio
n
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n
its
is
5
5
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8
4
8
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4
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t
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e
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ee
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m
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f
5
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7
$
as in
r
ef
er
e
n
ce
[
2
6
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[1
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W
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“
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M
.
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.
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[6
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“
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A
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a
n
d
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No
r,
“
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irs
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In
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n
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)
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[9
]
J.
A
.
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R.
C.
W
il
so
n
,
“
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n
a
p
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in
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th
e
rm
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ra
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n
g
s
y
ste
m
s,”
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E
T
ra
n
s.
Po
we
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p
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S
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.
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–
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1
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8
.
[1
0
]
K.
S
.
S
wa
ru
p
a
n
d
S
.
Ya
m
a
sh
iro
,
“
Un
it
c
o
m
m
it
m
e
n
t
so
lu
ti
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n
m
e
t
h
o
d
o
l
o
g
y
u
sin
g
g
e
n
e
ti
c
a
l
g
o
rit
h
m
,
”
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E
T
ra
n
s.
Po
we
r S
y
st.
,
v
o
l
.
1
7
,
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o
.
1
,
p
p
.
8
7
–
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1
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b
.
2
0
0
2
.
[1
1
]
H.
Ch
e
n
a
n
d
X.
W
a
n
g
,
“
Co
o
p
e
ra
ti
v
e
c
o
e
v
o
lu
ti
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n
a
ry
a
lg
o
rit
h
m
fo
r
u
n
it
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o
m
m
it
m
e
n
t,
”
IEE
E
T
ra
n
s.
P
o
we
r
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y
st
.,
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o
l.
1
6
,
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o
.
1
,
p
p
.
1
2
8
–
1
3
3
,
F
e
b
.
2
0
0
2
.
[1
2
]
D.
N.
S
im
o
p
o
u
lo
s,
e
t
a
l.
,
,
“
Un
it
c
o
m
m
it
m
e
n
t
b
y
a
n
e
n
h
a
n
c
e
d
sim
u
late
d
a
n
n
e
a
li
n
g
a
lg
o
rit
h
m
,
”
IEE
E
T
ra
n
s.
Po
we
r
S
y
st
.
,
v
o
l.
2
1
,
n
o
.
1
,
p
p
.
6
8
–
7
6
,
F
e
b
.
2
0
0
6
.
[1
3
]
B.
Zh
a
o
,
e
t
a
l.
,
“
A
n
I
m
p
ro
v
e
d
P
a
rti
c
le
S
w
a
r
m
Op
ti
m
iza
ti
o
n
A
l
g
o
rit
h
m
f
o
r
Un
it
Co
m
m
it
m
e
n
t,
”
El
e
c
t.
Po
we
r
En
e
rg
y
S
y
st
.
,
Vo
l.
2
8
,
No
.
7
,
p
p
.
4
8
2
–
4
9
0
,
2
0
0
6
.
[1
4
]
T
.
W
.
Lau
,
e
t
a
l.
,
“
Qu
a
n
tu
m
-
in
sp
ired
Ev
o
lu
t
io
n
a
ry
A
l
g
o
rit
h
m
A
p
p
ro
a
c
h
f
o
r
Un
it
Co
m
m
it
m
e
n
t,
”
IEE
E
T
ra
n
s.
Po
we
r S
y
st.
,
Vo
l.
2
4
,
No
.
3
,
p
p
.
1
5
0
3
–
1
5
1
2
,
A
u
g
.
2
0
0
9
.
[1
5
]
P
S
.
S
is
h
a
j,
e
t
a
l.
,
“
A
n
A
n
t
Co
lo
n
y
S
y
ste
m
A
p
p
ro
a
c
h
f
o
r
Un
it
Co
m
m
it
m
e
n
t
P
r
o
b
lem
,
”
In
t
J
El
e
c
tr
Po
we
r
En
e
rg
y
S
y
st
,
V
o
l.
2
8
,
No
.
5
,
p
p
.
3
1
5
–
2
3
,
2
0
0
6
.
[1
6
]
X
.
Yu
a
n
,
e
t
a
l.
,
“
A
p
p
li
c
a
ti
o
n
o
f
En
h
a
n
c
e
d
Disc
re
te
Diffe
re
n
ti
a
l
Ev
o
lu
ti
o
n
A
p
p
ro
a
c
h
t
o
Un
i
t
Co
m
m
it
m
e
n
t
P
r
o
b
lem
,
”
En
e
rg
y
Co
n
v
e
rs
M
a
n
a
g
e
,
V
o
l.
5
0
,
p
p
.
2
4
4
9
–
2
4
5
6
,
2
0
0
9
.
2
8
[1
7
]
H.
S
a
sa
k
i,
e
t
a
l.
,
“
A
S
o
lu
ti
o
n
M
e
th
o
d
o
f
Un
it
Co
m
m
it
m
e
n
t
b
y
A
rti
f
icia
l
N
e
u
ra
l
Ne
t
w
o
rk
s,”
IEE
E
T
ra
n
s
Po
we
r
S
y
st
,
V
o
l.
7
,
No
.
3
,
p
p
.
9
7
4
–
8
1
,
1
9
9
2
.
[1
8
]
A
.
Bo
rg
h
e
tt
i,
e
t
a
l.
,
“
L
a
g
r
a
n
g
ian
Re
lax
a
ti
o
n
a
n
d
T
a
b
u
S
e
a
rc
h
A
p
p
ro
a
c
h
e
s
f
o
r
Un
it
C
o
m
m
it
m
e
n
t
P
r
o
b
lem
,
”
IEE
E
p
o
rto
p
o
we
r tec
h
c
o
n
fer
e
n
c
e
,
P
o
rt
u
g
a
l,
2
0
0
1
.
[1
9
]
R.
Ha
b
a
c
h
i,
A
.
T
o
u
il
,
A
.
Ch
a
rk
a
o
u
i,
a
n
d
A
.
Ech
c
h
a
tb
i,
“
Eag
le
stra
teg
y
b
a
se
d
c
ro
w
se
a
r
c
h
a
lg
o
rit
h
m
f
o
r
so
lv
in
g
u
n
it
c
o
m
m
it
m
e
n
t
p
ro
b
lem
in
sm
a
rt
g
rid
s
y
ste
m
,
”
In
d
o
n
e
sia
n
J
o
u
rn
a
l
o
f
E
lec
trica
l
En
g
in
e
e
rin
g
a
n
d
Co
mp
u
ter
S
c
ien
c
e
.
,
v
o
l.
1
2
,
n
o
.
1
,
p
p
.
1
7
–
2
9
,
2
0
1
8
.
[2
0
]
S
.
S
.
S
a
k
th
i,
R.
K
.
S
a
n
th
i
,
N.
M
u
ra
li
Krish
n
a
n
,
S
.
G
a
n
e
sa
n
,
a
n
d
S
.
S
u
b
ra
m
a
n
ian
,
“
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in
d
I
n
teg
ra
ted
T
h
e
rm
a
l
Un
it
Co
m
m
it
m
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n
t
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o
l
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ti
o
n
Us
in
g
G
re
y
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f
Op
ti
m
i
z
e
r,
”
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ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
E
lec
trica
l
a
n
d
Co
m
p
u
t
e
r E
n
g
in
e
e
ri
n
g
(
IJ
ECE
)
,
v
o
l.
7
,
n
o
.
5
,
p
.
2
3
0
9
,
O
c
t.
2
0
1
7
.
[2
1
]
J.
Ke
n
n
e
d
y
,
R.
Eb
e
rh
a
rt,
“
P
a
rt
icle
s
w
a
r
m
o
p
ti
m
i
z
a
ti
o
n
,
”
in
:
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E
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
Ne
u
ra
l
Ne
two
rk
s
,
V
o
l
.
4
,
1
9
9
5
,
p
p
.
1
9
4
2
-
1
9
4
8
.
[2
2
]
R.
Eb
e
r
h
a
rt,
J.
Ke
n
n
e
d
y
,
“
A
n
e
w
o
p
ti
m
ize
r
u
sin
g
p
a
rti
c
le
sw
a
r
m
th
e
o
r
y
,
”
in
:
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c
e
e
d
i
n
g
s
o
f
th
e
S
ixt
h
In
ter
n
a
t
io
n
a
l
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y
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si
u
m o
n
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o
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a
c
h
i
n
e
a
n
d
H
u
ma
n
S
c
ien
c
e
,
1
9
9
5
,
p
p
.
3
9
-
4
3
.
[2
3
]
J.
Ke
n
n
e
d
y
a
n
d
R.
C.
Eb
e
rh
a
rt,
“
A
d
isc
re
te
b
in
a
r
y
v
e
rsio
n
o
f
th
e
p
a
rti
c
le
sw
a
r
m
a
lg
o
rit
h
m
,
”
IEE
E
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
S
y
ste
ms
,
M
a
n
,
a
n
d
Cy
b
e
rn
e
ti
c
s.
C
o
mp
u
ta
ti
o
n
a
l
Cy
b
e
rn
e
ti
c
s
a
n
d
S
im
u
la
t
io
n
,
Orl
a
n
d
o
,
F
L
,
USA
,
1
9
9
7
,
p
p
.
4
1
0
4
-
4
1
0
8
v
o
l
.
5
.
[2
4
]
Ha
n
K.H
a
n
d
Kim
J.H,
“
Qu
a
n
t
u
m
-
in
sp
ired
e
v
o
lu
ti
o
n
a
ry
a
l
g
o
rit
h
m
f
o
r
a
c
las
s
o
f
c
o
m
b
in
a
to
rial
o
p
ti
m
iza
ti
o
n
,
”
in
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Evo
l
u
ti
o
n
a
ry
Co
mp
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t
a
ti
o
n
,
v
o
l.
6
,
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o
.
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,
p
p
.
5
8
0
-
5
9
3
,
De
c
.
2
0
0
2
.
[2
5
]
L
.
S
p
e
c
to
r,
e
t
a
l.
,
“
F
i
n
d
i
n
g
a
b
e
tt
e
r
-
th
a
n
-
c
las
sic
a
l
q
u
a
n
t
u
m
A
N
D/OR
a
lg
o
rit
h
m
u
sin
g
g
e
n
e
ti
c
p
ro
g
ra
m
m
in
g
,
”
Pro
c
e
e
d
in
g
s
o
f
th
e
1
9
9
9
Co
n
g
re
ss
o
n
Evo
l
u
ti
o
n
a
ry
C
o
mp
u
ta
t
io
n
-
CEC9
9
(
Ca
t.
No
.
9
9
T
H
8
4
0
6
),
W
a
sh
in
g
to
n
,
DC,
USA
,
1
9
9
9
,
p
p
.
2
2
3
9
-
2
2
4
6
V
o
l.
3
.
[2
6
]
Y.
Je
o
n
g
,
e
t
a
l.
,
“
A
Ne
w
Qu
a
n
tu
m
-
In
sp
ired
Bin
a
ry
P
S
O:
A
p
p
li
c
a
ti
o
n
to
Un
it
C
o
m
m
it
m
e
n
t
P
ro
b
l
e
m
s
f
o
r
P
o
w
e
r
S
y
st
e
m
s,
”
in
IEE
E
T
r
a
n
s
a
c
ti
o
n
s
o
n
P
o
we
r S
y
ste
ms
,
v
o
l.
2
5
,
n
o
.
3
,
p
p
.
1
4
8
6
-
1
4
9
5
,
A
u
g
.
2
0
1
0
.
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I
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1155
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Evaluation Warning : The document was created with Spire.PDF for Python.