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.
157
~
165
I
S
S
N
:
2252
-
8938
,
D
O
I
:
10.11591/
ij
a
i.
v
10
.i
1
.pp
157
-
165
157
Jou
r
n
al
h
om
e
page
:
ht
tp
:
//
ij
ai
.
ia
e
s
c
or
e
.c
om
G
e
n
e
r
al
i
z
e
d
swar
m
i
n
t
e
l
l
i
ge
n
c
e
al
gor
i
t
h
m
s wit
h
d
om
ai
n
-
sp
e
c
i
f
i
c
h
e
u
r
i
st
i
c
s
P
. M
at
r
e
n
in
1
, V
. M
yas
n
ic
h
e
n
k
o
2
, N
. S
d
ob
n
ya
k
ov
3
, D
. S
ok
ol
ov
4
, S
. F
id
an
ova
5
, L
. K
ir
il
ov
6
, R
. M
ik
h
ov
7
1
Novosibirsk S
tate Technical Universit
y, Russia
2,3,4
Tver
State U
nivers
ity, Russ
ia
5,6,7
Bulgaria
n Acad
emy of Sc
iences,
Institute
of Inf
ormation
and Communi
cation T
echnolog
ies, Bulga
ria
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
O
c
t
2
4
, 20
20
R
e
vi
s
e
d
J
a
n
13
, 20
21
A
c
c
e
pt
e
d
F
e
b 1
6, 20
21
In
recent
years,
hybrid
approaches
on
population
-
based
algorithms
ar
e
more
often applied in industrial settings. In this paper, we present the a
pproach of a
combinat
ion
of
universal
,
problem
-
free
swarm
intelligence
(SI)
alg
orithms
with simpl
e deterministic
domain
-
specific heur
istic algorithms. The a
p
proach
focuses
on
improvin
g
efficiency
by
sharing
th
e
advantages
of
d
omain
-
specific heur
istic and swarm a
lgorithms. A heuristic a
lgorithm helps take into
account
the
specifics
of
the
problem
and
effectively
tran
slate
the
posit
ions
of
agents (p
article, an
t, bee)
into
the
problem
'
s solu
tion.
And a
s
warm alg
orithm
provides
an
increase
in
the
adaptability
and
efficiency
of
the
approach
due
to
stochastic
and
self
-
organized
properties.
We
demonstrate
this
approach
on
t
wo
non
-
trivial
optimization
tasks:
scheduling
problem
and
findi
ng
the
minimum distance
between
3D isomers.
K
e
y
w
o
r
d
s
:
D
om
a
in
-
s
pe
c
if
ic
he
ur
is
ti
c
J
ob
-
s
hop s
c
he
dul
in
g
N
a
noc
lu
s
te
r
s
P
a
r
ti
c
le
s
w
a
r
m
opt
im
iz
a
ti
on
P
ot
e
nt
ia
l
e
ne
r
gy s
ur
f
a
c
e
S
w
a
r
m
in
te
ll
ig
e
nc
e
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
:
P
. M
a
tr
e
ni
n
D
e
pa
r
tm
e
nt
of
I
ndus
tr
ia
l
P
ow
e
r
S
yppl
y S
ys
te
m
s
N
ovos
ib
ir
s
k S
ta
te
T
e
c
hni
c
a
l
U
ni
ve
r
s
it
y
N
ovos
ib
ir
s
k 630073, R
us
s
ia
E
m
a
il
:
m
a
tr
e
ni
n.2012@
c
or
p.ns
tu
.r
u
1.
I
N
T
R
O
D
U
C
T
I
O
N
S
w
a
r
m
in
te
ll
ig
e
nc
e
a
lg
or
it
hm
s
a
r
e
a
ppl
ie
d
in
a
lm
os
t
e
ve
r
y
a
r
e
a
of
s
c
ie
n
c
e
a
nd
e
ngi
ne
e
r
in
g,
s
in
c
e
in
pr
a
c
ti
c
e
,
th
e
y
ha
ve
s
ho
w
n
th
e
ir
hi
gh
e
f
f
ic
ie
nc
y
in
s
ol
vi
ng,
f
ir
s
t
of
a
ll
,
c
om
pl
e
x
r
e
a
l
-
li
f
e
e
ngi
ne
e
r
in
g
opt
im
iz
a
ti
on
pr
obl
e
m
s
[
1
-
3
]
.
C
om
pl
e
x
opt
im
iz
a
ti
on
p
r
obl
e
m
s
a
r
e
unde
r
s
to
od
a
s
hi
gh
-
di
m
e
ns
io
na
li
ty
pr
obl
e
m
s
w
it
h
a
la
r
ge
-
s
c
a
le
c
om
pl
e
x
to
pol
ogy
of
th
e
s
ol
ut
io
n
s
e
a
r
c
h
s
pa
c
e
,
nonl
in
e
a
r
c
r
it
e
r
ia
a
nd
c
on
s
tr
a
in
ts
.
A
ls
o,
th
e
s
e
pr
obl
e
m
s
m
a
y
h
a
ve
m
or
e
th
a
n
one
obj
e
c
ti
ve
f
unc
ti
on,
s
to
c
ha
s
ti
c
a
nd
dyna
m
ic
pr
ope
r
ti
e
s
.
A
s
c
ie
nt
is
t
w
it
h
a
n
unde
r
s
ta
ndi
ng
of
va
r
io
us
s
w
a
r
m
a
lg
or
it
hm
s
'
m
e
c
ha
ni
s
m
s
,
th
e
ir
w
e
a
k
a
nd
s
tr
ong
s
id
e
s
c
a
n
c
r
e
a
te
hybr
id
a
lg
or
it
hm
s
,
c
om
bi
ni
ng,
a
s
a
r
ul
e
,
two
s
w
a
r
m
a
lg
or
it
hm
s
or
s
w
a
r
m
a
nd
e
vol
ut
io
na
r
y
a
lg
or
it
hm
s
.
I
t
a
ll
ow
s
a
c
hi
e
vi
ng
a
s
yne
r
gi
s
ti
c
e
f
f
e
c
t,
in
c
r
e
a
s
in
g
th
e
ove
r
a
ll
e
f
f
ic
ie
nc
y
of
th
e
r
e
s
ul
ti
ng
hybr
id
a
lg
or
it
hm
[
4
]
.
T
he
r
e
a
r
e
s
e
ve
r
a
l
di
r
e
c
ti
ons
f
or
hybr
id
iz
a
ti
on.
E
a
c
h
a
lg
or
it
hm
in
th
e
e
ns
e
m
bl
e
w
or
ks
a
c
c
or
di
ng
to
it
s
o
w
n
r
ul
e
s
.
H
ow
e
ve
r
,
th
e
y
us
e
th
e
y
u
s
e
th
e
ge
ne
r
a
l
popula
ti
on
of
a
ge
nt
s
or
e
x
c
ha
nge
th
e
be
s
t
-
f
ound
s
ol
ut
io
ns
,
f
or
e
xa
m
pl
e
,
a
hybr
id
of
th
e
P
S
O
a
nd
th
e
ge
ne
ti
c
a
lg
or
it
hm
(
G
A
)
[
5
]
,
P
S
O
+
di
f
f
e
r
e
nt
ia
l
e
vol
u
ti
on
[
6
]
,
P
S
O
+
gr
e
y
w
ol
f
opt
im
iz
e
r
[
7]
,
P
S
O
+
bi
oge
ogr
a
phy
-
ba
s
e
d
opt
im
iz
a
ti
on
[
8
]
.
T
hi
s
a
ppr
oa
c
h
doe
s
not
r
e
qui
r
e
a
c
ha
nge
in
th
e
unde
r
ly
in
g
a
lg
or
it
hm
s
.
T
he
y
w
or
k
in
pa
r
a
ll
e
l,
e
xc
h
a
ngi
ng
da
ta
,
or
us
in
g
a
s
h
a
r
e
d
(
pub
li
c
)
popula
ti
on.
A
s
a
r
e
s
ul
t,
th
e
c
om
pl
e
xi
ty
of
th
e
a
lg
or
it
hm
s
doe
s
not
in
c
r
e
a
s
e
;
th
e
b
a
s
ic
a
lg
or
it
hm
s
c
a
n
b
e
e
a
s
il
y
r
e
pl
a
c
e
d.
S
im
ul
ta
ne
ous
ly
,
in
s
uc
h
a
n
a
ppr
oa
c
h, t
he
s
yne
r
gi
s
ti
c
e
f
f
e
c
t
m
a
y b
e
s
m
a
ll
be
c
a
us
e
of
t
he
w
e
a
k i
nt
e
gr
a
ti
on of
a
lg
or
it
hm
s
i
nt
o t
he
s
ys
te
m
.
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
:
157
–
165
158
A
ddi
ng
a
r
ul
e
or
s
t
a
ge
of
upda
ti
n
g
th
e
pos
it
io
ns
of
a
ge
nt
s
f
r
om
a
not
he
r
a
lg
or
it
hm
to
th
e
m
a
in
a
lg
or
it
hm
.
I
n
[
9
]
,
a
m
ut
a
ti
on
s
ta
ge
w
a
s
a
dde
d
to
th
e
c
la
s
s
ic
a
l
P
S
O
a
lg
or
it
hm
a
t
th
e
e
nd
o
f
e
a
c
h
it
e
r
a
ti
on,
s
im
il
a
r
t
o t
ha
t
in
G
A
;
s
im
il
a
r
ly
, t
he
m
ut
a
ti
on w
a
s
a
dde
d t
o t
he
gr
e
y w
ol
f
op
ti
m
iz
e
r
i
n [
10
]
;
th
e
s
tu
dy [
1
1
]
a
ls
o
a
dde
d
a
m
ut
a
ti
on
s
ta
g
e
to
th
e
P
S
O
a
lg
or
it
hm
,
but
a
c
c
or
di
ng
t
o
th
e
pr
in
c
ip
le
s
of
th
e
di
f
f
e
r
e
nt
ia
l
e
v
ol
ut
io
n.
P
a
pe
r
s
[
1
2
-
1
3
]
de
s
c
r
ib
e
P
S
O
w
it
h a
n a
ddi
ti
ona
l
a
ll
ow
a
nc
e
f
or
p
a
r
ti
c
le
a
c
c
e
le
r
a
ti
on, c
a
lc
ul
a
te
d u
s
in
g f
or
m
ul
a
s
f
r
om
th
e
gr
a
v
it
a
ti
ona
l
s
e
a
r
c
h
a
lg
or
it
hm
.
I
n
th
is
a
ppr
oa
c
h,
a
ne
w
a
lg
or
it
hm
is
c
r
e
a
te
d,
of
te
n
us
in
g
th
e
pr
in
c
ip
le
s
of
bot
h
s
w
a
r
m
i
nt
e
ll
ig
e
nc
e
a
nd e
vol
ut
io
na
r
y c
om
put
a
ti
on.
H
ybr
id
a
lg
or
it
hm
s
w
it
h
a
hi
ghe
r
de
gr
e
e
of
in
te
gr
a
ti
on
of
th
e
r
ul
e
s
a
nd
pr
in
c
ip
le
s
of
ope
r
a
ti
on
of
two
a
lg
or
it
hm
s
a
r
e
a
ls
o
pos
s
ib
le
:
F
ir
e
F
ly
+
P
S
O
a
lg
or
it
hm
[
1
4
]
,
P
S
O
+
a
r
ti
f
ic
ia
l
be
e
c
ol
ony
a
lg
or
it
hm
[
1
5
]
,
P
S
O
+
a
nt
c
ol
ony
o
pt
im
iz
a
ti
on
(
A
C
O
)
[
1
6]
,
P
S
O
+
w
ol
f
pa
c
k
a
lg
or
it
hm
[
1
7
]
.
T
hi
s
m
e
th
od
a
ll
ow
s
us
to
c
r
e
a
te
a
n
a
lg
or
it
hm
th
a
t
c
ons
id
e
r
s
pr
obl
e
m
’
s
f
e
a
tu
r
e
s
be
in
g
s
ol
ve
d
a
n
d
c
om
pe
ns
a
te
s
f
or
th
e
s
hor
tc
om
in
gs
of
on
e
a
lg
or
it
hm
by
a
ddi
ng
pr
ope
r
ti
e
s
of
a
not
he
r
to
it
.
N
e
ve
r
th
e
le
s
s
,
th
is
s
ig
ni
f
ic
a
nt
ly
c
om
pl
ic
a
te
s
th
e
c
r
e
a
te
d
a
lg
or
it
hm
f
or
s
ol
vi
ng
th
e
pr
obl
e
m
a
nd
s
e
le
c
ti
ng
th
e
he
ur
is
ti
c
pa
r
a
m
e
te
r
s
'
a
lg
or
it
hm
.
I
n
ot
he
r
w
or
ds
,
th
e
c
om
pl
e
xi
ty
of
t
he
hybr
id
a
lg
or
it
hm
e
xc
e
e
ds
t
he
s
um
of
t
he
c
om
pl
e
xi
ti
e
s
of
t
he
pa
r
ts
t
ha
t
le
a
ve
i
t.
U
s
in
g
m
e
ta
-
opt
im
iz
a
ti
on
w
he
n
one
a
lg
or
it
hm
pe
r
f
or
m
s
th
e
s
e
le
c
ti
on
of
p
a
r
a
m
e
te
r
s
of
a
not
he
r
a
lg
or
it
hm
.
F
or
e
xa
m
pl
e
,
in
[
1
8
]
,
lo
c
a
l
uni
m
oda
l
s
a
m
pl
in
g
w
a
s
us
e
d
to
s
e
le
c
t
th
e
va
lu
e
s
of
th
e
P
S
O
a
lg
or
it
hm
pa
r
a
m
e
te
r
s
;
in
th
e
a
r
ti
c
le
[
1
9
]
,
th
e
P
S
O
pa
r
a
m
e
te
r
s
a
r
e
s
e
le
c
te
d
us
in
g
G
A
;
in
[
20
]
,
th
e
A
C
O
pa
r
a
m
e
te
r
s
a
r
e
s
e
le
c
te
d
us
in
g
th
e
ba
c
te
r
ia
l
f
or
a
gi
ng
a
lg
o
r
it
hm
.
T
hi
s
a
ppr
oa
c
h
r
e
qui
r
e
s
a
ve
r
y
la
r
ge
e
xpe
ndi
tu
r
e
o
f
c
om
put
a
ti
ona
l
r
e
s
our
c
e
s
.
A
t
e
a
c
h
it
e
r
a
ti
on
of
th
e
a
lg
or
it
hm
,
a
ll
a
ge
nt
s
'
pos
it
io
ns
in
th
e
popula
ti
on
or
onl
y
th
e
be
s
t
a
ge
nt
s
a
r
e
us
e
d
a
s
a
n
in
it
ia
l
a
ppr
oxi
m
a
ti
on
f
or
th
e
lo
c
a
l
s
e
a
r
c
h
a
lg
or
it
hm
. I
n
[
21]
,
th
e
uns
tr
in
gi
ng
a
nd
s
tr
in
gi
ng
ope
r
a
to
r
w
a
s
u
s
e
d
f
or
th
e
A
C
O
w
it
h
th
e
lo
c
a
l
s
e
a
r
c
h;
th
e
us
e
of
va
r
io
us
l
oc
a
l
s
e
a
r
c
h
a
lg
or
it
hm
s
in
P
S
O
is
di
s
c
us
s
e
d
in
[
22]
;
F
ir
e
F
ly
+
gr
a
di
e
nt
de
s
c
e
nt
i
s
u
s
e
d i
n [
23]
;
T
he
P
S
O
+
lin
-
k
e
r
ni
gha
n a
lg
or
it
hm
w
a
s
c
ons
id
e
r
e
d i
n [
24]
.
S
w
a
r
m
a
nd
e
vol
ut
io
na
r
y
m
e
ta
he
ur
is
ti
c
a
lg
or
it
hm
s
th
e
m
s
e
lv
e
s
a
r
e
qui
te
c
om
pl
e
x
in
unde
r
s
ta
ndi
ng
th
e
ir
w
or
k
a
nd
f
in
e
-
tu
ni
ng
to
th
e
f
e
a
tu
r
e
s
of
th
e
t
a
s
ks
be
in
g
s
ol
ve
d.
H
ybr
id
s
f
r
om
di
f
f
e
r
e
nt
m
e
ta
he
ur
is
ti
c
a
lg
or
it
hm
s
tu
r
n
out
to
be
e
ve
n
m
or
e
c
om
pl
e
x
a
nd
le
s
s
uni
ve
r
s
a
l.
H
ow
e
ve
r
,
a
s
s
h
o
w
n
in
[
17]
,
th
e
m
e
ta
he
ur
is
ti
c
a
lg
or
it
hm
'
s
e
f
f
ic
ie
nc
y
c
a
n
s
om
e
ti
m
e
s
be
in
c
r
e
a
s
e
d
on
th
e
c
ont
r
a
r
y,
by
s
im
pl
i
f
yi
ng
it
.
P
e
r
ha
ps
th
a
t
is
w
hy
th
e
r
e
a
r
e
m
a
ny
w
or
ks
in
w
hi
c
h
c
om
pl
e
x
hybr
id
a
lg
or
it
hm
s
a
r
e
s
uc
c
e
s
s
f
ul
ly
a
ppl
ie
d
to
s
ol
ve
a
s
pe
c
if
ic
pr
obl
e
m
.
S
ti
ll
,
no
ne
of
th
e
m
ha
s
be
c
om
e
a
s
w
id
e
s
pr
e
a
d
a
s
l
e
s
s
c
om
pl
ic
a
te
d
A
C
O
a
nd
P
S
O
a
m
ong
S
I
a
lg
or
it
hm
s
[
4
]
or
G
A
a
m
ong e
vol
ut
io
na
r
y one
s
.
O
ur
a
ppr
oa
c
h
to
s
ol
vi
ng
opt
im
iz
a
ti
on
pr
obl
e
m
s
a
im
s
to
in
c
r
e
a
s
e
S
I
a
lg
or
it
hm
s
'
e
f
f
ic
ie
nc
y
a
nd
ve
r
s
a
ti
li
ty
w
it
hout
in
c
r
e
a
s
in
g
th
e
ir
c
om
pl
e
xi
ty
.
W
e
a
ppl
y
a
c
om
bi
na
ti
on
of
a
uni
ve
r
s
a
l,
pr
obl
e
m
-
f
r
e
e
S
I
a
lg
or
it
hm
w
it
h
s
im
pl
e
de
te
r
m
in
is
ti
c
dom
a
in
-
s
pe
c
if
ic
he
ur
is
ti
c
a
lg
or
it
hm
s
or
,
in
ot
he
r
w
or
ds
,
gr
e
e
dy
he
ur
is
ti
c
s
.
A
hybr
id
of
a
s
to
c
ha
s
ti
c
uni
ve
r
s
a
l
S
I
a
lg
or
i
th
m
a
nd
a
de
te
r
m
in
is
ti
c
s
im
pl
e
dom
a
i
n
-
s
pe
c
if
ic
a
lg
or
it
hm
a
c
hi
e
ve
s
a
gr
e
a
te
r
s
yn
e
r
gy e
f
f
e
c
t
th
a
n c
om
bi
ni
ng t
w
o
s
w
a
r
m
or
e
vol
ut
i
ona
r
y a
lg
or
it
hm
s
.
2.
G
E
N
E
R
A
L
I
Z
E
D
S
C
H
E
M
E
O
F
S
I
A
L
G
O
R
I
T
H
M
A
N
D
A
P
P
L
I
C
A
T
I
O
N
A
P
P
R
O
A
C
H
T
o
im
pl
e
m
e
nt
th
e
pr
opos
e
d
a
ppr
oa
c
h,
it
is
ne
c
e
s
s
a
r
y
to
m
a
ke
s
ur
e
th
a
t
it
doe
s
not
de
p
e
nd
on
th
e
c
hoi
c
e
of
a
S
I
a
lg
or
it
hm
a
nd
a
dom
a
in
-
s
pe
c
if
ic
h
e
ur
is
ti
c
a
lg
or
i
th
m
.
I
n
th
is
c
a
s
e
,
it
w
il
l
be
qui
te
ve
r
s
a
ti
le
a
nd
f
le
xi
bl
e
a
nd
w
il
l
not
r
e
qui
r
e
a
ny
m
odi
f
ic
a
ti
ons
to
th
e
a
lg
o
r
it
h
m
s
;
onl
y
th
e
ir
in
te
r
a
c
ti
on
f
e
a
tu
r
e
s
w
il
l
c
ha
nge
.
T
he
r
e
f
or
e
,
it
is
ne
c
e
s
s
a
r
y
to
de
f
in
e
a
ge
ne
r
a
li
z
e
d
S
I
a
lg
or
it
hm
m
ode
l
s
o
th
a
t
va
r
io
us
S
I
a
lg
or
it
hm
s
c
a
n
be
e
a
s
il
y
a
ppl
ie
d s
in
c
e
it
i
s
im
pos
s
ib
le
to
s
a
y
in
a
dva
nc
e
w
hi
c
h
on
e
w
il
l
be
be
tt
e
r
in
a
gi
v
e
n
ta
s
k.
N
e
xt
,
w
e
ne
e
d
to
de
f
in
e
a
ge
ne
r
a
l
uni
ve
r
s
a
l
s
c
he
m
e
of
in
te
r
a
c
ti
on
be
tw
e
e
n
a
S
I
a
lg
or
it
hm
a
nd
a
dom
a
in
-
s
pe
c
if
ic
he
ur
is
ti
c
w
it
hout
s
tr
ong de
pe
nde
nc
ie
s
.
2
.1.
G
e
n
e
r
al
iz
e
d
S
I
al
gor
it
h
m
m
od
e
l
A
n
S
I
a
lg
or
it
hm
is
s
p
e
c
if
ie
d
by
d
a
ta
s
tr
uc
tu
r
e
s
a
nd
ope
r
a
ti
ons
on
th
e
m
,
li
ke
m
a
ny
ot
he
r
a
lg
or
it
hm
s
.
S
I
us
e
s
th
e
s
w
a
r
m
,
i.
e
.,
a
popula
ti
on
of
a
ge
nt
s
a
s
a
ba
s
ic
d
a
t
a
s
tr
uc
tu
r
e
a
nd
r
ul
e
s
of
m
ovi
ng
a
ge
nt
s
a
s
a
n
a
lg
or
it
hm
f
o
r
t
r
a
ns
f
or
m
in
g t
he
da
ta
. A
di
s
ti
nc
ti
ve
f
e
a
tu
r
e
of
th
e
S
I
a
lg
or
it
hm
s
i
s
us
in
g a
n i
ndi
r
e
c
t
in
f
or
m
a
ti
o
n
e
xc
ha
nge
be
twe
e
n a
ge
nt
s
. F
or
e
xa
m
pl
e
, t
he
P
S
O
us
e
s
t
he
be
s
t
-
f
ou
nd pos
it
io
n i
n t
he
s
e
a
r
c
h s
pa
c
e
[
2
5
]
;
th
e
a
nt
c
ol
ony
opt
im
iz
a
ti
on
us
e
s
a
phe
r
om
one
gr
a
ph
[
2
6
]
;
th
e
m
onke
y
s
e
a
r
c
h
a
lg
or
it
hm
us
e
s
a
w
e
ig
ht
e
d
c
e
nt
e
r
of
a
ge
nt
s
’
pos
it
io
ns
[
2
7]
. I
t
is
pos
s
ib
le
t
o f
or
m
ul
a
te
ba
s
ic
p
a
r
ts
of
a
n S
I
a
lg
or
it
hm
:
−
A
s
e
t
of
a
ge
nt
s
S
.
−
A
n o
bj
e
c
t
f
or
t
he
i
ndi
r
e
c
t
in
te
r
a
c
ti
on
M
.
−
A
n a
lg
or
it
hm
of
a
ge
nt
s
’
m
ovi
ng a
nd i
nt
e
r
a
c
ti
on w
it
h opti
m
iz
a
ti
on pr
obl
e
m
A
.
−
H
e
ur
is
ti
c
pa
r
a
m
e
te
r
s
P
.
−
A
n i
nput
t
o obta
in
da
ta
f
r
om
t
he
opt
im
iz
a
ti
on pr
obl
e
m
be
in
g s
ol
ve
d
I
.
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
G
e
ne
r
al
iz
e
d
s
w
a
r
m
i
nt
e
ll
ig
e
nc
e
al
go
r
it
hm
s
w
it
h domain
-
s
pe
c
if
ic
he
ur
is
ti
c
s
(
P
. M
at
r
e
ni
n
)
159
−
A
n output
t
o s
e
nd s
ol
ut
io
ns
of
t
he
opt
im
iz
a
ti
on pr
obl
e
m
a
nd t
he
f
in
a
l
a
lg
or
it
hm
r
e
s
ul
t
O
.
A
ny S
I
a
lg
or
it
hm
w
or
ks
a
c
c
or
di
ng t
o t
he
f
ol
lo
w
in
g s
c
he
m
e
.
−
G
e
ne
r
a
ti
on
of
th
e
in
i
ti
a
l
popula
ti
on.
T
he
s
w
a
r
m
a
ge
nt
s
di
s
tr
i
but
e
r
a
ndoml
y
in
th
e
s
ol
ut
io
n
s
e
a
r
c
hi
ng
s
pa
c
e
.
−
C
a
lc
ul
a
ti
on
of
f
it
ne
s
s
-
f
unc
ti
ons
.
E
a
c
h
a
ge
nt
r
e
c
e
iv
e
s
th
e
v
a
lu
e
s
of
th
e
opt
im
iz
a
ti
on
pr
obl
e
m
c
r
it
e
r
io
n
(
c
r
it
e
r
ia
)
.
I
f
t
he
a
ge
nt
ha
s
a
be
tt
e
r
f
it
ne
s
s
t
ha
n a
ll
p
r
e
vi
ous
f
in
e
s
s
e
s
of
a
ll
a
ge
nt
s
, t
hi
s
s
ol
ut
io
n i
s
s
a
ve
d a
s
th
e
be
s
t
c
ur
r
e
nt
s
ol
ut
io
n.
−
A
ge
nt
s
’
m
ove
m
e
nt
. T
he
a
ge
nt
s
m
ove
i
n t
he
s
e
a
r
c
h
s
pa
c
e
u
s
in
g
in
di
r
e
c
t
in
te
r
a
c
ti
ons
.
−
I
f
th
e
s
to
p
c
ondi
ti
on
is
s
a
ti
s
f
ie
d,
th
e
a
lg
or
it
hm
ne
e
ds
to
be
f
in
i
s
he
d
or
ot
he
r
w
is
e
ne
e
d
s
to
be
p
a
s
s
e
d
to
S
te
p 2.
T
he
s
a
v
e
d be
s
t
s
ol
ut
io
n i
s
t
he
a
lg
or
it
hm
r
e
s
ul
t.
2.2. I
n
t
e
r
ac
t
io
n
b
e
t
w
e
e
n
a S
I
al
gor
it
h
m
an
d
a d
om
ai
n
-
s
p
e
c
if
ic
al
gor
it
h
m
T
he
f
ol
lo
w
in
g
in
te
r
f
a
c
e
a
nd
in
te
r
a
c
ti
on
s
te
ps
w
e
r
e
pr
opos
e
d
f
or
th
e
in
te
r
a
c
ti
on
of
a
n
S
I
a
lg
or
it
hm
a
nd a
doma
in
-
s
pe
c
if
ic
he
ur
is
ti
c
a
l
gor
it
hm
.
−
T
he
S
I
a
lg
or
it
hm
r
e
c
e
iv
e
s
a
di
m
e
ns
io
n
of
th
e
s
e
a
r
c
h
s
pa
c
e
of
a
n
opt
im
iz
a
ti
on
ta
s
k
vi
a
in
put
I
.
I
t
is
us
e
d
a
s
t
he
l
e
ngt
h of
t
he
ve
c
to
r
X
.
−
T
he
S
I
a
lg
or
it
hm
ge
ne
r
a
te
s
th
e
va
r
ia
nt
s
of
th
e
pr
obl
e
m
s
ol
ut
io
n
by
a
ge
nt
s
’
m
ove
m
e
nt
s
.
A
c
ount
o
f
va
r
ia
nt
s
i
s
a
c
ount
of
a
ge
nt
s
.
−
E
a
c
h pos
it
io
n i
s
s
e
nt
t
o a
doma
in
-
s
p
e
c
if
ic
he
ur
is
ti
c
a
lg
or
it
hm
of
a
n opti
m
iz
e
d s
ys
te
m
vi
a
out
put
O
pos
.
−
T
he
dom
a
in
-
s
pe
c
if
ic
he
ur
is
ti
c
a
lg
or
it
hm
e
nc
ode
s
th
e
pos
it
io
n
a
nd
us
e
s
it
f
or
s
ol
vi
ng
a
n
op
ti
m
iz
a
ti
on
pr
obl
e
m
a
nd
c
a
lc
ul
a
ti
ng
th
e
c
r
it
e
r
io
n
va
lu
e
s
.
T
hu
s
,
th
e
S
I
a
lg
o
r
it
hm
w
or
ks
a
s
a
m
e
ta
-
opt
im
iz
e
r
f
or
th
e
dom
a
in
-
s
pe
c
if
ic
a
lg
or
it
hm
.
−
A
ll
obt
a
in
e
d c
r
it
e
r
io
n va
lu
e
s
a
r
e
s
e
nt
t
o t
he
S
I
vi
a
I
.
−
T
he
S
I
a
lg
or
it
hm
r
e
c
e
iv
e
s
c
r
it
e
r
io
n
va
lu
e
s
a
nd
pe
r
f
or
m
s
a
ge
n
ts
’
m
ove
m
e
nt
,
i.
e
.,
w
e
go
to
th
e
s
e
c
ond
s
te
p of
t
hi
s
a
lg
or
it
hm
.
W
he
n
a
s
to
p
-
c
ondi
ti
on
is
s
a
ti
s
f
ie
d,
th
e
n
th
e
be
s
t
a
ge
nt
pos
it
io
n
is
tr
a
ns
m
it
te
d
to
out
pu
t
O
.
T
he
s
im
pl
e
s
t
s
to
ppi
ng c
ondi
ti
on i
s
t
he
e
x
e
c
ut
io
n of
a
gi
ve
n numbe
r
of
i
te
r
a
ti
ons
.
T
he
in
te
r
a
c
ti
on’
s
li
s
te
d
s
te
p
s
pr
ovi
de
th
e
in
de
pe
nde
n
c
e
of
u
s
e
d
a
lg
or
it
hm
s
.
T
h
e
a
ppr
oa
c
h
pr
opos
e
d
a
ll
ow
s
us
to
im
pl
e
m
e
nt
di
f
f
e
r
e
nt
S
I
a
lg
or
it
hm
s
qui
c
kl
y.
A
s
f
a
r
a
s
c
ha
ng
e
s
in
th
e
opt
im
iz
a
ti
on
pr
obl
e
m
do
not
c
a
us
e
th
e
ne
c
e
s
s
it
y
of
c
ha
ngi
ng
a
nyt
hi
ng
in
th
e
S
I
a
lg
or
it
hm
i
m
pl
e
m
e
nt
a
ti
on,
a
nd
vi
c
e
ve
r
s
a
.
T
he
a
bs
e
nc
e
of
c
lo
s
e
r
e
la
ti
ons
hi
ps
m
a
ke
s
i
t
pos
s
ib
le
t
o c
om
bi
ne
a
ny S
I
a
lg
or
it
hm
w
it
h doma
in
-
s
pe
c
if
ic
he
ur
is
ti
c
s
.
2.3.
M
ap
p
in
g of
age
n
t
s
’
p
os
it
io
n
s
I
n
th
e
pr
opos
e
d
a
ppr
oa
c
h,
w
e
us
e
th
e
s
e
a
r
c
h
s
p
a
c
e
c
on
s
tr
a
in
ts
f
r
om
0
to
1
f
or
e
a
c
h
di
m
e
ns
io
n.
T
he
in
tr
odu
c
e
d
r
e
s
tr
ic
ti
ons
a
r
e
ne
c
e
s
s
a
r
y
f
or
s
uc
c
e
s
s
f
ul
a
da
pt
a
ti
o
n
a
nd
s
im
pl
e
in
te
gr
a
ti
on
of
th
e
a
lg
or
it
hm
f
or
s
ol
vi
ng
va
r
io
us
opt
im
iz
a
ti
on
pr
obl
e
m
s
.
T
he
f
a
c
t
is
th
a
t
s
om
e
S
I
pa
r
a
m
e
te
r
s
ha
ve
a
di
f
f
e
r
e
nt
e
f
f
e
c
t
de
pe
ndi
ng
on
th
e
s
c
a
le
of
opt
im
iz
a
ti
on
va
r
ia
bl
e
s
.
F
or
e
x
a
m
pl
e
,
in
th
e
f
ir
e
f
ly
opt
im
iz
a
ti
on
a
lg
or
it
hm
[
2
8
]
,
th
e
di
s
ta
nc
e
be
twe
e
n
a
ge
nt
s
a
f
f
e
c
ts
a
g
e
nt
s
’
a
tt
r
a
c
ti
on
nonl
in
e
a
r
ly
.
T
he
r
e
f
or
e
,
if
a
r
a
nge
of
s
e
a
r
c
h
s
pa
c
e
is
f
r
om
0
to
100
,
th
e
di
s
ta
nc
e
f
r
om
th
e
m
id
dl
e
(
50)
to
th
e
hi
gh
e
dge
(
100)
w
il
l
b
e
75.
W
hi
le
if
th
i
s
di
s
ta
nc
e
is
s
c
a
le
d
f
r
om
0
to
1,
th
e
n
th
e
s
a
m
e
di
s
ta
nc
e
w
il
l
be
e
qu
a
l
to
0.75,
a
nd
th
e
d
e
gr
e
e
of
a
tt
r
a
c
ti
on
be
tw
e
e
n
th
e
a
ge
nt
s
w
oul
d
be
c
om
pl
e
te
ly
di
f
f
e
r
e
nt
. A
t
th
e
s
a
m
e
t
im
e
, t
hi
s
di
s
ta
nc
e
i
s
e
qui
va
le
nt
t
o t
he
opt
im
iz
a
ti
on t
a
s
k. A
ls
o, t
he
r
a
di
us
of
th
e
n
e
ig
hbor
hood
r
e
gi
on
w
id
th
of
th
e
b
e
e
’
s
a
lg
or
it
hm
[
29
]
.
T
he
la
r
ge
r
th
e
di
s
ta
nc
e
be
twe
e
n
th
e
bounda
r
ie
s
of
a
s
e
a
r
c
h
s
pa
c
e
di
r
e
c
ti
on,
th
e
gr
e
a
te
r
th
e
ne
ig
hbor
hood
r
e
gi
on
w
id
th
s
houl
d
be
.
I
t
w
oul
d
be
ne
c
e
s
s
a
r
y
f
or
a
non
-
hom
oge
ne
ous
s
e
a
r
c
h
s
pa
c
e
t
o i
nt
r
oduc
e
di
f
f
e
r
e
nt
va
lu
e
s
of
t
he
pa
r
a
m
e
te
r
s
f
or
di
f
f
e
r
e
nt
di
r
e
c
ti
ons
.
A
s
a
r
e
s
ul
t,
th
e
a
lg
or
it
hm
pa
r
a
m
e
te
r
s
w
oul
d
ha
ve
to
be
c
ha
nge
d
e
ve
n
if
a
s
im
pl
e
c
ha
nge
of
m
e
a
s
ur
e
m
e
nt
uni
ts
in
th
e
t
a
s
k
(
hour
s
to
s
e
c
onds
,
a
nd
ki
lo
m
e
t
e
r
s
to
f
e
e
t)
.
W
e
s
ugg
e
s
t
s
pe
c
if
yi
ng
th
e
s
e
a
r
c
h
s
pa
c
e
bounde
d
f
r
om
0.0
to
1.0
in
a
ll
di
r
e
c
ti
ons
in
to
th
e
a
lg
or
it
hm
to
a
voi
d
th
is
.
A
nd
m
a
ppi
ng
of
th
e
a
ge
nt
s
’
c
oor
di
na
te
s
f
r
om
th
e
a
lg
or
i
th
m
in
to
th
e
va
lu
e
s
of
th
e
opt
im
iz
e
d
va
r
ia
bl
e
s
.
I
n
th
e
s
im
pl
e
s
t
va
r
ia
nt
,
th
is
c
a
n
be
done
a
s
f
ol
lo
w
s
. W
e
de
not
e
t
he
c
oor
d
in
a
te
ve
c
to
r
of
a
n
a
ge
nt
X
=
{
x
1
,
x
2
, …,
x
L
}
,
a
nd t
he
ve
c
to
r
of
opt
im
iz
e
d
va
r
ia
bl
e
s
Q
=
{
q
1
,
q
2
, ...,
q
L
}
. U
nde
r
t
he
r
e
s
tr
ic
ti
ons
a
i
≤
q
i
≤
b
i
, w
e
obt
a
in
a
m
a
p of
t
he
f
or
m
q
i
=
x
i
(
b
i
–
a
i
)
+
a
i
,
i
=
1, …,
L
.
A
m
or
e
s
ophi
s
ti
c
a
te
d
va
r
ia
nt
is
s
how
n
in
s
e
c
ti
ons
3
–
4.
T
he
pr
opos
e
d
pa
r
a
m
e
te
r
m
a
ppi
ng
is
ne
c
e
s
s
a
r
y
to
e
li
m
in
a
te
unne
c
e
s
s
a
r
y
r
e
la
ti
ons
hi
ps
be
tw
e
e
n
th
e
opt
im
iz
a
ti
on
pr
obl
e
m
m
ode
l
a
nd
th
e
opt
im
iz
a
ti
on a
lg
or
it
hm
s
.
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
:
157
–
165
160
3.
R
E
S
U
L
T
S
A
N
D
D
I
S
C
U
S
S
I
O
N
3.1.
A
p
p
li
c
at
io
n
e
xam
p
le
. j
ob
-
s
h
op
s
c
h
e
d
u
li
n
g
p
r
ob
le
m
T
hi
s
s
ubs
e
c
ti
on
in
tr
oduc
e
s
it
s
ow
n
s
ym
bol
ic
not
a
ti
on,
w
hi
c
h
s
houl
d
not
b
e
c
onf
us
e
d
w
it
h
th
e
not
a
ti
on i
n t
he
de
s
c
r
ip
ti
ons
of
t
he
S
I
a
lg
or
it
hm
s
(
S
e
c
ti
on
I
I
)
. A
s
m
e
nt
io
ne
d a
bove
, a
m
ode
l
of
a
n opti
m
iz
a
ti
on
pr
obl
e
m
a
nd
th
e
S
I
a
lg
or
it
hm
s
a
r
e
c
om
pl
e
te
ly
in
de
pe
nd
e
nt
.
T
he
jo
b
-
s
hop
s
c
he
dul
in
g
pr
obl
e
m
is
a
m
ong
th
e
m
os
t
c
ha
ll
e
ngi
ng
c
om
bi
na
to
r
ia
l
opt
im
iz
a
ti
on
pr
obl
e
m
s
.
S
c
he
dul
in
g
ta
s
ks
m
a
y
be
c
ha
r
a
c
te
r
iz
e
d
a
s
one
of
th
e
m
os
t
s
ig
ni
f
ic
a
nt
opt
im
iz
a
ti
on
pr
obl
e
m
s
s
in
c
e
pl
a
n
s
a
nd
s
c
he
dul
e
s
ne
e
d
to
be
a
r
r
a
nge
d
in
a
ll
f
ie
ld
s
.
T
h
e
pr
obl
e
m
c
ons
is
ts
of
s
c
he
dul
in
g a
s
e
t
of
j
obs
N
on a
s
e
t
of
m
a
c
hi
ne
s
M
to
m
in
im
iz
e
t
he
pr
oc
e
s
s
in
g t
im
e
na
m
e
d
a
s
t
he
m
a
ke
s
pa
n. I
t
is
t
he
t
im
e
ne
e
de
d t
o pr
oc
e
s
s
a
ll
j
obs
.
E
a
c
h
jo
b i
nc
lu
de
s
a
numbe
r
o
f
ope
r
a
ti
ons
a
nd ha
s
a
pr
e
de
f
in
e
d
ope
r
a
ti
on
or
de
r
.
T
he
o
r
de
r
de
f
in
e
s
a
s
pe
c
if
ic
m
a
c
hi
ne
a
nd
ti
m
e
in
te
r
va
l
f
or
e
a
c
h
ope
r
a
ti
on
a
nd
s
e
que
nc
e
of
ope
r
a
ti
on.
E
a
c
h
m
a
c
hi
ne
c
a
n
pr
oc
e
s
s
onl
y
one
op
e
r
a
ti
on
a
t
a
ti
m
e
.
I
t
ne
e
ds
to
f
in
d
th
e
s
hor
te
s
t
(
qui
c
ke
s
t)
s
c
he
dul
e
a
s
a
di
s
tr
ib
ut
io
n
of
th
e
ope
r
a
ti
on
s
to
ti
m
e
in
te
r
va
ls
o
n
th
e
m
a
c
hi
n
e
s
.
T
hi
s
pr
obl
e
m
be
lo
ngs
t
o t
he
N
P
-
ha
r
d c
la
s
s
[
30]
. L
e
t:
N
=
{
1, …,
n
}
i
s
t
he
s
e
t
of
j
obs
;
M
=
{
1, …,
m
}
i
s
t
he
s
e
t
of
m
a
c
hi
ne
s
;
O
=
{
o
0
,
…,
o
L
+1
}
de
not
e
th
e
s
e
t
of
th
e
a
ll
ope
r
a
ti
ons
,
0
a
nd
L
+
1
a
r
e
f
ic
ti
ons
ope
r
a
ti
ons
:
s
ta
r
t
a
nd
f
in
is
h,
L
is
t
he
t
ot
a
l
num
be
r
of
ope
r
a
ti
ons
of
a
ll
j
obs
[
31
-
32]
.
E
a
c
h
ope
r
a
ti
on
o
O
ha
s
it
s
pr
oc
e
s
s
in
g
ti
m
e
p
(
o
)
.
A
nd
A
de
not
e
s
th
e
s
e
t
of
or
de
r
e
d
p
a
ir
s
of
ope
r
a
ti
ons
c
ons
tr
a
in
e
d
by
th
e
pr
e
c
e
de
nc
e
r
e
la
ti
on
s
;
E
k
de
not
e
s
t
he
s
e
t
of
a
ll
pa
ir
s
of
ope
r
a
ti
ons
w
hi
c
h
r
e
qui
r
e
m
a
c
hi
ne
M
k
. N
e
xt
, l
e
t
t
(
o
)
i
s
t
he
s
ta
r
t
ti
m
e
of
t
he
ope
r
a
ti
on
o
,
t
(
o
0
)
=
0. T
he
pr
obl
e
m
i
s
t
o f
in
d a
s
c
h
e
du
le
:
m
a
x(
t
(
o
)
+
p
(
o
)
)
,
o
O;
(
1)
t
(
o
)
≥ 0,
∀
o
O;
(
2)
t
(
v
)
–
t
(
o
)
≥
p
(
o
)
,
∀
(
o
,
v
)
A
;
(
3)
t
(
w
)
–
t
(
o
)
≥
p
(
o
)
∨
t
(
o
)
–
t
(
w
)
≥
p
(
w
)
,
(
4)
∀
(
w
,
o
)
E
k
,
k
=
1, …,
m.
T
he
va
lu
e
of
m
a
x(
t
(
o
)
+
p
(
o
)
)
i
s
c
a
ll
e
d t
he
m
a
ke
s
pa
n.
3.1.1.
S
I
A
lg
or
it
h
m
w
it
h
t
h
e
gr
e
e
d
y h
e
u
r
is
t
ic
f
or
j
ob
-
s
h
op
s
c
h
e
d
u
li
n
g p
r
ob
le
m
T
he
f
ol
lo
w
in
g a
lg
or
it
hm
c
a
n be
us
e
d a
s
a
s
im
pl
e
gr
e
e
dy he
ur
is
t
ic
f
or
s
ol
vi
ng t
he
pr
obl
e
m
.
I
n
p
u
t
:
O
,
A
,
L
,
E
k
,
m
,
n
1.
Ψ
← {
}
2.
Ω
1:
L
-
1
← s
or
t(
O
)
i
n de
s
c
e
ndi
ng or
de
r
a
nd pr
e
s
e
r
vi
ng t
he
or
de
r
gi
ve
n i
n
E
k
,
k
=
1,…,
m
3.
Ω
0
←
o
0
,
Ω
L
←
o
L
4.
t
(
Ω
0
)
← 0,
Ψ
← {
o
0
}
5.
F
or
i
=
1 …
L
:
5.1. pla
c
e
t
he
ope
r
a
ti
on
Ω
i
:
t
(
Ω
i
)
← mi
n(
t
(
Ω
i
)
)
unde
r
c
ondi
ti
ons
:
t
(
v
)
–
t
(
Ω
i
)
≥
p
(
Ω
i
)
,
∀
(
v
)
Ψ
,
∀
(
Ω
i
,
v
)
A
;
t
(
w
)
–
t
(
Ω
i
)
≥
p
(
Ω
i
)
∨
t
(
Ω
i
)
–
t
(
w
)
≥
p
(
w
)
,
∀
(
w
)
Ψ
,
∀
(
w
,
Ω
i
)
E
k
,
k
=
1, …,
m
5.2.
Ψ
← Ψ
∪
{
Ω
i
}
O
u
t
p
u
t
:
Ψ
(
ve
c
to
r
of
di
s
tr
ib
ut
e
d ope
r
a
ti
ons
)
A
s
a
r
e
s
ul
t,
f
or
e
a
c
h
ope
r
a
ti
on
o
O
,
th
e
s
ta
r
t
ti
m
e
t
(
o
)
w
il
l
be
de
te
r
m
in
e
d,
a
nd
th
e
va
lu
e
of
th
e
opt
im
a
li
ty
c
r
it
e
r
io
n w
il
l
be
e
qua
l
to
t
(
o
L
).
T
hi
s
gr
e
e
dy
he
ur
is
ti
c
a
ll
ow
s
us
to
s
c
he
dul
e
a
c
ti
vi
ti
e
s
to
pr
io
r
i
ti
z
in
g
m
or
e
e
xt
e
nde
d
a
c
ti
vi
ti
e
s
.
T
he
lo
nge
r
th
e
e
xe
c
ut
io
n
ti
m
e
of
th
e
op
e
r
a
ti
on
p
(
o
)
,
th
e
m
or
e
di
f
f
ic
ul
t
it
is
to
f
in
d
a
f
r
e
e
m
a
c
hi
ne
f
or
it
;
th
e
r
e
f
or
e
,
pr
io
r
it
y
is
gi
ve
n
to
m
or
e
e
xt
e
nde
d
ope
r
a
ti
ons
.
T
he
a
dva
nt
a
ge
of
th
e
a
lg
or
it
hm
is
it
s
s
im
pl
ic
it
y
a
nd
th
e
a
bi
li
ty
to
a
dd
a
ddi
ti
ona
l
r
e
s
tr
ic
ti
ons
on
th
e
r
e
la
ti
ons
hi
p
of
ope
r
a
ti
on
s
to
it
.
H
ow
e
ve
r
,
s
uc
h
a
n
a
lg
or
i
th
m
c
a
n
gi
ve
s
ol
ut
io
ns
t
ha
t
a
r
e
f
a
r
f
r
om
opt
im
a
l.
T
he
a
lg
or
it
hm
'
s
e
f
f
ic
ie
nc
y
in
te
r
m
s
of
th
e
c
r
it
e
r
io
n
of
th
e
pr
obl
e
m
(
m
in
im
iz
a
ti
on
of
th
e
m
a
ke
s
pa
n)
c
a
n
be
s
ig
ni
f
ic
a
nt
ly
in
c
r
e
a
s
e
d
du
e
to
th
e
in
te
ll
ig
e
nt
pr
io
r
it
iz
a
ti
on
of
ope
r
a
ti
ons
.
I
n
th
is
c
a
s
e
,
th
e
s
a
m
e
he
ur
is
ti
c
s
c
h
e
m
e
c
a
n
be
a
ppl
ie
d
onl
y
to
or
de
r
th
e
ope
r
a
ti
on
s
n
ot
by
th
e
ir
dur
a
ti
on
but
w
it
h
pr
io
r
it
ie
s
,
w
hi
c
h
c
a
n
be
de
te
r
m
in
e
d
us
in
g
S
I
a
lg
o
r
it
hm
s
.
F
or
a
ppl
yi
ng
a
n
S
I
a
lg
or
it
hm
to
th
e
jo
b
-
s
hop
s
c
he
dul
in
g
pr
obl
e
m
,
a
n
a
ge
nt
pos
it
io
n
(
ve
c
to
r
X
)
is
ne
e
de
d
to
m
a
p
in
to
a
pos
s
ib
le
s
c
he
dul
e
.
T
h
e
ve
c
to
r
X
m
us
t
c
ont
a
in
a
s
m
a
ny
e
le
m
e
nt
s
a
s
t
ot
a
l
ope
r
a
ti
ons
i
n a
ll
j
obs
(
L
)
. T
he
m
a
ppi
ng pr
oc
e
s
s
c
ons
is
t
s
of
s
e
ve
r
a
l
s
te
ps
.
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
G
e
ne
r
al
iz
e
d
s
w
a
r
m
i
nt
e
ll
ig
e
nc
e
al
go
r
it
hm
s
w
it
h domain
-
s
pe
c
if
ic
he
ur
is
ti
c
s
(
P
. M
at
r
e
ni
n
)
161
I
n
p
u
t
:
O
, X
1.
OX
← c
onc
a
te
na
te
_e
le
m
e
nt
_by_
e
le
m
e
nt
(
O
,
X
)
2.
OX
← s
or
t(
OX
)
a
s
c
e
ndi
ng
x
.
3.
O
*
←
OX
1
:
L
, 1
(
r
e
m
ove
x
f
r
om
pa
ir
s
{
o
,
x
}
4.
F
or
i
=
1 …
L
:
r
e
pl
a
c
e
t
he
ope
r
a
ti
on o
i
by t
he
ope
r
a
ti
on o
k
th
a
t
s
houl
d be
on t
h
e
c
or
r
e
s
ponde
nc
e
or
de
r
f
or
t
hi
s
j
ob.
O
u
t
p
u
t
:
O
*
C
ons
id
e
r
a
n e
xa
m
pl
e
of
3 w
or
ks
, e
a
c
h of
w
hi
c
h c
on
s
is
ts
of
3 op
e
r
a
ti
ons
.
J
1
=
{
o
1
,
o
2
,
o
3
}
;
J
2
=
{
o
4
,
o
5
,
o
6
}
;
J
3
=
{
o
7
,
o
8
,
o
9
}.
L
e
t
X
=
{
0.11, 0.72, 0.57, 0.92, 0.43, 0.21, 0.12, 0.40, 0.3}
.
T
he
n
O
=
{
J
1
,
J
2
,
J
3
}
=
{
o
1
,
o
2
,
o
3
,
o
4
,
o
5
,
o
6
,
o
7
,
o
8
,
o
9
}
. A
f
te
r
s
o
r
ti
ng:
OX
=
{
{
o
4
,
0.92}
,
{
o
2
,
0.72
}
,
{
o
3
,
0.57}
,
{
o
5
,
0.43}
,
{
o
8
,
0.4
}
,
{
o
9
,
0.3}
,
{
o
6
,
0.21}
,
{
o
7
,
0.12}
,
{
o
1
,
0.11}
}
.
T
he
ope
r
a
ti
on
or
de
r
obt
a
in
e
d
c
a
nnot
be
us
e
d
a
s
a
s
c
he
dul
e
s
in
c
e
it
is
po
s
s
ib
le
to
vi
ol
a
te
th
e
s
e
qu
e
nc
e
of
ope
r
a
ti
ons
w
it
hi
n one
j
ob.
F
in
a
ll
y,
ta
ki
ng
in
to
a
c
c
ount
th
e
r
e
s
to
r
a
ti
on
of
or
de
r
w
it
hi
n
th
e
w
or
ks
,
w
e
obt
a
i
n
O
*
=
{
o
0
,
o
4
,
o
1
,
o
2
,
o
5
,
o
7
,
o
8
,
o
9
,
o
6
,
o
3
,
o
10
}
,
o
0
a
nd
o
10
a
r
e
f
ic
ti
ons
s
ta
r
t
a
nd f
in
is
h
ope
r
a
ti
ons
.
T
he
ve
c
to
r
O
*
doe
s
not
e
xa
c
tl
y
m
e
a
n
th
e
or
de
r
of
th
e
s
ta
r
ti
ng
o
f
th
e
s
ta
ge
s
.
I
t
m
e
a
ns
th
a
t
ope
r
a
ti
ons
a
r
e
e
xt
r
a
c
te
d
f
r
om
O
in
th
e
or
de
r
in
w
hi
c
h
th
e
y
a
r
e
lo
c
a
te
d
in
O
*
.
F
or
th
e
e
xt
r
a
c
te
d
ope
r
a
ti
on,
th
e
m
om
e
nt
of
th
e
f
a
s
te
s
t
po
s
s
ib
le
s
ta
r
t
is
de
te
r
m
in
e
d.
T
hus
,
th
e
ve
c
to
r
O
*
doe
s
not
s
pe
c
if
y
th
e
or
de
r
of
pr
oc
e
s
s
in
g
ope
r
a
ti
ons
,
but
th
e
or
de
r
of
de
te
r
m
in
in
g
th
e
s
ta
r
t
ti
m
e
f
o
r
th
e
m
.
S
in
c
e
th
e
ti
m
e
c
os
ts
f
or
pe
r
f
or
m
in
g
e
a
c
h
ope
r
a
ti
on
a
r
e
a
s
s
um
e
d
to
be
c
ons
ta
nt
,
th
e
ve
c
to
r
O
*
uni
que
ly
de
te
r
m
in
e
s
th
e
f
in
a
l
s
c
he
dul
e
.
T
he
r
e
f
or
e
,
th
e
ve
c
to
r
X
is
uni
que
ly
tr
a
ns
la
te
d
in
to
th
e
r
e
qui
r
e
d
di
s
c
r
e
te
s
c
he
dul
e
.
T
he
a
dva
nt
a
ge
of
th
e
a
bove
s
c
h
e
m
e
is
obt
a
in
in
g a
n a
ll
ow
a
bl
e
s
c
h
e
dul
e
f
or
a
ny va
lu
e
s
of
t
he
ve
c
to
r
X
.
3.1.2. E
xp
e
r
im
e
n
t
al
r
e
s
u
lt
s
T
he
P
S
O
a
lg
or
it
hm
w
a
s
us
e
d
to
s
ol
ve
th
e
s
e
t
of
jo
b
-
s
hop
pr
obl
e
m
in
s
ta
nc
e
s
[
33]
de
not
e
d
a
s
L
A
01
-
L
A
21
of
va
r
io
us
s
iz
e
s
pr
ovi
de
d
by
O
R
-
L
ib
r
a
r
y
[
34
]
(
L
A
be
c
a
us
e
th
e
a
ut
hor
is
S
.
L
a
w
r
e
nc
e
)
.
T
he
s
iz
e
s
of
in
s
ta
nc
e
s
a
r
e
f
r
om
10×
5
to
15×
10
(
n
×
m
)
.
T
a
bl
e
1
s
how
s
th
e
r
e
s
ul
ts
(
a
ve
r
a
ge
a
nd
th
e
b
e
s
t
s
ol
ut
io
ns
f
r
om
te
n
r
un
s
of
th
e
a
lg
or
it
hm
)
.
A
ls
o,
T
a
bl
e
1
li
s
t
th
e
be
s
t
w
e
ll
-
known
r
e
s
ul
ts
f
r
om
th
e
li
te
r
a
tu
r
e
[
34
]
.
T
he
va
lu
e
s
of
th
e
P
S
O
pa
r
a
m
e
te
r
s
:
popula
ti
on s
iz
e
50,
α
1
=
1.76,
α
2
=
1.38,
ω
=
0.73,
β
=
0.28 [
18]
.
T
he
s
um
m
a
r
y
de
vi
a
ti
on
be
twe
e
n
th
e
be
s
t
a
nd
w
e
ll
-
known
r
e
s
ul
ts
is
135
hour
s
(
0.71%
)
us
in
g
th
e
P
S
O
. T
he
r
e
s
ul
ts
a
r
e
c
lo
s
e
t
o t
he
be
s
t
(
de
vi
a
ti
on <
1%
)
f
or
m
os
t
ta
s
ks
(
81%
)
. T
hus
, t
he
P
S
O
a
lg
or
it
hm
a
ll
ow
s
s
ol
vi
ng
jo
b
-
s
hop
s
c
he
dul
in
g
pr
obl
e
m
s
ve
r
y
c
lo
s
e
to
th
e
be
s
t
-
known
r
e
s
ul
ts
.
M
or
e
ove
r
,
th
e
P
S
O
a
lg
or
it
hm
is
hi
gh
-
s
pe
e
d,
s
in
c
e
onl
y
100
P
S
O
it
e
r
a
ti
ons
w
e
r
e
us
e
d.
I
nc
r
e
a
s
in
g
th
e
it
e
r
a
ti
on
num
be
r
c
a
n
gi
ve
be
tt
e
r
r
e
s
ul
ts
f
or
a
lo
nge
r
ti
m
e
.
T
he
la
r
ge
s
t
ti
m
e
of
s
ol
vi
ng
one
in
s
ta
nc
e
w
a
s
a
bout
0.5
s
e
c
onds
us
in
g
2.4
G
H
z
I
nt
e
l
C
P
U
i7
.
T
he
m
in
im
um
ti
m
e
w
a
s
0.08
s
e
c
onds
.
S
uc
h
va
r
ia
t
io
n
is
e
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L
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593
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L
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926.03
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L
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L
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L
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L
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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
:
157
–
165
162
3.2.
A
p
p
li
c
at
io
n
e
xam
p
le
. e
xp
lo
r
in
g p
ot
e
n
t
ia
l
e
n
e
r
gy s
u
r
f
ac
e
of
n
an
oc
lu
s
t
e
r
i
s
o
m
e
r
s
T
hi
s
s
ubs
e
c
ti
on
di
s
c
us
s
e
s
two
r
e
la
te
d
pr
obl
e
m
s
.
T
he
f
ir
s
t
pr
obl
e
m
is
th
e
lo
c
a
l
m
in
im
a
s
e
a
r
c
h
on
th
e
pot
e
nt
ia
l
e
ne
r
gy
s
ur
f
a
c
e
,
w
hi
c
h
a
r
e
is
om
e
r
s
f
or
a
c
lu
s
te
r
of
a
gi
ve
n
c
om
pos
it
io
n.
T
he
s
e
c
ond
pr
obl
e
m
is
c
a
lc
ul
a
ti
ng t
he
«r
e
a
c
ti
on pa
th
» a
s
t
he
e
n
e
r
ge
ti
c
a
ll
y
m
os
t
f
a
vor
a
bl
e
pa
th
of
t
he
pha
s
e
poi
nt
m
ove
m
e
nt
be
twe
e
n
two
known
lo
c
a
l
m
in
im
a
.
T
he
lo
w
e
r
th
e
m
in
i
m
um
,
th
e
m
o
r
e
s
ta
bl
e
c
or
r
e
s
ponding
c
onf
ig
ur
a
ti
on
of
a
to
m
ic
nuc
le
i.
T
he
r
e
a
r
e
s
pe
c
i
a
li
z
e
d
s
of
twa
r
e
s
ol
ut
io
ns
in
th
e
f
ie
ld
of
bi
oi
nf
o
r
m
a
ti
c
s
f
or
e
xpl
or
in
g
li
ga
nd
bi
ndi
ng/
unbi
ndi
ng
pa
th
w
a
y
[
35
]
.
I
s
om
e
r
s
a
r
e
two
(
o
r
m
or
e
)
m
ol
e
c
ul
e
s
(
na
noc
lu
s
te
r
s
)
w
it
h
th
e
s
a
m
e
m
ol
e
c
ul
a
r
f
or
m
ul
a
, i
.e
., a
to
m
ic
c
om
pos
it
io
n.
I
s
om
e
r
s
a
r
e
di
vi
de
d i
nt
o t
w
o m
a
in
c
a
te
gor
ie
s
. S
tr
uc
tu
r
a
l
is
om
e
r
s
(
or
c
ons
ti
tu
ti
ona
l
is
om
e
r
)
ha
ve
th
e
s
a
m
e
f
or
m
u
la
,
but
th
e
a
to
m
s
a
r
e
bonde
d
to
ge
th
e
r
in
di
f
f
e
r
e
nt
or
de
r
s
.
S
te
r
e
oi
s
om
e
r
s
ha
ve
th
e
s
a
m
e
c
onn
e
c
ti
vi
ty
but
th
e
di
f
f
e
r
e
nt
s
p
a
ti
a
l
a
r
r
a
nge
m
e
nt
s
[
36]
.
I
s
om
e
r
s
c
a
n
ha
v
e
ve
r
y
di
f
f
e
r
e
nt
phys
ic
a
l
pr
ope
r
ti
e
s
,
s
uc
h
a
s
boi
li
ng
poi
nt
,
m
e
lt
in
g
poi
nt
,
a
nd
c
he
m
ic
a
l
r
e
a
c
ti
v
it
y.
I
n
m
e
ta
l
s
ys
t
e
m
s
,
th
e
pr
ope
r
ti
e
s
of
s
te
r
e
oi
s
om
e
r
s
, a
s
a
r
ul
e
, do not di
f
f
e
r
.
T
he
a
c
t
of
a
s
tr
uc
tu
r
a
l
pha
s
e
tr
a
ns
it
io
n
in
a
na
noc
lu
s
te
r
is
a
m
ut
ua
l
ge
om
e
tr
ic
r
e
a
r
r
a
nge
m
e
nt
of
a
to
m
s
oc
c
ur
r
in
g
in
ti
m
e
[
37]
.
A
c
c
or
di
ngl
y,
th
e
c
lu
s
te
r
'
s
e
ne
r
gy
a
nd
it
s
phy
s
i
c
oc
h
e
m
ic
a
l
pr
ope
r
ti
e
s
s
ubs
ta
nt
ia
ll
y
de
pe
nd
on
th
e
ge
om
e
tr
ic
a
r
r
a
nge
m
e
nt
of
th
e
a
to
m
s
.
E
ve
n
in
s
ig
ni
f
ic
a
nt
c
ha
nge
s
in
th
e
s
pa
ti
a
l
s
tr
uc
tu
r
e
of
a
c
lu
s
te
r
c
a
n l
e
a
d t
o
r
a
th
e
r
l
a
r
ge
c
ha
nge
s
i
n i
ts
t
ot
a
l
e
ne
r
gy. T
he
i
ni
ti
a
l
ge
om
e
tr
y'
s
s
ui
ta
bl
e
c
hoi
c
e
is
c
r
uc
ia
l
f
or
obt
a
in
in
g
r
e
li
a
bl
e
, c
a
lc
ul
a
te
d va
lu
e
s
of
a
c
lu
s
te
r
'
s
phys
ic
oc
he
m
ic
a
l
c
ha
r
a
c
t
e
r
is
ti
c
s
i
n a
s
ta
ti
ona
r
y
(
e
qui
li
br
iu
m
)
s
ta
te
.
F
or
a
s
uc
c
e
s
s
f
ul
ly
c
a
lc
ul
a
te
d
ge
om
e
tr
y,
c
ha
nge
s
in
e
ne
r
gy
va
lu
e
s
dur
in
g
th
e
opt
im
iz
a
ti
on
pr
oc
e
s
s
s
houl
d
be
in
s
ig
ni
f
ic
a
nt
(
le
s
s
th
a
n
a
gi
ve
n
va
lu
e
)
.
A
ls
o
,
f
or
a
n
opt
im
iz
e
d
ge
om
e
tr
y,
th
e
f
ir
s
t
e
ne
r
gy
de
r
iv
a
ti
ve
s
(
gr
a
di
e
nt
)
w
it
h
r
e
s
pe
c
t
to
a
ll
ge
om
e
tr
ic
di
s
to
r
ti
ons
s
houl
d
be
c
lo
s
e
to
z
e
r
o.
I
t
s
ugge
s
t
s
th
a
t
w
e
a
r
e
on
a
f
la
t
e
ne
r
gy
s
ur
f
a
c
e
.
W
h
e
n
c
on
s
id
e
r
in
g
th
e
br
oa
de
r
f
e
a
tu
r
e
s
of
th
e
pot
e
nt
ia
l
e
ne
r
gy
s
ur
f
a
c
e
(
P
E
S
)
,
in
c
lu
di
ng
to
pol
ogy
a
nd
to
pogr
a
phy,
it
ha
s
be
c
om
e
us
ua
l
to
r
e
f
e
r
to
th
e
P
E
S
a
s
th
e
«pot
e
nt
ia
l
e
ne
r
g
y
la
nds
c
a
pe
» [
38]
.
E
ne
r
gy
s
ur
f
a
c
e
s
a
nd
la
nd
s
c
a
pe
s
hol
d
th
e
k
e
y
to
unde
r
s
ta
ndi
ng
a
w
id
e
r
a
nge
of
m
ol
e
c
ul
a
r
phe
nom
e
na
.
T
o
c
on
s
tr
uc
t
th
e
P
E
S
,
it
is
c
onve
ni
e
nt
to
us
e
th
e
s
o
-
c
a
ll
e
d
in
te
r
na
l
c
oor
di
na
te
s
,
w
hi
c
h
in
c
lu
d
e
bond
le
ngt
hs
or
ot
he
r
in
te
r
a
to
m
ic
di
s
ta
nc
e
s
,
bond
a
nd
di
he
dr
a
l
a
ngl
e
s
of
a
c
lu
s
te
r
/m
ol
e
c
ul
e
.
T
h
e
num
be
r
of
3
n
-
6
(
w
he
r
e
n
is
th
e
num
be
r
of
a
to
m
ic
nuc
le
i)
of
in
de
pe
nde
nt
c
oor
d
in
a
te
s
s
houl
d
in
c
lu
de
th
os
e
s
tr
uc
tu
r
a
l
pa
r
a
m
e
te
r
s
th
a
t
c
ha
nge
m
os
t
dr
a
m
a
ti
c
a
ll
y
dur
in
g
th
e
tr
a
ns
f
o
r
m
a
ti
on
unde
r
in
ve
s
ti
ga
ti
on.
T
he
pa
pe
r
[
39]
de
s
c
r
ib
e
s
a
pot
e
nt
ia
l
e
ne
r
gy
s
ur
f
a
c
e
in
te
r
m
s
of
lo
c
a
l
m
in
im
a
a
nd
th
e
tr
a
ns
it
io
n
s
ta
te
s
th
a
t
c
onne
c
t
th
e
m
pr
ovi
de
s
a
c
onc
e
pt
ua
l
a
nd
c
om
put
a
ti
ona
l
f
r
a
m
e
w
or
k f
or
unde
r
s
ta
ndi
ng a
nd pr
e
di
c
ti
ng obs
e
r
va
bl
e
pr
ope
r
ti
e
s
.
A
pot
e
nt
ia
l
ba
r
r
ie
r
to
s
tr
uc
tu
r
a
l
tr
a
n
s
f
or
m
a
ti
on
is
th
e
e
ne
r
gy
of
th
e
tr
a
ns
it
io
n
s
ta
t
e
(
s
a
ddl
e
poi
nt
)
r
e
la
ti
ve
to
th
e
in
it
ia
l
m
in
im
um
of
th
e
pot
e
nt
ia
l
e
ne
r
gy
s
ur
f
a
c
e
.
I
t
is
th
e
pot
e
nt
ia
l
ba
r
r
ie
r
th
a
t
de
te
r
m
in
e
s
th
e
r
a
te
of
th
e
pr
oc
e
s
s
of
s
tr
uc
tu
r
a
l
tr
a
ns
f
or
m
a
ti
on.
I
n
th
e
A
r
r
he
ni
us
e
qua
ti
on,
th
e
s
e
a
r
e
th
e
a
c
ti
va
ti
on
e
n
e
r
gi
e
s
Е
А
:
k
=
k
0
e
xp(
-
Е
А
/
k
B
T
)
;
Е
А
is
th
e
e
n
e
r
gy
a
c
ti
va
ti
on,
k
0
i
s
th
e
p
r
e
-
e
xpone
nt
ia
l
f
a
c
to
r
f
or
th
e
r
e
a
c
ti
on,
k
B
i
s
th
e
B
ol
tz
m
a
nn c
ons
ta
nt
,
T
is
t
he
a
bs
ol
ut
e
t
e
m
pe
r
a
tu
r
e
(
in
K
e
lv
in
s
)
.
T
o
c
on
s
tr
uc
t
a
m
in
im
um
e
ne
r
gy
pa
th
be
twe
e
n
two
known
c
ons
ti
tu
ti
ona
l
i
s
om
e
r
s
,
a
n
e
f
f
ic
ie
nt
s
ol
ut
io
n
to
th
e
a
s
s
ig
nm
e
nt
pr
obl
e
m
in
a
b
ip
a
r
ti
te
gr
a
ph
is
r
e
qui
r
e
d.
E
a
c
h
a
to
m
of
is
om
e
r
A
(
r
e
a
ge
nt
)
is
a
s
s
oc
ia
t
e
d
w
it
h
one
a
nd
onl
y
one
a
to
m
of
is
om
e
r
B
(
pr
odu
c
t)
.
T
he
pr
obl
e
m
c
a
n
be
s
ol
ve
d
a
s
a
gl
oba
l
opt
im
iz
a
ti
on
pr
obl
e
m
.
A
ppl
yi
ng
tr
a
di
ti
ona
l
nu
m
e
r
ic
a
l
m
e
th
ods
is
im
pr
a
c
ti
c
a
l
be
c
a
us
e
th
e
y
ne
e
d
hu
ge
a
m
ount
s
of
c
om
put
a
ti
ona
l
r
e
s
our
c
e
s
l
ik
e
t
im
e
a
nd m
e
m
or
y [
40]
.
3.2.1.
G
r
e
e
d
y
h
e
u
r
is
t
ic
T
hus
,
th
e
s
e
a
r
c
h
f
or
is
om
e
r
s
c
or
r
e
s
ponding
to
lo
c
a
l
m
in
im
a
a
nd
th
e
c
ons
tr
uc
ti
on
of
th
e
m
in
im
u
m
e
ne
r
gy
pa
th
be
twe
e
n
th
e
m
a
r
e
th
e
ba
s
ic
s
ta
ge
s
of
th
e
P
E
S
c
o
ns
tr
uc
ti
on
pr
oc
e
s
s
.
I
t
is
ne
c
e
s
s
a
r
y
to
f
in
d
th
e
pe
r
m
ut
a
ti
on f
unc
ti
on
P
, w
hi
c
h w
oul
d a
s
s
oc
ia
te
w
it
h e
a
c
h a
to
m
a
i
f
r
om
A
(
i
=
1, …,
n
)
one
a
nd only one
a
to
m
b
p
(
i
)
f
r
om
B
, s
o t
ha
t
r
oot
m
e
a
d s
qua
r
e
d di
s
ta
nc
e
,
R
M
SD
(
f
)
=
(
Σ
i
n
=1
|a
i
–
b
j
*
|
2
)
1/
2
→
m
in
,
b
i
*
=
b
P
(
i
)
A
ddi
ti
ona
l
r
e
s
tr
ic
ti
ons
a
r
e
im
pos
e
d
on
c
ol
li
s
io
ns
of
th
e
tr
a
ns
it
io
n
pa
th
s
of
a
to
m
s
.
T
he
m
in
im
u
m
di
s
ta
nc
e
be
twe
e
n t
he
c
e
nt
e
r
s
of
t
he
ve
c
to
r
s
c
onne
c
ti
ng t
he
a
to
m
s
a
i
a
nd
b
P
(
i
)
(
i
=
1, …,
n
)
m
us
t
be
no l
e
s
s
t
ha
n
c
m
i
n
=
c
di
s
t
m
in
(
m
in
_di
s
anc
e
_A
,
m
in
_di
s
anc
e
_B
),
w
he
r
e
c
di
s
t
is
a
n
e
m
pi
r
ic
a
l
c
oe
f
f
ic
ie
nt
(
~
0.8)
,
m
in
_di
s
anc
e
_X
–
th
e
m
in
im
um
di
s
ta
nc
e
a
m
ong
a
ll
pa
ir
s
of
a
to
m
s
of
is
om
e
r
X
(
A
or
B
)
.
T
hi
s
li
m
it
a
ti
on,
hi
gh
di
m
e
ns
io
na
li
ty
a
nd
th
e
pr
e
s
e
nc
e
of
s
e
ve
r
a
l
ty
pe
s
of
a
to
m
s
do
not
a
ll
ow
th
e
e
xi
s
ti
ng
m
e
th
od
s
f
or
s
ol
vi
ng
a
s
s
ig
nm
e
nt
pr
obl
e
m
s
w
it
hout
t
he
ir
s
ig
ni
f
ic
a
nt
m
odi
f
ic
a
ti
on.
W
e
c
om
bi
ne
a
s
tr
a
ig
ht
f
or
w
a
r
d
gr
e
e
dy
he
ur
is
ti
c
a
lg
or
i
th
m
a
n
d
th
e
uni
ve
r
s
a
l
P
S
O
a
lg
or
it
hm
s
.
T
he
he
ur
is
ti
c
us
e
d
in
vol
ve
s
s
e
que
nt
ia
ll
y
s
or
ti
ng
th
e
a
to
m
s
of
is
o
m
e
r
B
a
nd
m
a
tc
hi
ng
e
a
c
h
of
th
e
m
w
it
h
t
he
ne
a
r
e
s
t
a
to
m
f
r
om
A
th
a
t
ha
s
not
ye
t
be
e
n m
a
tc
he
d.
T
hi
s
he
ur
is
t
ic
c
a
n be
w
r
it
te
n:
I
n
p
u
t
:
A
,
B
,
n, L
(
L
li
s
t
of
numbe
r
s
f
r
om
1 t
o
n
w
i
th
out
r
e
pe
ti
ti
ons
)
1.
ta
bu
← {
}
.
2.
F
or
i
=
1 …
n
;
j
=
1 …
n
:
D
ij
← |
a
i
–
b
j
|
2
(
f
or
a
to
m
s
of
di
f
f
e
r
e
nt
s
or
ts
, t
he
di
s
ta
nc
e
i
s
i
nf
in
it
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
G
e
ne
r
al
iz
e
d
s
w
a
r
m
i
nt
e
ll
ig
e
nc
e
al
go
r
it
hm
s
w
it
h domain
-
s
pe
c
if
ic
he
ur
is
ti
c
s
(
P
. M
at
r
e
ni
n
)
163
3.
F
or
i
=
1 …
n
:
3.1.
j
←
ar
gm
in
(
D
L
i
j
)
,
j
∉
ta
bu
3.2.
P
(
L
i
)
←
j
3.3.
ta
bu
←
ta
bu
∪
{
j
}.
O
u
t
p
u
t
:
P
S
te
p 3.2 me
a
ns
t
ha
t
L
i
a
to
m
of
B
goe
s
ove
r
t
o t
he
pos
it
io
n of
t
he
j
-
th
a
to
m
of
A
.
T
he
r
e
s
ul
ti
ng
ta
bl
e
f
unc
ti
on
P
is
th
e
de
s
ir
e
d
pe
r
m
ut
a
ti
on.
T
he
a
dva
nt
a
ge
of
s
uc
h
he
ur
is
ti
c
is
a
ve
r
y
hi
gh
s
pe
e
d
of
ope
r
a
ti
on
s
o
th
e
s
ol
ut
io
n
is
obt
a
in
e
d
in
one
pa
s
s
th
r
ough
th
e
a
to
m
s
of
is
om
e
r
B
.
I
f
th
e
pha
s
e
s
tr
uc
tu
r
e
of
two
is
om
e
r
s
is
c
lo
s
e
a
nd
is
om
e
r
B
is
not
r
ot
a
te
d
r
e
la
ti
ve
to
is
om
e
r
A
,
th
is
s
ol
ut
io
n
m
e
th
od a
ll
ow
s
to
f
in
d
th
e
opt
im
a
l
s
ol
ut
io
n
r
e
ga
r
dl
e
s
s
of
th
e
num
be
r
of
a
to
m
s
a
nd
num
b
e
r
s
or
ts
of
a
to
m
s
.
B
ut
it
is
not
s
ui
ta
bl
e
f
or
m
or
e
c
om
pl
e
x
p
r
obl
e
m
s
s
i
nc
e
a
t
th
e
ve
r
y
f
ir
s
t
it
e
r
a
ti
ons
of
th
e
w
or
k,
it
c
a
n
m
a
tc
h
a
to
m
s
o
f
is
om
e
r
B
to
s
uc
h
a
to
m
s
of
is
om
e
r
A
,
w
hi
c
h,
if
opt
im
a
ll
y
s
ol
ve
d,
s
houl
d
b
e
m
a
tc
he
d
w
it
h
ot
he
r
a
to
m
s
of
is
om
e
r
B
.
3.2.2.
S
I
al
gor
it
h
m
w
it
h
t
h
e
gr
e
e
d
y h
e
u
r
is
t
ic
T
he
r
e
s
ul
ti
ng a
lg
or
it
hm
c
a
n
be
w
r
it
te
n
:
I
n
p
u
t
:
A
,
B
,
n
,
m
, ps
o_i
te
r
s
1.
X
m
← {
x
1
,
x
2
, …,
x
n
}
, x
mk
←r
a
ndom(
0, 1)
,
m
=
1, …, |
S
|,
k
=
1,
…,
n
2.
F
or
i
=
1 …
ps
o_i
te
r
s
:
2.1.
F
or
m
=
1, …, |S
|.
2.1.1.
L
← c
r
e
a
te
_or
de
r
_l
is
t{
x
m
1
, x
m
2
, …
, x
m
n
}.
2.1.2. P
← gr
e
e
dy_he
ur
is
ti
c
(
A
,
B
,
n
,
L
)
2.1.3.
fi
tn
e
s
s
← R
M
S
D
(
A
,
P
(
B
))
2.1.4.
If
fi
tn
e
s
s
<
fi
tn
e
s
s
_m
in
fi
tn
e
s
s
_m
in
←
fi
tn
e
s
s
P
be
s
t
←
P
2.2. P
a
r
ti
c
le
s
’
m
ove
m
e
nt
O
u
t
p
u
t
:
P
be
s
t
T
he
de
ve
lo
pe
d
m
e
th
od
ha
s
be
e
n
te
s
te
d
on
s
om
e
is
om
e
r
c
onf
ig
ur
a
ti
ons
f
r
om
7
to
39
a
to
m
s
.
T
a
bl
e
2
s
how
s
th
e
va
lu
e
s
of
th
e
R
M
S
D
obt
a
in
e
d
by
th
e
gr
e
e
dy
h
e
u
r
is
ti
c
onl
y
a
nd
by
th
e
P
S
O
w
it
h
th
e
gr
e
e
dy
he
ur
is
ti
c
.
T
he
m
a
th
e
m
a
ti
c
a
l
m
ode
li
ng
c
onf
ir
m
e
d
th
a
t
th
e
c
o
m
bi
na
ti
on
of
gr
e
e
dy
he
ur
is
ti
c
s
ba
s
e
d
on
th
e
phys
ic
a
l
pr
ope
r
ti
e
s
of
th
e
pr
obl
e
m
a
nd
S
I
a
lg
o
r
it
hm
s
s
ig
ni
f
ic
a
nt
ly
im
pr
ove
d
th
e
r
e
s
ul
ts
r
e
ga
r
di
ng
a
ppl
yi
ng
th
e
s
e
m
e
th
ods
s
e
pa
r
a
te
ly
.
T
a
bl
e
2. R
e
s
ul
ts
of
f
in
di
ng t
he
s
hor
te
s
t
di
s
ta
n
c
e
be
twe
e
n i
s
om
e
r
s
of
t
he
bi
m
e
ta
ll
ic
c
lu
s
te
r
I
ns
t
a
nc
e
G
r
e
e
dy he
ur
i
s
t
i
c
, R
M
S
D
, A
ng
s
t
r
om
P
S
O
w
i
t
h t
he
gr
e
e
dy he
ur
i
s
t
i
c
, R
M
S
D
, A
ngs
t
r
om
A
g7
9,78
9,02
A
u19
24,52
20,80
A
u20
no va
l
i
d s
ol
ut
i
on f
ound
26,88
A
u12A
g12
no va
l
i
d s
ol
ut
i
on f
ound
98,41
C
u15A
g15
63,85
61,72
C
o16C
u16
no va
l
i
d
s
ol
ut
i
on f
ound
67,61
A
u6A
g33
no va
l
i
d s
ol
ut
i
on f
ound
48,17
4.
C
O
N
C
L
U
S
I
O
N
I
n
th
is
a
r
ti
c
le
,
a
hybr
id
a
ppr
oa
c
h
is
pr
opos
e
d
ut
il
iz
in
g
th
e
s
tr
e
ngt
hs
of
S
I
a
nd
dom
a
in
-
s
pe
c
if
ic
he
ur
is
ti
c
a
lg
or
it
hm
s
. T
he
m
a
in
id
e
a
be
hi
nd
d
e
ve
lo
pi
ng
i
s
:
(a
)
to
he
lp
th
e
S
I
a
lg
or
it
hm
to
ta
ke
in
to
a
c
c
ount
th
e
s
pe
c
if
ic
s
of
th
e
s
ol
ve
d
pr
obl
e
m
th
a
nks
to
th
e
dom
a
in
-
s
pe
c
if
ic
a
lg
or
it
hm
a
nd
(
b
)
to
im
p
r
ove
th
e
e
f
f
ic
ie
nc
y
of
th
e
dom
a
in
-
s
pe
c
if
ic
a
lg
or
it
hm
by
in
tr
oduc
in
g
s
to
c
ha
s
ti
c
a
nd
s
e
lf
-
or
ga
ni
z
e
d
pr
ope
r
ti
e
s
f
r
om
th
e
S
I
a
lg
or
it
hm
.
D
if
f
e
r
e
nt
S
I
a
lg
o
r
it
hm
s
c
a
n
be
e
a
s
il
y
a
ppl
ie
d
due
to
S
I
a
lg
or
it
hm
’
s
lo
w
c
oupl
in
g
a
nd
th
e
dom
a
in
-
s
pe
c
if
ic
he
ur
is
ti
c
a
lg
or
it
hm
.
T
he
a
ppr
oa
c
h’
s
a
ppl
ic
a
ti
on
is
d
e
m
ons
tr
a
te
d
on
th
e
jo
b
-
s
hop
s
c
he
dul
in
g
pr
obl
e
m
a
nd
th
e
pr
obl
e
m
of
c
ons
tr
uc
ti
on
of
th
e
m
in
im
um
e
ne
r
gy
p
a
th
be
twe
e
n
two
is
om
e
r
s
.
T
he
e
xpe
r
im
e
nt
s
c
onf
ir
m
e
d
th
a
t
th
e
pr
opos
e
d
a
ppr
oa
c
h
a
ll
ow
s
th
e
us
e
of
S
I
a
lg
or
it
hm
s
a
s
a
m
e
ta
-
opt
im
iz
e
r
th
a
t
in
c
r
e
a
s
e
s
dom
a
in
-
s
p
e
c
if
ic
he
ur
is
ti
c
a
lg
or
it
hm
s
’
e
f
f
ic
ie
nc
y.
A
C
K
N
O
WL
E
D
G
E
M
E
N
T
S
T
hi
s
w
or
k
w
a
s
pa
r
ti
a
ll
y
f
unde
d
by
R
us
s
ia
n
F
e
de
r
a
ti
on
of
B
a
s
i
c
R
e
s
e
a
r
c
h,
pr
oj
e
c
t
20
-
37
-
70007;
by
th
e
M
in
is
tr
y
of
S
c
ie
nc
e
a
nd
H
ig
he
r
E
duc
a
ti
on
of
th
e
R
us
s
i
a
n
F
e
de
r
a
ti
on
in
th
e
f
r
a
m
e
w
or
k
of
th
e
S
ta
te
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
:
157
–
165
164
P
r
ogr
a
m
in
th
e
F
ie
ld
o
f
th
e
R
e
s
e
a
r
c
h
A
c
ti
vi
ty
pr
oj
e
c
t
08
17
-
2020
-
0007;
N
a
ti
ona
l
S
c
ie
nt
i
f
ic
P
r
og
r
a
m
“
In
f
or
m
a
ti
on
a
nd
C
om
m
uni
c
a
ti
on
T
e
c
hnol
ogi
e
s
f
or
a
S
in
gl
e
D
ig
it
a
l
M
a
r
ke
t
in
S
c
ie
nc
e
,
E
duc
a
ti
on
a
nd
S
e
c
ur
it
y
(
I
C
T
in
S
E
S
)
”
,
M
in
is
tr
y
o
f
E
duc
a
ti
on
a
nd
S
c
ie
nc
e
–
B
ul
ga
r
ia
a
nd
th
e
B
ul
ga
r
ia
n
N
S
F
unde
r
th
e
g
r
a
nt
D
F
N
I
-
D
N
02/
10;
a
nd N
ovos
ib
ir
s
k S
ta
te
T
e
c
hni
c
a
l
U
ni
v
e
r
s
it
y de
ve
lo
pm
e
nt
pr
ogr
a
m
,
pr
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