I
AE
S In
t
er
na
t
io
na
l J
o
urna
l o
f
Art
if
icia
l In
t
ellig
ence
(
I
J
-
AI
)
Vo
l.
1
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,
Feb
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0
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6
,
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383
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:
h
ttp
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//ij
a
i
.
ia
esco
r
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co
m
Centrality
-
o
pti
mi
zed coa
lition
forma
tion
:
a
g
eneti
c
a
lg
o
rithm
a
ppro
a
ch wit
h l
ea
dership a
t
tribu
tes
Ano
n Suk
s
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So
ra
p
a
k
P
u
k
des
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S
c
h
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f
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n
f
o
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ma
t
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o
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Te
c
h
n
o
l
o
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y
a
n
d
I
n
n
o
v
a
t
i
o
n
,
B
a
n
g
k
o
k
U
n
i
v
e
r
s
i
t
y
,
P
a
t
h
u
m
Th
a
n
i
,
Th
a
i
l
a
n
d
Art
icle
I
nfo
AB
S
T
RAC
T
A
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ticle
his
to
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y:
R
ec
eiv
ed
Oct
3
0
,
2
0
2
4
R
ev
is
ed
No
v
3
,
2
0
2
5
Acc
ep
ted
J
an
1
0
,
2
0
2
6
In
g
ra
p
h
t
h
e
o
r
y
,
c
e
n
tralit
y
is
o
fte
n
a
ss
e
ss
e
d
u
sin
g
trad
it
i
o
n
a
l
m
e
th
o
d
s su
c
h
a
s
c
lo
se
n
e
ss
c
e
n
tralit
y
,
w
h
ich
m
e
a
su
re
s
th
e
a
v
e
ra
g
e
sh
o
rtes
t
p
a
th
len
g
t
h
b
e
twe
e
n
n
o
d
e
s
i
n
a
n
e
two
r
k
.
In
t
h
is
stu
d
y
,
we
p
rima
ril
y
fo
c
u
s
o
n
d
e
v
e
lo
p
in
g
th
e
p
ro
p
o
se
d
a
p
p
r
o
a
c
h
a
n
d
d
e
m
o
n
stra
ti
n
g
it
s
e
ffe
c
ti
v
e
n
e
ss
th
r
o
u
g
h
in
i
ti
a
l
e
x
p
e
rime
n
tal
re
su
lt
s
.
A
n
o
v
e
l
g
e
n
e
ti
c
a
lg
o
r
it
h
m
(G
A)
–
b
a
se
d
m
e
th
o
d
n
a
m
e
d
c
e
n
tralit
y
–
o
p
t
imiz
e
d
lea
d
e
rsh
i
p
c
o
a
li
ti
o
n
fo
rm
a
ti
o
n
(COLCF
)
h
a
s
b
e
e
n
d
e
sig
n
e
d
.
It
e
m
p
h
a
siz
e
s
a
c
tu
a
l
a
g
e
n
t
d
istan
c
e
s
a
c
c
o
rd
in
g
t
o
c
lo
se
n
e
ss
c
e
n
tralit
y
a
n
d
lea
d
e
rsh
ip
a
tt
ri
b
u
tes
in
g
r
o
u
p
f
o
rm
a
ti
o
n
.
We
d
e
tail
t
h
e
COLCF
a
lg
o
ri
th
m
,
p
re
se
n
t
e
m
p
i
rica
l
c
a
se
stu
d
ies
,
a
n
d
p
r
o
v
i
d
e
e
fficie
n
c
y
c
o
m
p
a
riso
n
s
.
In
a
c
c
o
rd
a
n
c
e
wi
th
o
u
r
sim
u
lati
o
n
re
su
lt
s,
th
e
p
ro
p
o
se
d
a
lg
o
rit
h
m
is
c
a
p
a
b
le
o
f
c
a
p
i
tali
z
in
g
o
n
t
h
e
id
e
a
l
c
o
a
li
t
io
n
stru
c
tu
re
fo
r
a
c
h
iev
in
g
h
i
g
h
c
l
o
se
n
e
ss
c
e
n
tralit
y
wh
e
n
in
c
o
r
p
o
ra
te
d
with
lea
d
e
rsh
i
p
a
tt
rib
u
tes
.
Th
e
e
x
p
e
rime
n
tal
re
su
lt
s
d
e
m
o
n
stra
te
t
h
e
a
lg
o
rit
h
m
’
s
ro
b
u
st
n
e
ss
a
n
d
e
ffe
c
ti
v
e
n
e
ss
in
a
d
d
re
ss
in
g
c
o
m
p
lex
c
o
a
l
it
io
n
f
o
rm
a
ti
o
n
c
h
a
ll
e
n
g
e
s
.
K
ey
w
o
r
d
s
:
C
lo
s
en
ess
ce
n
tr
ality
Gen
etic
alg
o
r
ith
m
Gr
o
u
p
f
o
r
m
atio
n
L
ea
d
er
s
h
ip
attr
ib
u
tes
Op
tim
izatio
n
alg
o
r
ith
m
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
An
o
n
Su
k
s
tr
ien
wo
n
g
Sch
o
o
l o
f
I
n
f
o
r
m
atio
n
T
ec
h
n
o
lo
g
y
an
d
I
n
n
o
v
atio
n
,
B
an
g
k
o
k
Un
iv
er
s
ity
9
/
1
Mo
o
5
,
Ph
ah
o
n
y
o
th
in
R
o
a
d
,
Kh
lo
n
g
Nu
en
g
,
Kh
lo
n
g
L
u
a
n
g
Dis
tr
ict,
Path
u
m
T
h
an
i,
T
h
ailan
d
E
m
ail:
an
o
n
.
s
u
@
b
u
.
ac
.
th
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
co
n
ce
p
t
o
f
“
co
alitio
n
f
o
r
m
atio
n
”
h
as
b
ee
n
m
o
d
eled
as
an
ess
en
tial
to
o
l
th
r
o
u
g
h
m
a
th
em
atica
l
th
eo
r
ies
o
f
co
alitio
n
b
eh
a
v
io
r
,
allo
win
g
g
r
o
u
p
s
t
o
o
b
tain
t
h
e
g
r
ea
test
b
en
ef
it
.
Acc
o
r
d
i
n
g
ly
,
it
h
as
b
ee
n
ap
p
lied
ac
r
o
s
s
d
iv
er
s
e
co
n
tex
ts
an
d
d
o
m
ain
s
.
I
n
p
ar
ticu
lar
,
it
is
em
p
lo
y
ed
in
altr
u
is
tic
d
ec
is
io
n
-
m
a
k
in
g
in
m
u
lti
-
ag
e
n
t
s
y
s
tem
s
[
1
]
,
s
h
ar
ed
r
eso
u
r
ce
m
an
ag
em
en
t
i
n
co
n
g
esti
o
n
p
r
o
b
lem
s
wh
er
e
m
u
ltip
le
ag
en
ts
co
m
p
ete
f
o
r
lim
ited
r
eso
u
r
ce
s
[
2
]
,
p
u
b
lic
allo
ca
tio
n
g
u
id
ed
b
y
in
f
o
r
m
atio
n
d
esig
n
[
3
]
,
an
d
ca
p
ab
ilit
y
-
b
ased
m
o
d
elin
g
f
o
r
c
o
m
p
lex
g
r
o
u
p
task
s
[
4
]
.
I
n
th
e
r
eal
-
w
o
r
ld
ap
p
licatio
n
s
,
th
e
ter
m
“
c
o
alitio
n
f
o
r
m
atio
n
”
is
alter
n
ativ
ely
r
ef
er
r
e
d
to
as
team
f
o
r
m
atio
n
,
s
tr
ateg
ic
alli
an
ce
s
,
jo
in
t
v
en
t
u
r
e
f
o
r
m
atio
n
,
g
r
o
u
p
f
o
r
m
atio
n
,
p
ar
tn
er
s
h
ip
f
o
r
m
atio
n
,
an
d
co
llab
o
r
ativ
e
g
r
o
u
p
in
g
[
5
]
–
[
8
]
.
Am
o
n
g
th
ese,
“
team
f
o
r
m
atio
n
”
is
a
ter
m
o
f
te
n
u
s
ed
in
th
e
co
n
tex
t
o
f
g
am
es
.
I
t
r
ef
er
s
to
o
p
tim
izin
g
g
r
o
u
p
o
u
tco
m
es
t
h
r
o
u
g
h
co
o
p
er
ativ
e
ef
f
o
r
ts
b
ased
o
n
th
e
attr
ib
u
tes
o
f
th
e
g
am
e
’
s
p
ar
ticip
an
ts
[
9
]
,
[
1
0
]
.
I
n
th
e
b
u
s
in
ess
co
n
tex
t,
it
is
o
f
ten
r
ef
er
r
ed
to
as
s
tr
ateg
ic
allian
ce
s
,
wh
er
e
allian
ce
co
m
p
an
ies
co
llab
o
r
ate
to
d
e
v
elo
p
in
n
o
v
atio
n
an
d
e
n
h
an
c
e
m
ar
k
et
p
er
f
o
r
m
a
n
ce
b
y
s
h
ar
in
g
s
tr
en
g
th
s
an
d
m
u
tu
al
b
e
n
ef
its
.
I
t
ca
n
also
b
e
ca
lled
“
jo
in
t
v
en
tu
r
e
f
o
r
m
atio
n
”
wh
e
n
r
e
f
er
r
in
g
to
a
f
o
r
m
al
b
u
s
in
ess
ar
r
an
g
em
e
n
t
[
1
1
]
.
Similar
ly
,
th
e
ter
m
“
p
a
r
tn
er
s
h
ip
f
o
r
m
atio
n
”
is
u
s
ed
in
ter
ch
a
n
g
ea
b
ly
with
“
g
r
o
u
p
f
o
r
m
atio
n
,
”
b
u
t
it
m
o
s
t
c
o
m
m
o
n
ly
d
escr
ib
es
o
f
f
icial
ag
r
ee
m
en
ts
b
etwe
en
two
o
r
m
o
r
e
p
ar
ties
f
o
r
lo
n
g
-
ter
m
co
llab
o
r
atio
n
[
1
2
]
.
T
h
e
ter
m
“
g
r
o
u
p
f
o
r
m
atio
n
”
is
co
m
m
o
n
ly
u
s
ed
in
ed
u
ca
tio
n
as
well,
p
ar
ticu
lar
ly
in
co
llab
o
r
ativ
e
lear
n
i
n
g
an
d
co
m
p
u
ter
-
s
u
p
p
o
r
te
d
co
llab
o
r
ati
v
e
lear
n
in
g
(
C
SC
L
)
en
v
ir
o
n
m
en
ts
.
Fo
r
ex
am
p
le,
s
o
m
e
tech
n
o
lo
g
y
co
m
p
an
ies
jo
in
to
g
eth
er
to
s
h
ar
e
th
eir
s
k
ills
an
d
id
ea
s
to
cr
ea
te
n
ew
in
n
o
v
atio
n
s
.
T
h
er
ef
o
r
e
,
co
alitio
n
s
ch
em
es
h
av
e
b
ec
o
m
e
ess
en
tial
to
o
ls
,
o
f
f
er
in
g
p
r
o
m
is
in
g
s
o
lu
tio
n
s
to
d
ea
l
with
co
m
p
lex
c
h
allen
g
es,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8
9
3
8
I
n
t J Ar
tif
I
n
tell
,
Vo
l.
1
5
,
No
.
1
,
Feb
r
u
ar
y
2
0
2
6
:
383
-
3
9
8
384
esp
ec
ially
in
e
d
u
ca
tio
n
,
w
h
er
e
c
o
llab
o
r
atio
n
is
em
p
l
o
y
ed
to
ac
h
iev
e
o
p
tim
al
l
ea
r
n
in
g
o
b
jectiv
es
.
T
h
is
is
b
ec
au
s
e
en
h
an
cin
g
t
h
e
p
er
f
o
r
m
an
ce
o
f
d
iv
e
r
s
e
s
tu
d
en
ts
th
r
o
u
g
h
g
r
o
u
p
wo
r
k
l
ies
at
th
e
co
r
e
o
f
ed
u
ca
tio
n
al
d
ev
el
o
p
m
en
t
.
C
h
ai
et
a
l
.
[
1
3
]
co
n
d
u
cted
a
s
y
s
tem
atic
r
ev
iew
o
f
em
p
ir
ical
r
e
s
ea
r
ch
f
o
cu
s
in
g
o
n
co
m
p
u
ter
-
b
ased
ass
ess
m
en
t
o
f
co
llab
o
r
ativ
e
p
r
o
b
lem
-
s
o
l
v
in
g
(
C
PS
)
s
k
ills
.
T
h
e
au
t
h
o
r
s
p
o
in
te
d
o
u
t
th
at
co
llab
o
r
ativ
e
m
eth
o
d
s
s
h
o
u
l
d
p
r
io
r
itize
r
ea
l
-
wo
r
l
d
s
k
ills
an
d
e
f
f
ec
tiv
ely
ca
p
tu
r
e
s
tu
d
en
ts
’
co
llab
o
r
ativ
e
b
eh
av
io
r
s
an
d
o
u
tco
m
es
.
W
i
th
in
en
g
in
ee
r
in
g
,
t
h
e
ter
m
“
co
alitio
n
f
o
r
m
atio
n
”
d
escr
ib
e
s
h
o
w
a
u
to
n
o
m
o
u
s
ag
en
ts
s
elf
-
o
r
g
an
ize
in
to
ta
s
k
-
o
r
ien
ted
g
r
o
u
p
s
to
im
p
r
o
v
e
ef
f
icien
cy
an
d
r
esp
o
n
s
iv
en
ess
in
co
m
p
lex
en
v
ir
o
n
m
en
ts
[
1
4
]
,
[
1
5
]
.
T
h
e
p
ap
er
s
em
p
h
asize
h
o
w
task
co
m
p
letio
n
is
o
p
tim
ized
b
y
g
r
o
u
p
in
g
m
em
b
e
r
s
b
ased
o
n
s
k
ills
an
d
c
o
n
tex
tu
al
in
f
o
r
m
atio
n
.
C
o
n
s
eq
u
en
tly
,
s
ev
er
al
r
esear
c
h
er
s
h
av
e
in
v
esti
g
ated
v
ar
io
u
s
m
eth
o
d
o
lo
g
ies,
r
u
les,
p
o
lici
es,
d
o
m
ain
k
n
o
wled
g
e,
a
n
d
g
u
id
elin
es
f
o
r
s
elec
tin
g
ap
p
r
o
p
r
iate
alg
o
r
ith
m
s
f
o
r
co
alitio
n
f
o
r
m
atio
n
to
ac
h
iev
e
th
eir
r
esp
ec
tiv
e
o
b
jectiv
es
.
Fo
r
e
x
am
p
le,
B
au
s
ch
[
1
6
]
p
r
o
p
o
s
es
r
u
les
in
th
e
c
o
n
tex
t
o
f
p
o
liti
cs
r
eg
ar
d
in
g
h
o
w
lead
er
s
ar
e
r
e
-
s
elec
ted
an
d
h
o
w
th
ey
f
o
r
m
th
e
b
est
co
alitio
n
s
o
f
d
if
f
e
r
en
t
s
izes
with
in
l
ar
g
e
g
r
o
u
p
s
.
T
h
ese
s
elec
ted
lead
er
s
ar
e
in
ten
d
e
d
to
f
ac
ilit
ate
ef
f
ec
tiv
e
co
o
r
d
in
atio
n
an
d
en
h
an
ce
o
v
er
a
ll
g
r
o
u
p
c
o
h
esio
n
.
Din
g
et
a
l
.
[
1
7
]
em
p
l
o
y
co
alit
io
n
f
o
r
m
atio
n
to
o
p
tim
ize
a
d
i
s
tr
ib
u
ted
n
etwo
r
k
i
n
a
jam
m
i
n
g
en
v
i
r
o
n
m
e
n
t
o
n
m
u
lti
-
ag
en
t b
eh
a
v
io
r
.
T
h
e
au
t
h
o
r
s
p
r
esen
t d
is
tr
ib
u
ted
alg
o
r
it
h
m
s
th
at
en
ab
le
u
s
er
s
to
m
ak
e
d
ec
is
io
n
s
r
esu
ltin
g
in
ef
f
icien
t
n
etwo
r
k
p
er
f
o
r
m
an
ce
.
R
o
s
s
i
et
a
l
.
[
1
8
]
r
ev
i
ew
s
ev
er
al
alg
o
r
ith
m
ic
s
tr
ateg
ies
f
o
r
co
alitio
n
f
o
r
m
atio
n
a
n
d
class
if
y
m
u
lti
-
ag
en
t
alg
o
r
ith
m
s
f
o
r
co
llectiv
e
b
eh
av
io
r
,
h
ig
h
lig
h
tin
g
th
eir
r
o
le
in
d
is
tr
ib
u
ted
d
ec
is
io
n
-
m
ak
in
g
.
Sev
er
al
s
tu
d
ies
f
o
cu
s
o
n
o
n
lin
e
co
aliti
o
n
f
o
r
m
atio
n
f
r
o
m
t
h
eo
r
etic
al
an
d
alg
o
r
ith
m
ic
p
er
s
p
ec
tiv
es,
as
d
etailed
b
y
B
u
llin
g
er
a
n
d
R
o
m
e
n
[
1
9
]
.
T
h
i
s
lin
e
o
f
s
tu
d
y
,
in
clu
d
i
n
g
a
b
r
o
ad
er
o
v
er
v
iew,
is
g
en
er
ally
s
u
p
p
o
r
ted
b
y
th
e
s
u
r
v
ey
o
n
co
alitio
n
f
o
r
m
atio
n
in
m
u
lti
-
ag
en
t sy
s
tem
s
[
6
]
,
[
2
0
]
,
[
2
1
]
.
I
n
co
n
test
ab
ly
,
a
ch
iev
in
g
th
ei
r
co
m
m
o
n
o
b
j
ec
tiv
es
th
r
o
u
g
h
jo
in
in
g
p
r
o
p
er
m
em
b
er
s
in
tan
d
em
an
d
h
av
in
g
th
e
r
i
g
h
t
in
d
iv
id
u
als
in
th
e
g
r
o
u
p
s
m
ak
es
s
tr
o
n
g
co
llab
o
r
ativ
e
co
n
n
ec
tio
n
s
[
2
2
]
.
Fo
r
m
in
g
g
r
o
u
p
s
o
f
in
d
iv
id
u
als
in
a
v
ir
tu
al
en
v
ir
o
n
m
e
n
t
h
as
b
ee
n
v
alid
ated
as
to
o
l
f
o
r
g
e
n
er
atin
g
p
o
s
itiv
e
o
u
tc
o
m
es
b
y
m
ax
i
m
izin
g
o
p
p
o
r
tu
n
ities
f
o
r
s
h
ar
in
g
ea
ch
m
em
b
er
’
s
ex
p
er
ien
ce
an
d
s
atis
f
y
in
g
ad
e
q
u
ate
lear
n
in
g
p
e
r
f
o
r
m
an
ce
[
9
]
,
[
2
3
]
–
[
2
5
]
.
I
t
is
wid
ely
ac
k
n
o
wled
g
ed
th
a
t,
u
p
to
th
e
p
r
esen
t
tim
e,
th
e
r
e
ar
e
v
ar
io
u
s
ap
p
r
o
ac
h
es
to
es
tab
lis
h
in
g
g
r
o
u
p
f
o
r
m
ati
o
n
,
in
clu
d
in
g
r
a
n
d
o
m
g
r
o
u
p
in
g
,
s
elf
-
s
elec
tio
n
,
an
d
cr
iter
io
n
-
b
ased
g
r
o
u
p
in
g
.
R
am
ír
ez
et
a
l
.
[
2
6
]
ex
am
in
ed
t
h
ese
ap
p
r
o
ac
h
es
i
n
s
ec
o
n
d
ar
y
ed
u
ca
tio
n
,
h
ig
h
lig
h
tin
g
th
eir
ch
ar
ac
te
r
is
tics
an
d
im
p
licatio
n
s
.
T
h
e
r
an
d
o
m
tech
n
iq
u
e
is
an
ea
s
y
an
d
s
tr
aig
h
tf
o
r
war
d
m
eth
o
d
s
in
ce
ev
er
y
o
n
e
is
ass
ig
n
ed
to
g
r
o
u
p
s
r
a
n
d
o
m
ly
.
I
t
allo
ws
all
m
em
b
er
s
to
b
e
m
i
x
ed
to
ac
h
ie
v
e
h
eter
o
g
en
eity
in
th
e
s
ep
ar
ated
g
r
o
u
p
in
g
s
[
2
7
]
–
[
2
9
]
.
T
h
is
g
o
al,
h
o
wev
er
,
is
n
o
t
alwa
y
s
s
atis
f
ied
,
as
r
an
d
o
m
ly
ass
ig
n
in
g
s
t
u
d
en
ts
to
g
r
o
u
p
s
ca
n
lead
to
is
s
u
es,
w
ith
s
o
m
e
m
em
b
er
s
b
ein
g
r
elu
ctan
t
to
jo
in
th
e
g
r
o
u
p
to
wh
ich
t
h
ey
h
av
e
b
ee
n
allo
ca
ted
.
T
h
e
s
ec
o
n
d
m
eth
o
d
,
s
elf
-
s
elec
ted
g
r
o
u
p
f
o
r
m
atio
n
,
allo
ws
p
eo
p
le
to
estab
lis
h
g
r
o
u
p
s
in
d
e
p
en
d
e
n
tly
.
T
h
i
s
ap
p
r
o
ac
h
en
ab
les
ev
er
y
o
n
e
to
f
o
r
m
g
r
o
u
p
s
b
ased
o
n
th
eir
o
wn
d
ec
is
io
n
s
,
p
r
ef
er
en
ce
s
,
o
r
f
am
iliar
ity
with
o
t
h
er
s
[
2
7
]
,
[
2
9
]
–
[
3
1
]
.
T
h
e
th
ir
d
m
eth
o
d
,
cr
iter
io
n
-
b
ased
g
r
o
u
p
in
g
,
p
er
m
its
th
e
f
o
r
m
atio
n
o
f
g
r
o
u
p
s
b
ased
o
n
s
p
ec
if
ied
cr
iter
ia
an
d
alg
o
r
ith
m
s
d
ee
m
e
d
s
cien
tific
a
lly
ac
cu
r
ate
[
2
9
]
,
[
3
1
]
,
[
3
2
]
.
C
o
n
s
eq
u
en
tly
,
v
ar
i
o
u
s
g
r
o
u
p
i
n
g
cr
iter
ia
h
a
v
e
b
ee
n
p
r
o
p
o
s
ed
to
cr
ea
te
well
-
s
tr
u
c
tu
r
ed
g
r
o
u
p
s
th
at
f
o
s
ter
co
lla
b
o
r
atio
n
,
en
h
an
ce
task
e
f
f
ici
en
cy
,
a
n
d
im
p
r
o
v
e
o
v
er
all
p
er
f
o
r
m
an
ce
.
Fro
m
a
n
o
th
er
p
e
r
s
p
ec
tiv
e
,
a
m
u
lti
-
tar
g
et
o
p
tim
izatio
n
tech
n
i
q
u
e
was
p
r
o
p
o
s
ed
b
y
Mir
an
d
a
et
a
l
.
[
3
3
]
to
f
ac
ilit
ate
th
e
g
r
o
u
p
f
o
r
m
atio
n
p
r
o
b
lem
,
wh
ile
ac
co
u
n
tin
g
f
o
r
n
u
m
er
o
u
s
o
b
jectiv
e
f
u
n
ctio
n
s
s
u
ch
as
in
ter
-
h
o
m
o
g
en
eity
,
in
tr
a
-
h
eter
o
g
en
eity
,
an
d
em
p
ath
y
.
T
h
eir
e
x
p
er
im
en
ts
wer
e
co
n
d
u
cted
o
n
v
ar
y
in
g
s
izes a
n
d
co
m
p
lex
itie
s
,
aim
in
g
to
m
ax
im
ize
th
e
av
e
r
ag
e
s
im
ilar
ity
o
f
g
r
o
u
p
m
e
m
b
er
s
.
Fo
llo
win
g
th
at,
B
o
o
n
g
asam
e
et
a
l
.
[
3
4
]
p
r
esen
ted
a
f
ascin
atin
g
wo
r
k
in
v
o
lv
in
g
g
r
o
u
p
f
o
r
m
ati
o
n
with
th
e
ch
ar
ac
ter
is
tic
o
f
a
co
alitio
n
lead
er
.
T
h
e
au
th
o
r
s
f
o
cu
s
ed
o
n
a
b
u
y
er
co
aliti
o
n
s
ch
em
e
to
g
ain
ad
d
itio
n
al
d
is
co
u
n
ts
f
o
r
th
eir
g
r
o
u
p
p
u
r
ch
aser
s
.
Ho
wev
er
,
we
ar
e
in
ter
ested
b
y
th
e
f
ac
t
t
h
at
a
g
r
o
u
p
o
f
in
d
i
v
id
u
als
d
is
tr
ib
u
ted
in
d
if
f
e
r
en
t
g
eo
lo
g
ical
lo
ca
tio
n
s
m
u
s
t
f
o
r
m
a
g
r
o
u
p
b
ased
o
n
th
e
r
esu
lts
o
f
co
s
t
a
n
d
r
ewa
r
d
,
wh
er
e
ea
ch
m
em
b
er
is
p
lace
d
ad
jace
n
t
to
ea
ch
o
th
er
.
Fo
r
m
in
g
g
r
o
u
p
s
o
f
m
em
b
e
r
s
b
ased
o
n
t
h
eir
g
e
o
g
r
ap
h
ical
lo
ca
tio
n
,
o
f
co
u
r
s
e,
d
em
an
d
s
a
g
r
o
u
p
ce
n
tr
ality
m
ea
s
u
r
em
en
t
in
o
r
d
er
to
id
e
n
tify
s
ig
n
if
ica
n
t
in
d
iv
id
u
als
wh
o
p
o
s
s
ess
lead
er
s
h
ip
attr
ib
u
tes
an
d
a
h
ig
h
s
co
r
e
i
n
clo
s
en
ess
ce
n
tr
a
lity
am
o
n
g
a
lar
g
e
n
u
m
b
er
o
f
p
ar
ticip
an
ts
.
T
h
is
is
b
ec
au
s
e
g
r
o
u
p
m
em
b
er
s
ca
n
b
e
d
ir
ec
tly
in
f
lu
e
n
ce
d
b
y
th
e
g
r
o
u
p
'
s
lead
er
.
T
h
e
r
ef
o
r
e
,
ea
c
h
p
er
s
o
n
'
s
lead
er
s
h
ip
attr
ib
u
te
is
s
p
ec
if
ied
in
o
r
d
e
r
to
ass
es
s
clo
s
en
ess
ce
n
tr
ality
.
A
m
em
b
er
ca
n
b
e
d
ef
in
ed
a
s
a
n
o
d
e
in
g
r
a
p
h
th
eo
r
y
.
All
n
o
d
es
m
ay
h
a
v
e
a
lead
er
at
th
eir
ce
n
ter
,
as
a
q
u
alif
ied
lead
er
ca
n
co
o
r
d
in
ate
g
r
o
u
p
ac
tiv
ities
an
d
c
o
m
f
o
r
tab
ly
co
m
m
u
n
icate
to
all
m
em
b
er
s
.
I
n
a
d
d
itio
n
,
g
r
o
u
p
lead
er
s
h
ip
is
o
n
e
o
f
th
e
m
o
s
t
ess
en
tial
ch
ar
ac
ter
is
tic
s
o
f
team
ef
f
icien
c
y
.
So
m
e
au
th
o
r
s
in
[
3
5
]
,
[
3
6
]
h
a
v
e
af
f
ir
m
e
d
th
at
lead
e
r
s
h
ip
co
r
r
elate
s
to
b
etter
team
p
e
r
f
o
r
m
an
ce
.
Fra
n
s
en
et
a
l
[
3
5
]
v
e
r
if
ied
th
at
it
is
b
en
ef
icial
to
d
esig
n
ate
a
lead
er
in
a
g
r
o
u
p
to
em
p
o
wer
team
m
em
b
e
r
s
s
in
ce
lead
er
s
h
ip
ab
ilit
ies
ar
e
m
o
r
e
b
r
o
ad
ly
d
is
p
er
s
ed
o
v
er
tim
e
am
o
n
g
tea
m
m
em
b
er
s
.
T
h
e
r
elev
an
ce
o
f
clo
s
en
ess
in
th
e
n
etwo
r
k
g
r
a
p
h
[
3
7
]
,
is
u
s
ed
to
d
eter
m
in
e
a
n
o
d
e'
s
p
o
wer
,
ac
tiv
ities
,
an
d
co
m
m
u
n
icatio
n
co
n
v
e
n
ien
ce
.
Mo
r
eo
v
er
,
th
e
au
th
o
r
s
claim
ed
th
at
g
r
o
u
p
ac
tiv
ities
ar
e
alwa
y
s
ass
o
ciate
d
with
g
o
o
d
lead
er
s
h
ip
,
s
tr
o
n
g
p
o
p
u
lar
ity
,
o
r
th
e
r
ep
u
tatio
n
o
f
a
n
etwo
r
k
.
Me
s
h
ch
e
r
y
a
k
o
v
a
a
n
d
Sh
v
y
d
u
n
[
3
8
]
als
o
em
p
h
asized
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J Ar
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I
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tell
I
SS
N:
2252
-
8
9
3
8
C
en
tr
a
lity
-
o
p
timiz
ed
co
a
liti
o
n
fo
r
ma
tio
n
:
a
g
en
etic
a
lg
o
r
ith
m
a
p
p
r
o
a
c
h
w
ith
…
(
A
n
o
n
S
u
kstr
ien
w
o
n
g
)
385
im
p
o
r
tan
ce
o
f
ce
n
tr
ality
m
etr
i
cs
in
ev
alu
atin
g
in
d
iv
id
u
al
r
o
l
es
with
in
a
n
etwo
r
k
.
T
h
e
au
th
o
r
s
h
ig
h
lig
h
ted
t
h
at
clo
s
en
ess
,
b
etwe
en
n
ess
,
an
d
eig
en
v
ec
to
r
ce
n
tr
ality
ea
c
h
o
f
f
er
u
n
i
q
u
e
in
s
ig
h
ts
in
to
an
in
d
iv
id
u
al'
s
in
f
lu
en
ce
an
d
co
m
m
u
n
icatio
n
ef
f
icien
c
y
.
C
o
m
p
lem
en
tin
g
th
is
,
I
s
tr
ate
et
a
l
.
[
3
9
]
p
r
o
p
o
s
ed
a
g
am
e
-
th
eo
r
etic
f
r
am
ewo
r
k
f
o
r
an
aly
zin
g
ce
n
tr
ality
b
y
m
o
d
elin
g
in
d
i
v
id
u
als
an
d
th
eir
co
n
n
ec
tio
n
s
as
co
alitio
n
s
,
th
e
r
eb
y
en
h
an
cin
g
th
e
m
ea
s
u
r
em
en
t o
f
in
f
lu
e
n
ce
an
d
ef
f
ec
tiv
en
ess
with
in
g
r
o
u
p
in
t
er
ac
tio
n
s
.
T
h
e
r
esear
ch
in
[
4
0
]
,
[
4
1
]
em
p
h
asized
th
e
im
p
o
r
tan
ce
o
f
clo
s
en
ess
ce
n
tr
ality
in
le
ad
er
s
h
ip
.
Mitter
lech
n
er
h
i
g
h
lig
h
ted
h
o
w
lead
er
s
p
o
s
itio
n
ed
clo
s
er
to
o
th
e
r
s
in
th
e
n
etwo
r
k
ca
n
b
etter
co
o
r
d
in
ate
ac
tiv
ities
an
d
in
f
lu
en
ce
g
r
o
u
p
d
y
n
am
ics,
w
h
ile
Yu
an
a
n
d
K
n
ip
p
en
b
er
g
[
4
1
]
d
is
cu
s
s
ed
h
o
w
a
lead
er
’
s
ce
n
tr
a
l
p
o
s
itio
n
in
a
n
etwo
r
k
p
o
s
itiv
ely
im
p
ac
ts
team
p
er
f
o
r
m
an
ce
,
with
team
s
ize
ac
tin
g
as
a
m
o
d
er
atin
g
f
ac
to
r
.
T
h
e
p
ap
er
s
p
r
o
v
id
e
u
s
with
a
p
er
s
p
ec
tiv
e
o
n
h
o
w
ce
n
t
r
ality
u
n
d
er
s
co
r
es
th
e
im
p
o
r
tan
ce
o
f
in
co
r
p
o
r
atin
g
lead
er
s
h
ip
attr
ib
u
tes
wh
e
n
ev
a
lu
atin
g
n
etwo
r
k
s
tr
u
ctu
r
es
.
T
h
er
ef
o
r
e,
in
clu
d
in
g
lead
e
r
s
h
ip
a
ttrib
u
tes
is
cr
itical
in
th
is
wo
r
k
.
C
o
n
s
eq
u
en
tly
,
t
h
e
d
is
tan
ce
b
etwe
en
m
em
b
er
s
an
d
th
eir
g
r
o
u
p
lead
e
r
is
,
th
u
s
,
th
e
p
r
im
a
r
y
f
a
cto
r
in
o
u
r
wo
r
k
f
o
r
f
o
r
m
in
g
o
p
tim
al
g
r
o
u
p
s
s
o
th
at
cl
o
s
en
ess
ce
n
tr
ality
ca
n
b
e
ac
h
iev
e
d
.
H
o
wev
er
,
cr
ea
tin
g
a
n
o
p
tim
al
g
r
o
u
p
f
o
r
m
atio
n
b
ase
d
o
n
th
e
clo
s
en
ess
ce
n
tr
ality
o
f
th
e
lead
er
is
a
d
em
an
d
in
g
p
r
o
b
lem
th
at
r
eq
u
ir
es
a
s
o
p
h
is
ticated
alg
o
r
ith
m
.
T
h
e
r
ef
o
r
e,
th
e
d
ev
elo
p
m
en
t
o
f
e
f
f
icien
t
alg
o
r
ith
m
s
to
tack
le
t
h
is
p
r
o
b
lem
is
cr
u
cial
in
v
ar
io
u
s
d
o
m
ain
s
.
T
h
is
p
ap
er
is
o
r
g
an
ized
in
to
f
iv
e
s
ec
tio
n
s
,
in
clu
d
in
g
th
is
i
n
tr
o
d
u
ct
o
r
y
s
ec
tio
n
.
Sectio
n
2
in
clu
d
es
b
ac
k
g
r
o
u
n
d
th
eo
r
y
as
well
as
an
o
v
e
r
v
iew
o
f
liter
atu
r
e
r
elat
ed
to
o
u
r
wo
r
k
.
Sectio
n
3
d
es
cr
ib
es
o
u
r
p
r
o
p
o
s
ed
g
en
etic
-
lik
e
alg
o
r
ith
m
f
o
r
g
en
er
atin
g
o
p
tim
al
g
r
o
u
p
s
o
f
ag
e
n
ts
in
ter
m
s
o
f
clo
s
en
ess
ce
n
tr
ality
to
a
q
u
alif
ie
d
lead
er
.
A
clo
s
en
ess
ce
n
tr
ality
-
b
ased
m
ea
s
u
r
e
t
h
at
we
e
m
p
lo
y
ed
in
th
e
f
itn
ess
f
u
n
ctio
n
is
also
d
etailed
.
Fo
llo
win
g
th
at,
s
ec
tio
n
4
p
r
esen
ts
an
em
p
ir
ical
ca
s
e
s
tu
d
y
to
v
alid
ate
th
e
p
r
o
p
o
s
ed
alg
o
r
it
h
m
.
T
h
e
co
n
clu
s
io
n
an
d
d
is
cu
s
s
io
n
ar
e
p
r
o
v
i
d
ed
in
s
ec
tio
n
5
.
2.
B
ACK
G
RO
UND
AN
D
RE
L
AT
E
D
WO
RK
S
T
h
is
s
ec
tio
n
p
r
o
v
id
es
a
b
r
ief
b
ac
k
g
r
o
u
n
d
o
f
g
r
o
u
p
f
o
r
m
atio
n
r
eg
ar
d
i
n
g
a
co
alitio
n
lead
er
as
well
a
s
clo
s
en
ess
ce
n
tr
ality
in
th
e
n
et
wo
r
k
to
c
o
m
p
r
e
h
en
d
t
h
e
co
alit
io
n
d
ev
el
o
p
m
en
t
o
f
o
u
r
p
r
o
p
o
s
ed
alg
o
r
ith
m
.
2
.
1
.
G
ro
up
f
o
rma
t
io
n
Gr
o
u
p
f
o
r
m
atio
n
co
n
ce
p
ts
i
n
v
o
lv
e
th
e
ch
allen
g
e
o
f
g
r
o
u
p
in
g
m
em
b
er
s
ef
f
ec
tiv
ely
to
e
n
s
u
r
e
s
u
cc
ess
f
u
l
co
llab
o
r
atio
n
to
wa
r
d
a
c
o
m
m
o
n
g
o
al
[
2
9
]
,
[
3
1
]
,
[
4
2
]
,
[
4
3
]
.
Su
cc
ess
f
u
l
g
r
o
u
p
f
o
r
m
atio
n
d
ep
e
n
d
s
n
o
t
o
n
l
y
o
n
in
d
i
v
id
u
al
s
k
ills
b
u
t
also
o
n
th
e
s
tr
ateg
ic
p
o
s
itio
n
in
g
o
f
m
e
m
b
er
s
with
in
t
h
e
s
o
cial
n
etwo
r
k
t
o
m
ax
im
ize
in
ter
ac
tio
n
an
d
in
f
l
u
en
ce
[
4
4
]
,
[
4
5
]
.
C
u
r
r
en
tly
,
n
u
m
er
o
u
s
s
tu
d
ies
e
n
d
ea
v
o
r
to
estab
lis
h
o
p
tim
ized
g
r
o
u
p
s
with
a
v
ar
iety
o
f
aim
s
an
d
tech
n
iq
u
es
.
Fo
r
in
s
tan
ce
,
Seth
i
an
d
Nich
o
ls
o
n
[
4
6
]
in
v
e
s
tig
ated
h
y
p
o
th
esis
test
in
g
u
s
in
g
s
tr
u
ctu
r
al
eq
u
atio
n
m
o
d
elin
g
in
o
r
d
er
to
attain
ex
ce
p
tio
n
al
p
er
f
o
r
m
a
n
ce
.
T
h
e
au
th
o
r
s
p
r
o
v
id
ed
f
in
d
in
g
s
r
eg
ar
d
in
g
team
s
tr
u
ctu
r
al
ch
ar
ac
ter
is
tics
an
d
co
n
tex
tu
al
f
ac
to
r
s
th
at
co
r
r
elat
e
to
an
tece
d
en
ts
o
f
ch
ar
g
ed
b
e
h
av
io
r
in
ch
a
r
g
e
d
p
r
o
d
u
ct
d
ev
elo
p
m
en
t
team
s
.
I
s
o
tan
i
et
a
l
.
[
4
7
]
f
o
c
u
s
ed
o
n
tech
n
o
lo
g
y
d
ev
elo
p
m
e
n
t
th
at
en
h
an
ce
s
co
llab
o
r
atio
n
an
d
class
co
m
m
u
n
icatio
n
.
T
h
e
au
t
h
o
r
s
s
tated
th
at
g
r
o
u
p
f
o
r
m
atio
n
is
cr
itical
to
th
e
ac
ce
p
tab
ilit
y
o
f
g
r
o
u
p
ac
tiv
ities
an
d
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
lear
n
in
g
p
r
o
ce
s
s
.
I
n
ad
d
itio
n
,
th
ey
claim
ed
th
at
s
ev
er
al
co
llab
o
r
ativ
e
lear
n
in
g
ap
p
r
o
ac
h
es
h
av
e
f
ailed
d
u
e
to
in
s
u
f
f
icien
t
g
r
o
u
p
f
o
r
m
atio
n
.
L
ee
m
an
d
C
h
en
[
4
8
]
p
r
o
p
o
s
ed
a
s
im
ilar
ity
-
co
ef
f
icien
t
-
b
a
s
ed
s
tr
ateg
y
f
o
r
m
ac
h
in
e
g
r
o
u
p
in
g
in
o
r
d
er
to
g
en
er
ate
ef
f
icien
t
m
ac
h
in
e
ce
l
ls
an
d
p
ar
t
f
am
ilies
th
at
o
p
tim
ize
s
im
ilar
ity
v
alu
es
.
Gu
o
et
a
l
.
[
4
9
]
p
r
o
p
o
s
ed
an
ap
p
r
o
ac
h
f
o
r
f
o
r
m
in
g
lo
g
ical
g
r
o
u
p
in
g
s
.
T
h
e
a
u
th
o
r
s
d
ev
el
o
p
ed
a
m
o
b
ile
a
p
p
licatio
n
n
a
m
ed
Gr
o
u
p
Me
th
at
en
ab
les
in
d
iv
id
u
als
to
o
r
g
a
n
i
ze
s
o
cial
ac
tiv
itie
s
.
T
s
en
g
et
a
l
.
[
5
0
]
s
u
g
g
ested
a
u
n
iq
u
e
m
eth
o
d
f
o
r
m
u
lti
-
f
u
n
ctio
n
al
p
r
o
ject
team
f
o
r
m
a
tio
n
wh
er
e
th
er
e
ar
e
n
o
clea
r
t
ask
s
b
etwe
en
cu
s
to
m
er
r
eq
u
ir
em
en
ts
an
d
p
r
o
ject
ch
ar
ac
ter
is
tics
.
Fu
zz
y
s
et
th
eo
r
y
is
u
tili
ze
d
in
th
eir
wo
r
k
to
d
ea
l
with
am
b
ig
u
o
u
s
s
itu
atio
n
s
,
wh
ile
g
r
ey
d
ec
is
io
n
th
eo
r
y
(
u
n
ce
r
tai
n
ty
o
r
in
c
o
m
p
lete
in
f
o
r
m
atio
n
)
i
s
em
p
lo
y
ed
to
ch
o
o
s
e
d
esire
d
team
m
e
m
b
er
s
.
I
n
d
r
awa
n
et
a
l
.
[
5
1
]
p
r
o
v
i
d
ed
a
f
r
am
ewo
r
k
to
f
ac
ilit
ate
m
u
lti
-
attr
ib
u
te
co
alitio
n
n
eg
o
tiatio
n
in
th
e
e
-
m
ar
k
etp
lace
.
Yu
et
a
l
.
[
5
2
]
d
ev
elo
p
e
d
a
m
u
lti
-
attr
ib
u
te
co
alitio
n
f
o
r
m
atio
n
-
b
ased
n
eg
o
tiatin
g
p
r
o
t
o
co
l
aim
ed
at
m
in
im
izin
g
th
e
w
o
r
k
lo
ad
an
d
tim
e
c
o
n
s
u
m
p
tio
n
f
o
r
m
a
n
u
f
ac
t
u
r
er
ag
en
ts
.
I
n
a
r
elate
d
c
o
n
tex
t,
Po
n
ce
et
a
l.
[
5
3
]
p
r
o
v
id
e
d
a
co
m
p
r
eh
e
n
s
iv
e
an
aly
s
is
o
f
h
o
w
cr
o
s
s
-
s
ec
to
r
o
r
g
an
izatio
n
al
s
tr
u
ctu
r
es
s
u
p
p
o
r
t
ef
f
ec
tiv
e
g
r
o
u
p
f
o
r
m
atio
n
a
n
d
co
alitio
n
s
f
o
r
s
u
s
tain
ab
ilit
y
o
u
tco
m
es,
wh
ich
ca
n
also
b
e
ad
a
p
ted
in
s
u
s
tain
ab
le
b
u
s
in
ess
m
o
d
els alig
n
ed
with
t
h
e
SDGs
.
W
h
en
f
o
r
m
in
g
an
ef
f
e
ctiv
e
g
r
o
u
p
o
f
ten
b
eg
i
n
s
b
y
id
en
t
if
y
in
g
a
ca
p
ab
le
lead
er
,
we
r
eq
u
ir
e
a
q
u
alif
ied
lead
er
t
o
s
u
p
p
o
r
t
t
h
e
g
r
o
u
p
’
s
d
e
v
elo
p
m
e
n
t
b
as
ed
o
n
th
e
g
r
o
u
p
’
s
o
b
jectiv
es
[
5
4
]
.
I
n
c
o
m
m
o
n
u
n
d
er
s
tan
d
i
n
g
,
a
lea
d
er
r
e
f
er
s
to
a
p
er
s
o
n
wh
o
ca
n
e
n
co
u
r
a
g
e
m
em
b
e
r
s
to
wo
r
k
co
o
p
er
at
iv
ely
to
war
d
s
th
ei
r
g
o
als,
wh
ich
is
s
u
p
p
o
r
ted
b
y
s
o
m
e
p
ap
er
s
;
f
o
r
e
x
am
p
le
in
[
5
5
]
,
[
5
6
]
p
r
o
v
i
d
ed
em
p
ir
ical
ev
id
en
ce
s
h
o
win
g
th
at
co
ac
h
in
g
a
n
d
en
tr
e
p
r
en
e
u
r
ial
lead
er
s
h
ip
s
ty
les
f
o
s
ter
co
llectiv
e
ef
f
icac
y
with
in
te
am
s
.
As
s
h
o
wn
in
Pér
ez
et
a
l
.
[
5
7
]
,
th
is
is
f
u
r
th
er
s
u
p
p
o
r
ted
b
y
an
al
y
s
es
o
f
e
s
p
o
r
ts
team
s
,
wh
er
e
k
e
y
s
tr
u
c
tu
r
es
an
d
p
r
o
ce
s
s
es
em
p
h
asize
th
e
cr
itical
r
o
le
o
f
lead
er
s
h
ip
in
p
r
o
m
o
tin
g
co
o
p
er
atio
n
an
d
team
ef
f
ec
tiv
e
n
e
s
s
.
Gen
er
ally
,
th
er
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
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2252
-
8
9
3
8
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tif
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tell
,
Vo
l.
1
5
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No
.
1
,
Feb
r
u
ar
y
2
0
2
6
:
383
-
3
9
8
386
ar
e
co
u
n
tles
s
o
p
p
o
r
tu
n
ities
f
o
r
ev
er
y
o
n
e
to
d
ev
el
o
p
lea
d
er
s
h
ip
ab
ilit
ies
in
p
r
ep
a
r
atio
n
f
o
r
b
ec
o
m
in
g
a
lead
er
.
So
m
e
in
d
iv
i
d
u
als
m
ay
p
o
s
s
ess
s
p
ec
if
ic
attr
ib
u
tes
t
h
at
m
a
k
e
t
h
em
m
o
r
e
q
u
alif
ied
to
b
e
th
e
l
ea
d
er
o
f
t
h
e
g
r
o
u
p
.
C
er
tain
lead
er
s
h
ip
b
eh
a
v
io
r
s
an
d
attr
ib
u
tes,
s
u
ch
as
s
u
p
p
o
r
tin
g
o
th
er
s
’
lear
n
in
g
,
m
a
y
co
n
tr
ib
u
te
to
an
in
d
iv
id
u
al
’
s
s
u
itab
ilit
y
f
o
r
a
lead
er
s
h
ip
r
o
le
[
5
8
]
,
[
5
9
]
.
As
a
r
esu
lt,
s
ev
er
al
p
ap
e
r
s
f
o
cu
s
o
n
th
e
lead
er
ch
ar
ac
ter
is
tics
th
at
in
f
lu
en
ce
g
r
o
u
p
f
o
r
m
atio
n
.
B
o
o
n
g
asam
e
et
a
l
.
[
34
]
c
o
n
d
u
cted
a
n
in
tr
ig
u
in
g
s
tu
d
y
t
h
at
ex
am
in
ed
g
r
o
u
p
f
o
r
m
atio
n
in
co
n
n
ec
tio
n
to
a
co
alitio
n
lead
er
.
T
h
e
a
u
th
o
r
s
aim
ed
to
f
o
r
m
a
b
u
y
er
c
o
alitio
n
u
tili
zin
g
a
s
ce
n
ar
io
an
d
r
elate
d
s
im
u
latio
n
to
o
ls
i
n
wh
ic
h
l
ea
d
er
s
h
ip
c
h
ar
ac
ter
is
tics
ar
e
e
x
am
in
ed
.
A
r
ec
en
t
wo
r
k
b
y
Xie
et
a
l
.
[
6
0
]
in
tr
o
d
u
ce
d
a
c
o
alitio
n
f
o
r
m
atio
n
f
r
a
m
ewo
r
k
f
o
r
d
y
n
am
ic
task
allo
ca
tio
n
,
s
h
o
win
g
th
at
ag
en
t
-
lev
el
lead
er
s
h
i
p
b
eh
a
v
io
r
s
s
u
p
p
o
r
t m
o
r
e
ef
f
ec
tiv
e
co
ali
tio
n
f
o
r
m
atio
n
.
I
n
ad
d
itio
n
,
R
az
in
an
d
Piccio
n
e
[
6
1
]
m
ea
s
u
r
e
d
co
alitio
n
f
o
r
m
ati
o
n
u
n
d
er
p
o
wer
r
e
latio
n
s
b
y
d
eter
m
in
in
g
t
h
e
ch
ar
ac
ter
izati
o
n
o
f
s
tr
o
n
g
ly
s
tab
le
s
o
cial
o
r
d
er
s
u
s
in
g
th
e
p
a
r
titi
o
n
f
u
n
ctio
n
f
o
r
a
co
o
p
er
ativ
e
g
am
e
ass
o
ciate
d
with
in
d
iv
id
u
al
an
d
g
r
o
u
p
p
o
wer
.
B
r
eb
a
n
an
d
Vass
ilev
a
[
6
2
]
p
r
esen
ted
an
in
ter
-
ag
e
n
t
tr
u
s
t
r
elatio
n
s
h
ip
co
alitio
n
-
b
u
ild
i
n
g
m
eth
o
d
.
A
co
alitio
n
-
b
u
ild
i
n
g
p
r
o
ce
s
s
was
p
r
esen
ted
a
n
d
ass
ess
ed
b
y
t
h
e
au
th
o
r
s
,
tak
in
g
in
to
ac
co
u
n
t
th
e
tr
u
s
t
r
elatio
n
s
h
ip
s
b
etwe
e
n
ag
en
ts
.
Nar
d
i
n
an
d
Sich
m
a
n
[
6
3
]
ass
ess
ed
th
e
tr
u
s
t
d
eg
r
ee
o
f
th
eir
lead
er
an
d
in
v
esti
g
ated
h
o
w
tr
u
s
t
in
f
lu
en
ce
s
co
alitio
n
f
o
r
m
atio
n
.
T
a
r
k
o
wsk
i
et
al
.
[
6
4
]
co
n
d
u
cte
d
th
e
s
u
r
v
ey
in
o
r
d
er
to
an
aly
z
e
a
v
ar
iety
o
f
g
am
e
-
th
eo
r
etic
ce
n
tr
ality
m
etr
ics,
d
etailin
g
h
o
w
a
g
en
ts
ca
n
b
e
e
v
alu
ated
a
n
d
s
elec
t
ed
b
ased
o
n
th
eir
co
alitio
n
-
f
o
r
m
in
g
p
o
te
n
tial
.
Mo
lin
er
o
et
a
l
.
[
6
5
]
f
u
r
th
er
d
ev
elo
p
e
d
th
is
asp
ec
t
b
y
u
s
in
g
in
f
lu
e
n
ce
-
g
am
e
m
o
d
els
.
T
h
e
au
th
o
r
s
also
em
p
lo
y
e
d
th
e
ce
n
tr
ality
o
f
m
em
b
er
s
to
co
alitio
n
s
tr
en
g
th
an
d
s
tab
il
ity
.
2
.
2
.
Clo
s
eness
ce
ntr
a
lity
I
n
a
n
etwo
r
k
g
r
a
p
h
,
th
e
clo
s
en
ess
ce
n
tr
ality
o
f
a
n
o
d
e
in
d
icat
es h
o
w
clo
s
e
it is
to
all
o
th
er
n
o
d
es
.
I
t is
d
ef
in
ed
as
th
e
av
er
a
g
e
v
al
u
e
o
f
th
e
s
h
o
r
test
p
ath
len
g
t
h
s
b
et
wee
n
ea
ch
n
o
d
e
in
th
e
n
etwo
r
k
[
4
2
]
,
[
6
6
]
–
[
7
0
]
.
I
t
h
as
th
e
ad
v
an
tag
e
o
f
id
e
n
tify
i
n
g
p
r
o
m
in
en
t
n
o
d
es
if
th
e
y
ar
e
m
o
r
e
ce
n
tr
al
a
n
d
clo
s
er
to
th
e
m
ajo
r
ity
o
f
n
o
d
es
in
th
e
n
etwo
r
k
.
As
a
r
esu
lt,
it
o
f
ten
d
eter
m
in
es
wh
ich
n
o
d
e
h
as
th
e
m
o
s
t
in
f
lu
en
ce
am
o
n
g
o
th
er
s
in
a
g
iv
en
n
etwo
r
k
[
6
6
]
.
Fo
r
t
h
is
p
r
esen
t
s
tu
d
y
,
clo
s
en
ess
ce
n
tr
ality
m
ak
es
p
er
f
ec
t
s
en
s
e
in
ter
m
s
o
f
in
f
lu
en
ce
.
T
h
is
is
b
ec
au
s
e
th
e
m
o
s
t
in
f
lu
en
tial
p
er
s
o
n
r
ef
er
s
to
a
p
e
r
s
o
n
wh
o
ca
n
ef
f
o
r
tles
s
ly
r
ea
ch
o
u
t
to
o
th
er
s
.
T
h
er
ef
o
r
e,
a
p
er
s
o
n
lo
ca
te
d
in
th
e
ce
n
ter
o
f
th
e
g
r
o
u
p
m
a
y
h
a
v
e
a
h
ig
h
r
e
latio
n
s
h
ip
with
o
th
e
r
p
e
r
s
o
n
s
.
L
et
=
(
,
)
b
e
a
n
etwo
r
k
m
o
d
eled
as
a
s
im
p
l
e
g
r
a
p
h
with
=
|
V
|
v
er
tices,
w
h
er
e
V
is
th
e
s
et
o
f
n
o
d
es
an
d
E
is
t
h
e
s
et
o
f
ed
g
es
.
B
y
f
in
d
in
g
th
e
s
h
o
r
te
s
t
r
o
u
tes
b
etwe
en
all
p
air
s
o
f
n
o
d
es
in
th
e
g
r
ap
h
,
th
e
clo
s
en
ess
ce
n
tr
ality
alg
o
r
ith
m
co
m
p
u
tes
th
e
f
ar
n
e
s
s
o
f
a
v
er
tex
,
wh
ich
is
d
ef
in
e
d
as
th
e
s
u
m
o
f
ea
ch
n
o
d
e'
s
s
h
o
r
test
p
ath
len
g
th
s
to
all
o
th
er
n
o
d
es
.
T
h
e
f
ar
n
ess
o
f
a
v
e
r
tex
is
d
ef
in
ed
as
(
1
)
.
(
)
=
∑
(
,
)
∈
(
,
)
≠
∞
(
1
)
W
h
er
e
(
,
)
r
ep
r
esen
ts
th
e
s
h
o
r
test
d
is
tan
ce
b
etwe
en
th
e
n
o
d
es
an
d
.
T
h
e
f
ar
n
ess
is
th
en
r
ev
er
s
ed
to
ca
lcu
late
th
e
clo
s
en
ess
ce
n
tr
ality
s
co
r
e
o
f
t
h
e
n
o
d
e
.
T
h
e
eq
u
atio
n
p
r
esen
ted
in
(
2
)
d
ef
in
es c
lo
s
en
ess
o
f
a
n
o
d
e
.
(
)
=
1
(
)
(
2
)
Ho
wev
er
,
(
)
=
0
if
x
ca
n
n
o
t
r
ea
ch
a
n
y
v
er
tex
in
th
e
g
r
a
p
h
.
W
e
ca
n
o
b
s
er
v
e
th
at,
if
th
e
f
ar
n
ess
is
lar
g
e,
th
e
clo
s
en
ess
ce
n
tr
ality
b
ec
o
m
es sm
all
an
d
v
ice
v
er
s
a
.
3.
DE
T
AI
L
E
D
C
AL
C
UL
A
T
I
O
N
M
E
T
H
O
DS A
ND
P
RO
P
O
SE
D
G
E
NE
T
I
C
A
L
G
O
RI
T
H
M
T
h
e
p
r
o
p
o
s
ed
ce
n
tr
ality
–
o
p
tim
ized
lead
er
s
h
ip
co
alitio
n
f
o
r
m
atio
n
(
C
OL
C
F)
alg
o
r
ith
m
le
v
er
ag
es th
is
m
ea
s
u
r
e
to
ef
f
ec
tiv
ely
id
en
tif
y
o
p
tim
al
g
r
o
u
p
s
tr
u
ctu
r
es
wh
ile
s
im
u
ltan
eo
u
s
ly
s
elec
tin
g
q
u
alif
ied
lead
er
s
f
o
r
ea
ch
g
r
o
u
p
,
e
n
h
an
ci
n
g
o
v
er
al
l
g
r
o
u
p
p
er
f
o
r
m
a
n
ce
an
d
co
o
r
d
in
atio
n
.
T
h
e
m
ath
em
atica
l
m
o
d
el
an
d
g
en
etic
alg
o
r
ith
m
(
GA)
,
u
s
ed
in
th
is
s
tu
d
y
,
in
clu
d
in
g
th
e
ca
lcu
latio
n
ex
am
p
le
o
f
alg
o
r
ith
m
,
ar
e
d
eta
iled
in
as f
o
llo
ws
.
3
.
1
.
M
a
t
hema
t
ica
l
m
o
del
L
et
=
{
1
,
2
,
3
,
.
.
.
,
}
d
en
o
te
a
s
et
o
f
ag
en
ts
,
wh
er
e
n
is
th
e
to
tal
n
u
m
b
er
o
f
ag
en
ts
.
I
n
th
is
wo
r
k
,
th
e
ter
m
"
ag
en
t
"
r
ef
e
r
s
to
"
a
p
er
s
o
n
".
Ho
wev
er
,
in
o
t
h
er
d
o
m
ain
s
,
it
m
ig
h
t
r
ef
er
to
an
in
d
iv
id
u
al
in
a
f
ac
to
r
y
o
r
a
r
o
b
o
t
th
at
ca
n
j
o
in
to
g
eth
er
i
n
a
g
r
o
u
p
with
a
s
h
ar
ed
g
o
al
.
E
ac
h
a
g
en
t
i
s
co
m
p
r
is
ed
o
f
a
b
in
ar
y
-
v
alu
e
lead
e
r
attr
ib
u
te
.
Als
o
,
an
ag
e
n
t
f
o
r
1
≤
≤
,
co
n
tain
s
attr
ib
u
tes
r
ep
r
esen
ted
in
th
e
f
o
r
m
o
f
=
(
,
,
1
,
2
,
…
,
)
,
wh
er
e
is
th
e
n
u
m
b
er
o
f
attr
i
b
u
tes
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ar
tif
I
n
tell
I
SS
N:
2252
-
8
9
3
8
C
en
tr
a
lity
-
o
p
timiz
ed
co
a
liti
o
n
fo
r
ma
tio
n
:
a
g
en
etic
a
lg
o
r
ith
m
a
p
p
r
o
a
c
h
w
ith
…
(
A
n
o
n
S
u
kstr
ien
w
o
n
g
)
387
C
o
n
s
id
er
a
n
o
n
-
em
p
ty
s
et
,
wh
er
e
1
≤
≤
r
ep
r
esen
tin
g
a
d
iv
id
ed
s
u
b
g
r
o
u
p
o
f
f
o
r
a
ce
r
tain
co
alitio
n
f
o
r
m
atio
n
.
Hen
ce
,
⋃
=
1
=
,
wh
er
e
is
th
e
to
tal
n
u
m
b
er
o
f
s
u
b
g
r
o
u
p
s
.
An
y
ag
en
t
is
n
o
t
p
er
m
itted
to
b
elo
n
g
to
m
o
r
e
t
h
an
o
n
e
g
r
o
u
p
,
wh
ich
is
⋂
=
1
=
∅
.
T
y
p
ically
,
to
p
ar
titi
o
n
a
s
et
o
f
d
is
tin
ct
ag
en
ts
in
to
g
r
o
u
p
s
as
eq
u
al
s
ize
as
p
o
s
s
ib
le,
th
e
to
tal
n
u
m
b
er
o
f
d
if
f
e
r
en
t
g
r
o
u
p
in
g
is
ca
lcu
lated
b
y
co
n
s
id
er
in
g
all
p
er
m
u
tatio
n
,
!
(
(
+
1
)
!
)
∙
(
!
)
−
∙
!
∙
(
−
)
!
,
wh
er
e
=
⌊
⌋
r
ep
r
esen
ts
th
e
s
ize
o
f
th
e
s
m
allest
g
r
o
u
p
,
=
r
ep
r
esen
ts
th
e
n
u
m
b
e
r
o
f
g
r
o
u
p
s
th
at
h
av
e
o
n
e
e
x
tr
a
ag
e
n
t
.
T
h
er
e
f
o
r
e,
th
er
e
a
r
e
g
r
o
u
p
s
o
f
+
1
an
d
−
g
r
o
u
p
s
o
f
.
Fo
r
ex
am
p
le,
if
=
10
,
=
3
,
th
en
we
g
et
=
⌊
10
3
⌋
=
3
,
an
d
=
10
3
=
1
.
T
h
is
m
ea
n
s
th
at
o
n
e
g
r
o
u
p
will
h
av
e
4
m
em
b
er
s
.
An
d
,
th
er
e
will
b
e
two
g
r
o
u
p
s
co
n
tain
in
g
3
m
em
b
er
s
.
Hen
ce
,
th
e
n
u
m
b
er
o
f
d
i
f
f
er
en
t
way
s
to
s
ep
ar
ate
3
g
r
o
u
p
s
o
f
1
0
a
g
en
ts
is
10
!
(
(
3
+
1
)
!
)
1
∙
(
3
!
)
3
−
1
∙
1
!
∙
(
3
−
1
)
!
=
10
!
4
!
∙
(
3
!
)
2
∙
1
!
∙
2
!
=
3
6
2
8
8
0
0
10368
=
350
.
T
h
is
m
ea
n
s
th
er
e
ar
e
3
5
0
d
is
tin
ct
way
s
to
s
ep
ar
ate
1
0
ag
en
ts
in
to
3
g
r
o
u
p
s
o
f
n
ea
r
ly
eq
u
al
s
ize
.
As we
ca
n
s
ee
,
an
in
cr
ea
s
e
in
r
esu
lts
in
a
co
m
b
in
ato
r
ial
g
r
o
wth
in
th
e
n
u
m
b
e
r
o
f
d
is
tin
ct
g
r
o
u
p
f
o
r
m
atio
n
s
,
r
esu
ltin
g
in
e
x
p
o
n
e
n
tial
co
m
p
le
x
ity
.
I
n
o
u
r
s
p
ec
if
ic
p
r
o
b
lem
,
g
r
o
u
p
f
o
r
m
atio
n
b
ased
o
n
a
lead
er
,
ea
ch
ag
en
t
is
r
ep
r
esen
t
ed
b
y
a
v
ec
to
r
o
f
th
e
f
o
r
m
((
l
atitu
d
e,
lo
n
g
itu
d
e
)
,
L
ea
d
er
_
attr
ib
u
te
)
.
T
h
e
L
ea
d
er
_
attr
ib
u
te
is
a
b
in
ar
y
v
ar
iab
le
th
at
in
d
icate
s
wh
eth
er
th
e
ag
e
n
t
ca
n
s
er
v
e
as
th
e
lead
er
o
f
th
e
g
r
o
u
p
.
I
n
ad
d
itio
n
,
ea
ch
d
iv
id
e
d
g
r
o
u
p
m
u
s
t
c
o
n
tain
a
q
u
alif
ied
ag
e
n
t
lead
e
r
,
wh
o
h
as
a
lead
er
attr
ib
u
te
.
Hen
ce
,
we
u
s
e
th
e
ter
m
“
co
m
p
lete
”
t
o
r
ef
er
to
th
e
d
iv
id
ed
g
r
o
u
p
if
it
co
n
tain
s
a
t
least
o
n
e
ag
en
t
with
th
e
lead
er
attr
ib
u
te
=
1
.
Oth
er
wis
e,
th
e
g
r
o
u
p
is
lab
eled
with
th
e
ter
m
“
f
ail
”
m
ea
n
in
g
th
at
it
h
as
n
o
q
u
alif
ied
lead
er
o
r
n
o
o
n
e
in
th
is
g
r
o
u
p
co
n
tain
s
lead
er
attr
ib
u
te
=
0
.
L
et
L
b
e
a
co
llectio
n
o
f
all
q
u
alif
ied
lead
e
r
s
,
wh
er
e
⊂
.
T
h
e
f
o
r
m
atio
n
o
f
a
g
r
o
u
p
will
b
e
s
u
cc
ess
f
u
l
if
a
n
d
o
n
ly
if
t
h
e
n
u
m
b
er
o
f
co
m
p
eten
t le
ad
e
r
s
is
at
least
,
wh
ich
eq
u
als |
L
|
.
I
n
o
th
er
w
o
r
d
s
,
if
|
|
≥
.
g
r
o
u
p
f
o
r
m
atio
n
f
ails
.
T
h
e
p
r
o
b
le
m
o
f
g
r
o
u
p
f
o
r
m
at
i
o
n
b
as
e
d
o
n
t
h
e
c
lo
s
e
n
ess
c
en
tr
a
lit
y
o
f
t
h
e
g
r
o
u
p
le
ad
e
r
an
d
at
tr
ib
u
t
es
ca
n
b
e
a
c
h
al
le
n
g
i
n
g
a
n
d
tim
e
-
co
n
s
u
m
in
g
tas
k
,
es
p
ec
i
all
y
wh
en
a
n
o
p
ti
m
a
l
s
o
l
u
ti
o
n
is
r
e
q
u
i
r
e
d
.
As
t
h
e
n
u
m
b
er
o
f
a
g
e
n
ts
a
n
d
s
u
b
g
r
o
u
p
s
g
r
o
w
s
b
i
g
g
e
r
,
t
h
e
s
ea
r
c
h
s
p
a
ce
o
f
t
h
e
p
r
o
b
le
m
b
ec
o
m
es
la
r
g
er
.
H
en
ce
,
t
h
is
p
r
o
b
l
em
b
e
co
m
es
m
o
r
e
co
m
p
le
x
,
h
a
v
i
n
g
t
h
e
d
i
f
f
ic
u
l
ty
o
f
f
i
n
d
i
n
g
t
h
e
o
p
t
im
al
s
o
l
u
ti
o
n
.
C
o
n
s
e
q
u
e
n
tly
,
i
t
h
as
b
e
c
o
m
e
a
m
o
r
e
c
h
a
lle
n
g
i
n
g
t
ask
f
o
r
u
s
to
f
o
r
m
th
e
o
p
ti
m
a
l
g
r
o
u
p
s
t
h
a
t
o
b
tai
n
q
u
ali
f
ie
d
le
ad
er
s
wi
th
in
th
e
d
i
v
i
d
e
d
s
m
all
er
g
r
o
u
p
,
w
h
e
r
e
t
h
e
m
ea
n
d
is
ta
n
c
e
b
et
we
en
g
r
o
u
p
m
e
m
b
e
r
s
an
d
a
g
r
o
u
p
l
ea
d
e
r
is
as l
o
w
as
p
o
s
s
ib
l
e
.
I
n
o
u
r
wo
r
k
,
a
g
r
o
u
p
f
o
r
m
atio
n
is
s
u
cc
ess
f
u
l if
an
d
o
n
l
y
if
it
s
atis
f
ies th
e
f
o
llo
win
g
co
n
d
iti
o
n
s
:
i)
E
ac
h
estab
lis
h
ed
g
r
o
u
p
c
o
n
tai
n
s
a
q
u
alif
ied
lead
e
r
.
ii)
T
h
e
n
u
m
b
er
o
f
q
u
alif
ied
lead
e
r
s
is
at
least p
,
i
.
e
.
,
|
|
≥
.
iii)
All
d
iv
id
ed
g
r
o
u
p
s
a
r
e
b
alan
c
ed
in
ter
m
s
o
f
th
e
d
is
tan
ce
b
etwe
en
th
eir
m
em
b
er
s
an
d
t
h
eir
g
r
o
u
p
lead
er
s
.
T
h
is
en
s
u
r
es th
at
th
e
s
p
lit g
r
o
u
p
s
ar
e
m
o
r
e
ce
n
tr
al,
m
ea
n
in
g
th
at
all
ag
en
ts
ar
e
n
ea
r
th
eir
a
g
en
t le
ad
er
.
iv
)
Fin
ally
,
we
ass
u
m
e
th
at
all
ag
en
ts
ca
n
co
m
m
u
n
icate
d
ir
ec
tly
with
ea
ch
o
th
er
,
with
o
u
t a
n
y
l
im
itatio
n
s
.
3
.
2
.
G
enet
ic
a
lg
o
rit
h
m
des
ig
n
GA,
a
well
-
k
n
o
wn
o
p
tim
izat
io
n
tech
n
i
q
u
e,
a
r
e
em
p
l
o
y
ed
f
o
r
estab
lis
h
in
g
o
p
tim
al
g
r
o
u
p
in
g
s
o
f
ag
en
ts
th
at
f
u
lf
ill th
e
s
p
ec
if
ied
cr
iter
ia
an
d
task
r
eq
u
ir
em
en
ts
f
o
r
ef
f
ec
tiv
e
co
alitio
n
f
o
r
m
ati
o
n
[
2
2
]
,
[
7
1
]
–
[
7
3
]
.
T
h
e
ev
o
lu
tio
n
o
f
a
GA
b
eg
in
s
with
a
f
u
lly
r
an
d
o
m
in
itial
s
et
o
f
p
o
ten
tial
s
o
lu
ti
o
n
s
,
wh
ich
ar
e
r
ef
er
r
e
d
to
as
th
e
p
o
p
u
latio
n
.
T
h
e
r
o
le
o
f
th
e
in
itial
p
o
p
u
latio
n
with
d
if
f
er
en
t
in
itializatio
n
tech
n
iq
u
e
s
ca
n
h
av
e
a
g
r
ea
t
im
p
ac
t
o
n
t
h
e
ef
f
icien
c
y
an
d
ef
f
ec
tiv
en
ess
o
f
GA
s
[
7
4
]
,
[
7
5
]
.
GAs
lev
er
ag
e
e
v
o
lu
tio
n
ar
y
p
r
in
cip
les
b
y
u
s
in
g
s
elec
tio
n
,
cr
o
s
s
o
v
er
,
a
n
d
m
u
tatio
n
to
iter
ativ
ely
im
p
r
o
v
e
c
an
d
id
ate
s
o
lu
tio
n
s
o
v
er
s
u
cc
e
s
s
iv
e
g
en
er
atio
n
s
.
Hen
ce
,
o
u
r
GA
is
d
esig
n
ed
u
s
i
n
g
o
n
l
y
two
p
r
o
ce
s
s
es
:
s
elec
ti
o
n
an
d
m
u
tatio
n
,
as sh
o
wn
in
Fig
u
r
e
1
.
As
th
e
p
u
r
p
o
s
e
o
f
al
g
o
r
ith
m
is
to
h
av
e
all
ag
en
ts
lo
ca
ted
as
clo
s
e
as
p
o
s
s
ib
le
to
th
eir
lead
e
r
in
g
r
o
u
p
th
ey
b
elo
n
g
to
,
it
is
th
er
ef
o
r
e
n
ec
ess
ar
y
to
ca
lcu
late
th
e
v
al
u
e
o
f
(
)
f
o
r
all
d
iv
i
d
ed
g
r
o
u
p
s
.
Kee
p
in
m
in
d
th
at
an
ag
en
t
lead
er
(
)
o
f
a
g
r
o
u
p
co
n
tain
s
a
lead
e
r
attr
ib
u
t
e
=
1
.
T
h
e
in
itial
p
o
p
u
latio
n
is
r
an
d
o
m
ly
s
elec
ted
,
an
d
its
f
itn
ess
v
alu
e
will
b
e
ca
lcu
lated
.
I
n
th
e
s
elec
tio
n
p
r
o
ce
s
s
,
th
e
alg
o
r
ith
m
s
elec
ts
ca
n
d
id
ates
b
ased
o
n
f
itn
ess
v
alu
e,
a
n
d
o
n
ly
a
ce
r
tain
p
er
ce
n
tag
e
o
f
in
d
i
v
id
u
als
with
th
e
b
est
f
itn
ess
v
alu
e
ar
e
p
ick
ed
.
B
y
d
o
in
g
th
is
,
m
o
r
e
f
it
in
d
iv
i
d
u
a
ls
ar
e
s
to
ch
asti
ca
lly
s
elec
ted
f
r
o
m
cu
r
r
en
t
p
o
p
u
latio
n
t
o
b
e
in
n
ex
t
g
en
e
r
atio
n
.
T
h
e
n
ex
t
o
p
er
ato
r
is
th
e
m
u
tatio
n
p
r
o
ce
s
s
,
wh
ich
is
u
s
ed
to
in
tr
o
d
u
ce
d
iv
e
r
s
ity
in
to
th
e
p
o
p
u
latio
n
.
Per
m
u
tatio
n
m
u
tatio
n
is
ad
o
p
ted
in
th
is
d
esig
n
to
en
s
u
r
e
t
h
at
all
ag
en
ts
ar
e
s
elec
ted
.
T
h
e
n
ew
g
e
n
er
atio
n
o
f
ca
n
d
id
ate
s
o
lu
tio
n
s
is
th
e
n
u
s
ed
in
n
ex
t
g
e
n
er
atio
n
.
B
y
ev
a
lu
atin
g
th
e
f
itn
ess
f
u
n
ctio
n
o
f
ea
ch
ch
r
o
m
o
s
o
m
e
an
d
iter
ativ
ely
e
v
o
lv
in
g
th
e
p
o
p
u
latio
n
t
h
r
o
u
g
h
s
elec
tio
n
a
n
d
m
u
tatio
n
,
th
e
alg
o
r
ith
m
ca
n
co
n
v
er
g
e
o
n
a
s
et
o
f
ch
r
o
m
o
s
o
m
es
th
at
r
e
p
r
esen
t
g
o
o
d
s
o
lu
tio
n
s
to
p
r
o
b
lem
o
f
g
r
o
u
p
f
o
r
m
atio
n
.
T
h
is
ca
p
a
b
ilit
y
,
p
ar
ticu
lar
ly
in
GA
-
lik
e
alg
o
r
ith
m
s
,
h
as
b
ee
n
s
u
p
p
o
r
te
d
ac
r
o
s
s
v
ar
io
u
s
wo
r
k
s
in
th
e
liter
atu
r
e
[
7
1
]
–
[
8
0
]
.
T
h
e
alg
o
r
ith
m
ter
m
in
ates
wh
en
eith
er
a
m
a
x
im
u
m
n
u
m
b
er
o
f
g
en
e
r
atio
n
s
(
Ma
x
_
Ge
n
<G
en
?
)
h
as
b
ee
n
p
r
o
d
u
ce
d
o
r
a
s
atis
f
ac
to
r
y
f
itn
ess
lev
el
h
as
b
ee
n
r
ea
ch
ed
f
o
r
th
e
p
o
p
u
latio
n
.
I
m
p
o
r
tan
tly
,
th
e
ch
r
o
m
o
s
o
m
e
r
ep
r
esen
tatio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8
9
3
8
I
n
t J Ar
tif
I
n
tell
,
Vo
l.
1
5
,
No
.
1
,
Feb
r
u
ar
y
2
0
2
6
:
383
-
3
9
8
388
u
s
ed
in
th
is
p
ap
er
is
d
esig
n
ed
as
a
f
ix
ed
-
s
ize
a
r
r
ay
,
as
p
r
ese
n
ted
in
Fig
u
r
e
2
,
c
o
n
tain
in
g
al
l
ag
en
ts
.
T
h
e
v
alu
e
o
f
f
o
r
1
≤
≤
in
d
icate
s
th
at
th
e
ag
en
t
lo
ca
ted
in
th
is
g
en
e
is
th
e
lead
er
o
f
g
r
o
u
p
j
.
Fig
u
r
e
1
.
Flo
wch
ar
t
f
o
r
C
OL
C
F
Fig
u
r
e
2
.
C
h
r
o
m
o
s
o
m
e
r
ep
r
es
en
tatio
n
ass
o
ciate
d
with
th
e
ar
r
ay
o
f
lea
d
er
p
o
s
itio
n
s
,
wh
er
e
f
o
r
1
≤
≤
T
h
e
a
l
g
o
r
i
t
h
m
i
n
i
t
i
a
l
i
z
e
s
w
i
t
h
G
e
n
=
0
.
A
n
d
i
t
r
u
n
s
r
e
p
e
a
t
e
d
l
y
u
n
t
i
l
t
h
e
g
e
n
e
r
a
t
i
o
n
h
i
t
s
t
h
e
M
a
x
_
G
e
n
.
F
o
r
t
h
i
s
i
n
v
e
s
t
i
g
a
t
i
o
n
,
t
h
e
f
i
t
n
e
s
s
i
s
a
s
s
o
c
i
a
t
e
d
w
i
t
h
t
h
e
c
l
o
s
e
n
e
s
s
c
e
n
t
r
a
l
i
t
y
a
s
p
r
e
s
e
n
t
e
d
i
n
(
1
)
a
n
d
(
2
)
.
T
o
c
a
l
c
u
l
a
t
e
t
h
e
d
i
s
t
a
n
c
e
b
e
t
w
e
e
n
t
w
o
g
e
o
g
r
a
p
h
i
c
a
l
l
o
c
a
t
i
o
n
s
i
n
k
i
l
o
m
e
t
e
r
s
,
w
e
t
h
e
n
u
s
e
t
h
e
h
a
v
e
r
s
i
n
e
f
o
r
m
u
l
a
g
i
v
e
n
b
y
(
3
)
.
=
2
×
6371
×
(
√
2
(
2
)
+
c
os
(
1
)
×
c
os
(
2
)
×
2
(
2
)
)
(
3
)
W
h
er
e
d
is
d
is
tan
ce
b
etwe
en
t
wo
p
o
in
ts
in
k
il
o
m
eter
s
,
∆
=
2
−
1
is
d
if
f
er
en
ce
in
latitu
d
e
,
∆
=
2
−
1
is
d
if
f
er
en
ce
in
lo
n
g
itu
d
e
,
1
an
d
2
ar
e
th
e
latitu
d
es
o
f
th
e
two
p
o
in
ts
in
r
ad
ian
s
,
1
an
d
2
ar
e
th
e
lo
n
g
itu
d
es o
f
th
e
two
p
o
in
ts
in
r
ad
ian
s
.
E
x
am
p
le
:
let
two
g
e
o
g
r
a
p
h
ic
al
p
o
in
ts
in
(
latitu
d
e,
lo
n
g
itu
d
e
)
f
o
r
m
at
b
e
d
ef
in
e
d
as
f
o
l
lo
ws
.
T
h
e
d
is
tan
ce
b
etwe
en
th
em
is
ca
lc
u
lated
as f
o
llo
ws
:
–
Po
in
t 1
(
13
.
6
5
8
5
9
2
6
2
0
5
6
2
0
2
7
,
1
0
0
.
6
4
8
6
0
6
1
2
8
3
2
0
0
)
.
–
Po
in
t 2
(
13
.
6
1
9
6
1
6
2
8
8
0
1
0
3
1
,
1
0
0
.
7
3
1
3
4
6
0
4
9
3
7
8
1
5
).
First,
co
n
v
er
t
th
e
latitu
d
e
an
d
lo
n
g
itu
d
e
v
alu
es
f
r
o
m
d
eg
r
ee
s
to
r
ad
ian
s
u
s
in
g
th
e
co
n
v
er
s
io
n
f
ac
to
r
(
/
180
)
.
E
ac
h
p
o
in
t
in
r
ad
ian
is
th
en
r
ep
r
esen
ted
in
th
e
f
o
r
m
(
,
)
.
Valu
es
r
o
u
n
d
e
d
to
5
d
ec
im
al
p
lace
s
f
o
r
r
ea
d
ab
ilit
y
.
Po
in
t 1
in
r
a
d
ian
s
:
(
ϕ
1
,
λ
1
)
=
(
0
.
23839
,
1
.
75665
)
Po
in
t 2
in
r
a
d
ian
s
:
(
2
,
2
)
=
(
0
.
23771
,
1
.
75809
)
∆
=
2
−
1
≈
0
.
23771
−
0
.
23839
=
−
0
.
00068
r
a
dia
n
s
∆
=
2
−
1
≈
1
.
75809
−
1
.
75665
=
0
.
00144
r
a
dia
n
s
=
2
×
6371
×
(
√
2
(
−
0
.
00068
2
)
+
(
0
.
23839
)
×
(
0
.
23771
)
×
2
(
0
.
00144
2
)
)
=
2
×
6371
×
(
√
0
.
0000001156
+
0
.
97197
×
0
.
97203
×
0
.
0000005184
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ar
tif
I
n
tell
I
SS
N:
2252
-
8
9
3
8
C
en
tr
a
lity
-
o
p
timiz
ed
co
a
liti
o
n
fo
r
ma
tio
n
:
a
g
en
etic
a
lg
o
r
ith
m
a
p
p
r
o
a
c
h
w
ith
…
(
A
n
o
n
S
u
kstr
ien
w
o
n
g
)
389
=
2
×
6371
×
a
r
c
s
in
(
√
0
.
0000006057
)
=
2
×
6371
×
a
r
c
s
in
(
0
.
0007781
)
≈
2
×
6371
×
0
.
0007781
≈
9
.
91421
(
)
T
h
e
r
e
f
o
r
e
,
t
h
e
d
i
s
t
a
n
c
e
b
e
t
w
e
e
n
p
o
i
n
t
1
a
n
d
p
o
i
n
t
2
,
w
r
i
t
t
e
n
a
s
(
P
o
in
t
1
,
P
o
in
t
2
)
,
i
s
a
p
p
r
o
x
i
m
a
t
e
l
y
9
.
9
1
4
2
1
k
m
.
T
h
e
C
OL
C
F
alg
o
r
ith
m
ca
lcu
lates
th
e
clo
s
en
es
s
ce
n
tr
ality
b
etwe
en
a
lead
er
an
d
th
e
o
th
er
m
em
b
er
s
with
in
th
e
d
iv
id
e
d
g
r
o
u
p
.
Su
b
s
eq
u
en
tly
,
th
e
ch
r
o
m
o
s
o
m
e
th
at
y
ield
s
a
h
ig
h
e
r
s
co
r
e
o
f
clo
s
en
ess
ce
n
tr
ality
will
b
e
co
n
s
id
er
e
d
th
e
b
est
c
an
d
id
ate
f
o
r
f
o
r
m
i
n
g
o
p
tim
al
g
r
o
u
p
in
g
s
o
f
ag
en
ts
.
I
t
s
h
o
u
ld
b
e
n
o
ted
th
at
in
(
4
)
a
n
d
(
5
)
,
th
e
v
ar
ia
b
le
is
ass
ig
n
ed
to
th
e
lea
d
er
a
g
en
t
o
f
t
h
e
d
iv
i
d
ed
g
r
o
u
p
.
As
ca
n
b
e
s
ee
n
,
(
)
is
th
e
s
u
m
o
f
th
e
d
is
tan
ce
s
b
etwe
en
th
e
ag
en
t
lead
er
an
d
th
e
o
th
e
r
s
in
th
e
g
r
o
u
p
.
T
h
e
v
al
u
e
o
f
(
)
ca
n
b
e
lar
g
e
.
T
h
er
ef
o
r
e,
(
)
is
d
ef
in
ed
as
1
d
iv
id
ed
b
y
(
)
,
r
esu
ltin
g
in
a
v
alu
e
i
s
les
s
th
an
1
.
T
h
e
f
itn
ess
v
alu
e
o
f
th
e
ch
r
o
m
o
s
o
m
e
is
d
eter
m
in
ed
b
y
tak
in
g
th
e
m
ea
n
v
alu
e
o
f
all
clo
s
en
ess
ce
n
tr
alitie
s
o
f
th
e
d
iv
id
ed
g
r
o
u
p
s
,
wh
ich
is
also
less
th
an
1
.
T
h
e
cl
o
s
en
ess
ce
n
tr
ality
b
etwe
en
th
e
a
g
en
t
lead
er
an
d
th
e
o
t
h
er
ag
e
n
ts
is
n
o
r
m
alize
d
b
y
d
iv
id
in
g
b
y
th
e
m
ax
im
u
m
p
o
s
s
ib
le
d
is
tan
ce
(
n
–
1
)
,
wh
er
e
n
is
th
e
n
u
m
b
er
o
f
a
g
en
ts
in
th
e
d
iv
id
ed
g
r
o
u
p
.
T
h
is
m
ea
n
s
th
at
th
e
m
ax
im
u
m
p
o
s
s
ib
le
v
alu
e
f
o
r
th
e
clo
s
en
ess
ce
n
tr
ality
o
f
ea
c
h
g
r
o
u
p
is
1
.
(
ℎ
)
=
1
(
∑
(
)
=
1
)
(
4
)
T
h
en
,
s
u
b
s
titu
tin
g
(
1
)
a
n
d
(
2
)
i
n
to
(
4
)
,
we
o
b
tai
n
:
(
ℎ
)
=
1
(
∑
(
1
∑
(
,
)
∈
(
,
)
≠
∞
)
=
1
)
(
5
)
wh
er
e
is
an
ag
en
t le
ad
er
o
f
th
e
d
iv
id
ed
g
r
o
u
p
an
d
is
th
e
to
tal
n
u
m
b
er
o
f
s
u
b
g
r
o
u
p
s
.
3
.
4
.
Ste
p
-
by
-
s
t
ep
ex
a
m
ple a
nd
ca
lcula
t
io
n o
f
t
he
a
lg
o
rit
hm
T
o
illu
s
tr
ate
th
e
o
p
er
ati
o
n
o
f
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
,
c
o
n
s
id
er
th
e
f
o
llo
win
g
e
x
am
p
le
.
S
u
p
p
o
s
e
we
d
iv
id
e
th
r
ee
eq
u
al
g
r
o
u
p
s
(
p
=
3
)
f
r
o
m
n
in
e
a
g
en
ts
in
G
=
{a
,
b
,
c,
d
,
e,
f
,
g
,
h
,
i}
,
wh
e
r
e
o
n
ly
a
,
b
,
c,
an
d
d
p
o
s
s
ess
th
e
lead
er
attr
ib
u
te,
an
d
th
ey
ar
e
s
ca
tter
ed
ac
r
o
s
s
th
e
m
ap
.
T
h
e
l
o
ca
tio
n
o
f
ea
c
h
a
g
en
t
is
p
r
esen
ted
,
as
illu
s
tr
ated
in
Fig
u
r
e
3
.
W
e
ass
u
m
e
th
at
ea
ch
ag
en
t
’
s
lo
ca
tio
n
is
r
ep
r
esen
ted
in
t
h
e
(
x,
y
)
co
o
r
d
in
ates,
an
d
th
eir
v
ec
to
r
r
ep
r
esen
tatio
n
s
ar
e
in
th
e
f
o
r
m
o
f
(
L
ea
d
e
r
_
attr
ib
u
te,
(
x,
y
)
)
.
T
h
er
ef
o
r
e,
it is
s
tr
aig
h
tf
o
r
war
d
to
ca
lcu
late
th
e
d
is
tan
ce
b
etwe
en
an
y
two
ag
en
ts
.
Fo
r
b
etter
u
n
d
e
r
s
tan
d
in
g
an
d
s
im
p
licity
,
we
th
en
em
p
lo
y
t
h
e
E
u
clid
ea
n
d
is
tan
ce
f
o
r
m
u
la
in
s
tead
o
f
th
e
Hav
er
s
in
e
f
o
r
m
u
la
to
ca
lc
u
late
d
is
tan
ce
s
b
etwe
en
two
m
em
b
er
s
o
n
th
e
2
D
m
ap
.
Hen
ce
,
th
e
v
ec
to
r
s
o
f
th
e
ag
en
ts
ar
e
d
ef
in
ed
as
f
o
llo
ws
:
a
=(
1
,
(
2
,
5
))
,
b
=(
1
,
(
1
,
1
))
,
c
=(
1
,
(
5
,
4
))
,
d
=(
1,
(
2
,
2
))
, e
=(
0
,
(
3
,
4
))
, f
=(
0
,
(
6
,
3
))
, g
=(
0
,
(
3
,
3
))
,
h
=(
0
,
(
4
,
2
))
,
an
d
i
=(
0
,
(
4
,
5
)).
Fig
u
r
e
3
.
L
o
ca
tio
n
o
f
ea
ch
a
g
e
n
t o
n
th
e
2
D
m
ap
T
o
f
o
r
m
th
r
ee
g
r
o
u
p
s
o
f
e
q
u
al
s
ize,
o
u
r
g
en
etic
-
b
ased
alg
o
r
ith
m
ex
p
lo
r
es
d
if
f
er
en
t
p
o
s
s
ib
le
co
n
f
ig
u
r
atio
n
s
wh
ile
s
atis
f
y
in
g
th
e
g
iv
en
co
n
s
tr
ain
ts
.
T
h
e
alg
o
r
ith
m
in
itializes
th
e
p
o
p
u
latio
n
with
a
s
et
o
f
r
an
d
o
m
l
y
g
en
e
r
ated
ch
r
o
m
o
s
o
m
es,
ea
ch
o
f
wh
ich
r
ep
r
esen
ts
a
p
o
s
s
ib
le
g
r
o
u
p
in
g
o
f
th
e
ag
en
ts
.
B
y
u
s
in
g
(
3
)
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8
9
3
8
I
n
t J Ar
tif
I
n
tell
,
Vo
l.
1
5
,
No
.
1
,
Feb
r
u
ar
y
2
0
2
6
:
383
-
3
9
8
390
th
e
f
itn
ess
f
u
n
ctio
n
o
f
th
e
ch
r
o
m
o
s
o
m
e
is
ev
alu
ate
d
b
ased
o
n
th
e
cl
o
s
en
ess
ce
n
tr
ality
o
f
ea
ch
g
r
o
u
p
'
s
lead
er
,
r
ef
lectin
g
th
eir
im
p
o
r
tan
ce
i
n
th
e
o
v
e
r
all
n
etwo
r
k
.
T
h
e
ch
r
o
m
o
s
o
m
e
s
h
o
wn
in
Fig
u
r
e
4
en
co
d
es
th
e
ch
r
o
m
o
s
o
m
e
th
at
G
1
=
{b
,
d
,
g
},
G
2
=
{a
,
e,
i},
an
d
G
3
=
{c
,
f
,
h
}
.
Ad
d
itio
n
ally
,
t
h
e
lead
er
o
f
G
1
is
b
,
th
e
lead
er
o
f
G
2
is
a,
an
d
t
h
e
lead
er
o
f
G
3
is
c,
an
d
th
e
n
etwo
r
k
ca
n
b
e
d
is
p
lay
ed
in
Fig
u
r
e
5
.
Fig
u
r
e
4
.
T
h
e
ch
r
o
m
o
s
o
m
e
r
e
p
r
esen
tin
g
G
1
=
{b
,
d
,
g
}
,
G
2
=
{a
,
e,
i},
an
d
G
3
=
{c
,
f
,
h
},
wh
er
e
b
,
a,
a
n
d
c
ar
e
th
e
lead
er
s
o
f
G
1
, G
2
,
an
d
G
3
,
r
esp
ec
tiv
ely
F
i
g
u
r
e
5
.
A
l
l
g
r
o
u
p
i
n
g
s
d
e
c
o
d
ed
f
r
o
m
c
h
r
o
m
o
s
o
m
e
i
n
F
i
g
u
r
e
4
o
n
t
h
e
2
D
m
a
p
,
s
h
o
w
i
n
g
e
a
ch
g
r
o
u
p
’
s
c
e
n
t
r
a
l
i
t
y
Fo
r
ea
ch
o
f
th
e
th
r
ee
g
r
o
u
p
s
,
o
n
e
r
ep
r
esen
tativ
e
ag
en
t,
wh
o
is
th
e
lead
er
o
f
th
e
g
r
o
u
p
,
will b
e
u
s
ed
to
co
m
p
u
te
th
e
s
h
o
r
test
p
ath
d
is
tan
ce
s
to
th
e
o
th
er
n
o
d
es with
in
th
e
s
am
e
g
r
o
u
p
.
T
h
e
s
u
m
s
o
f
th
ese
d
is
tan
ce
s
ar
e
th
en
in
v
e
r
ted
,
an
d
th
e
a
v
er
ag
e
o
f
t
h
e
th
r
ee
r
esu
lts
is
tak
en
as
th
e
f
itn
ess
v
al
u
e
.
B
y
u
s
in
g
(
7
)
,
th
e
f
itn
ess
is
ca
lcu
lated
as
1
3
(
1
1
+
√
8
+
1
√
2
+
2
+
1
√
2
+
√
5
)
,
wh
ich
e
v
alu
at
es
to
ap
p
r
o
x
im
ately
0
.
2
7
6
0
2
.
W
e
ca
n
o
b
s
er
v
e
th
at
th
e
o
f
f
s
p
r
in
g
y
ield
s
a
h
ig
h
er
f
itn
ess
v
alu
e,
in
d
icatin
g
th
at
th
e
ce
n
tr
ality
o
f
d
iv
id
e
d
g
r
o
u
p
s
ass
o
ciate
d
with
th
e
g
r
o
u
p
lead
er
is
b
etter
th
an
th
at
o
f
its
p
ar
en
t
.
Gen
er
ally
,
th
e
o
f
f
s
p
r
in
g
with
a
h
ig
h
er
f
itn
ess
v
alu
e
h
as
a
g
r
ea
ter
ch
an
ce
o
f
b
ein
g
s
elec
ted
f
o
r
t
h
e
n
ex
t g
e
n
er
atio
n
c
o
m
p
ar
e
d
to
th
eir
p
ar
e
n
ts
.
(
ℎ
)
=
1
3
(
∑
(
1
∑
(
,
)
∈
(
,
)
≠
∞
)
3
=
1
)
=
1
3
(
1
(
,
)
+
(
,
)
+
1
(
,
)
+
(
,
)
+
1
(
,
)
+
(
,
ℎ
)
)
=
1
3
(
1
1
+
√
8
+
1
√
2
+
2
+
1
√
2
+
√
5
)
≈
0
.
27602
W
e
th
en
ap
p
ly
th
e
p
er
m
u
tatio
n
m
u
tatio
n
to
g
en
er
ate
an
o
f
f
s
p
r
in
g
.
I
n
g
en
er
al,
th
e
o
f
f
s
p
r
in
g
is
s
im
i
lar
to
its
p
ar
en
t
ex
ce
p
t
f
o
r
th
e
m
u
tated
g
en
e
.
Su
p
p
o
s
e
th
at
th
e
p
er
m
u
tatio
n
m
u
tatio
n
m
o
d
if
ies
o
n
ly
th
e
f
ir
s
t
g
r
o
u
p
.
An
ex
a
m
p
le
o
f
o
f
f
s
p
r
in
g
r
esu
ltin
g
f
r
o
m
th
e
m
u
tatio
n
is
s
h
o
wn
in
Fig
u
r
e
6
,
wh
er
e
G
1
co
n
s
is
ts
o
f
{d
,
b
,
g
},
wh
ile
G
2
an
d
G
3
r
e
m
ain
u
n
c
h
an
g
e
d
.
T
h
en
,
we
c
an
d
em
o
n
s
tr
ate
all
g
r
o
u
p
m
e
m
b
er
s
co
n
n
ec
ted
t
o
th
eir
lead
er
,
as
p
r
esen
ted
in
Fig
u
r
e
7
.
I
t
is
im
p
o
r
tan
t
to
n
o
t
e
th
at,
f
o
r
a
g
r
o
u
p
to
b
e
co
n
s
id
er
ed
q
u
alif
ied
,
t
h
e
lead
er
m
u
s
t
p
o
s
s
ess
th
e
lead
e
r
s
h
ip
attr
ib
u
te
.
Fo
r
ex
am
p
le,
if
th
e
g
r
o
u
p
was
r
ep
r
esen
ted
as
G
1
=
{g
,
b
,
d
},
it
wo
u
ld
b
e
u
n
q
u
alif
ied
b
ec
au
s
e
g
'
s
lead
er
s
h
ip
attr
ib
u
te
is
e
q
u
al
to
0
.
T
o
en
s
u
r
e
th
e
q
u
al
ity
o
f
th
e
o
f
f
s
p
r
in
g
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ar
tif
I
n
tell
I
SS
N:
2252
-
8
9
3
8
C
en
tr
a
lity
-
o
p
timiz
ed
co
a
liti
o
n
fo
r
ma
tio
n
:
a
g
en
etic
a
lg
o
r
ith
m
a
p
p
r
o
a
c
h
w
ith
…
(
A
n
o
n
S
u
kstr
ien
w
o
n
g
)
391
g
en
er
ated
b
y
th
e
alg
o
r
ith
m
,
t
h
e
ch
r
o
m
o
s
o
m
es
co
n
tain
in
g
n
o
u
n
q
u
alif
ied
s
u
b
g
r
o
u
p
s
lik
e
th
is
ar
e
elim
in
ated
f
r
o
m
t
h
e
ca
n
d
id
ate
ch
r
o
m
o
s
o
m
es
.
As
a
r
esu
lt,
o
n
l
y
th
e
o
f
f
s
p
r
in
g
with
th
e
q
u
alif
ie
d
g
r
o
u
p
s
b
ased
o
n
th
is
ar
e
co
n
s
id
er
ed
f
o
r
f
u
r
th
er
ev
o
lu
tio
n
.
As
m
en
tio
n
ed
p
r
ev
io
u
s
ly
,
th
e
C
OL
C
F
alg
o
r
ith
m
co
n
s
id
er
s
th
e
ch
r
o
m
o
s
o
m
e
th
at
p
r
o
d
u
ce
s
th
e
g
r
ea
test
clo
s
en
ess
ce
n
tr
ality
s
co
r
e
b
etwe
en
an
ag
en
t
lead
er
an
d
th
e
o
th
e
r
s
with
in
th
e
d
iv
id
ed
g
r
o
u
p
s
.
T
h
er
ef
o
r
e,
th
e
ch
r
o
m
o
s
o
m
e
th
at
p
r
o
d
u
ce
s
th
e
g
r
ea
test
s
co
r
e
f
o
r
clo
s
en
ess
ce
n
tr
ality
is
d
ee
m
ed
th
e
m
o
s
t
s
u
itab
le
o
p
tio
n
f
o
r
cr
ea
tin
g
id
ea
l
ag
en
t
g
r
o
u
p
s
.
T
h
is
ca
n
b
e
v
er
if
ied
t
h
r
o
u
g
h
th
e
f
o
llo
win
g
ca
lcu
latio
n
.
L
et
u
s
ex
am
in
e
th
e
m
ap
illu
s
tr
ated
in
Fig
u
r
e
7
.
W
e
ca
n
s
ee
th
at
d
in
th
e
g
r
o
u
p
o
f
{d
,
b
,
g
}
h
as
th
e
lo
west
to
tal
d
is
tan
ce
to
all
o
th
er
s
.
T
h
e
f
itn
ess
i
s
ca
lcu
lated
as
1
3
(
1
1
+
√
5
+
1
√
2
+
2
+
1
√
2
+
√
5
)
,
wh
ich
ev
alu
ates
to
ap
p
r
o
x
im
ately
0
.
2
9
1
9
5
.
As
we
ca
n
s
ee
,
d
ca
n
b
e
a
lea
d
er
o
f
th
e
g
r
o
u
p
as
its
clo
s
en
ess
ce
n
tr
ality
is
th
e
h
ig
h
est
.
Deta
ils
o
f
t
h
e
ch
r
o
m
o
s
o
m
e'
s
f
itn
ess
v
alu
e
ca
lcu
latio
n
ar
e
p
r
esen
ted
as f
o
llo
ws
.
(
)
=
1
3
(
1
(
,
)
+
(
,
)
+
1
(
,
)
+
(
,
)
+
1
(
,
)
+
(
,
ℎ
)
)
=
1
3
(
1
1
+
√
5
+
1
√
2
+
2
+
1
√
2
+
√
5
)
≈
0
.
29195
Fig
u
r
e
6
.
Per
m
u
tatio
n
m
u
tatio
n
Fig
u
r
e
7
.
R
ep
r
esen
tatio
n
o
f
ea
ch
g
r
o
u
p
o
n
th
e
2
D
m
ap
b
ased
o
n
th
e
c
h
r
o
m
o
s
o
m
e
s
h
o
wn
in
Fig
u
r
e
6
T
h
e
f
itn
ess
v
alu
e
o
f
th
e
o
f
f
s
p
r
in
g
is
ap
p
r
o
x
im
ately
0
.
2
9
1
9
5
,
wh
ich
is
h
ig
h
er
th
a
n
th
at
o
f
its
p
ar
en
t
(
0
.
2
7
6
0
2
)
.
T
h
is
im
p
r
o
v
em
en
t
s
h
o
wed
th
at
th
e
o
f
f
s
p
r
in
g
h
ad
a
b
etter
g
r
o
u
p
in
g
s
o
lu
tio
n
co
m
p
ar
ed
to
its
p
ar
en
t
.
Du
r
in
g
ea
ch
g
en
er
atio
n
,
th
e
f
itn
ess
f
u
n
ctio
n
o
f
ea
ch
ch
r
o
m
o
s
o
m
e
is
ev
alu
ate
d
,
a
n
d
th
e
p
o
p
u
latio
n
is
iter
ativ
ely
ev
o
l
v
in
g
th
r
o
u
g
h
s
elec
tio
n
an
d
m
u
tatio
n
.
T
h
e
alg
o
r
ith
m
c
o
n
tin
u
e
d
t
o
e
v
o
lv
e
th
e
p
o
p
u
latio
n
u
n
til
it
r
ea
ch
ed
th
e
cr
iter
io
n
;
m
ax
im
u
m
n
u
m
b
er
o
f
g
en
er
atio
n
s
.
At
t
h
is
p
o
in
t,
t
h
e
C
OL
C
F
alg
o
r
ith
m
h
ad
f
o
u
n
d
a
s
et
o
f
ch
r
o
m
o
s
o
m
es
th
at
r
ep
r
esen
ted
g
o
o
d
s
o
lu
tio
n
s
to
th
e
p
r
o
b
lem
o
f
g
r
o
u
p
f
o
r
m
atio
n
,
an
d
t
h
e
o
p
tim
al
s
o
lu
tio
n
co
u
ld
b
e
f
o
u
n
d
.
I
ts
ab
ilit
y
to
ex
p
l
o
r
e
a
n
d
e
x
p
lo
it
th
e
s
ea
r
ch
s
p
ac
e,
w
h
ile
in
tr
o
d
u
cin
g
d
iv
er
s
ity
t
h
r
o
u
g
h
m
u
tatio
n
,
m
a
d
e
it a
n
ef
f
ec
tiv
e
to
o
l f
o
r
f
in
d
in
g
g
o
o
d
s
o
lu
ti
o
n
s
to
th
e
p
r
o
b
lem
.
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
o
d
em
o
n
s
tr
ate
th
e
s
ca
lab
ilit
y
o
f
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
,
we
co
n
d
u
cte
d
a
s
er
ies
o
f
e
x
p
er
im
en
ts
g
u
id
ed
b
y
in
s
ig
h
ts
an
d
m
eth
o
d
o
lo
g
ies
r
ep
o
r
te
d
in
r
ec
en
t
co
m
p
r
eh
en
s
iv
e
s
u
r
v
e
y
s
an
d
s
tu
d
ies
[
8
1
]
–
[
8
7
]
.
O
u
r
em
p
ir
ical
ex
p
e
r
im
en
ts
v
ar
ie
d
t
h
e
n
u
m
b
er
o
f
ag
en
ts
,
g
r
o
u
p
s
,
i
n
itial
p
o
p
u
latio
n
s
ize,
an
d
m
a
x
im
u
m
g
en
er
atio
n
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8
9
3
8
I
n
t J Ar
tif
I
n
tell
,
Vo
l.
1
5
,
No
.
1
,
Feb
r
u
ar
y
2
0
2
6
:
383
-
3
9
8
392
to
ev
alu
ate
t
h
e
alg
o
r
ith
m
’
s
p
e
r
f
o
r
m
a
n
ce
u
n
d
er
d
if
f
e
r
en
t
s
ca
l
ab
le
co
n
d
itio
n
s
.
T
h
e
d
etailed
ex
p
er
im
en
tal
s
etu
p
is
s
u
m
m
ar
ized
in
T
ab
le
1
.
T
ab
le
1
.
I
n
itial p
ar
am
eter
s
etu
p
f
o
r
t
h
e
alg
o
r
ith
m
b
ased
o
n
t
h
e
ex
p
er
im
e
n
tal
r
esu
lts
Ex
p
e
r
i
m
e
n
t
n
o
.
N
u
mb
e
r
o
f
a
g
e
n
t
s
N
u
mb
e
r
o
f
l
e
a
d
e
r
–
t
y
p
e
a
g
e
n
t
s
N
u
mb
e
r
o
f
g
r
o
u
p
s
I
n
i
t
i
a
l
c
h
r
o
mo
s
o
m
e
p
o
p
u
l
a
t
i
o
n
(
M
)
M
a
x
_
G
e
n
1
1
0
0
84
(
84
%)
10
3
0
0
2
0
0
2
2
0
0
1
5
2
(
76
%)
20
3
0
0
4
0
0
3
4
0
0
3
3
0
(
75
%)
40
3
0
0
4
0
0
I
n
o
u
r
ex
p
er
im
en
ts
,
we
c
o
n
s
id
e
r
ed
a
f
u
lly
c
o
n
n
ec
te
d
n
etw
o
r
k
o
f
m
u
ltip
le
ag
en
ts
.
T
h
e
g
o
al
was
to
ev
alu
ate
th
e
p
r
o
p
o
s
ed
alg
o
r
it
h
m
’
s
ab
ilit
y
to
p
ar
titi
o
n
a
v
a
r
y
in
g
n
u
m
b
er
o
f
a
g
en
ts
in
to
o
p
tim
al
s
u
b
g
r
o
u
p
s
,
aim
in
g
to
ac
h
iev
e
h
ig
h
clo
s
en
ess
ce
n
tr
ality
b
y
in
co
r
p
o
r
ati
n
g
lead
er
s
h
ip
attr
ib
u
tes
b
ase
d
o
n
ea
ch
ag
e
n
t
’
s
lo
ca
tio
n
.
B
y
v
ar
y
in
g
th
e
n
u
m
b
er
o
f
ag
en
ts
,
we
ass
ess
ed
h
o
w
ef
f
ec
tiv
ely
th
e
alg
o
r
ith
m
s
ca
led
an
d
ad
ap
ted
t
o
d
if
f
er
en
t
n
etwo
r
k
s
izes
.
i)
E
x
p
er
im
en
t
1
:
we
s
tar
ted
wi
th
1
0
0
a
g
en
ts
an
d
d
iv
id
ed
t
h
em
eq
u
ally
i
n
to
1
0
s
u
b
g
r
o
u
p
s
,
wh
er
e
th
e
n
u
m
b
er
o
f
lead
er
-
ty
p
e
ag
en
ts
is
8
4
.
I
n
o
r
d
er
to
ac
h
iev
e
o
p
tim
al
g
r
o
u
p
in
g
s
o
f
ag
en
ts
th
at
f
u
lf
ill
ce
r
tain
r
eq
u
ir
em
e
n
ts
,
th
e
C
OL
C
F
a
lg
o
r
ith
m
wa
s
em
p
lo
y
e
d
.
W
e
in
itialized
th
e
alg
o
r
ith
m
with
s
p
ec
if
ic
p
ar
am
eter
s
as
p
r
esen
ted
in
T
a
b
le
1
.
T
h
e
m
ax
im
u
m
n
u
m
b
e
r
o
f
g
e
n
er
atio
n
s
(
Max
_
Gen
)
wa
s
2
0
0
,
wh
ile
th
e
in
itial
ch
r
o
m
o
s
o
m
e
p
o
p
u
latio
n
(
M
)
was
3
0
0
.
T
h
e
ex
p
er
im
en
tal
r
esu
lts
ar
e
s
h
o
wn
in
Fig
u
r
e
8
,
in
d
icatin
g
th
at
th
e
alg
o
r
ith
m
q
u
ick
ly
co
n
v
er
g
e
d
to
t
h
e
o
p
tim
al
s
o
lu
tio
n
af
ter
ap
p
r
o
x
im
atel
y
1
5
0
g
en
er
atio
n
s
.
Ad
d
itio
n
ally
,
t
h
e
e
x
ec
u
tio
n
tim
e
f
o
r
th
is
ex
p
er
im
en
t
was
ab
o
u
t
4
s
ec
o
n
d
s
.
T
h
e
b
est
f
itn
ess
v
alu
e
f
o
u
n
d
b
y
th
e
alg
o
r
ith
m
was
0
.
6
2
4
8
9
5
.
Mo
r
eo
v
er
,
th
e
a
g
en
t
lead
er
o
f
ea
c
h
d
iv
id
ed
g
r
o
u
p
was
d
etailed
u
n
d
er
t
h
e
g
r
a
p
h
r
esu
lt
.
Fo
r
in
s
tan
ce
,
1
0
–
48
–
1
–
19
–
8
–
20
–
6
–
7
–
78
–
6
2
im
p
lie
s
th
at
th
e
f
ir
s
t
g
r
o
u
p
was a
g
en
t #
1
0
an
d
th
e
s
ec
o
n
d
g
r
o
u
p
was a
g
en
t #
4
8
.
Fig
u
r
e
8
.
Gr
o
u
p
f
o
r
m
atio
n
o
f
1
0
0
ag
en
ts
u
s
in
g
th
e
C
OL
C
F a
lg
o
r
ith
m
(
e
x
a
m
p
le
1
)
ii)
E
x
p
er
im
en
t
2
:
as
we
aim
ed
to
ev
alu
ate
th
e
s
ca
lab
ilit
y
o
f
o
u
r
p
r
o
p
o
s
ed
alg
o
r
ith
m
b
y
in
cr
ea
s
in
g
th
e
n
u
m
b
er
o
f
ag
e
n
ts
an
d
s
u
b
g
r
o
u
p
s
,
th
e
n
u
m
b
er
o
f
a
g
en
ts
wa
s
in
cr
ea
s
ed
to
2
0
0
,
wh
ich
wer
e
d
iv
id
ed
in
to
2
0
s
u
b
g
r
o
u
p
s
.
I
n
th
is
ex
p
er
i
m
en
t,
a
to
tal
o
f
1
5
2
ag
en
ts
(
76
%
o
f
all
ag
en
ts
)
p
o
s
s
ess
ed
a
lead
er
s
h
ip
attr
ib
u
te
.
T
h
e
in
itial
p
o
p
u
latio
n
o
f
ch
r
o
m
o
s
o
m
es
(
M
)
was
k
ep
t
at
3
0
0
,
wh
ile
th
e
m
ax
im
u
m
n
u
m
b
er
o
f
g
en
er
atio
n
s
(
Max
_
Gen
)
was
s
et
to
4
0
0
.
T
h
e
e
x
p
er
im
e
n
tal
r
e
s
u
lt,
p
r
esen
ted
in
Fig
u
r
e
9
,
d
e
m
o
n
s
tr
ates
th
e
alg
o
r
ith
m
’
s
ab
ilit
y
to
h
a
n
d
le
l
ar
g
er
p
r
o
b
lem
s
with
m
o
r
e
ag
e
n
ts
an
d
s
u
b
g
r
o
u
p
s
wh
ile
s
till
co
n
v
er
g
in
g
t
o
th
e
o
p
tim
al
s
o
lu
tio
n
.
I
n
a
d
d
it
io
n
,
it
s
h
o
ws
th
at
o
u
r
alg
o
r
ith
m
s
u
cc
ess
f
u
lly
co
n
v
er
g
ed
t
o
th
e
o
p
tim
al
s
o
lu
tio
n
af
ter
2
0
0
g
en
e
r
atio
n
s
.
T
h
is
ex
p
er
im
en
t
to
o
k
ap
p
r
o
x
im
ately
1
5
s
ec
o
n
d
s
to
co
m
p
lete,
an
d
th
e
b
est f
itn
ess
v
alu
e
ac
h
iev
ed
wa
s
0
.
7
7
4
1
7
7
.
Evaluation Warning : The document was created with Spire.PDF for Python.