TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 16, No. 3, Dece
mbe
r
2
015, pp. 565
~ 573
DOI: 10.115
9
1
/telkomni
ka.
v
16i3.914
1
565
Re
cei
v
ed
Jun
e
21, 2015; Revi
sed O
c
tob
e
r 6, 2015; A
c
cepted O
c
to
ber 28, 20
15
Tissue-like P System Based DNA-GA for Clus
tering
Caiping Hou*
1
, Xi
y
u
Liu
2
Schoo
l of Man
agem
ent Scie
n
c
e and En
gi
ne
erin
g, Shan
don
g Normal U
n
iv
ersit
y
, Jin
an, S
han
do
ng, Chi
n
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: sdnuhc
p@1
6
3
.com
1
, sdxy
liu@163.com
2
A
b
st
r
a
ct
In recent yea
r
s, DNA-GA
algorithm
is
dra
w
ing
attention from
scholars. Th
e a
l
gorithm
com
b
ine
s
the
DNA en
co
di
ng a
nd
Gen
e
t
ic Algo
rithm
,
whi
c
h
solves the p
r
em
ature con
v
ergen
ce
of geneti
c
al
gorithm
s, the
wea
k
lo
cal
sea
r
ch capa
bility and
bin
a
ry
Ham
m
i
ng cliff pro
b
le
m
s
effectivel
y. How to d
e
si
g
n
a m
o
re ef
fective
wa
y t
o
im
prove th
e perfo
rm
an
ce of
DNA
-G
A
algorithm
is
m
o
re wo
rth studyin
g.As is
kno
w
n to
all,t
he tissue
-like
P system
ca
n sea
r
ch for t
h
e
optim
al clu
s
tering
pa
rtitio
n with
the
h
e
lp of it
s p
a
rallel
com
puting a
d
vantag
e effecti
v
el
y. This
pape
r is un
d
e
r thi
s
prem
ise a
nd p
r
e
s
e
n
ts DNA-
GA
algorithm
ba
sed
on tissu
e
-like P system
s
(TP
D
NA
-
G
A
)
wit
h
a
loop
st
ru
ct
u
r
e of
cell
s,
which
aim
s
to co
m
b
ine the p
a
ralleli
sm
an
d the
evol
utiona
ry
rules of tissue
-like P syste
m
s
to
im
prove perfo
rm
ance of the DNA
-GA algo
rith
m.
The obj
ecti
ve
of this pap
er is to use the
TPDNA
-GA
algorithm
to sup
port
clu
s
tering i
n
order to
find the best
clu
s
terin
g
ce
nter.Thi
s algo
rithm
is of particula
r intere
st to when
d
ealing
with la
rge
and
heteroge
neou
s d
a
ta
sets an
d wh
en b
e
ing fa
c
ed
with an
u
n
kn
own num
ber
of cl
uste
rs.
Expe
rim
ental re
sults sho
w
that the p
r
o
p
o
se
d TP
DNA
-GA al
gorith
m
for clu
s
teri
ng i
s
supe
rio
r
o
r
com
petitive to cla
ssi
cal
k-m
eans algo
rit
h
m
and several evol
utiona
ry clu
s
te
ring al
gorithm
s.
Ke
y
w
ord:
DN
A computin
g, g
enetic a
l
g
o
rith
m,
tissue-l
i
ke P
system, cluste
ring ce
nter
Copy
right
©
2015 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
This
research concerns the
capability of the tissue-l
ike
P
system
com
putational model
to provide a
framework for DNA-GA algorith
m
.
Th
e gene
ral flo
w
of the tra
d
itional ge
ne
tic
algorith
m
is to get the optimal sol
u
tion
schem
e in several
candi
date
grou
ps. In
each
gene
ration,th
e geneti
c
alg
o
rithm is
sel
e
cted a
c
co
rd
ing to fitness and gen
etic recon
s
tru
c
tion
method to ge
nerate n
e
w
candid
a
te indi
viduals. In
the cycle of evolution
gen
etic algo
rithm, the
fitness fu
ncti
on facilitate
s
the ca
ndid
a
te
individual to
evolution. It
can form
ne
w
individual
s aft
e
r
contin
uou
s it
erative p
r
o
c
e
ss
and th
ese
individual
s h
a
ve improved
adapta
b
ility comp
ared to
the
previou
s
i
ndi
vidual in
ge
n
e
ral. T
h
is pe
rforman
c
e
of
geneti
c
al
gori
t
hm ge
nerally use the
G
e
n
e
tic
Algorithm a
s
the body of algorithm
whe
n
we will imp
r
o
v
e the algorit
hm.
Membrane computing (kn
o
wn as
P systems)
i
s
a
cla
ss
of dist
ribut
ed pa
rallel
co
mputing
model
s, it focuse
s
on th
e
communi
catio
n
in th
e me
m
b
ran
e
s,
cell
s,
tissue
s o
r
ot
her
structu
r
e
s
of
orga
nisms.In
this p
r
o
c
e
ss, the su
bsta
n
c
e in
cell m
e
mbrane
occur
cha
nge
s
randomly
and
in
parall
e
l,su
ch
as diverting
,
variation and so
o
n
, whi
c
h ma
ke
s the algo
rithm have greatly
parall
e
lism,
so a la
rge
nu
mber
of ope
ration can b
e
compl
e
ted at
a mome
nt. Compa
r
ed to t
hese
benefits of m
e
mbrane
co
mputing, th
e
tissu
e-li
ke
P system
is
in a
maximally parall
e
l way and
can find th
e best
candi
dat
e individual
s i
n
a sh
orte
r time, whi
c
h m
u
st be effe
ctive to choo
se
the
optimal clu
s
te
ring cente
r
.
2. A Brief O
u
tline of Tiss
ue-like P Sy
stems
Tissue
-like P system
s we
re
presented by
Martin-Vide
et
al.
in [[
1]
],whi
c
h is an
other type
of P system due to the stru
ctur
e of their mem
b
ra
ne. Instead
of con
s
ide
r
in
g a hiera
r
chi
c
al
stru
cture, me
mbra
ne
s are
cha
nge
d as a
general a
graph. They exist two biolo
g
i
c
al in
spiratio
ns
(s
ee [[
2]
]): inter cell
ula
r
co
mmuni
cation
and coop
erati
on between n
euro
n
s.
The inte
r
cellular comm
unication i
s
ba
sed
on
sympo
r
t/antip
ort rules,
which
are
introdu
ce
d a
s
the
comm
unication rul
e
s b
e
twe
en
cell
s. Sympo
r
t rule
s m
e
a
n
s that o
b
je
cts
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 16, No. 3, Dece
mb
er 201
5 : 565 – 573
566
coo
perate to traverse a m
e
mbrane
tog
e
ther in the
same directio
n
,
where
a
s in t
he antipo
r
t ru
les,
obje
c
ts a
c
ro
ss a memb
ran
e
resi
ding at
both sid
e
s of
it but in oppo
site dire
ction
s
[[
3]
].
Formally, a tissue-li
ke P system with
in
put of degre
e
q >0 is a con
s
tru
c
t:
Π
=
(A,w
1
,...,
w
q
,R
1
,..
.,R
q ,R’,I,O )
Whe
r
e:
(1) A is a finit
e
alpha
bet, whose symbol
s are call
ed ob
jects;
(2) w
i
(1
≤
i
≤
q
)
is finite set of strings ove
r
A, whic
h re
prese
n
ts multiset of objects
pre
s
ent
in cell i at the initial configuration;
(3) R
i
(1
≤
i
≤
q
)
is finite set of evolution rul
e
s in cell i;
(4)
R’ is
finite s
e
t of c
o
mmunic
ation
rules of the form (i,u/v,j), for i,j
∈
{0,1,2,...,q},
i
≠
j, u,v
∈
A,|
u | + |v| is the
length of the comm
uni
cati
on rule
(i,u/v,
j);
(5) I
∈
{1,2,...,
q} is
the input c
e
ll;
(6) O in
dicate
s the output region of t
he
whol
e system
in the enviro
n
ment.
A tissue
-
like P system of degree q
>
0
can b
e
viewed as a
set
of q cells la
b
e
led by
1,2,...,q, each of which
consist
s
of an el
ementary
membrane. We
will use I
to express the input
cell
and
O
to
den
ote the
o
u
tput region.
In above
defi
n
ition, R
i
(1
≤
i
≤
q) is finite
set of evolutio
n
rules in
cell
i, whose
rul
e
is
of the form
u
→
v,u,v
∈
A. The ap
plicatio
n of the
rule
mean
s that u
will
be evolved to
v. In most of the existing t
i
ssue-li
ke P
systems a
nd v
a
riant
s, evolu
t
ion rule
of the
form is
ba
se
d on
string
o
f
object
s
.Moreover,
the q cell
s
will be arrang
ed
a
s
a
loop
to
polo
g
y
based on th
e
commu
nication rul
e
s d
e
scrib
ed b
e
low.
The commu
nicatio
n
rul
e
(i,u/v,j) can b
e
applie
d
ove
r
two cell
s
la
b
e
led by
i and
j su
ch
th
at
u
is containe
d
in cell i
an
d v
is containe
d
in
cell j. The ap
plicatio
n of this rule me
an
s that
the objects of the mul
t
is
ets re
prese
n
ted by u and
v
are inte
rchan
ged bet
wee
n
the two cell
s. Note that
if either i = 0
or j = 0 the
n
the object
s
are
interchan
ged
betwe
en a ce
ll and the env
ironm
ent [[
4]
].
The rule
s of
a system like de
scrib
e
d
are used in
the non-d
e
termini
s
tic m
a
ximally
parall
e
l manner
when there are
several
possi
bilities,
as usual
i
n
t
he framework of m
e
mbrane
comp
uting.In
each
step, all
cell
s
whi
c
h
can evolve
must evolve i
n
a maximally parallel
way. T
h
at
is to say, in e
a
ch
step e
a
ch obje
c
t in a
membrane
ca
n only be u
s
e
d
for on
e rul
e
, but the syst
em
applie
s a mul
t
iset of rule
s whi
c
h is maxi
mal: no furthe
r rule
can b
e
adde
d [[
5]
].
In a tissue-li
ke P system
o
f
degre
e
d,a
comp
utation i
s
a
seq
uen
ce
of step
s whi
c
h
start
with the
c
e
lls
1,...,q c
ontaining the multisets
w
1
,...,w
q
and
whe
r
e, d
u
ring
ea
ch
st
ep, one
or m
o
re
rule
s a
r
e a
p
p
lied to the
cu
rre
nt multisets of
sy
mbol obje
c
ts.
Th
e comp
utation start
s
from
th
e
initial configu
r
ation an
d proce
e
d
s
as d
e
fined
befo
r
e
;
only halting computatio
n
s
(rea
ching
a
config
uratio
n
whe
r
e n
o
ru
le ca
n be
ap
plied)
give a
re
sult, and t
he re
sult i
s
encode
d by the
multiset of ob
jects. A comp
utati
on is su
cce
ssful if and
only if it halts. When it halts, it produ
ce
s a
final result in output cell.
3. DNA Algo
rithm Bas
e
d
on Tissue
-
like P s
y
stem (TPDNA-GA)
3.1. DN
A Co
ding
The m
a
in g
e
netic m
a
teri
a
l
of organi
sms i
s
DNA
that contain
s
a
wealth
of gen
etic
informatio
n. The ba
sic el
ements of th
e DNA is
Nu
cleotid
e. Nucl
eotide co
ntai
ns four b
a
se
s:
A
(ade
nine
), G (gua
nine
), C
(cyto
s
ine
)
an
d T (t
hymine). Where A p
a
irs
with T, and C pai
rs
wi
th
G.The sequ
e
n
ce of the
DNA mole
cule
s can be a
b
stracted
as th
e strin
g
co
m
posed by the
four
bases. DNA
encode
s u
s
e
the potential
solutio
n
of t
he four ba
se t
o
optimizatio
n pro
b
lem, which
is an effe
ctive method to ex
pre
ss i
ndividu
al and ma
ke i
t
more suitabl
e to recombi
n
e and vari
ate.
Adding DNA
enco
d
ing t
o
the geneti
c
algo
rithm i
s
more suit
able for exp
r
essin
g
co
m
p
lex
knowledge, whi
c
h has
hi
gher coding
accuracy.It is easy to m
a
i
n
ta
in the diversity of i
ndivi
dual
s
and m
o
re
ea
sily to intro
d
u
ce th
e g
ene
tic mani
pul
ati
on. A key
problem
of imp
a
ct on
a
c
curacy
and
conve
r
g
ence rate
of probl
em
sol
v
ing is t
he l
ength of the
DNA
stra
nd
. This p
ape
r use
quante
r
na
ry
encodin
g
in t
he literature
[[
6]
] instead
o
f
E’={0,1,2,3}
1
,1 is the l
e
n
g
th of the
DNA
seq
uen
ce. Th
is allo
ws to e
x
press the
so
lution of
the proble
m
as a i
n
teger
strin
g
of quatern
a
ry
.
Gene
rally, the optimizatio
n probl
em ca
n be de
scribe
d as follo
ws:
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Tissue
-like P System
Base
d DNA
-GA fo
r Clu
s
teri
ng (Caipi
ng Ho
u)
567
)
x
,...,
x
,
f(x
Min
n
,...,
2
1,
=
i
,
maxi
X
≤
X
≤
mini
X
n
2
1
i
In the pra
c
tical optimizatio
n pro
b
lem
s
,
t
he variabl
e x
i
is
an integer
s
t
ring
with length L.[x
min i
,x
max
i
] is the bou
nda
ri
es of x
i
. x
min i
is a
cod
e
string of 0 an
d
x
ma
x
i
is a co
de stri
ng of 4
l
-1.
Duri
ng th
e en
codi
ng p
r
o
c
e
ss, thi
s
a
r
e
a
of x
ma
x
i
-
x
mi
n i
is t
r
an
slate
d
into 4
l
se
g
m
ents.
T
here
f
ore,
the accu
ra
cy
of variable x
i
is
(x
max
i
-
x
mi
n
i
)/4
l
an
d th
e length
of e
a
ch i
ndividua
l n-dim
e
n
s
ion
a
l
variable i
s
L=n × l[[
7]
].
3.2. Fitness
Function
Geneti
c
alg
o
r
ithm exist
s
su
ch a
fun
c
tion t
hat pl
ays d
e
ci
sive role in th
e e
v
olution
dire
ction of g
enetic al
gorit
hm. This fun
c
tion is
the fitness functio
n
. Fitness may be the obje
c
ti
ve
function
and
it may also b
e
a fun
c
tion
of the obj
ecti
ve functio
n
related. Mo
re
over, it can
a
l
so
have nothin
g
to do with the
objective fun
c
tion. Ge
n
e
tic algorithm ev
aluate
s
the candid
a
te by the
size of the value of the fitness fun
c
tion. G
enetic algorithm
s
can d
e
termi
n
e the cha
n
ce of
can
d
idate
so
lutions into t
he next gen
eration of
g
e
netic ba
se
d on the value
of the fitness
function. It is about wh
eth
e
r the quality
of candi
d
a
te
solution
s m
a
y have a better cha
n
ce of
geneti
c
evol
u
t
ion.Also,it is
about
wh
ethe
r the
exce
ll
en
t cha
r
a
c
teri
sti
c
s of the
po
p
u
lation
ca
n b
e
contin
ued.
As the di
re
ct
ion of
sea
r
ch and
evolut
i
onary
guidin
g
the TP
DNA-GA alg
o
rit
h
m, the
desi
gning of t
he fitness fun
c
tion is very i
m
porta
n
t. This
paper us
e a fitnes
s
func
tion as
follows
:
F (x
) =1/(
1+f
(
x
)
)
Whe
r
e, f(x) i
s
the
obj
ecti
ve functio
n
of the
o
p
timization
proble
m
of minimi
zing. After this
treatment, the range of fitness
func
tion values
is
[0,1].
After en
codi
n
g
n
individu
al
s of
the i
n
itia
l
pop
ulation
i
n
to qu
aternary seq
uen
ce,
w
e
so
rt
the fitness va
lues by the fitness fun
c
tion
value.
Reserve the minimum value of individual fitn
ess
(the worst ind
i
vidual) a
nd t
he maximum
individual
(th
e
be
st individ
ual)(a total of
two individu
a
l
s)
as limit individual
s. The remainin
g (N-2) indi
vidu
al
s co
ndu
ct T
P
processin
g
.
Reserving t
h
e
individual of t
he wo
rst fitness value i
s
in ord
e
r to
m
a
intain the di
versity of the
offsprin
g, which
make it po
ssi
ble for the alg
o
rithm to escape from
lo
ca
l optimum an
d avoid falling into premat
ure
conve
r
ge
nce.
3.3. Tissue-li
ke P Proces
sing
After the ope
ration, the two limit individ
uals
rem
a
in
s in the area
s betwe
en the
basi
c
outer mem
b
rane and the
surfa
c
e m
e
m
b
ran
e
. The re
mainin
g (N-2) individu
als are put into m
basi
c
m
e
mbrane
s eq
ually, whi
c
h fo
rms
a P syst
e
m
.And ea
ch i
ndiv
i
dual in
ea
ch
membrane
can
be viewed
a
s
a
cell.In th
is
se
ction,the
memb
ran
e
s will b
e
a
r
ra
nged
as a l
o
op top
o
logy.The
individual
s h
a
v
e som
e
evol
ution rules to
evolve ea
ch
other i
n
the
system, whil
e
comm
uni
cati
o
n
rule
s betwee
n
individual m
e
mbrane
s are use
d
to exchang
e and
sh
are the info
rmation.
In this p
ape
r,
the tissue
-li
k
e P sy
stem u
s
e
s
a sin
g
le
-l
ayer
m
e
mb
ra
ne stru
cture becau
se
the layers of
the tissue
-like P
system
s a
r
e rela
ted
to the mag
n
itude of po
pu
lation si
ze
N.
In
orde
r to make the runni
ng
time of each
membrane
re
lative to the average of the
runni
ng time,
w
e
define the nu
mber of the
membrane
s a
s
follows:
Z=
2
N
Whe
r
e
N i
s
the total num
ber of i
ndivid
uals
of in
itial
popul
ation,
Z is the
sq
u
a
re
root of
(N-2
)
(ro
und do
wn)
[[
6]
]. When
N is l
a
rg
e en
ough,
we
can
get the s
qua
re root of N
d
i
rectly. Using
this
way to d
e
fine
the nu
mbe
r
Z ca
n mai
n
ta
in simil
a
r limi
t
individual
s
betwe
en int
r
a
m
embrane
a
nd
extramemb
r
a
ne, whi
c
h can
redu
ce the o
v
erall co
nvergen
ce time.
3.3.1. Rules
At the same t
i
me, the evol
ution rul
e
of the
mem
b
ra
n
e
is defin
ed.
The role of e
v
olution
rule
s is to evolve the individuals in th
e membrane
s to gene
rat
e
new in
dividuals u
s
e
d
in the
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NI
KA
Vol. 16, No. 3, Dece
mb
er 201
5 : 565 – 573
568
cal
c
ulatio
n of
fitness.
Du
ri
ng the evol
u
t
ion,
each m
e
mbrane
mai
n
tains th
e same
size (th
e
numbe
r of individual
s). Every individual
in each
me
mbra
ne will b
e
evolved after executing
the
sele
ction, cro
s
sover a
nd
mutation in t
u
rn.
When th
e individual
s
are evolve
d,each memb
rane
sen
d
s its
be
st individual to the neigh
boring
memb
ra
n
e
s (su
c
h a
s
membrane i
-
1 and me
mbrane
i+1)
and by u
s
ing the
com
m
unication ru
le,
we ret
r
ieve the best in
dividual from
the neigh
bori
n
g
membrane
s
whi
c
h con
s
titute a matchi
ng pool of
th
e individual
s
in the next calcul
ation ste
p
. A
matchin
g
po
o
l
is made
up
of all individu
als in e
a
ch m
e
mbrane a
n
d
the best indi
viduals from i
t
s
two adja
c
ent
membra
ne
s. The individuals in
mat
c
hing pool
wi
ll be evolved by executi
n
g
sele
ction, cro
s
sover an
d mutation ope
ration
s in turn.In orde
r to maintain the size of individual
s
in ea
ch
mem
b
ran
e
, tru
n
ca
tion op
eratio
n is u
s
ed t
o
con
s
titute n
e
w
in
dividual
pool
acco
rdin
g to
the fitness fu
nction. T
he in
dividual
s in n
e
w in
di
vidual pool will
be regarded as
t
he
individ
uals
to
be evolved in
next computi
ng step [[
8]
].
The sp
eci
a
l logical stru
ctu
r
e ca
n bri
ng the followi
ng b
enefits:
(1) T
he
co-evolution of indi
viduals in th
e
m memb
ran
e
s
can a
c
cele
rate the
conv
erge
nce
of the propo
sed TPDNA-G
A
algorithm.
(2) The
indivi
dual
sha
r
in
g
mech
ani
sm o
f
the local n
e
i
ghbo
rho
od
st
ructu
r
e
can e
nhan
ce
the diversity of individuals
in the entire system.
After all the in
dividual
s in the tissue
-
li
ke P sy
stem are
evolved, the best individu
a
l
will be
comm
uni
cate
d to the environment. Th
ey will ste
p
to
n
e
xt round
ope
ration tog
e
the
r
with the i
n
itial
2 limit individuals. As it in
volves multipl
e
best
individ
uals in the
e
v
olut
ion of the system
s, the
t
i
ssu
e-li
ke P
sy
st
em
can e
f
f
e
ct
iv
ely
solv
e
the probl
em
of local opti
m
um algo
rith
m.
3.3.2. Selection Opera
t
or
In this pape
r, we adopt th
e limit individual re
se
rvatio
ns an
d the fitness fun
c
tion
as the
sele
ction o
p
e
r
ator.
Choo
se the sm
alle
st fitness
value of the indi
viduals in
ea
ch g
ene
ratio
n
to
comp
are with
the be
st in
di
vidual from
the p
r
ev
iou
s
gene
ration
a
nd
sele
ct the
minimum
fitness
value of the i
ndividual
s a
s
the limit indivi
dual
s to
pa
rti
c
ipate i
n
sele
cting of th
e n
e
xt gene
ratio
n
. It
will not rel
e
a
s
e the be
st i
ndividual to the extram
e
m
bran
e until it rea
c
he
s the
con
d
ition
s
of the
membrane
di
ssolution
(wh
en it rea
c
he
s the
ma
xim
u
m exe
c
utio
n ste
p
n
u
mb
er
G). T
he
b
e
st
individual
will
carry o
n
the
iteration
op
era
t
ion out
side
the me
mbran
e
. In the
oute
r
me
mbrane,
we
adopt the limi
t
individual re
servatio
ns a
s
well.
3.3.3. Cross
o
v
e
r Operators
In this pa
per,
we
use th
e re
con
s
tru
c
tion
cro
s
s
o
ver operator. Before the
rec
o
ns
truc
tion
o
f
the cro
s
s op
eration, t
w
o i
ndividual
s fro
m
the
p
opul
ation
shoul
d be sele
cted as
th
e
pa
ren
t
s.
Since the m
a
in purpo
se
of the reco
n
s
tru
c
tion is
t
o
cha
nge th
e simila
rity of the outstan
din
g
individual, the
choi
ce of the
parent
s is no
t random,
whi
c
h is to say we need
cho
o
se the relatively
simila
r indivi
dual
s. Firstly, choo
se o
n
e
indi
vidual
as o
ne of the pa
rent
s randomly in t
he
individual
s wi
th better fitness. And ra
nd
omly sele
ct two individu
al
s as a candid
a
te pare
n
ts. Then
by comp
ari
n
g
the simila
rity betwe
en
ca
ndidate
par
e
n
ts an
d the
known pa
rent
s, we sele
ct the
individual tha
t
is more
si
milar to the
kno
w
n p
a
ren
t
s as a
nothe
r pa
rent of the re
co
nst
r
u
c
tion
operation.
Here
we
defin
e that the
si
milarity
bet
ween in
dividu
als i
s
the
di
stan
ce
between
individual
s. T
he smalle
r th
e dista
n
ce is,
the mo
re
si
milar the t
w
o
bodie
s
a
r
e
b
e
lieved.After
th
e
two pa
rent
s are d
e
termin
ed, we defin
e the indivi
d
ual with bett
e
r fitness a
s
the parent A and
anothe
r indivi
dual is d
e
fine
d as pa
rent B
.
The sp
ecifi
c
descri
p
tion of
the re
con
s
truction
cro
s
so
ver o
peration
process i
s
shown in
the Figure 1.
At first, we choose one ba
se rand
omly in the la
tter of the parent A that is the [L/2, L] and
cut the seq
u
e
n
ce fra
g
ment
R behind thi
s
ba
se fr
om the parent A.
Then pa
ste the fragm
ent into
the front of t
he pa
rent B,
whi
c
h fo
rm in
termedi
ate in
dividual A a
n
d
interm
ediat
e individu
al B
.
In
the DNA ge
n
e
tic alg
o
rithm
,
the length o
f
the individu
al is fixed. Th
erefo
r
e it ne
e
d
s to g
ene
rat
e
a
seq
uen
ce fra
g
ment R’ in t
he latter of interme
d
iate ind
i
vidual A which contai
ns th
e same n
u
mb
er
of base
s
with
R. At
the sa
me time,we cut a seque
nce fragme
n
t from the latter of intermedia
t
e
individual B t
hat also
cont
ains th
e
sam
e
num
ber of
ba
ses with
R.The
r
eby,it
forms two
ne
w
individual
s: p
r
oge
ny A a
n
d
progeny
B.In this
pap
er
,
we ad
opt the
same
pro
babili
ty of crossov
e
r
operator in
sid
e
and out
side
the membra
ne.
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TELKOM
NIKA
ISSN:
2302-4
046
Tissue
-like P System
Base
d DNA
-GA fo
r Clu
s
teri
ng (Caipi
ng Ho
u)
569
Figure 1. The
reco
nst
r
u
c
tio
n
cro
s
sove
r o
peratio
n
It should be
noted that d
ue to the re
constructi
o
n
o
f
the cro
s
sover ope
ratio
n
is more
compl
e
x and
the cha
nge
s are la
rge
r
for the populat
i
on individual
s, so the execution pro
babil
i
ty
Pr of the reco
nstru
c
tion
cro
ss
sho
u
ld cho
o
se
a
smalle
r value. Here
we defin
e Pr=0.05.
3.3.4. Mutati
on Opera
t
or
In the genetic algo
rithm, mutation ope
rator i
s
main
ly to ensure
the diversity of the
grou
ps in a
certain
deg
ree
.
In ord
e
r to
fully
displ
a
y the pe
rforman
c
e
of the
cro
s
sover
ope
ra
to
r
pre
s
ente
d
in
this pap
er, th
e mutation o
perato
r
u
s
e t
he co
mmon v
a
riant
s (n
orm
a
l mutation, NM)
operator that
is com
m
only
use
d
in the DNA geneti
c
al
gorithm.
This o
perator is simila
r to
the flip variati
on of the bin
a
ry GA,whi
ch
is to mutate
every
base in th
e
individual
wit
h
proba
bility p
m
into another base. T
he
probability of performi
n
g
variation of th
e wh
ole in
dividual i
s
p
m
×L. For exa
m
ple,
the ba
se
C i
s
repla
c
ed
by base A in th
e
individual.
The si
ngle
-
p
o
int mutation
is used to
reali
z
e the
mutations
of individual
s. If v is a
mutation poi
n
t determi
ned accord
i
ng to
mutation probability
p
m
, its value
become
s
, after
mutating.
0
≠
v
,
v
×
δ
×
2
v
0
=
v
,
δ
×
2
v
Whe
r
e the
si
gns
“+” o
r
“-”
oc
cur
with e
q
ual proba
bility, and
δ
is
a real num
be
r in
the ran
ge [0,
1
],
gene
rated
with uniform di
st
ribution.
3.4. The Implementa
tion
Steps
o
f
the TPDNA-GA Algorithm
The procedu
re of TPDNA-GA can b
e
su
mmari
zed a
s
follows:
(1) Before runnin
g
the
algorith
m
,we
need
to
se
t the pa
ram
e
ters of the
algo
rithm
(initializi
ng t
he po
pulatio
n), in
cludi
ng
popul
ation
size N, th
e
larg
est p
o
p
u
lation evol
u
t
ion
algebrai
c
G,
reconstruction cros
s
execution probabilit
y P, common
variant execution
probabil
i
ty
p
m
;
(2)
Ra
ndomly
prod
uce N i
n
dividual
s with
the lengt
h
of L=n x l, which ma
ke up
th
e initial
popul
ation. And the cu
rren
t evolut
ion ge
neratio
n is se
t to 1;
(3)
DNA en
co
ding:calculate
the value of
each individu
al's fitness an
d sortin
g;
(4) Sel
e
ct an
d re
serve t
w
o individual
s
with
the maxi
mum and mi
nimum fitness value.
The rem
a
inin
g (N-2) in
dividual
s are p
u
t into m membran
e
s e
quall
y
, which form
s a tissue-li
ke P
system
s. We
set the maxi
mum execution st
ep n
u
mb
er as T
1
insi
d
e
the membrane
s;
(5) The pro
p
o
se
d
ge
netic operation
s
were ca
rri
ed o
u
t for ea
ch
of the individu
a
l
s withi
n
the membran
e
s: sel
e
ctio
n, cro
s
sove
r an
d mutation.
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 16, No. 3, Dece
mb
er 201
5 : 565 – 573
570
(6)
Run th
e
step of (5) i
n
each of th
e memb
ran
e
repe
atedly until the me
mbra
ne
operation re
ach
e
s the m
a
ximum evol
ution gen
er
at
ion and p
r
od
uce a b
e
st i
ndividual
whi
c
h
con
s
titutes a
matchin
g
po
o
l
with the indi
vidual
s in th
e
adjacent me
mbra
ne
s. Th
e matchi
ng p
ool
con
s
i
s
ts
of al
l individual
s i
n
on
e me
mbrane
and
the t
w
o
be
st indiv
i
dual
s fro
m
t
h
e
a
d
ja
cent t
w
o
membranes. The
individuals
in mat
c
hing pool
will be evolved
by executing sele
ction, crossover
and m
u
tation
ope
ration
s in
turn. In o
r
d
e
r
to mai
n
tain
the si
ze
of in
dividual
s in e
a
ch
memb
ra
ne,
truncation o
p
e
ration i
s
u
s
e
d
to co
nstitut
e
ne
w individ
ual po
ol a
c
co
rding to th
e fi
tness fun
c
tio
n
.
The individu
a
l
s in ne
w indi
vidual pool
will be reg
a
r
d
e
d
as the in
di
viduals to be
evolved in n
e
xt
comp
uting st
ep.
(7)
Run the
st
ep of (5
) in the matchi
ng p
ool
until it rea
c
he
s the max
i
mum execution step
numbe
r (with
the sam
e
m
e
mbrane exe
c
ution
step n
u
mbe
r
T1 in
side the mem
b
ran
e
).Th
en
t
he
membrane
s are dissolve
d.
The fin
a
l
be
st indivi
dual(a total
of one
) i
s
relea
s
ed to
the
environ
ment
whi
c
h compo
s
e
s
the elite popul
ati
on wit
h
the initial two limit individuals.
(8) Elite
po
pulation
co
n
duct the
ge
netic m
anip
u
lation: cro
s
sover an
d
mutation,
sele
ction. We
set the maximum execution
step n
u
mb
er as T
2
outsi
de the memb
rane.
(9)
Ru
n the step of (7
) re
p
eatedly until the op
eratio
n
rea
c
he
s the t
e
rmin
ation
co
ndition.
And the optimal solutio
n
is gen
er
ate
d
.The TPDNA-GA algorithm
end
s.
4. Applicatio
n of TPDNA-GA Algo
rith
m in Clusteri
ng
4.1. Introduc
tion of Clu
s
tering and Cl
usterin
g
Me
asure
From n
o
w
o
n
, let us a
s
sume that we
are
con
c
e
r
n
ed with a
dat
a set D,
whi
c
h h
a
s n
sampl
e
p
o
int
s
a
nd i
s
p
a
rtit
ioned
into
k
clusters,
C
1
,C
2
,...
,C
k
. Each
of them i
s
re
pre
s
ente
d
a
s
an
m-dime
nsi
o
n
a
l vecto
r
of
real nu
mbe
r
s,
say x
1
, x
2
,...
,x
n
, where
x
i
= [
x
i1
, x
i2
,..
.,
x
in
]. Denote
by
z
1,
z
2,
...,z
k
the corre
s
po
n
d
ing
clu
s
ter
cente
r
s. If th
e dista
n
ces
of sam
p
le p
o
int x
i
to c
l
us
ter
cent
e
r
s z
p
(p =
1,2,...,k
) s
a
tis
f
y:
p,
≠
j
an
d
k
1,2,...,
=
p
||,
p
z
-
i
x
||
≤
||
j
z
-
i
x
||
Then sampl
e
point x
i
is assigned to cl
ust
e
r C
j
, i =
1,2,...,n.
Gene
rally
sp
eaki
ng, pa
rtitional
clu
s
teri
ng alg
o
rithm
sea
r
che
s
fo
r the o
p
timal
clu
s
ter
cente
r
s in th
e solution
sp
ace
a
c
cordi
n
g to
some
cl
usteri
ng
mea
s
ure in
orde
r to solve dat
a
clu
s
terin
g
pro
b
lem. A com
m
only use
d
cl
usteri
ng me
a
s
ure is:
M(C
1
,C
2
,...,C
k
) =
k
1x
i
||
z
-
x
||
j
iC
i
j
The smalle
r the M value, t
he hig
her th
e
clu
s
terin
g
q
uality. In this work, the
cl
usteri
ng
measure is a
l
so u
s
e
d
to e
v
aluate the i
ndividual
s
of
the syste
m
d
u
ring
mem
b
rane evol
ution
.
If
the M value of an membra
ne is the sma
ller, the me
mbrane is
the better, otherwis
e
, it is
worse.
Since data
set D has
k cluster
cent
ers and e
a
ch clu
s
ter
cente
r
is a m-dim
ensi
onal
vector, ea
ch
membrane in
the system i
s
co
nsi
der
ed
as a (k×m)-di
mensi
onal
re
al vector of the
form:
km
k2
k1
im
i2
i1
1m
12
11
z
,...,
z
,
z
,...,
z
,...,
z
,
z
,...,
z
,...,
z
,
z
z
Whe
r
e z
11,
z
12,
...,
z
1d,
are d co
mpone
nts of
ith
clu
s
t
e
r ce
nt
er
i
z
, i=
1,2,...,k
. For
s
i
mplic
i
ty, s
u
ppos
e
that each
cell
has the sam
e
numbe
r of obje
c
ts, whi
c
h is den
oted
by D [[
9]
].
Initially, the system will ra
n
domly gene
ra
tes m
initial o
b
ject
s for ea
ch cell.When a
n
initial
obje
c
t z is g
enerated,
(k×d)
ran
dom
re
al nu
mbe
r
s a
r
e
pro
d
u
c
ed
repe
atedly to
form
it with
the
c
o
ns
traint of:
B
≤
z
≤
A
,...,
B
≤
z
≤
A
,...,
B
≤
z
≤
A
d
id
d
j
ij
j
1
i1
1
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Tissue
-like P System
Base
d DNA
-GA fo
r Clu
s
teri
ng (Caipi
ng Ho
u)
571
Whe
r
e
j
A
and
j
B
are
lower bou
n
d
an
d u
ppe
r bou
nd
of
jth
dimensi
onal
compon
ent of
dat
a
points
,
res
pec
tively, j =
1,2,...
,d.
4.2. Cluste
ring Ba
s
e
d on
TPDNA-GA
Acco
rdi
ng to
the compo
n
ents
discu
s
sed ab
ove, th
e de
sign
ed t
i
ssue-li
ke
P
system
based
DNA
can be fo
rmall
y
used fo
r
clu
s
terin
g
to
cho
o
se th
e be
st
clu
s
terin
g
ce
nter. The
opti
m
al
solutio
n
in
th
e environm
e
n
t refe
rs to t
he o
p
timal
cl
usteri
ng th
at
we
co
uld
obt
ain fro
m
the
data
given [[
10
]
]. The objective function f(x) will be
reali
z
ed by evaluating the
distances
between two
individual
s fro
m
each oth
e
r.
Steps that use TPDNA
-GA
to solve the
probl
em of cl
usteri
ng a
r
e a
s
follows:
(1) Fi
rst of all
,
give the data sets that
n
eed to be cl
u
s
tere
d and
condu
ct DNA encodin
g
for data;
(2) Cal
c
ulate the
obje
c
tive
function;
(3) Determin
e the fitne
s
s
function
a
cco
rding
to the
o
b
jective fun
c
t
i
on, whi
c
h
is
use
d
to
evaluate the
poste
rity of the geneti
c
alg
o
ri
thm
s
and g
r
asp the evol
utionary di
re
ction.
(4) Introd
uce
TPDNA-GA
algo
rithm o
perat
io
n a
n
d
determine t
he o
perating
ope
rato
r
(sel
ect op
erator, cross op
erator,mutation operator).
(5)
Perfo
r
m TPDNA
-GA algorith
m
to gene
rate
th
e
optimal
sol
u
tion that is th
e optimal
c
l
us
te
r
i
ng
c
e
n
t
e
r
.
Based
on
the
propo
sed
T
P
DNA-GA, th
e be
st o
b
je
ct in the
envi
r
o
n
ment i
s
reg
a
rde
d
a
s
the system o
u
tput, which is t
he found o
p
timal clu
s
ter centers.
5. Experiment Re
sults a
nd Analy
s
is
In this se
ction
,
the propo
se
d TPDNA
-GA
algorit
hm i
s
evaluated for
clu
s
terin
g
on
the five
real
-life data
sets p
r
ovide
d
in UCI [[
11]
] (inclu
ding th
e Iris, Brea
st
Can
c
er,
Win
e
, New T
h
yroid
and Live
r Di
sorde
r
s) an
d
comp
ared with cla
ssi
cal
k-m
ean
s alg
o
rithm a
nd several
clu
s
te
ring
algorith
m
s, in
cludi
ng GA [[
12]
] an
d PSO
[[
13]
]. In ord
e
r to te
st the
robu
stne
ss of
these
cl
uste
ring
algorith
m
s,
we re
peat th
e
experim
ents
50 time
s fo
r
each d
a
ta
set
.
The M
valu
e is al
so u
s
e
d
to
measure the
clu
s
terin
g
qu
ality of each
clu
s
terin
g
al
g
o
rithm. Th
at is to
say, if the M value
of
one
individual i
s
the smalle
r than othe
rs,the fitnes
s value
s
will be
smalle
r, wh
ich me
ans t
h
e
individual will
be better tha
n
others. So the clu
s
ter
ce
nters
will also
be better. Th
ese al
gorithm
s
are impl
emen
ted in Matlab
7.1.
Table
1.
The perfo
rman
ce comp
ari
s
o
n
s of
tissue
-
like P systems of
different deg
rees
Data sets
4 cells
8 cells
16 cells
20 cells
Iris
96.84
96.81
96.75
96.77
±0.0751
±0.0435
±0.0428
±0.0361
Breast Cancer
2974.24
2971.14
2970.24
2969.06
±1.5431
±1.5287
±1.1225
±1.0970
Wine
16309.01
16303.42
16292.25
16301.97
±2.5053
±1.9595
±0.1529
±2.8563
Ne
w
Th
yr
oid
1885.69
1870.37
1869.29
1871.18
±14.3773
±1.7355
±0.9215
±2.2496
Liver Disorders
9860.54
9859.02
9851.78
9857.08
±5.7239
±0.5116
±0.0347
±0.1043
In the exp
e
ri
ments,
we
u
s
e f
our
kind
s o
f
tissu
e-li
ke P
syste
m
s with
deg
ree
s
4, 8,
16
and
20 re
sp
ective
ly. The purpo
se i
s
to evalu
a
te the effe
ct
s of the n
u
mb
er of cells
(dif
ferent de
gree
s)
on cl
uste
ring
quality. The
four tissue
-li
k
e P syst
em
s
are a
pplie
d to find out the
optimal cl
ust
e
r
centers for the five data
sets re
spectivel
y
. The average values
ar
e used to illust
rate the average
perfo
rman
ce
of the algorit
hms while st
anda
rd devia
tions indi
cate
their robu
stn
e
ss. As we can
see, T
able
1
provide
s
exp
e
rime
ntal results of th
e tissue
-like P
system
s of fou
r
deg
ree
s
on f
i
ve
data
sets
re
spectively. It can be
furth
e
r ob
serve
d
th
at the tissue
-l
ike P
system
with d
egree
16
obtains the smallest average valu
es and standard
deviations on a
ll of data set
s
, whi
c
h illustrate
that the tissu
e-like P syste
m
with deg
re
e 16 ha
s goo
d clu
s
terin
g
q
uality and hig
h
robu
stne
ss.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 16, No. 3, Dece
mb
er 201
5 : 565 – 573
572
For thi
s
re
ason, we
will d
o
experim
ent
on TPDNA-GA, k-me
an
s, GA, and PSO with
degree 1
6
. In the experi
m
e
n
ts, the pa
ra
meters of TP
DNA
-GA a
r
e
set a
s
follo
ws. The pop
ulati
on
size i
s
200
(N = 20
0). T
h
e
l
a
rge
s
t
pop
ula
t
ion evolutio
n
alge
braic G i
s
set
as 30
0,
whi
c
h i
s
to
say
that the m
a
ximum evol
utio
n ge
ne
ral i
n
side A1
an
d o
u
tside
A2 i
s
150. T
he
parameters
of th
e
mutation op
e
r
ator i
s
set as pm
=0.0
1. And the
crossover probability
is set
as
Pr=0.05.
The
numbe
r of m
e
mbrane
s i
s
15(m
=
1
5
). In
ord
e
r to
stud
y performan
ces of ti
ssue-li
ke P
system
s of
different d
egrees, fou
r
ca
ses a
r
e
co
nsi
d
ered
in the
e
x
perime
n
ts: q
=
4; 8; 1
6
; 2
0
. And for
ea
ch
test probl
em, we ru
n 50 times for the five algorithm
s of
TPDNA-GA, k-m
ean
s, GA and PSO
.
The
results a
r
e sh
own in Ta
ble
2.
Table 2. The
results obtai
n
ed by the alg
o
ri
thms
for 50 runs
on the five data s
e
ts
Data sets
TPDNA-
G
A
GA
PSO
k-means
Iris
96.80
99.83
97.23
104.11
±0.1436
±5.5239
±0.3513
±12.4563
Breast Cancer
2997.36
3249.26
3050.04
3251.21
±2.1345
±229.734
±110.801
±251.143
Wine
16292.25
16298.42
16292.25
16312.43
±0.1530
±2.1523
±0.1531
±9.4269
Ne
w
Th
yr
oid
1870.36
1875.11
1872.51
1886.25
±0.9215
±13.5834
±11.0923
±16.2189
Liver Disorders
9851.81
9856.14
9851.73
9868.32
±0.0348
±1.9523
±0.0356
±7.9274
In orde
r to fu
rther
evaluat
e clu
s
teri
ng p
e
rform
a
n
c
e, the propo
se
d
TPDNA
-GA a
l
gorithm
is compa
r
ed
with GA-ba
s
e
d
and PSO
-b
ase
d
clu
s
te
ri
ng algo
rithm
s
as well a
s
cl
assical k-me
ans
algorith
m
. Ta
ble 2
give
s t
he
com
pari
s
o
n
results
of t
he tissu
e
-li
k
e
P
system
of
deg
re
e 1
6
with
other fou
r
cl
u
s
terin
g
alg
o
rit
h
ms o
n
the fi
ve data set
s
, respe
c
tively.
From
the re
sults,
we can see
that the TPDNA-GA p
r
ovi
des the o
p
timum aver
a
g
e
value and
smalle
st stan
dard d
e
viatio
n in
comp
are to those of othe
r a
l
gorit
hm
s.Fo
r instan
ce, the
optimum valu
e is 96.80
whi
c
h is o
b
taine
d
in mo
st of ru
ns
of TPDNA
-
GA al
gorith
m
, however
,
other th
ree
al
gorithm
s fail t
o
attain the
value
even on
ce
wi
thin 50 run
s
. And the resul
t
s on the
Win
e
also sho
w
that the TPDNA-GA algo
rith
m
provide
s
the
optimum valu
e of 16292.2
5
while
the
PSO, GA and k-m
ean
s o
b
tain 162
98.
42,
1629
2.25
an
d 16
312.4
3
resp
ectively. In ad
dition, t
he tissu
e
-li
k
e
P sy
stem
o
b
tains smalle
st
standard deviation on each
data set in compare to other three al
gorithm
s
, whi
c
h illustrates that it
has
high
rob
u
stne
ss. Thi
s
is
a st
ron
g
eviden
ce
t
o
prove th
e
signifi
cant
su
perio
rity of the
prop
osed alg
o
rithm.
6. Conclusio
n
In this pape
r, a new DNA-GA algorithm
based
o
n
tissue
-like P system (TP
D
NA-GA) is
prop
osed
by combi
n
ing
DNA-GA
with t
i
ssue-li
ke
P
s
y
s
t
em for the firs
t time and we us
e it
for
clu
s
terin
g
. Di
stingui
sh
ed f
r
om th
e existing evol
utio
nary
clu
s
teri
ng te
chniq
u
e
s
, two i
nhe
rent
mech
ani
sm
s
of
t
i
ssu
e-li
ke
P
sy
st
em a
r
e
ex
ploit
ed to realize the TP
DNA
-GA alg
o
r
ithm, incl
udi
ng
evolution an
d com
m
uni
cation me
cha
n
ism
s
. A
nd t
he two i
nhe
rent rule
s a
r
e used b
e
tween
membrane
s that contain
th
e ave
r
age
n
u
m
ber of
i
ndividual
s.Moreov
er, the
comm
unication
rule
s
imply
re
alize a
lo
cal neig
h
borh
ood
stru
cture,
nam
ely, each m
e
mb
rane
ex
chan
ges an
d
sha
r
es
the be
st obj
e
c
ts
with its two adja
c
e
n
t m
e
mbrane.
Un
der th
e
control of two
rul
e
s a
nd the
fitness
function
of in
dividual
s, the
TPDNA
-GA
algorith
m
is
a
b
le to search
for the optim
al clu
s
ter
ce
n
t
ers
for a d
a
ta set to be
clu
s
tere
d.In ad
d
i
tion, the local neig
hbo
rh
ood
stru
cture
can
guid
e
the
exploitation o
f
the optimal
obje
c
t an
d e
nhan
ce
the
d
i
versity of ev
olution
obje
c
ts. The
r
efo
r
e,
the
TPDNA
-GA
a
l
gorithm pre
s
ented
in
thi
s
pape
r can be
viewed
as
a
su
ccessful in
stan
ce fo
r da
ta
c
l
us
te
r
i
ng
.
After repe
ate
d
verification,
the TPDNA
-GA
algorith
m
performs
wel
l
when the p
o
pulation
size is la
rge
enou
gh. The
future work is to im
prove the algo
rithm
efficien
cy wh
en the pop
ula
t
ion
size is small.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Tissue
-like P System
Base
d DNA
-GA fo
r Clu
s
teri
ng (Caipi
ng Ho
u)
573
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proac
h to data cluste
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