Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
Vol.
5, No. 6, Decem
ber
2015, pp. 1424~
1
432
I
S
SN
: 208
8-8
7
0
8
1
424
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Te
st Ca
se
Re
duc
tio
n
Using
Ant Colo
ny
Optimiz
a
tion for
Obje
ct
Oriented Program
Sudhir
Kum
a
r Moh
a
p
a
tr
a*, Srinivas
Prasad
**
* Res
ear
ch S
c
ho
lar,
S
OA Univer
s
i
t
y
, Bhub
anes
war, Odis
h
a
,
India
** Dept. of Com
puter Science
&Engineer
ing, G
M
RIT, Andhra Pradesh, India
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
May 6, 2015
Rev
i
sed
Ju
l 18
,
20
15
Accepte
d Aug 2, 2015
Software testing
is one in all t
h
e vita
l stages of sy
st
em
devel
opm
ent. In
software develo
pment, de
velopers continually
d
e
pe
nd upon testin
g to reveal
bugs. Within
the mainten
a
nce stage test
suite size grow due
to in
tegration of
new function
a
lities. Addition of
latest te
chnique
force to mak
e
n
e
w test case
which incre
a
se t
h
e cost of test suite
. In
regression
testing new test
case could
also be added to the test suite thr
oughout the entir
e testing pr
ocess. These
additions of tes
t
cases produce risk
of presen
ce of redundant test cases.
Because of l
i
m
i
t
a
tion of tim
e an
d resource, r
e
du
ction t
echniqu
es should be
accus
t
om
ed de
te
rm
ine and tak
e
awa
y
. Anal
ys
is
s
hows
that a s
e
t
of the tes
t
case in a suit should satisf
y
all the
test o
b
jectives that is named a
s
representativ
e set. Redund
ant
test case in
cr
ease th
e execution
price of the tes
t
s
u
ite,
in s
p
ite
o
f
NP
-com
pleten
es
s
of the probl
em
there
are f
e
w s
e
ns
ible
reduction techniques are av
ailable. Du
ring th
is paper the pr
evious GA
primarily
based
techn
i
que propo
sed is
improved to search out
co
st optimum
represent
a
tiv
e se
t using
ant
colon
y
optim
iz
ation
.
Keyword:
An
t co
lon
y
o
p
t
i
m
izat
io
n
Rep
r
esen
tativ
e set
Soft
ware
testin
g
Test su
ite reductio
n
Copyright ©
201
5 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Su
dhi
r K
u
m
a
r M
oha
pat
r
a
,
Depa
rt
em
ent
of C
o
m
put
er
Sci
e
nce &
E
ngi
ne
eri
n
g,
SO
A
Uni
v
ersit
y
, O
d
isha
, I
n
dia.
Em
ail: sudhirm
ohapatra@hotm
a
il.com
1.
INTRODUCTION
So
ft
ware testing
an
d
retesting is do
n
e
frequen
tly
du
rin
g
th
e so
ftware
de
velopm
ent lifecycle and i
n
part
i
c
ul
a
r
i
n
re
gressi
o
n
t
e
st
i
n
g.
I
n
re
g
r
essi
o
n
t
e
st
i
n
g s
o
ft
w
a
re
gr
ow
s a
n
d
evol
ves,
t
h
at
c
r
eat
e ne
w t
e
st
cases
an
d add
e
d
t
h
em
to
a test suite to
ex
ercise th
e latest
c
h
a
nge
s t
o
t
h
e
so
ft
ware
.
Ov
er
m
a
ny
ver
s
i
o
ns
o
f
t
h
e
devel
opm
ent of the softwa
re, test cases in the test su
ite can
b
e
r
e
du
nd
an
t .Th
e
r
e
dun
dan
t
test case
may
in
respect
t
o
t
h
e t
e
st
i
ng
re
qui
re
m
e
nt
s f
o
r
w
h
i
c
h t
h
ey
we
re
ge
nerate
d,
beca
use these
re
quire
m
ents are
now als
o
satisfied
b
y
n
e
w test cases in th
e test su
ite th
at were n
e
wly ad
d
e
d
to
co
ver ch
ang
e
s in
t
h
e later v
e
rsion
s
of
so
ft
ware. Du
e to
limitat
i
o
n
o
f
ti
m
e
an
d
resou
r
ce
fo
r
rete
stin
g th
e
software ev
ery ti
m
e
before a n
e
w
v
e
rsion
is
release, it is re
ally
i
m
p
o
r
tan
t
to
search
for tech
n
i
q
u
e
s th
at en
sure m
a
n
a
g
eab
le test su
its size b
y
p
e
rio
d
ically
rem
ovi
ng
re
du
nda
nt
t
e
st
case
s
. T
h
i
s
p
r
oce
s
s i
s
cal
l
e
d
test su
ite mi
n
i
miza
tio
n
. Th
e test
su
ite m
i
n
i
miz
a
tio
n
pr
o
b
lem
[1]
can
be
fo
rm
al
ly stated
as fo
llows:
Given.
A test su
ite T
o
f
test
cases {t
1
,t
2
,t
3
,…..,t
m
}, a set
o
f
testing
req
u
irem
en
ts {r
1
,r
2
,r
3
….,r
n
} tha
t
m
u
st
be sat
i
s
fi
ed t
o
p
r
ovi
de
t
h
e de
si
red
t
e
s
t
cove
ra
ge
of
t
h
e p
r
og
ram
,
and
su
bset
s {
T
1
,T
2
,..
,T
n
}
of T, one
associated
with each
of the
r
i’
s
suc
h
t
h
at any
one
of t
h
e tests
t
j
b
e
long
ing
to T
i
satisfies
r
i
.
Problem.
Find a
m
i
n
i
m
a
l card
i
n
a
lity su
b
s
et
o
f
T t
h
at ex
ercises all r
i’
s exercised by the
unm
i
nimized
test su
ite T.
The r
i
’s can
rep
r
esen
t eith
er all o
f
th
e
p
r
og
ram
’
s
test case requirem
ents or
those re
qui
rem
e
nts
related
to
pro
g
ram
m
o
d
i
ficati
o
n
s
. A
represen
tativ
e set o
f
t
e
st cases th
at satisfies th
e r
i
’s
m
u
st contain
at least
one
test case
from
each T
i
.
Such
a
set is called
a
h
ittin
g set of th
e group
of sets T
l
, T
2
, .
. .
, T. A
m
a
x
i
m
u
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Test Ca
se Redu
ctio
n Using
An
t Co
l
o
n
y
Op
timiza
tion
f
o
r
Ob
ject Orien
t
ed… (S
ud
h
i
r Kuma
r Mo
hap
a
t
ra
)
1
425
redu
ction
is ach
i
ev
ed
b
y
find
in
g th
e sm
alles
t
rep
r
esen
tativ
e set of test cases.
Howev
e
r, t
h
is su
bset of t
h
e test
su
ite is th
e
m
i
n
i
m
u
m
card
i
n
a
lity h
i
t
tin
g
set o
f
th
e T,’s an
d th
e p
r
o
b
l
em
o
f
find
ing
th
e
min
i
m
u
m
card
i
n
a
lity
h
ittin
g
set
is NP-co
m
p
l
ete [2
]. Th
erefore, sin
ce
we ar
e
un
aware of an
y app
r
ox
im
a
t
e so
lutio
n
t
o
th
e prob
lem
,
we d
e
v
e
lop
a
h
e
uristic [3
],
[4
] to
find
a
represen
ta
tiv
e set
th
at ap
pro
x
i
m
a
tes th
e min
i
m
u
m card
i
n
a
lity h
ittin
g
set.
Th
e
d
e
v
e
l
o
p
m
en
t team
if ab
le to
fi
n
d
ou
t red
und
an
t test ca
se and eliminate them
from
the test case
th
en
t
h
e test suite size can
b
e
redu
ced
.
wh
ile fi
n
d
i
n
g
th
e
rep
r
esen
tativ
e
set th
e team
mu
st en
su
re that all
test req
u
i
rem
e
n
t
s are satisfied
b
y
th
e
red
u
c
ed
test su
ite,
to
m
a
k
e
testin
g
m
o
re efficien
t. Th
at is, g
i
ven
th
e
o
r
i
g
in
al test suite T={t
1
, t
2
, t
3
, ..
.,
t
n
} an
d
a set
o
f
t
e
st
r
e
qui
rem
e
nt
s R
=
{r
1
,
r
2
,
r
3
, .
..,
r
m
}, th
e go
al
is to
f
i
n
d
a
s
u
b
s
e
t
o
f
t
h
e
t
e
s
t
s
u
i
t
e
T
,
d
e
n
o
t
e
d
b
y
a
r
e
p
r
esen
tativ
e set RS, to
satisfy all t
h
e test requ
iremen
ts
sat
i
s
fi
ed
by
T.
The
p
r
oce
ss
of
fi
n
d
i
n
g t
h
e r
e
p
r
es
en
tativ
e set
is called
test suite redu
ctio
n [5]-[8
].
The
or
gani
zat
i
on o
f
t
h
i
s
pa
per i
s
as fol
l
o
ws. I
n
sect
i
o
n
2 rel
a
t
e
d w
o
r
k
s i
s
di
scuss
f
o
l
l
o
we
d by
sect
i
on
3
whi
c
h c
ont
ai
n
t
e
st
case re
duct
i
o
n
pr
o
b
l
e
m
usi
ng a
n
t
col
ony
o
p
t
i
m
i
zat
i
on. T
h
e
pr
op
ose
d
m
odel
i
s
di
scuss
e
d i
n
s
ect
i
on 4 a
nd e
xpe
ri
m
e
nt
al
resul
t
i
n
sect
i
o
n
5. I
n
l
a
st
sect
i
on t
h
e fi
n
d
i
n
gs o
f
t
h
e pa
pe
r are
summ
arized.
2.
REVIEW
RE
LATED W
O
RK
The
Gree
dy
al
go
ri
t
h
m
[9]
,
[
10]
rem
oves t
h
e t
e
st case
c
ontinuously. T
h
e algorithm
stop
when a
represen
tativ
e set i.e RS wh
ich
cov
e
rs th
e
en
tire requ
ir
e
m
ent
i
s
deri
ve
d.
In C
h
e
n
an
d La
u [
1
1]
al
g
o
ri
t
h
m
choose
all im
porta
nt test case
first t
h
en appl
y gree
dy
algorith
m
o
v
e
r th
e
rem
a
in
in
g
test
case fo
r rest
of test
case selection [
12]
f
r
om
that. In [
5
]
Jeffrey
a
nd
Gu
pta p
r
o
d
u
ce re
prese
n
tative set for test suite red
u
ctio
n
usin
g
selective redundancy.
Harrol
d, Gupt
a and Soffa [1] find
re
prese
n
tative test
cases for eac
h subset and include
them in the represe
n
tative se
t. In [14] the authors
use irre
placeability to
evaluate the im
portance of t
e
sts and
p
r
esen
t an
algo
rith
m
th
at u
l
ti
m
a
tely p
r
o
d
u
ces red
u
c
ed
test su
ites wit
h
a su
bstan
tially d
ecrease i
n
the
execut
i
o
n c
o
st
.
Usi
n
g
ge
net
i
c
al
go
ri
t
h
m
i
n
pape
r
[1
3]
,
[15]-[16] the a
u
thors a
r
e a
b
le t
o
m
i
nimize test case
whic
h cover t
h
e entire re
quirem
e
nt
that can be c
ove
re
d by all the te
st cases. In [17], [18] Prasa
d
and
M
oha
pat
r
a
ha
s pr
o
pose
d
a
genet
i
c
al
g
o
i
t
h
m
t
echni
que
t
o
fi
n
d
re
pre
s
ent
a
t
i
v
e set
.
AC
O
use i
n
wi
rel
e
ss
net
w
or
k gi
ve
s a cl
ear pi
ct
ure
of usi
n
g i
t
i
n
opt
i
m
i
zati
on p
r
o
b
l
e
m
by
Dac-N
h
u
o
ng Le [
1
9]
and M
i
na J
a
fari
,
Hassa
n Kh
ot
an
l
ou [
20]
.
3.
TEST CASE
REDUCTION PROBLEM
US
ING ANT COLONY
OPTIMIZ
A
TION
A test req
u
i
remen
t
m
a
trix
called
as TR tab
l
e is fi
rst c
r
e
a
ted from
the requirem
ent and test case
of
asoft
w
are
.
Tes
t
requi
rem
e
nt
tabl
e (TR
)
i
s
a t
w
o di
m
e
nsi
o
n
a
l
0-1
val
u
e t
a
bl
e of si
ze ( m
* n)
. The t
e
st
sui
t
e
T={ t1, t2, t
3
…..,tm
}
is represente
d in r
o
w and the
requirem
ent R={r1, r
2
,
…
..
,r
n} is represe
n
ted i
n
the
colum
n
. That is each row of
the table
repre
s
ent re
quirem
e
n
ts fulfill by a
pa
rticular
test
case. Entry i
n
to the
TR tab
l
e is
d
e
term
in
ed
b
y
:
TR(i,j)
0
1
(
1
)
In Ta
bl
e 1 a t
e
st
sui
t
e
of f
o
ur t
e
st
case an
d t
h
ei
r fi
ve re
qui
rem
e
nt
s are gi
ve
n. Eac
h
t
e
st
case i
s
represen
tin
g
in row wh
ere as th
e requ
irem
e
n
t fu
lfilled
b
y
th
e test case a
r
e m
a
rk
ed
as 1
in
th
e requ
ire
m
en
t
co
lu
m
n
o
t
herwise 0
.
Tab
l
e
1
.
An
exa
m
p
l
e o
f
test case and
requ
iremen
ts fu
l
f
ill by it with
executio
n
tim
e
Test case
Require
m
e
nts to b
e
satisfied
Ti
m
e
No
r1
r2
r3
r4
r5
t1
1 1 1
0 0 2
t2
0 1 1
1 0 5
t3
1 0 0
0 1 2
t4
0 0 1
0 1 2
t5
1 0 1
0 1 1
As p
e
r th
e TR tab
l
e with
m
ro
ws an
d
n
co
lum
n
s, it
is essen
tial
to
select a
su
bset o
f
rows to
co
v
e
r all
o
f
th
e co
l
u
m
n
s in
t
h
e m
a
trix
with
m
i
n
i
m
a
l e
x
ecu
tion ti
m
e
. Sup
p
o
s
e th
e v
e
cto
r
elem
en
t rep
r
esen
ts t
h
e
row i i
n
the vector x i
s
selected and xi=0
m
eans not
, t
h
ere
f
o
r
e,
t
h
e set
cove
r
a
ge p
r
o
b
l
e
m
can be
rep
r
ese
n
t
e
d as
st
anda
rd
o
p
t
i
m
i
zat
i
on p
r
obl
e
m
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJECE
Vol. 5, No. 6, D
ecem
ber
2015 :
1424 –
1432
1
426
M
i
n z(
x)=
∑
C
X
S.t
∑
a
x
i
1
,
i
=
1,2,
3,
4,
……
(2
)
(Ensure that e
v
ery col
u
m
n
is cove
re
d
by at least one row)
xj
∈
0,1
,
j=
1,
2
,
3,…
…
..
The t
e
st
sui
t
e
red
u
ct
i
on
pr
o
b
l
e
m
i
s
conve
rt
ed t
o
set
co
vera
ge p
r
obl
e
m
, and t
h
e
n
con
v
e
r
t
e
d t
o
stan
d
a
rd
op
ti
mizatio
n
prob
lem
.
Th
e id
ea o
f
p
r
op
o
s
ed
algorith
m
start fro
m th
is. It is an
op
ti
m
i
zatio
n
alg
o
r
ith
m
th
at can
u
s
e An
t co
l
o
n
y
op
timizatio
n
to
so
lv
e th
is red
u
c
ti
o
n
pro
b
l
em
.
The test case reduction
problem
can be
m
odel
as a com
p
l
e
t
e
graph
net
w
o
r
k
G
(
V
,
E
) with
E
represe
n
ts all the test case. T
h
e e
dges
e
ij
re
prese
n
t
s
a
pat
h
fr
om
one t
e
st
case t
o
ot
her
.
From
t
a
bl
e n
o
1 t
h
e
g
e
n
e
rated co
m
p
lete graph
is:
Fi
gu
re
1.
The
t
e
st
case re
d
u
ct
i
o
n
p
r
obl
em
m
odel
by
a
com
p
l
e
t
e
gra
p
h
An
t al
go
rith
m
s
u
s
e a
g
r
ou
p
o
f
artificial an
t
fo
r op
tim
u
m
answer
,
out
o
f
al
l
ant
i
ndi
vi
d
u
al
ant
deri
ve
d
an e
n
tire ans
w
er in s
o
m
e
ste
p
s. T
e
m
p
ans
w
er is t
h
at the
ans
w
er
de
rive
d by a
n
t
k in s
o
m
e
n steps.
At eve
r
y
st
ep eve
r
y
a
n
t
k c
o
m
put
es a
gr
o
up
o
f
p
o
ssi
bl
e ex
pa
nsi
o
ns
to its curre
nt
state and m
o
ves to at least one
of
th
o
s
e in
ch
an
ce.Each
an
t k
m
o
v
e
s fro
m
o
n
e
v
e
rtex
i to
an
o
t
h
e
r
v
e
rtex j
with
a tran
sitio
n
p
r
ob
ab
ility ru
le
p
kij
(t
), w
h
i
c
h
i
s
desc
ri
be
d by
t
h
e
f
o
rm
ul
a:
∑
∈
,
∈
0,
∈
(3)
The t
e
m
p
sol
u
t
i
on
of t
h
e
pr
o
b
l
em
i
s
a part
of
sol
u
t
i
o
n an
d t
h
e pa
rt
i
a
l
sol
u
t
i
on i
s
a su
bset
of
vert
i
ces,
wh
ich
con
s
titute a so
lu
tio
n
o
f
th
e p
r
ob
lem
.
Param
e
ters
α
and
β
wh
ich
is u
s
ed
in
th
e tran
sitio
n
p
r
ob
ab
i
lity ru
le
pki
j(t) express
e
d
by (3), indi
cate about
th
is, how im
p
o
r
tan
t
th
e
ph
ero
m
o
n
e
trail
τ
ij
and
th
e attractiv
en
ess
μ
ij
are d
u
ri
n
g
t
r
a
n
si
t
i
on f
r
o
m
one t
o
a
n
ot
he
r st
at
e. Val
u
e
s
of t
h
ese
par
a
m
e
t
e
rs
α
and
β
should
be set by
expe
ri
m
e
nt
and t
u
ne
d t
o
t
h
e
t
e
st
case re
d
u
ct
i
o
n
p
r
obl
em
wi
t
h
m
i
nim
u
m
coveri
ng
cost
.
After a solution
has
been
found each ant
de
posits a
ph
erom
one with a
quantity
Δτ
on
all v
e
rtices,
wh
ich
co
nstitu
te th
e so
lu
tion
Vs, i
n
acco
r
d
a
n
ce
with
th
e
p
a
ttern
:
τ
t
τ
t
∆
τ
(4)
Thus these ve
rtices which were included i
n
to a
sol
u
tion have receive
d an
additional qua
ntity
of
a
p
h
e
ro
m
o
n
e
and
can
b
e
cho
s
en
to
a so
l
u
tion
th
at wo
u
l
d
be co
n
s
t
r
u
c
ted
n
e
x
t
with
a h
i
g
h
e
r pro
b
a
b
ility th
an
ot
he
rs
vert
i
ces
fr
om
t
h
e set
V
T
.
An ev
apo
r
ation
m
ech
an
ism
is in
corporated
in
t
o
an
an
t alg
o
rith
m
in
o
r
d
e
r to avo
i
d
a t
o
o fast
co
nv
erg
e
n
ce t
o
a su
b-o
p
timal so
lu
tion
.
An
in
ten
s
ity o
f
ev
aporatio
n
is co
n
t
ro
lled b
y
a p
a
ram
e
ter
ρ
and a
qua
ntity of a pherom
one on e
ach ve
rtex
from the set VT is update at th
e end
of eac
h cy
cle in accordance with
th
e p
a
ttern
:
τ
1
ρ
τ
t
,
ρ
∈
0
,
1
(5)
Th
us a
di
ve
rsi
t
y
of
a s
o
l
u
t
i
o
n
i
s
gra
n
t
e
d
.
Val
u
es
of
a
param
e
t
e
r
ρ
s
h
o
u
l
d
b
e
set
by
e
x
peri
m
e
nt
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Test Ca
se Redu
ctio
n Using
An
t Co
l
o
n
y
Op
timiza
tion
f
o
r
Ob
ject Orien
t
ed… (S
ud
h
i
r Kuma
r Mo
hap
a
t
ra
)
1
427
A q
u
a
n
tity
o
f
d
e
po
sited
ph
ero
m
o
n
e
Δτ
d
e
pen
d
s
o
n
a
q
u
ality o
f
so
lu
tion
Q and
if the b
e
tter is a
sol
u
t
i
o
n t
h
an
t
h
e m
o
re
phe
ro
m
one i
s
de
posi
t
ed an
d i
n
ge
ne
ral
can
be
st
at
ed as
f
o
rm
ul
a:
∆
τ
f
Q
(6)
and i
n
pa
rt
i
c
ul
ar can
be e
x
p
r
essed
by
som
e
speci
fi
c f
o
rm
ul
a, w
h
i
c
h t
a
k
e
i
n
t
o
acco
u
n
t
t
h
e co
veri
ng
cost.
3.
1. Al
g
o
ri
t
h
m
begin
w
h
ile (
All th
e
requ
irem
en
t Co
v
e
red
)
do
f
o
r (
k
:=1
t
o
n
Ants
)
do
while (
A so
lu
ti
o
n
is
n
o
t
C
o
m
p
lete )
do
Upd
a
te Av
ailab
l
e
Vertices;
C
h
o
o
se ne
xt
v
e
rt
ex
i
with
prob
ab
ility
p
(
i
) a
n
d c
o
n
s
i
s
t
e
ncy
c
h
ecki
ng;
Ad
d t
o
a
Tem
p
Sol
u
t
i
on;
Upd
a
te Tem
p
So
lu
tion
;
If
(
r
e
qui
rem
e
nt C
o
vere
d)
Retu
rn Best Solu
tio
n
Foun
d
e
d
Term
inate;
end
end
Upd
a
te C
u
rrent Best So
lu
tion;
end
Upd
a
te Best;
Use a
n
e
v
a
p
oration m
echanis
m;
Up
dat
e
P
h
e
r
o
m
one;
end
Retu
rn Best Solu
tio
n
Foun
d
e
d;
end
3.2. Theore
tical Example
From
Fi
g
u
re
1
l
e
t
5 ant
st
art
f
r
o
m
fi
ve ve
rt
ex
rep
r
ese
n
t
e
d i
n
t
h
e fi
gu
re,
he
re
n
o
of
ve
rt
ex
(n
)=
no
o
f
an
t(k
)
. In
first
ex
ecu
tion
let al
l th
e an
t
d
e
riv
e
d
th
e fo
llowing so
l
u
tio
n in
t
w
o
step
s.
Tab
l
e
2
.
An
exa
m
p
l
e o
f
test case, requ
irem
e
n
ts an
d it co
st
Ants
Test
Case
Fa
ult
detect
ed
Execution
ti
me
A1 {
T
1-
T2}
4
7
A2 {
T
2-
T3}
5
7
A3 {
T
3-
T5}
3
3
A4 {
T
4-
T1}
4
4
A5 {
T
5-
T4
}
3
3
In
th
e resu
t it i
s
clearly v
i
sib
l
e th
at an
t A2
co
v
e
rs all th
e req
u
i
rem
e
n
t
with
ex
ecu
tion
ti
me o
f
th
e two
test case 7
Sec
.
If it is a
ti
me
co
nstrain
e
d
red
u
c
tion
th
e
n
the algorithm
ca
n exec
ute
fu
rth
e
r fo
r getting a
result
with
less ex
ecutio
n
tim
e o
t
h
e
rwise we can
st
o
p
our ex
ecu
ti
o
n
as all th
e req
u
i
rem
e
n
t
is fulfilled
b
y
an
t A2
.
4.
OUR P
R
OP
O
S
ED
MO
DEL
Fi
gu
re 2
desc
r
i
be t
h
e p
r
oce
d
ure
of e
x
ecut
i
on
of
AC
O
-
R
e
duce al
go
ri
t
h
m
.
B
e
fore a
p
p
l
y
i
ng t
h
e
five test suite
reduction techniques,
we c
o
l
l
ected
the test case-re
quirement m
a
trices fro
m
th
e p
r
ev
iou
s
execution
of t
h
e test case T over
prog
ram
P. In case
o
f
re
g
r
essio
n
testi
ng
the test cases T is reduce
using
ACO-Reduce
and
give re
duc
e
test cases T’. These test
cases are run on the m
odified program
P’ in the
maintenance st
age.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJECE
Vol. 5, No. 6, D
ecem
ber
2015 :
1424 –
1432
1
428
Fi
gu
re
2.
M
o
d
e
l
fo
r e
x
ecut
i
o
n
of
AC
O-R
e
d
u
ce
pr
oce
d
u
r
e
5.
E
X
PERI
MEN
T
RES
U
LTS
Thi
s
t
e
c
hni
que
i
s
i
m
pl
em
ent
e
d
usi
n
g M
A
T
L
AB
whi
c
h
tak
e
th
e test su
it po
o
l
T
X R as inp
u
t
and
u
s
ing
th
e above an
t co
lo
n
y
op
ti
m
i
zatio
n
tec
h
n
i
q
u
e
f
i
nd
out a r
e
p
r
esen
tativ
e set, w
h
ich is n
a
m
e
d
as
A
C
O-
R
e
duce
.
The f
o
l
l
o
wi
ng fo
u
r
exi
s
t
i
ng
t
e
c
hni
que
a
r
e
al
so
a
ppl
i
e
d usi
n
g M
A
TLAB
fo
r
com
p
ari
s
on o
f
res
u
l
t
bet
w
ee
n
ou
r a
p
pr
oac
h
a
n
d
t
h
e
exi
s
t
i
n
g
ap
pr
oa
ch.
1)
Ha
rr
ol
d
et
al
.’s
he
uri
s
t
i
c
To m
a
ke cons
i
s
t
e
ncy
wi
t
h
ot
her resea
r
che
s
[2
2]
,
[2
3]
, we use ‘
G
A
’
t
o
den
o
t
e
Har
r
ol
d et
al
.’s
Heuristic [21
]
.
Th
e aim
o
f
th
is h
e
uristic alg
o
rith
m
is
to
find the minim
u
m
size of re
prese
n
tative set of t
h
e test
su
ite. Th
e
b
a
si
s of t
h
is algorith
m
is to
fi
n
d
essen
tial test
ca
ses,
whic
h a
r
e
defi
ned as t
h
os
e test cases t
h
a
t
when
rem
oved,
som
e
t
e
st
req
u
i
r
em
ent
s
ca
n
neve
r
b
e
sat
i
s
fi
ed.
2)
C
h
e
n
a
n
d
L
a
u’s
GR
E
he
u
r
i
s
t
i
c
Thi
s
heu
r
i
s
t
i
c
al
go
ri
t
h
m
i
s
prop
ose
d
by
C
h
e
n
a
nd
Lau i
n
[
2
2]
. ‘
G
R
E
’
i
s
us
ed t
o
de
not
e t
h
ei
r he
uri
s
t
i
c
[2
2]
,
[2
3]
. T
h
e
al
go
ri
t
h
m
i
s
b
a
sed
o
n
t
h
e
m
i
x
of
t
h
ree
strat
e
g
i
es: th
e
greed
y
strateg
y
, the essen
tial strateg
y
,
an
d
th
e 1-
to
-1
r
e
dun
d
a
n
c
y
strateg
y
.
3)
M
a
ns
ou
r a
n
d El
-
F
aki
n
’s
a
p
p
r
oach
Genet
i
c
al
g
o
ri
t
h
m
s
are based o
n
t
h
e m
e
chani
s
m
of nat
u
ral
ev
ol
ut
i
o
n,
whe
r
e re
pr
o
d
u
ct
i
on a
n
d
sel
ect
i
on o
p
er
at
i
ons are a
p
pl
i
e
d t
o
p
o
pul
at
i
ons
o
v
er s
u
cc
essi
ve ge
ner
a
t
i
ons
f
o
r e
vol
vi
ng
o
p
t
i
m
a
l
solut
i
o
n
s
[24
]
. Man
s
ou
r
an
d
El
-Fak
in
[2
5
]
ad
ap
t th
e
hyb
rid
g
e
n
e
tic
alg
o
rith
m
to
so
lv
e th
e test su
ite redu
ction
prob
lem
.
In
t
h
i
s
pape
r,
we
use
‘M
EF
’
t
o
de
n
o
t
e
M
a
n
s
ou
r a
n
d El
-
F
a
k
i
n
’s a
p
p
r
oach
.
4) Black et al.’s approac
h
On
e recen
t
strateg
y
fo
r test
su
ite red
u
c
ti
o
n
is pr
opo
sed
by Black
et al.
[
2
6
]
, in wh
ich, tw
o in
teg
e
r
l
i
n
ear p
r
o
g
ra
m
m
i
ng (ILP
)
m
odel
s
are pr
ovi
ded
.
I
n
t
h
i
s
pape
r,
we u
s
e ‘B
A
A
’ t
o
den
o
t
e
B
l
ack
et
al
.’s
approach.
All th
e im
p
l
emen
ted
techn
i
q
u
e
s
were
ex
ecu
t
ed on
a PC
with an In
tel
Pen
tiu
m
2
.
2
6
GHz CPU an
d
5
1
2
M
m
e
m
o
r
y
r
u
nn
ing
th
e W
i
nd
ow
s 2000
Pro
f
essi
on
al o
p
e
r
a
ting
syste
m
. Tab
l
e 3
sh
ow
s th
e d
e
t
a
ils o
f
subject progra
m
s
and the col
l
ected te
st cas
e-req
u
i
rem
e
n
t
matrices. Co
lu
m
n
1
lists
all
t
h
e subj
ect p
r
og
ram
s
.
Co
lu
m
n
2
lists th
e nu
m
b
er of lin
es of co
d
e
(LOC
) of
eac
h subject program
. Colu
m
n
3 lists the size of t
h
e
cor
r
es
po
n
d
i
n
g
su
bject
pr
o
g
r
a
m
’
s t
e
st
sui
t
e
po
ol
whe
r
e T
denotes the num
b
er of all the test cases
and R
den
o
t
e
s t
h
e
n
u
m
ber of t
e
st
r
e
qui
rem
e
nt
s. Fi
ve p
r
o
g
ram
s
were st
udi
e
d
,
r
a
ngi
ng
fr
om
142
5 t
o
3
0
9
5
l
i
nes o
f
code
(L
OC
). T
h
ese fi
ve Ja
va
pro
g
r
am
s i
n
our ex
peri
m
e
nt are binary search tr
ee (BST) with
all o
p
eratio
n
and
a
ppl
i
cat
i
o
n ,
po
wer
e
qua
l
i
zer (PE
Q
), t
r
ansm
i
ssi
on co
nt
r
o
l
(TC
)
,
st
ack i
m
pl
em
ent
a
t
i
on
fo
r
j
o
b
(
S
TAC
K
),
st
ock
i
n
dex
p
r
e
d
i
c
t
i
on
(ST
O
C
K
).
T
h
e
feat
ure
o
f
t
h
ese
p
r
og
r
a
m
s
has
been
g
i
ven i
n
Ta
bl
e
3
.
Tabl
e
3.
Sum
m
a
ry
o
f
pr
o
g
ram
s
use
d
i
n
e
xpe
r
i
m
e
nt
at
i
on
Progra
m
Source
file
(LOC
)
Test suite
pool
(T X
R)
BST
1864
1694 X 983
PEQ
1456
674 X 124
TC
2987
2287 X 157
STACK
1425
719 X 70
STOC
K
3095
3970 X 128
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Test Ca
se Redu
ctio
n Using
An
t Co
l
o
n
y
Op
timiza
tion
f
o
r
Ob
ject Orien
t
ed… (S
ud
h
i
r Kuma
r Mo
hap
a
t
ra
)
1
429
Th
e
resu
lt an
al
ysis is d
o
n
e
b
a
sin
g
upo
n th
e scalab
ility an
d
size o
f
th
e
represen
tativ
e set
[27
]
. All t
h
e
test case red
u
ctio
n
techn
i
que is scale wit
h
th
e co
m
p
lexity o
f
th
e test
su
it. To
m
e
a
s
u
r
e scalab
ilit
y th
ese
alg
o
rith
m
are i
m
p
l
e
m
en
ted
with
test su
it o
f
d
i
fferen
t
co
m
p
lex
ity an
d
record
t
h
eir tim
e.
A co
m
p
lex
ity o
f
test
su
it is
Com
p
lexity
(t)=log
1
0
(m
X
n
)
(7
)
In
Eq
u
a
tion
(7), m
is th
e n
u
m
b
e
r o
f
test ca
ses in
th
e test
su
ite (t), and
n is th
e
m
a
x
i
m
u
m n
u
m
b
e
r of
test
requ
irem
e
n
ts
th
at
can
b
e
satisfied
b
y
t. Ag
ai
n
we
co
mp
are th
e size of rep
r
esen
tativ
e
set p
r
od
u
c
e b
y
all th
e
al
go
ri
t
h
m
usi
n
g
ou
r sel
ect
ed
pr
o
g
ram
.
5
.
1
.
Sca
l
a
b
ility
Fig
u
re
3
.
Scalab
ility o
f
ACO-Red
,
GA,
GRE, MEF, BAA
fo
r 5 program
From
Figure
3, we can observe AC
O-Reduce needs the minim
u
m
tim
e
to
calculate representative set
s
,
wh
ile MEF and
BAA tak
e
s ap
pro
x
i
m
a
tel
y
s
a
m
e
ti
me. GA alg
o
rith
m
tak
e
s
m
o
re ti
m
e
th
an
o
t
h
e
r in
all o
f
t
h
e
com
p
arison
wi
th differe
n
t size of the test cases. Thus,
t
h
e tim
e
efficiency of th
ese four algorithm
s
can be
summ
arized as tACO-Red
≤
t G
R
E
≤
tMEF
≤
tBAA
≤
t
GA
. The
com
p
lexity of t
h
e
progra
m
s
are calculated
by
Equ
a
tio
n (7
).
5.
2.
Repre
s
ent
a
ti
ve Se
t Si
z
e
Fi
gu
re
4
de
pi
ct
s t
h
e si
zes
of t
h
e
rep
r
ese
n
t
a
t
i
v
e set
s
g
e
nerat
e
d
by
t
h
e
fi
ve t
e
st
s
u
i
t
e
re
duct
i
o
n
t
echni
q
u
es f
o
r
t
h
e di
ffe
rent
s
u
bject
p
r
o
g
r
am
s. In eve
r
y
si
ngl
e di
agram
i
n
Figu
re 4, t
h
e h
o
r
i
z
ont
al
axi
s
de
not
es
th
e test su
ite’s
size wh
ereas the v
e
rtical ax
is
d
e
no
tes th
e size o
f
represen
tativ
e set g
e
n
e
rat
e
d
b
y
th
e
5
test
su
ite
red
u
ct
i
o
n t
ech
ni
q
u
es.
Det
a
i
l
s
of
o
u
r e
xpe
ri
m
e
nt
wi
t
h
the fi
ve p
r
o
g
r
a
m
s
usi
ng
fi
v
e
di
ffe
re
nt
re
duct
i
o
n
algorithm
are summarize in the Table
4.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJECE
Vol. 5, No. 6, D
ecem
ber
2015 :
1424 –
1432
1
430
Fi
gu
re
4.
Si
zes
o
f
re
p
r
esent
a
t
i
ve set
s
o
f
AC
O
-
R
e
d,
G
A
,
GR
E, M
E
F
,
B
A
A
fo
r
5
pr
o
g
ram
Tabl
e
4.
Sum
m
a
ry
o
f
e
xpe
ri
m
e
nt
d
o
n
e
usi
n
g
fi
ve
p
r
o
g
r
am
s
fo
r
di
ffe
re
nt
re
duct
i
o
n al
g
o
ri
t
h
m
P
r
ogra
m
Reducti
on
Techniq
ue
BST PEQ
TC
STACK
STO
C
K
Tes
t
Cas
e
R
S
%
Reducti
on
Tes
t
Cas
e
R
S
%
Reducti
on
Tes
t
Cas
e
RS %
Reducti
on
Tes
t
Cas
e
R
S
%
Reducti
on
Tes
t
Cas
e
RS %
Reducti
on
ACO-
Reduce
169
4
72
0
58
674
45
6
33
228
7
156
7
32
719
53
7
26
397
0
267
2
33
GA
169
4
75
6
56
674
45
6
33
228
7
160
8
30
719
58
9
19
397
0
268
4
33
GRE
169
4
81
0
53
674
46
7
39
228
7
158
2
31
719
53
7
26
397
0
270
1
32
MEF
169
4
72
1
58
674
48
7
28
228
7
160
1
30
719
56
5
22
397
0
267
2
33
BAA
169
4
73
4
57
674
47
8
30
228
7
160
9
30
719
58
1
20
397
0
267
9
33
6.
CO
NCL
USI
O
N
In
t
h
is p
a
p
e
r an
algo
rith
m
fo
r test cases reductio
n
is
prese
n
ted and im
ple
m
ented.
It is com
p
ared wit
h
ou
r
ot
her t
e
c
h
n
i
que
[1
7]
, [
2
8]
. It
fi
n
d
s
out
re
prese
n
t
a
t
i
v
e se
t
of t
h
e t
e
st
cas
e fr
om
t
h
e gi
v
e
n set
o
f
t
e
st
case. It
225
50
7
69
8
10
24
122
8
0
10
0
20
0
30
0
40
0
50
0
60
0
Se
l
e
c
t
T
e
s
t
Su
i
t
Si
z
e
R
epr
es
ent
at
i
v
e S
i
z
e
BST
AC
O
-
R
e
d
GA
GR
E
ME
F
BAA
70
145
240
45
0
52
4
0
50
10
0
15
0
20
0
25
0
Se
l
e
c
t
T
e
s
t
S
u
i
t
Si
z
e
R
epr
es
ent
at
i
v
e
S
i
z
e
PEQ
A
C
O-
R
e
d
GA
GR
E
ME
F
BA
A
30
2
67
8
79
0
1
229
18
09
0
10
0
20
0
30
0
40
0
50
0
60
0
70
0
80
0
90
0
10
00
S
e
l
e
ct
T
e
st
S
u
i
t
S
i
z
e
R
epr
e
s
ent
at
i
v
e
S
i
z
e
TC
AC
O
-
R
e
d
GA
GR
E
MEF
BA
A
50
277
324
513
687
0
50
100
150
200
250
300
350
Se
l
e
ct T
e
st
Su
i
t
S
i
z
e
R
epres
ent
at
i
v
e
S
i
z
e
ST
A
C
K
AC
O
-
R
e
d
GA
GR
E
MEF
BA
A
567
716
102
9
1289
1607
0
100
200
300
400
500
600
700
800
900
Se
l
e
c
t
T
e
s
t
Su
i
t
Si
z
e
R
epr
es
ent
at
i
v
e Si
z
e
ST
O
C
K
AC
O
-
R
e
d
GA
GR
E
ME
F
BA
A
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Test Ca
se Redu
ctio
n Using
An
t Co
l
o
n
y
Op
timiza
tion
f
o
r
Ob
ject Orien
t
ed… (S
ud
h
i
r Kuma
r Mo
hap
a
t
ra
)
1
431
uses a sim
p
l
e
AC
O m
e
t
hod t
o
red
u
ce t
h
e t
e
st
case i
n
regre
ssi
on t
e
st
i
n
g. M
o
re
ove
r, t
h
e
gene
rat
e
d t
e
st
sui
t
e
i
s
minimized gre
a
tly. Therefore
it can redu
ce
test cost of re
gressi
on testing
and im
prove
the efficiency
of the
so
ft
ware wit
h
th
e o
p
tim
ized
test su
ite. W
e
h
a
v
e
ev
alu
a
t
e
d
t
h
e effect
i
v
e
n
ess of o
u
r
pr
o
pos
ed re
g
r
essi
on t
e
st
case red
u
ct
i
o
n
t
echni
q
u
e usi
ng se
veral
m
oderat
e
si
zed
o
b
ject
e
d
o
r
i
e
nt
e
d
Java
pr
o
g
ra
m
s
. It
i
s
obser
ver f
r
o
m
th
e exp
e
rim
e
n
t
th
at th
e AC
O-Red
u
ce al
go
rith
m
sh
ow
p
r
o
m
isin
g
resu
lts in
term
s
o
f
ex
ecu
tio
n
t
i
m
e
as
com
p
ared
wi
t
h
ot
h
e
r
re
duct
i
o
n al
go
ri
t
h
m
.
A
C
O-R
e
duce
al
g
o
rith
m
redu
ce th
e test case
1
0
% effectiv
el
y th
en
o
t
h
e
r algo
rit
h
m
an
d
its ex
ecu
tio
n ti
m
e
is fa
s
t
e
r
wh
en
co
mp
a
r
e w
ith o
t
h
e
r a
l
g
o
r
ith
ms
.
REFERE
NC
ES
[1]
M. J. Harrold
, R
.
Gupta, and
M. L. Soff
a, “A
Methodolog
y
for
Controlling
the
Size of
a T
e
st S
u
ite”,
ACM Trans.
Software
Eng. And Methodo
logy,
Vol. 2, No. 3
,
p
p
. 270-285
, 199
3.
[2]
T. H. Cormen, C. E. Leiser
son, R. L. Rivest, and C.
Stein, “Introduction to Algorithms”, seco
nd ed. MIT Press,
2001.
[3]
GUP
TA R., “
A
reconfigur
able
LI
W
archit
ectur
e a
nd its
com
p
iler
”
, Tech
. Rep
.
87-3
,
Dept
. Computer Science, Univ
.
Pittsburgh, Pit
t
sburgh, Pa., 1987
.
[4]
Gum
A. R., an
d S
o
ffa M
.
L.
,
“
C
om
pile-tim
e techniqu
es
for
im
proving s
cal
ar ac
ces
s
perfor
m
ance in par
a
ll
el
me
mori
e
s
”
,
IEEE Trans. Parallel and Distribu
ted Systems 2
,
pp
.
138-148, 1991
.
[5]
D. Jeffrey
,
and
N. Gupta, “Improving
Fault Detection Capab
ility
b
y
Selectiv
ely Retaining Test
Cases During Test
Suite R
e
duction
”,
I
E
EE Trans. o
n
Software Engineering,
Vol. 33
, No. 2
,
pp
. 108-
123, 2007
.
[6]
J
.
W
.
Lin
,
and
C. Y. Huang
,
“
A
nal
y
s
i
s
of
Tes
t
S
u
it
e Red
u
ction wi
th En
hanced
Ti
e-Bre
a
king T
echn
i
qu
es
”,
Information and
Software Techno
logy,
Vol. 51, No. 4
,
pp
. 679-69
0, 2009
.
[7]
M. R. Gar
e
y
,
and D. S.
Johnson, “Computers and Intr
actability
: A Gu
ide to the
Th
eor
y
of NP-Completeness”,
Freeman and
Co
mpan
y
,
1979.
[8]
R. M.
Karp,
“
R
educib
ilit
y
am
on
g Com
b
inatori
a
l
Problem
s”,
Complexity of Comp
uter Co
mputatio
ns, Plenum Pres
s,
pp. 85-103
, 197
2.
[9]
V.
Chvatal,
“A Greedy
Heuristic
for th
e Set-Co
vering Problem”,
Math
ematics O
p
erations Res
e
a
r
ch,
Vol. 4, No.
3,
pp. 233-235
, Au
gust 1979.
[10]
S. Yoo, and M.
Harm
an, “
R
egressi
on Testing
Minim
i
zation
,
S
e
le
ction
and Pri
o
ritiz
at
ion: a S
u
rve
y
”,
So
ftwar
e
Testing,
Verifica
tion and
Reliability,
Vol. 22
, No.
2, 2012
.
[11]
T
.
Y
.
C
h
e
n
,
a
n
d
M
.
F
.
L
a
u
,
“
A
New Heuristic
for Test Suite R
e
duct
i
on”,
In
formation and Software Technolog
y,
Vol. 40
, No. 5-6, pp. 347-354, 19
98.
[12]
J. A. Jones, an
d M. J. Harrold
, “T
est-Suite
Reduction
and
Prioritiza
tion
for Modified
Condition/Decis
i
on
Coverage”,
IEEE Trans. on So
ftware Engin
eerin
g,
Vol. 29
No. 3
,
pp. 195-209, 20
03.
[13]
Ma X.
Y.
, He
Z.
F.,
Sheng B.
K., Ye C
.
Q., “A genetic
algorith
m for test-suite r
e
duction
”, In
: P
r
o
c
.
t
h
e
International Co
nference on
Systems, Man and
C
y
bernetics,
pp. 1
33–139, 2005
.
[14]
Chu-Ti Lin
,
Kai-Wei Tang
, Cheng-Ding Chen,
and Gregor
y
M. Kapfhammer, “Reducing
the C
o
st of Regression
Te
sting by
Ide
n
tify
ing Irre
p
la
c
eable
Te
st Ca
se
s”,
In Proc. Of
th
e
6th ICGEC ’12
.
[15]
Y
.
Z
h
a
n
g
,
J
.
L
i
u
,
Y
.
C
u
i
,
X
.
Hei, ”An
improved
quantum genetic al
gorith
m
for test
suite
reduction“,
IEEE
International Co
nference on
Co
mputer
Science and
Automation Engineering
(
C
SAE)
,
2011.
[16]
Dan Hao, Tao Xie, Lu Zhang
,
Xiao
y
i
nWang, Jiasu Sun, Hong
Mei, “Test i
nput reduction for result inspection to
faci
lit
ate
fau
l
t
lo
cal
iza
tion”
,
Auto
mated Software
Engineering
, V
o
l. 17
, No
. 1
,
pp
5-31,
2010.
[17]
S.
K.
Moha
patra,
S.
Pra
s
a
d
,
“M
i
n
im
izing T
e
st C
a
ses to R
e
duce
t
h
e Cost of R
e
gr
ession Testing
”
,
Pr
oceed
ings
of
t
h
e
8th INDIACom,
2014.
[18]
S. K. Mohap
a
tr
a, S.
Prasad,
“
E
volution
a
r
y
se
arch
algori
t
hm
for Test
Case
Prioritiz
atio
n“
,
2013 Internatio
na
l
Confer
enc
e
on
Machine
Int
e
ll
ig
ence
R
e
s
e
ar
ch a
nd Advan
cemen
t
.
[19]
Dac-Nhuong Le, “GA and AC
O
Algorithms App
lied to Optimiz
ing Location of
Controllers
in Wireless Networks”,
International Jo
urnal of
Electrical
and Computer Engin
eering
(
I
JECE)
,
Vol. 3, No. 2
,
pp
. 221-22
9, 2013
.
[20]
Mina
Ja
fa
ri, Ha
ssa
n Khota
n
lou,
“A R
outing Alg
o
rithm
Bas
e
d on
Ant Colon
y
,
Lo
cal
S
ear
ch and
F
u
zz
y Inf
e
ren
c
e
t
o
Improve Energ
y
Consumption in
Wireless Sensor Networks”,
I
n
ternational
Jou
r
nal of Electrical and Computer
Engineering (
I
JECE)
,
Vol. 3, No. 5
,
pp
. 640-65
0, 2013
.
[21]
M.
J.
Ha
rrold,
R.
Gupta,
M.
L.
S
o
ffa
,
“A me
thod
olog
y
for con
t
rolling th
e size of
a test suite”,
AC
M Transactions on
Software
Engineering and M
e
tho
dology
, Vol. 2 N
o
. 3
,
pp
. 270–28
5, 1993
.
[22]
T. Y. Ch
en, M.
Lau, “A new he
uristic for
test su
ite r
e
duct
i
on”
,
I
n
formation and Software Techno
logy
, Vol. 40, N
o
.
5-6, 347–354
, 1
998.
[23]
T. Y. Ch
en,
M.
Lau
,
“
A
sim
u
la
tion stud
y on
som
e
heuristi
cs fo
r test
suite
redu
ction
”
,
In
formation and Software
Technology
, Vol. 40
, No. 13, pp.
777–787, 1998
.
[24]
D. Goldberg
, “Genetic Algor
ithms in Sear
ch, Optimi
zation
and
Machine Learning
”, Addison-Wesley
, 1989
.
[25]
N. M
a
ns
our, K.
El-F
akih
, “
S
im
ulat
ed
annealing
and genetic algo
rithms
for optimal regr
ession tes
ting”,
Journal o
f
Software Ma
intenance
, Vol. 11,
No. 1, pp. 19–34
, 1999
.
[26]
J. Black
, E. Melachrinoud
is, D.
Kaeli, “Bi-criter
ia models for all-
uses test suite r
e
duction
”
,
In: Pr
oceed
ings
of 26t
h
International Conference on Software E
ngineerin
g, IEEE
Computer Society,
Washington, DC,
USA, pp. 106–11
5,
2004.
[27]
H. Zhong, L. Zhang,
and H. M
e
i, “A
n Experimental Stud
y
of
Four Ty
pical
Test Suite Reduction Techniqu
es
”,
Information and
Software Techno
logy,
Vol. 50, No. 6
,
pp
. 534-54
6, 2008
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJECE
Vol. 5, No. 6, D
ecem
ber
2015 :
1424 –
1432
1
432
[28]
S
.
K. M
ohapa
tr
a, S
.
P
r
as
ad, B
.
P
.
Kar
,
”Tes
t
S
u
it Redu
ction
B
y
F
i
nding C
o
s
t
Optim
al Re
pres
enta
tive
S
e
t
”
,
International Jo
urnal of
Advan
c
ed Techno
logy &
E
ngineering Research
(
I
JAT
ER)
,
Vol. 4, No.
3, 2014
.
BIOGRAP
HI
ES
OF AUTH
ORS
Sudhir Kumar Mohapatra an
M.Tech(Computer
Science) holder from Ut
kal University
is
currently
persuing P.hD from SOA University
,Odi
sha, Ind
i
a in the dep
a
rtment of Computer
Science & Engg
.
Srinivas Prasad has done his PhD in Comput
er
Scien
ce
,UU, Orissa. He has 20
y
e
ars of
experi
enc
e
in
in
dustr
y
as wel
l
a
s
institut
i
on.
Cu
rrentl
y
he is
wor
k
ing
as
prof
essor and He
ads of
Department
in D
e
pt. of Com
puter
Scien
c
e &Eng
in
eering
,
GMRIT,
Andhra Pradesh, India.
Evaluation Warning : The document was created with Spire.PDF for Python.