Inter
national
J
our
nal
of
Electrical
and
Computer
Engineering
(IJECE)
V
ol.
9,
No.
3,
May
2019,
pp.
2075
2082
ISSN:
2088-8708,
DOI:
10.11591/ijece.v9i3.pp2075-2082
r
2075
Memetic
chick
en
swarm
algorithm
f
or
job
shop
scheduling
pr
oblem
Soukaina
Cherif
Bourki
Semlali,
Mohammed
Essaid
Riffi,
F
ayc
¸
al
Chebihi
Laroseri
Laboratory
,
Department
of
Computer
Sciences,
F
aculty
of
Sciences,
Uni
v
ersity
of
Chouaib
Doukkali,
El
Jadida,
Morocco
Article
Inf
o
Article
history:
Recei
v
ed
Aug
10,
2018
Re
vised
No
v
10,
2018
Accepted
No
v
10,
2018
K
eyw
ords:
Chick
en
sw
arm
optimization
Job-shop
scheduling
Combinatorial
optimization
2-opt
Mak
espan
ABSTRA
CT
This
paper
presents
a
M
emetic
Chick
en
sw
arm
optimization
(MeCSO)
to
solv
e
job
shop
scheduling
problem
(JSSP).
The
aim
is
to
find
a
better
solution
which
minimizes
the
maximum
of
the
completion
time
also
called
Mak
espan.
In
this
paper
,
we
adapt
the
chick
en
sw
arm
algorithm
which
tak
e
into
consideration
the
hierarchical
order
of
chick
en
sw
arm
while
seeking
for
food.
Moreo
v
er
,
we
inte
grate
2-opt
method
to
im-
pro
v
e
the
mo
v
ement
of
the
rooster
.
The
ne
w
algorithm
is
applied
on
some
instances
of
OR-Library
.
The
empirical
results
sho
w
the
forcefulness
of
MeCSO
comparing
to
other
metaheuristics
from
literature
in
term
of
run
time
and
quality
of
solution.
Copyright
c
2019
Institute
of
Advanced
Engineering
and
Science
.
All
rights
r
eserved.
Corresponding
A
uthor:
Soukaina
Cherif
Bourki
Semlali,
Laroseri
Laboratory
,
Department
of
mathematics,
F
aculty
of
Sciences,
Uni
v
ersity
of
Chouaib
Doukkali,
El
Jadida,
Morocco.
Email:
Soukaina.cherif.b
.s@ucd.ac.ma
1.
INTR
ODUCTION
The
job-shop
scheduling
problem
(JSSP)
w
as
formulated
for
the
first
time
by
Muth
and
Thompson
in
1963.
The
JSSP
is
one
of
the
NP-Hard
problems
[1]
and
the
most
kno
wn
of
the
classical
scheduling
problems
in
the
conte
xt
of
manuf
acturing
[2],
which
help
to
impro
v
e
competiti
v
eness
of
man
y
companies
and
or
g
anizations.
The
aim
purpose
of
the
job-shop
scheduling
problem
is
to
find
a
schedule
which
minimizes
the
time
required
to
complete
a
group
of
jobs
(the
mak
espan).
Historically
,
se
v
eral
algorithms
are
proposed
in
literature
to
solv
e
the
job
shop
scheduling
problem
by
optimizing
the
mak
espan
such
as:
branch
and
bound
(BB)[3],
simulated
annealing
(SA)
[4],
T
ab
u
search
(TS)[5][6],
genetic
algorithms
(GA)[7][8][9],neural
netw
orks
(NN)[10],ant
colon
y
optimization
(A
CO)[11],P
article
sw
arm
optimization
(PSO)[12],
Bee
colon
y
optimization
(BCO)[13]
and
firefly
algorithm(F
A)
[14].
Addition-
ally
,
some
researchers
ha
v
e
de
v
eloped
an
h
ybrid
optimization
strate
gy
for
JSSP
such
as
parallel
GRASP
with
path-relinking[15]
and
ne
w
h
ybrid
genetic
algorithm
[16].
2.
JOB-SHOP
SCHEDULING
PR
OBLEM
The
JSSP
can
be
briefly
introduced
[17]
as
a
sequential
allocation
of
a
production
schedule
for
a
gi
v
en
set
of
jobs
and
resources
that
optimizes
the
completion
time
of
all
jobs
which
helps
to
minimize
the
mak
espan.
As
result,
the
mak
espan
(the
maximum
job
completion
time)
C
max
is
the
duration
between
the
time
of
completion
of
last
job
and
the
starting
time
of
the
first
job
(1).
C
max
=
max
t
ij
(
t
ij
+
p
ij
)
(1)
Where
t
ij
is
denoted
as
the
starting
time
and
p
ij
as
the
uninterrupted
processing
time.
J
ournal
homepage:
http://iaescor
e
.com/journals/inde
x.php/IJECE
Evaluation Warning : The document was created with Spire.PDF for Python.
2076
r
ISSN:
2088-8708
The
JSSP
can
be
formulated
by
assigning
a
set
of
n
jobs
J
=
f
J
1
;
:
:
:
;
J
n
g
to
a
set
of
m
machines
M
=
f
M
1
;
:
:
:
:;
M
m
g
,each
machine
can
process
at
most
one
operation
at
time.As
well
,
each
job
consists
of
a
set
of
O
ik
,
which
contains
m
operations
where
i
denotes
the
job
of
a
specific
operation
and
k
represents
the
current
machine
M
k
.
Each
operation
must
be
processed
during
an
uninterrupted
period
of
time
on
a
gi
v
en
machine.
In
the
jssp,
the
order
and
the
uninterrupted
processing
time
must
be
tak
e
into
consideration.
The
schedule
as
a
solution
for
the
JSSP
can
be
modeled
as
a
v
ector
of
a
seqence
of
operation
(
C
11
;
;
C
j
i
;
:::;
C
nm
+1
)
then
the
main
goal
is
to
find
the
minimum
time
of
all
processes,
the
problem
is
for
-
mulated
as
follo
ws:
minC
nm
+1
(2)
Where
C
k
l
C
j
i
d
k
l
;
j
=
1
;
:
:
:
;
n
;
i
=
1
;
:
:
:
;
m
;
k
l
2
P
j
i
(3)
X
j
i
2
O
(
t
)
r
j
i
1;
i
2
M
;
t
0
(4)
C
j
i
0;
j
=
1
;
:
:
:
;
n
;
i
=
1
;
:
:
:
;
m
(5)
The
constraint
(2)
minimizes
the
finish
time
of
operation
o
nm
+1
(the
mak
espan).
The
constraint
(3)
represents
the
f
act
that
between
operations
the
precedence
relations
should
be
re-
spected.
The
constraint
(4)
describes
that
each
machine
can
process
one
operation
at
a
each
time.
The
constraint
(5)
guarantees
that
the
finish
times
to
be
positi
v
e.
The
remainder
of
this
paper
is
or
g
anised
as
follo
ws:
The
section
2
represents
the
literature
re
vie
w
of
the
problem.
The
Section
3
describes
the
proposed
memetic-CSO
algorithm.
The
Section
4
present
s
the
results
of
the
e
xperimental
study
.
The
Section
5
gi
v
es
a
discussion
of
the
empirical
results.
Finally
,
the
Section
6
gi
v
es
the
conclusion
and
the
prospects
for
further
w
orks.
3.
FORMULA
TION
OF
THE
PR
OBLEM
In
the
job-shop
scheduling
problem
(JSSP),the
solution
can
be
depicted
as
a
sequence
of
n
m
operations,which
optimizes
the
completion
time
of
all
jobs
and
then
helps
tp
find
a
schedule
with
minimum
mak
espan.
let’
s
consider
the
follo
wing
e
xample
with
m
=
3
machines
and
n
=
3
jobs,
where:
J
=
f
J
ob
0
;
J
ob
1
;
J
ob
2
g
and
M
=
f
0
;
1
;
2
g
J
ob
0
=
f
(0;
3)
;
(1;
2)
;
(2;
2)
g
J
ob
1
=
f
(0;
2)
;
(2;
1)
;
(1;
4)
g
J
ob
2
=
f
(1;
4)
;
(2;
3)
g
The
representation
of
the
matrix
will
be
as
bello
w:
0
B
B
B
B
@
0
1
2
3
4
5
6
7
0
0
0
1
1
1
2
2
0
1
2
0
1
2
0
1
0
1
2
0
2
1
1
2
3
2
2
2
1
4
4
3
1
C
C
C
C
A
The
first
line
contains
the
operati
on
number
,the
second
line
contains
the
job
number
,the
third
line
con-
tains
the
sequence
number
,the
forth
line
contains
the
machine
number
and
the
last
line
contains
the
processing
time
of
each
operation.
As
indicated
in
the
Gantt
chart
representation
Figure
1,
the
solution
S
=
f
0
;
6
;
3
;
4
;
1
;
5
;
2
;
7
g
is
gi
v
en
by
a
permutation
of
a
set
of
operations
on
each
machine,
in
this
e
xample
the
minimum
mak
espan
Cmax=11.
In
this
paper
,
the
chick
en
can
search
food
in
a
set
of
solutions
S
defined
as
the
search
space.
IJECE,
V
ol.
9,
No.
3,
May
2019
:
2075
–
2082
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708
r
2077
Figure
1.
Gantt
chart
representation
4.
CHICKEN
SW
ARM
OPTIMIZA
TION
The
Chick
en
sw
arm
optimization
(
CSO)
w
as
introduced
by
Meng,
X.B.
And
al.
[18]
and
inspired
by
the
beha
vior
of
a
chick
en
sw
arm
while
searching
for
food.
Each
sw
arm
is
di
vided
into
se
v
eral
groups,
which
comprises
one
rooster
,hens
and
chi
cks.The
hierarchical
order
in
the
sw
arm
is
established
by
the
fitness
v
alue.
W
e
refer
the
number
of
roosters,
hens,
chicks
and
mother
hens
by
RN,
HN,
CN
and
MN.
The
position
update
equation
of
the
rooster
can
be
formulated
as:
x
t
+1
i;j
=
x
t
i;j
(1
+
R
andn
(0
;
2
))
(6)
2
=
(
1
;
if
f
i
f
k
;
exp(
f
k
f
i
j
f
i
j
"
)
other
w
ise
k
2
[1
;
N
]
;
k
6
=
i
(7)
where
R
andn
(0
;
2
)
is
a
Gaussian
distrib
ution
2
is
a
standard
de
viation
The
rooster
inde
x
k
is
randomly
selected
from
the
rooster’
s
group.
f
is
the
fitness
v
alue
of
the
corresponding
x.
The
position
update
equation
of
the
hen
can
be
formulated
as
bello
w
:
x
t
+1
i;j
=
x
t
i;j
+
S
1
R
and
(
x
t
r
1
;j
x
t
i;j
)
+
S
2
R
and
(
x
t
r
2
;j
x
t
i;j
)
(8)
and
S1=
exp(
f
i
f
r
1
j
f
i
j
+
"
)
and
S2=
exp((
f
r
2
f
i
)
)
where
R
and
2
[0
;
1]
,
r
1
is
the
inde
x
of
the
rooster
and
r
2
is
the
inde
x
of
a
random
chick
en
from
the
sw
arm
(where
r1
6
=
r2).
Finally
,
the
position
update
equation
of
the
chick
is
formulated
in
[19]
as
follo
ws
:
x
t
+1
i;j
=
W
x
t
i;j
+
F
L
(
x
t
m;j
x
t
i;j
))
+
C
(
x
t
r
;j
x
t
i;j
))
(9)
Where
W
is
a
self-learni
n
g
f
actor
for
chicks,
F
L
2
[0
;
2]
is
a
randomly
selected
parameter
to
refer
to
the
relationship
between
the
chicks
and
its
mother
with
the
inde
x
m
where
m
2
[1
;
N
]
.
Otherwise,
C
is
a
learning-
f
actor
from
the
rooster
with
the
inde
x
r
.
Memetic
c
hic
k
en
swarm
algorithm...
(Soukaina
Cherif
Bourki
Semlali)
Evaluation Warning : The document was created with Spire.PDF for Python.
2078
r
ISSN:
2088-8708
5.
AD
APT
A
TION
OF
CHICKEN
SW
ARM
ALGORITHM
T
O
JOB
SHOP
SCHEDULING
PR
OB-
LEM
During
the
discretization
of
the
original
v
ersion
of
the
chick
en
sw
arm
algorithm
in
order
to
solv
e
the
jop
shop
scheduling
problem,
the
redefinition
of
operators
is
represented
by
the
subtraction
,the
multiplica-
tion
and
the
addition
used
in
the
original
v
ersion
[19].
Furthermore,
we
used
the
uniform
crosso
v
er
(UX)
[20]
in
the
position
update
equation
of
hens
and
chicks
for
the
mo
v
ement
to
w
ards
the
leaders
of
groups
and
the
sequential
constructi
v
e
crosso
v
er
(SCX)
[21]
to
simulate
the
mo
v
ement
to
w
ards
the
neighbors.
operator
represents
the
crosso
v
er
operator
and
operator
as
applying
the
chosen
crosso
v
er
to
the
equation.the
addition
operator
indicates
that
the
randomly
chosen
crosso
v
er
is
applied
to
the
mo
v
ement.
The
application
of
UX
and
SCX
ensure
the
competit
ion
between
groups
in
the
sw
arm.
As
well
,
we
inte
grate
the
2-opt
neighborhood
operator
to
realize
the
auto-im
pro
v
ement
mechanism
in
the
position
equation
of
the
roosters
and
the
chicks.
In
this
ne
w
adaptation
each
schedule
of
a
group
i
s
chosen
randomly
.
The
MeCSO
in
pseudo-code
is
represented
by
algorithm
1.
Algorithm
1
:
MeCSO
for
jssp
1.
Initialize
P
the
size
of
sw
arm
2.
Generate
P
chick
ens
3.
initialize
parameters:
P
,
G
,FL
,
C
and
w
.
4.
Ev
aluate
the
fitness
v
alues
at
t=0
for
each
chick
en
5.
Rank
and
establish
a
hierarchal
order
6.
Create
groups
and
assign
chicks
to
mother
-hens
7.
Update
the
position
by
equations
6
,8
and
9
8.
Update
the
ne
w
solution
if
the
fitness
v
alue
is
better
.
9.
Rank
if
G
is
reatched
until
stop
criterion
.
10.
Return
results
of
MeCSO
6.
EXPERIMENT
AL
RESUL
TS
AND
DISCUSSION
6.1.
Experimental
en
vir
onment
The
proposed
algorithm
MeCSO
w
as
coded
in
p
ython
and
run
on
a
DELL
in
visual
studio
2017
and
simulated
with
Intel(R)
Core(TM)
i7-6500
U
CPU
2.5GHZ
(4
CPUs)
2.6
GHz
and
16.00
GB
of
RAM
and
Microsoft
W
indo
ws
10
Professional
(64-bit)
operating
system.
The
performance
of
MeCSO
w
as
tested
on
dif
ferent
instances
of
OR-Library
[22]
20
times
in
100
iterations.
6.2.
Default
parameters
The
table
1
sho
ws
the
parameter
v
alues
used
in
the
ne
w
adaptation
MeCSO.
W
e
e
x
ecute
dif
ferent
tests
on
instances
Abz5
and
Orb1
in
order
to
choose
the
v
alues
which
guarantee
to
obtain
good
results
and
con
v
er
ge
to
w
ards
the
global
optimum
.
T
able
1.
The
P
arameters
for
the
Memetic-CSO
Algorithm
P
arameters
of
MeCSO
V
alues
P
:
Population
size
500
RN
:
Number
of
roosters
(
%
)
12
HN
:
Number
of
hens
(
%
)
25
CN
:
Number
of
chicks
(
%
)
63
G
:
Number
of
iterations
to
update
the
algorithm
10
W
:
Self-learning
f
actor
0.5
FL
:
Learning
f
actor
from
the
mother
hens
0.4
C
:
Learning
f
actor
from
the
rooster
0.65
IJECE,
V
ol.
9,
No.
3,
May
2019
:
2075
–
2082
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708
r
2079
where
C
N
=
P
(
N
R
+
N
H
)
(10)
6.3.
RESUL
TS
AND
DISCUSSION:
W
e
applied
MeCSO
on
some
instances
of
OR-library
,the
table
2
summarizes
the
obtained
results
of
20
runs.The
first
column
represents
dif
ferent
instances
instance
in
OR-Library
,
the
second
column
indicates
the
best
Kno
wn
solution
(BKS)
,the
third
column
describes
the
a
v
erage
of
the
best
found
solution
av
g
,
t
he
remaining
columns
represent
the
measures
use
to
perform
the
quality
of
the
solution.
The
proposed
algorithm
MeCSO
allo
ws
to
find
the
best-kno
wn
solution
about
51.08
%
from
all
tested
instances.
T
able
2.
Numerical
Results
by
MeCSO
Applied
to
Some
Instances
of
OR-library
n
m
Instance
BKS
av
g
T
av
g
(
s
)
Err(
%
)
10
10
Abz5
1234
1236
139
0.068
10
10
Abz6
943
949
521
0.821
10
10
Orb1
1059
1093
807
1.045
10
10
Orb2
888
907
157
0.981
10
10
Orb3
1005
1011
408
0.056
10
10
Orb4
1005
1024
101
0.328
10
10
Orb5
887
891
633
0.766
10
10
Orb6
1010
1016
412
0.831
10
10
Orb7
397
402
595
0.907
10
10
Orb8
899
907
276
0.837
10
10
Orb9
934
944
166
0.741
6
6
Ft06
55
55
1
0
10
10
Ft10
930
939
102
0.801
10
5
LA01
666
666
1
0
10
5
LA02
655
655
1
0
10
5
LA03
597
599
21
0.086
10
5
LA04
590
590
3
0
10
5
LA05
593
593
1
0
15
5
LA06
926
926
1
0
15
5
LA07
890
890
2
0
15
5
LA08
863
863
1
0
15
5
LA09
951
951
1
0
15
5
LA10
958
958
1
0
20
5
LA11
1222
1222
2
0
20
5
LA12
1039
1039
1
0
20
5
LA13
1150
1150
1
0
20
5
LA14
1292
1292
1
0
20
5
LA15
1207
1207
3
0
10
10
LA16
945
950
12
0.551
10
10
LA17
784
784
84
0
10
10
LA18
848
851
534
0.021
10
10
LA19
842
850
126
0.352
10
10
LA20
902
911
782
0.045
15
10
LA21
1046
1085
477
0.755
The
mathematical
formulation
of
the
percentage
of
error
ERR
(11)
is
represented
as
bello
w:
Memetic
c
hic
k
en
swarm
algorithm...
(Soukaina
Cherif
Bourki
Semlali)
Evaluation Warning : The document was created with Spire.PDF for Python.
2080
r
ISSN:
2088-8708
[H]
E
r
r
=
(
av
g
B
K
S
)
B
K
S
100
(11)
where
B
K
S
is
the
best
kno
wn
v
alue
,
av
g
the
a
v
erage
of
the
best
found
solution.
The
proposed
algorithm
MeCSO
seems
to
be
promising
to
solv
e
jssp
in
a
reasonable
time
compared
to
GB
algorithm
[23]
as
repres
ented
in
Figure
2.
Furthermore,
the
algorithm
allo
ws
to
obtain
good
results
in
term
of
the
global
optimum
compared
to
other
algorithms
from
literature,
such
as
[24]
and
[25]
as
represented
in
table
3
and
GB
algorithm
[23]
as
represented
in
Figure
3.
T
able
3.
A
v
erage
of
the
BFS
of
Some
Algorithms
in
the
Literature
Compared
to
MeCSO
Instance
MeCSO
Bondal(GA)
[25]
Udomsakdigool
and
Kachitvich
yanukul
[24]
Abz5
1236
1339
-
Abz6
949
1043
-
Ft06
55
55
55
Ft10
939
944
1099
LA01
666
666
666
LA02
655
658
716
LA03
599
603
638
LA04
590
590
619
LA05
593
593
593
LA16
950
977
1033
Figure
2.
A
v
erage
time
(s)
of
MeCSO
and
GB
algorithm
IJECE,
V
ol.
9,
No.
3,
May
2019
:
2075
–
2082
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708
r
2081
Figure
3.
Err
(%)
of
MeCSO
and
GB
algorithm
7.
CONCLUDING
REMARKS
In
this
paper
,we
proposed
a
Memetic
Chic
k
e
n
sw
arm
optimization
algorithm
based
on
the
origi
nal
v
ersion
of
chick
en
sw
arm
optimization
(CSO)
and
2-opt
mechanism
in
order
to
solv
e
the
job
shop
scheduling
problem.
The
empirical
results
sho
w
that
MeCSO
algorithm
is
ef
ficient
to
solv
e
this
type
of
problem
than
the
other
algorithms
from
literature
such
as
GB
algorithm
and
GA
in
term
of
the
quality
of
solutions
and
the
computing
time.
In
further
research,
we
suggest
to
inte
grat
e
the
simulating
annealing
with
the
chick
en
sw
arm
algorithm
to
ensure
the
redistrib
ution
of
the
sw
arm.
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