Indonesian
J
our
nal
of
Electrical
Engineering
and
Computer
Science
V
ol.
24,
No.
2,
No
v
ember
2021,
pp.
1161
1172
ISSN:
2502-4752,
DOI:
10.11591/ijeecs.v24.i2.pp1161-1172
r
1161
Artificial
neural
netw
ork
based
meta-heuristic
f
or
perf
ormance
impr
o
v
ement
in
ph
ysical
inter
net
supply
chain
netw
ork
Chouar
Abdelsamad
1
,
T
etouani
Samir
2
,
Soulhi
Aziz
3
,
Elalami
J
amila
4
1,2
Laboratoire
d’Analyse
des
Syst
`
emes,
T
raitement
de
l’Information
et
Management
Int
´
egr
´
e
(LASTIMI),
Uni
v
ersit
´
e
Mohammed
V
-Agdal
Ecole
Mohammadia
d’Ing
´
enieurs,
Rabat,
Morocco
1,2
Centre
d’Excellence
en
Logistique
(CELOG),
´
Ecole
Sup
´
erieure
de
l’industrie
du
T
e
xtile
et
d’Habillement
(ESITH),
Casablanca,
Morocco
3
Superior
National
School
of
Mines,
Rabat,
Morocco
4
National
Center
for
Scientific
and
T
echnical
Research
(CNRST),
Rabat,
Morocco
Article
Inf
o
Article
history:
Recei
v
ed
Jun
3,
2021
Re
vised
Sep
11,
2021
Accepted
Sep
15,
2021
K
eyw
ords:
Artificial
neural
netw
orks
Slime
mould
algorithm
Supply
chain
management
Ph
ysical
internet
ABSTRA
CT
No
w
adays,
reducing
total
costs
while
enhancing
customer
satisf
action
is
a
major
task
for
man
y
supply
chain
systems.
T
o
deal
with
this
issue,
the
ph
ysical
internet
(PI)
paradigm
can
be
represented
as
a
potential
replacement
for
the
current
logistics
sys-
tem.
This
paper
de
v
oted
the
cost
reduction
and
lead
time
impro
v
ement
in
a
PI-SCN
using
a
h
ybrid
frame
w
ork
based
on
an
artificial
neural
netw
ork
(ANN)
and
an
im-
pro
v
ed
slime
mould
algorithm
(ISMA).
T
o
address
the
performance
of
the
proposed
frame
w
ork,
a
real-case
study
in
Morocco
is
considered.
The
ne
w
trainer
ISMA
’
s
per
-
formance
has
been
in
v
estig
ated
in
three
approximation
datasets
from
the
Uni
v
ersity
of
California
at
Irvine
(UCI)
machine-learning
repository
re
g
arding
nine
recent
meta-
heuristics.
The
e
xperimental
results
highlight
the
ef
fecti
v
eness
of
ISMA
according
to
other
meta
heuristics
for
training
feed-forw
ard
neural
netw
orks
(FNNs)
to
con
v
er
ge
speed
and
to
a
v
oid
local
minima.
This
is
an
open
access
article
under
the
CC
BY
-SA
license
.
Corresponding
A
uthor:
Chouar
Abdelsamad
Centre
d’Excellence
en
Logistique
(CELOG)
´
Ecole
Sup
´
erieure
de
l’industrie
du
T
e
xtile
et
d’Habillement
(ESITH)
Casablanca,
Morocco
Email:
chouar@esith.ac.ma
1.
INTR
ODUCTION
No
w
adays,
the
major
strength
for
the
global
logistics
operations
is
to
ensure
a
sustainable
syst
ems
through
inte
grating
the
de
v
eloped
technologies
and
methodologies
to
the
real
w
orld
practices.
F
or
a
lar
ge
logistics
scale,
t
he
logistics
web
aims
to
connect
the
supply
chain’
s
netw
ork
including
the
dif
ferent
actors,
ph
ysical
items
and
digital
technologies
in
order
to
assist
the
global
requirements.
From
a
broadly
perspecti
v
e,
the
ph
ysical
internet
(PI)
aims
to
optimize
the
supply
cha
in
processes
according
to
a
defined
frame
w
ork
to
enhance
the
logistics
web
ef
ficienc
y
,
ef
fecti
v
eness
and
sustainability
which
de
v
elop
the
required
reliability
,
resilience
and
adaptability
.
The
purpose
of
the
inno
v
ati
v
e
Ph
ysical
Internet
(PI
or
)
initiati
v
e
is
to
re
v
erse
the
situation
of
e
xisting
unsustainable
in
current
logistics
systems.
Indeed,
due
to
the
dynamic
nature
of
real-w
orld
problems,
logistics
web
design
models
must
tak
e
into
consideration
the
risks
of
disruption
and
unforeseen
e
v
ents
to
ensure
the
resilience
and
ef
ficienc
y
of
the
entire
logistics
web
chain.
F
or
e
xample,
taking
into
account
J
ournal
homepage:
http://ijeecs.iaescor
e
.com
Evaluation Warning : The document was created with Spire.PDF for Python.
1162
r
ISSN:
2502-4752
uncertainties
(demand
and
road
traf
fic)
and
assessing
the
risks
of
disruptions
caused
by
major
crises,
such
as
the
crisis
of
the
corona
virus
disease
(CO
VID-19)
epidemic.
The
capacity
to
measure
the
strate
gical,
tactical
and
operational
performance
is
considered
as
a
main
frame
w
ork
to
assert
ine
vitably
in
order
to
strengthen
the
enterprises
competiti
v
eness
within
ph
ysical
internet
supply
chain
netw
orks.
This
allo
ws
the
long-term
outputs
ef
fects
ass
essment
to
further
support
the
competi-
ti
v
eness
and
decision-making
po
wer
[1].
Therefore,
a
well-defined
set
of
performance
indicators
is
mandatory
to
consolidate
the
required
objecti
v
es
for
the
o
v
erall
performance
measurement.
The
underpinning
to
unco
v
er
these
indicators
i
n
order
to
increase
the
chances
of
success
is
an
o
v
erall
analysis
of
the
compan
y’
s
en
vironment
processes
[2].
Thus,
correction’
s
adv
antages
are
performed
through
e
v
aluation
perspecti
v
es
which
must
g
ather
financial
and
non-financial
measures.
Since
the
presence
of
man
y
criteria,
the
performance
measurement
in
ph
ysical
internet
supply
chain
netw
ork
(PISCN)
is
defined
as
a
problem
which
belongs
to
multiple
criteria
de-
cision
making.
In
f
act,
multiple
methodologies
ha
v
e
been
de
v
eloped
to
e
v
aluate
a
multiple
criteria
scheme
such
as
data
en
v
elopment
analysis
(DEA)
[3].
Accordingly
,
the
DEA
contrib
utes
to
assess
the
ef
ficienc
y
surf
aces
through
a
mathematical
programming
model.
Wherea
s,
the
resolution
process
can
be
af
fected
statistical
noises
which
e
xtent
to
wrap
the
deri
v
ed
frontier
[4].
Due
to
the
panoply
of
choice
for
decision-making
processes,
the
non-parametric
tool
for
non-linear
relations
between
inputs
and
outputs
modeling
approach
has
been
widely
de
v
eloped
with
the
artificial
neural
netw
ork
(ANN)
[5].
In
f
act,
the
ANN
presents
a
wide
v
ariety
in
the
literature
such
as
spiking
neural
net-
w
orks
[6]
and
recurrent
neural
netw
orks
[7],
though,
the
most
popular
type
is
the
feed-forw
ard
neural
netw
orks
(FNNs)
[8].
Besides,
the
learning
process
(i.e.,
training
process)
has
a
huge
impact
on
the
process
performance
of
ANNs.
As
a
whole,
training
algorithms
can
be
arranged
into
tw
o
cate
gories:
gradient-based
algorithms
v
ersus
stochastic
search
algorithms.
It
can
be
noted
from
[9]
that
the
widely
adopted
gradient-based
training
algorithm
is
back-propag
ation
(BP).
T
o
some
e
xtent,
the
cons
of
this
method
are
e
vinced,
for
instance,
through
the
tardy
con
v
er
gence
beha
vior
and
hanging
on
local
minima.
Besides,
for
optimization
problems,
considering
some
nature-inspired
metaheuristics
algorithms
as
alternati
v
e
trainers
ha
v
e
pro
v
ed
a
higher
ef
ficienc
y
to
di
v
er
ge
from
local
minima.
The
lar
ge
potential
of
meta-
heuristic
methods
to
train
the
feed-forw
ard
neural
netw
orks
(FNNs)
has
been
widely
asserted
in
the
literature.
In
t
his
respect,
the
krill
herd
algorithm
(KHA)
has
been
established
for
data
classification
to
train
t
he
FNNs
[10].
Not
l
ong
ago
in
2016,
a
nature-inspi
red
algorithm
kno
wn
as
multi
v
erse
optimizer
(MV
O)
has
been
used
for
training
the
FNNs
[11].
It
is
w
orth
mentioning
that
through
the
reported
numerical
results,
the
MV
O
re
v
eals
a
high
competiti
v
eness
and
it
performs
better
than
another
training
algorithms
in
most
of
datasets.
In
spite
of
the
high
quality
of
the
pre
vious
presented
w
orks,
the
local
optima
entrapment’
s
issue
con-
tinues
to
be
f
aced.
Besides,
as
mentioned
by
[12],
a
theorem
kno
wn
as
No
Free
Lunch
within
the
heuristics
area
highlights
t
he
lack
of
a
generic
problem
solving
optimization
algorithm.
Gi
v
en
that,
the
performance
g
ap
between
algorithms
occurs
after
FNNs
training
for
multiple
data
sets.
Thus,
ne
w
algorithms
ef
ficiencies
for
learning
FNNs
are
considered
as
a
w
orth
y
field
to
be
addressed
by
researchers.
In
this
respect,
this
paper
aims
to
embed
the
ne
wly
slime
mould
algorithm
(SMA)
algorithm
[13]
into
FNNs.
This
paper
appraises
the
ph
ysical
internet
supply
chain
netw
ork
performance
(PI-SCN).
The
proposed
structre
is
tw
o
steps
based.
Firstly
,
we
depict
three
fe
atures’
cate
gories
(i.e.,
economic,
social,
and
en
viron-
mental)
in
addition
to
the
tar
get
v
ariables
(reducing
costs
and
lead
time
impro
v
ement)
af
fecting
the
ph
ysical
internet
supply
chain
netw
ork
(PI-SCN).
Secondly
and
in
order
to
train
the
FNNs,
a
ne
w
method
formulation
has
been
applied
using
the
impro
v
ed
slime
mould
algorithm
(ISMA)
to
reach
the
ef
ficienc
y
v
alues.
The
remainder
of
this
article
is
or
g
anized
as
follo
ws.
The
performance
measurement
system
is
dis-
cussed
in
the
sec
tion
2.
Section
3
details
the
methodologies
applied
in
this
study
.
Sect
ion
4
presents
numerical
computations
and
discussion.
At
the
end,
section
5
summarizes
the
conclusions
and
points
out
future
re-
searches.
2.
PHYSICAL
INTERNET
SUPPL
Y
CHAIN
NETW
ORK
(PI-SCN)
PERFORMANCE
SYSTEM
The
assessment
of
operations’
performance
in
a
ph
ysical
internet
supply
chain
netw
ork
stands
among
the
main
manageri
al
b
usiness
af
f
air
.
But,
it
is
v
ery
tough
to
e
v
aluate
an
or
g
anization’
s
performance
when
se
v
eral
measures
belongs
to
a
defined
system
or
operation
[14].
Besides,
the
e
xpanding
competiti
v
eness
in
the
supply
c
hain
domain
requires
more
adv
anced
performance
le
v
el.
According
to
the
global
objecti
v
es
of
the
compan
y
,
the
related
system
of
performance
measurement’
s
indicator
will
be
dra
wn
[15].
The
importance
Indonesian
J
Elec
Eng
&
Comp
Sci,
V
ol.
24,
No.
2,
No
v
ember
2021
:
1161
–
1172
Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian
J
Elec
Eng
&
Comp
Sci
ISSN:
2502-4752
r
1163
of
financial
measures
to
assess
the
or
g
anizations’
profits
point
out
their
e
xistence
within
man
y
performance
measurement
frame
w
orks
proposed
for
ph
ysical
supply
chain
netw
ork.
This
study
highlights
the
objecti
v
es
to
rely
on
as
well
as
the
in
v
olv
ed
performance
indicators
to
reach
the
tar
geted
PI-SCN
performances.
The
whole
steps
are
presented
in
Figure
1.
Figure
1.
Ph
ysical
internet
supply
chain
netw
ork
system
3.
RESEARCH
METHOD
In
this
part,
we
illustrate
the
recommended
frame
w
ork
to
e
v
aluate
the
performance
of
(PI-SCN).
3.1.
F
eed-f
orward
neural
netw
ork
One
of
the
most
popular
type
of
ANNs
is
the
FNNs.
In
this
netw
ork,
the
information
has
a
unique
progression’
s
direction
which
start
from
the
inputs
to
outputs
by
mo
ving
across
set
“neurons”
[16]
in
hidden
layer
.
Ne
v
ertheless,
the
netw
ork
does
not
intend
an
y
c
ycles
or
loops.
The
Figure
2
illustrates
an
elementary
FNN
with
a
single
hidden
layer
.
As
highlighted,
the
sum
of
the
inputs’
weight
are
computed
by
each
neuron
considering
a
bias.
Subsequently
,
the
sum
is
pass
ed
across
sigmoid
function
and
then
reach
the
output
of
NN.
The
procedure
is
represented
by
(1)-(3):
H
j
=
R
X
i
=1
!
i;j
I
j
+
b
j
(1)
Where
R
is
the
number
of
nodes
of
input
layers,
!
i;j
denotes
the
connection
weight
between
the
i
th
neuron
of
the
input
layer
and
j
th
neuron
of
the
hidden
layer
,
b
j
is
the
threshold
(bias)
in
hidden
layers
and
I
i
is
the
i
th
input
data.
f
(
x
)
=
1
1
+
e
x
(2)
Here
f
(
x
)
is
the
sigmoid
function.
The
output
of
the
netw
ork
is
calculated
as
follo
ws:
y
k
=
f
k
(
N
X
j
=1
i;j
H
j
+
b
k
)
(3)
Artificial
neur
al
network
based
meta-heuristic
for
performance
impr
o
vement...
(Chouar
Abdelsamad)
Evaluation Warning : The document was created with Spire.PDF for Python.
1164
r
ISSN:
2502-4752
Where
i;j
denotes
the
connection
weight
between
the
j
th
neuron
of
the
hidden
layer
and
k
th
neuron
of
the
output
layer
,
b
k
is
the
threshold
(bias)
in
output
layers.
As
long
as
some
error
criterion
is
not
reached,
the
training
procedure
is
performed
to
re
gulate
t
he
weights
and
bias.
As
a
matter
of
f
act,
pick
up
the
proper
training
algorithm
is
the
principal
challenge.
Moreo
v
er
,
the
design
comple
xity
of
the
neural
netw
ork
increases
gi
v
en
that
man
y
elements
af
fect
the
training
performance,
for
instance,
the
total
nodes
in
hidden
layers,
in
addition
to
the
error
and
acti
v
ation
functions.
Figure
2
sho
ws
a
simple
FNN
structure.
Figure
2.
FNN
architecture
3.2.
Brief
description
of
SMA
A
ne
wly
optimization
technique
has
been
presented
not
long
ago
by
[13]
called
the
SMA,
the
general
concept
is
simulated
from
slime
moulds,
ph
ysarum
polyce
p
ha
lum
intelligent
beha
viour
.
Henceforw
ard,
this
algorithm
which
is
based
on
a
population
stochastic
search
procedure
has
been
emplo
yed
into
man
y
comple
x
engineering
problems
in
the
field
of
optimizati
on.
The
principal
concepts
of
SMA
are
outlined
in
the
follo
wing
subsection.
3.2.1.
A
ppr
oach
f
ood
T
o
model
the
approaching
beha
vior
of
slime
mould
as
a
mathematical
equation,
the
follo
wing
rule
is
proposed
to
imitate
the
contraction
mode
by
using
(4):
X
t
+1
=
X
b
(
t
)
+
v
b
:
(
W
:X
A
(
t
)
X
B
(
t
))
r
<
p
v
c
:X
t
r
p
(4)
where
v
b
is
a
parameter
with
a
range
of
[
a;
a
]
,
v
c
decreases
linearly
from
one
to
zero.
The
t
represents
the
current
iteration,
X
b
represents
the
indi
vidual
location
with
the
highest
odor
concentration
currently
found,
X
represents
the
location
of
slime
mould,
X
A
and
X
B
represent
tw
o
indi
viduals
randomly
selected
from
the
sw
arm,
W
represents
the
weight
of
slime
mould.
The
formula
of
p
is
as
follo
ws
using
(5):
p
=
tanh
j
S
(
i
)
D
F
j
(5)
where
i
2
1
;
2
;
:
:
:
;
n
,
S
(
i
)
represents
the
fitness
of
X
,
D
F
represents
the
best
fitness
obtained
in
all
iterations.
The
formula
of
v
b
is
as
follo
ws
by
(6):
v
b
=
[
a;
a
]
(6)
The
formula
of
a
is
as
follo
ws
by
(7):
a
=
arctanh
t
max
t
+
1
(7)
The
formula
of
W
is
listed
as
follo
ws
by
(8):
W
(
S
mel
l
I
ndex
(
i
))
=
1
+
r
log
((
b
F
S
(
i
))
=
(
b
F
w
F
)
+
1)
condition
1
r
log
((
b
F
S
(
i
))
=
(
b
F
w
F
)
+
1)
other
s
(8)
Indonesian
J
Elec
Eng
&
Comp
Sci,
V
ol.
24,
No.
2,
No
v
ember
2021
:
1161
–
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Eng
&
Comp
Sci
ISSN:
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r
1165
S
mel
l
I
ndex
=
sor
t
(
S
)
(9)
where
condition
indicates
that
S
(
i
)
ranks
first
half
of
the
population,
r
denotes
the
random
v
alue
in
the
interv
al
of
[0,1],
b
F
and
w
F
illustrates,
respecti
v
ely
,
the
obtained
optimal
and
w
orst
fitnesses
in
the
current
iterati
v
e
process,
while
S
mel
l
I
nde
x
denotes
the
sorted
sequence
of
fitness
v
alues
(ascends
in
the
minimum
v
alue
problem).
3.2.2.
Wrap
f
ood
The
mathematical
formula
for
updating
the
location
of
slime
mould
is
described
by
(10):
X
=
8
<
:
r
and
(
U
B
LB
)
+
LB
r
and
<
z
X
b
(
t
)
+
v
b
(
W
X
A
(
t
)
X
B
(
t
))
r
<
p
v
c
X
(
t
)
r
p
(10)
where
LB
and
U
B
outline
the
lo
wer
and
upper
boundaries
of
the
search
range,
rand
and
r
define
the
random
v
alue
within
[0
:
1]
.
3.2.3.
Oscillation
The
v
alue
of
v
b
oscillates
randomly
between
[
a;
a
]
and
it
gradually
con
v
er
ges
to
w
ard
zero
as
well
as
the
iterations
increase.
The
v
alue
of
v
c
oscillates
between
[
1
;
1]
and
tends
to
zero
e
v
entually
.
The
main
steps
of
the
SMA
are
illustrated
in
the
figure
and
the
algorithm.
3.3.
L
´
evy
flights
Le
vy
flights
is
a
non-Gaussian
stochasti
c
process,
the
related
step
sizes
are
distrib
uted
based
on
a
Le
vy
stable
distrib
ution
to
generate
ne
w
solutions.
Once
a
no
v
el
solution
is
defined,
the
follo
wing
Le
vy
flight
is
carried
out
in
(11):
X
t
+1
=
X
t
Lev
y
(
)
(11)
where
indicates
t
he
step
size
related
to
the
problem’
s
scales.
The
product
means
entry-wise
multiplications.
The
pre
v
ailing
idea
is
that
Le
vy
flights
furnish
a
random
w
alk
gi
v
en
that
for
lar
ge
steps.
In
this
study
,
the
algorithm
proposed
by
[16]
will
be
used
on
account
of
its
prominent
ef
ficient
hi
ghlighted
with
Le
vy
flights
implementation.
3.4.
Impr
o
v
ed
slime
mould
algorithm
The
pre
v
ailing
criteria
for
an
ef
ficient
optimization
algorithm
are
based
on
the
strong
e
xploration
ability
in
addition
to
a
f
ast
e
xploitation
rate.
W
ith
the
aim
for
SMA
performance’
s
impro
v
ement
and
to
e
xpand
the
algorithm
e
xploration,
an
update
position-based
accelerated
particle
sw
arm
optimization
(APSO)
[17]
and
L
´
evy
flight
technique
are
included
into
the
SMA.
The
principal
intention
of
the
suggested
algorithm
is
in
that
w
ay
.
The
basic
idea
of
the
proposed
algorithm
is
as
follo
ws.
First,
a
fraction
of
the
population
is
chosen
according
to
the
w
orst
fitness
v
alue.
Then
a
L
´
evy
flight
is
performed
according
section
2.2,
while
the
standard
SMA
is
applied
to
the
rest
of
better
solutions.
Secondly
,
an
update
position-based
is
implemented
based
on
APSO.
Generally
,
APSO
has
the
ability
to
prospect
rapidly
the
search
space
and
find
out
ef
ficiently
the
optimal
solution.
Hence,
the
position
is
updated
by
the
follo
wing
(12):
X
t
+1
=
(1
)
X
t
+
g
+
r
(12)
The
v
elocity
is
not
included
in
the
equation
12,
thereof,
the
APSO
does
not
require
v
elocities’
initiali
zation,
in
this
re
g
ard,
it
a
v
oids
the
dra
wbacks
related
to
re
gular
PSO
v
elocities.
At
this
stage
the
third
term
r
compels
the
system
to
be
more
mobile
and
to
a
v
oid
entrapment
within
an
y
local
optima
if
its
selection
has
been
performed
properly
,
the
corresponding
definition
of
r
can
be
dra
wn
from
a
statistical
distrib
ution.
According
to
the
other
parameters
such
as
and
are
choosing
according
to
[17]
as
follo
w
in
(13):
=
t
(13)
where
=
0
:
2
0
:
7
and
=
0
:
1
0
:
99
.
Here
t
2
[0
;
t
max
]
.
The
proposed
method
is
outlined
in
Algorithm
1:
Artificial
neur
al
network
based
meta-heuristic
for
performance
impr
o
vement...
(Chouar
Abdelsamad)
Evaluation Warning : The document was created with Spire.PDF for Python.
1166
r
ISSN:
2502-4752
Algorithm
1
Proposed
ISMA
trainer
Inputs
:
N
:
Population
size
and
max
t
:
maximum
number
of
iterations
Outputs
:
The
best
solution
Slime
mould
positions
X
i
(
i
=
1
;
2
;
:
:
:
;
n
)
at
t
=
0
while
(stop
criterion)
do
Calculate
the
fitness
of
all
slime
mould
f
or
(each
portion
N
pop
F
r
action
of
w
orst
of
solutions)
do
Perform
Le
vy
flight
for
X
i
to
generate
a
ne
w
slime
X
0
i
using
Eq.
(11
)
X
i
X
0
i
f
i
f
0
i
end
f
or
Calculate
the
W
by
(8
)
Update
bestFitness
and
X
b
f
or
(each
portion
3
N
pop
F
r
action
of
rest
of
solutions)
do
Update
p
,
v
b
,
v
c
Update
positions
by
:
8
<
:
(1
)
X
t
+
X
b
+
r
r
and
<
z
X
b
(
t
)
+
v
b
(
W
X
A
(
t
)
X
B
(
t
))
r
<
p
v
c
X
(
t
)
r
p
end
f
or
end
while
Retur
n
bestFitness
and
X
b
4.
ISMA
FOR
TRAIN
FNNS
4.1.
Ar
chitectur
e
of
FNNs
During
NNs
emplo
yment,
the
structure
should
be
essentially
defined
according
to
the
layers’
number
in
addition
to
layers’
neurons
number
.
The
NN
comple
xity’
s
is
correlated
to
the
number
of
neurons
in
the
hidden
layers.
As
long
as
the
number
is
important,
the
comple
xity
increases.
In
this
study
,
the
characteristic
of
a
problem-dependent
has
been
associated
to
the
input
and
output
neurons’
number
in
MLP
netw
ork
so
that
the
K
olmogoro
v
theorem
[18]
has
been
adopted
to
compute
the
number
of
hidden
nodes
through
the
(14):
H
=
2
I
+
1
(14)
The
netw
ork’
s
weights
and
bias
ha
v
e
been
optimized
through
SMA.
Moreo
v
er
,
D
reflects
each
or
g
anism’
s
dimension:
D
=
(
I
H
)
+
(
H
O
)
+
H
bias
+
O
bias
(15)
Notice
that
I
,
H
and
O
describe
respecti
v
ely
the
input,
hidden
and
output
FNN’
s
neurons.
While
H
bias
and
O
bias
presents
the
biases’
number
and
output
layers.
Figure
3
sho
ws
the
FNN
architecture
for
PI-SCN.
Figure
3.
PI-SCN
system
ANN
based
representation
Indonesian
J
Elec
Eng
&
Comp
Sci,
V
ol.
24,
No.
2,
No
v
ember
2021
:
1161
–
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ISSN:
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r
1167
4.2.
Method
e
v
aluation
The
e
v
aluation
according
to
ISMA
of
each
slime
mould
is
performed
gi
ving
its
fitness
which
reflect
s
to
its
status.
The
corresponding
process
is
the
follo
wing;
the
v
ector
that
include
the
weights
and
biases
is
passed
to
FNNs,
afterw
ard,
the
neural
netw
ork
prediction
emplo
ying
the
training
dataset
is
used
to
figure
out
the
mean
squared
error
(MSE)
criterion.
The
optimal
solution
is
reached
after
consecuti
v
e
iterations
which
describe
the
neural
netw
ork
weights
and
biases.
The
(16)
presents
the
MSE
criterion,
M
describes
the
samples’
number
in
training
dataset
and
(
b
Y
;
Y
)
are
respecti
v
ele
y
to
the
estimated
and
the
original
v
alues
according
to
the
suggested
model.
M
S
E
=
1
M
M
X
i
=1
(
y
r
b
y
r
)
(16)
4.3.
Encoding
strategy
Dif
ferent
encoding
strate
gies
ha
v
e
been
introduced
by
[19].
F
or
instance,
in
the
field
of
e
v
olut
ionary
algorithm,
the
FNNs’
weights
and
biases
for
e
v
ery
agent
can
be
structured
in
multiple
forms
such
as
v
ector
,
matrix,
or
binary
.
The
Figure
4
highlights
an
encoding
strate
gy
which
belongs
to
v
ector
structure,
this
method
has
been
adopted
for
the
present
study
.
In
this
respect,
the
FNNs’
weights
and
biases
stand
for
each
mould
which
con
v
erted
afterw
ards
into
a
real
number
single
v
ector
.
Figure
4.
Solution
representation
4.4.
Pr
oposed
model
In
this
part,
the
suggested
model
is
e
xplored
according
to
a
t
hree
part.
Firstly
,
three
cate
gories
of
fea-
tures
are
ide
n
t
ified
(i.e.,
economic,
s
ocial,
and
en
vironmental)
and
the
tar
get
v
ariables
(reducing
costs
and
lead
time
impro
v
ement)
that
af
fect
our
system.
At
the
end,
the
ef
ficienc
y
scores
are
determined
while
implementing
ISMA
as
no
v
el
method
to
train
FNNs.
The
related
al
gorithm
for
the
proposed
h
ybrid
frame
w
ork
is
reported
in
the
Figure
5.
Figure
5.
Proposed
h
ybrid
frame
w
ork
Artificial
neur
al
network
based
meta-heuristic
for
performance
impr
o
vement...
(Chouar
Abdelsamad)
Evaluation Warning : The document was created with Spire.PDF for Python.
1168
r
ISSN:
2502-4752
5.
RESUL
T
AND
DISCUSSION
In
this
part,
the
suggested
h
ybrid
frame
w
ork
ef
ficienc
y
i
s
e
xplored
to
e
v
aluate
the
PI-SCN
perfor
-
mance.
The
proposed
method
is
compared
ag
ainst
recent
nine
algorithms
such
as
GA
[20],
GW
O
[21],
SCA
[22],
W
O
A
[23],
HHO
[24],
SMA
[13],
MV
O
[25],
MFO
[26].
The
whole
algorithms
were
programmed
in
MA
TLAB
R2014a.
The
e
xperiments
computations
ha
v
e
been
performed
through
20
distinct
runs;
the
other
algorithms’
parameters
are
tak
en
the
same
as
the
published
paper’
s
v
alues.
The
dataset
sho
wn
in
T
able
1
has
been
g
athered
e
xploiting
a
brainstorming.
Because
of
condientiality
concerns,
the
first
data
has
been
changed
and
partitioned
into
66%
for
training
and
34%
for
testing.
T
able
1.
T
e
xtile
datasets
Features
T
ar
gets
Economic
Social
En
vironment
SG
PG
R
OC
G
L
TTF
R
OS
R
OCS
Spo
E
WWS
SSD
Spi
Costs
L
T
10
2
6
6
8
3
6
1
6
2
4
5
4
69
68
9
6
6
9
1
2
6
3
9
2
5
7
6
76
61
10
9
6
3
5
2
3
9
1
8
3
5
3
70
53
6
2
5
10
1
5
2
9
5
1
10
1
6
79
73
3
2
9
7
9
6
9
4
6
8
6
1
10
66
53
1
10
10
8
3
7
3
6
3
1
6
6
9
74
73
7
8
6
5
1
3
8
3
9
8
1
8
5
71
55
3
10
8
4
9
1
2
1
6
1
3
5
4
51
51
In
order
to
compare
all
algorithms
and
during
all
benchmarks,
the
a
v
erage
(A
VE)
and
the
standar
g
de
viation
(STD)
ha
v
e
been
emplo
yed.
These
tw
o
mesures
ha
v
e
been
implemented
to
highlight
the
algorithm’
s
ef
fecti
v
eness
to
escape
from
local
minima
entrapment.
A
case
study
has
been
applied
based
on
100
companies
operating
in
te
xtile
industry
in
order
to
v
alidate
our
model.
The
results
of
dataset
are
reported
in
T
able
2.
By
analysi
n
g
the
results
of
the
T
able
2,
the
pre
v
ailing
element
to
share
is
the
best
performance
outlined
by
the
proposed
method
as
well
as
MFO
and
HHO.
This
beha
vior
is
depicted
by
the
highest
abi
lity
to
escape
local
optima
which
is
fundamentally
finer
comparing
to
another
algorithms.
Besides,
a
con
v
er
gence
comparati
v
e
e
xperimentation
w
as
implem
ented
to
appro
v
e
that
ISMA
has
greater
con
v
er
gence
performance
than
the
other
algorithms.
Figure
6
sho
ws
the
con
v
er
gence
curv
es.
T
able
2.
Experimental
results
for
te
xtile
compan
y
dataset
GA
GW
O
SCA
W
O
A
HHO
SMA
MV
O
MFO
ISMA
Min
9,86E-04
9,80E-04
1,02E-03
1,13E-03
5,02E-04
9,71E-04
9,64E-04
5,00E-04
5,00E-04
Max
9,86E-04
9,80E-04
1,02E-03
1,13E-03
5,02E-04
9,71E-04
9,64E-04
5,00E-04
5,00E-04
A
V
G
9,86E-04
9,80E-04
1,02E-03
1,13E-03
5,02E-04
9,71E-04
9,64E-04
5,00E-04
5,00E-04
Std
1,6E-02
4,0E-03
5,0E-02
4,7E-02
8,9E-04
3,9E-02
2,7E-02
8,5E-04
8,1E-04
Error
8,45
8,32
13,19
11,56
5,45
9,36
8,10
5,40
5,25
p-v
alue
8,60E-08
6,09E-03
6,80E-08
1,06E-07
5,31E-01
7,41E-09
4,60E-04
6,61E-0
N/A
Figure
6.
Con
v
er
gence
curv
es-case
study
Indonesian
J
Elec
Eng
&
Comp
Sci,
V
ol.
24,
No.
2,
No
v
ember
2021
:
1161
–
1172
Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian
J
Elec
Eng
&
Comp
Sci
ISSN:
2502-4752
r
1169
Additionally
,
the
proposed
method
has
led
to
higher
ef
ficac
y
threshold.
This
result
has
been
demon-
strated
through
a
benchmark
with
three
selected
standard
classification
data
sets
from
the
Uni
v
ersity
of
Cal-
ifornia
at
Irvine
(UCI)
machine
learning
repository
[27]:
sigmoid,
cosine
and
sine.
The
dataset
i
s
sho
wn
in
T
able
3.
T
able
3.
Function
approximation
dataset
Function
approximation
dataset
T
raining
samples
T
est
samples
Sigmoid:
y
=
1
=
(1
+
e
x
)
61:
x
2
[3
:
0
:
1
:
3]
121:
x
2
[3
:
0
:
05
:
3]
Cosine:
y
=
(
cos
(
x
=
2))
7
31:
x
2
[1
:
25
:
0
:
05
:
2
:
75]
38:
x
2
[1
:
25
:
0
:
04
:
2
:
75]
Sine:
y
=
sin
(2
x
)
126:
x
2
[
2
:
0
:
1
:
2
]
252:
x
2
[
2
:
0
:
05
:
2
]
5.1.
Sigmoid
function
The
sigmoid
dataset
belongs
to
the
interv
al
[
3
;
3]
with
increases
of
0.1
which
sum
up
the
number
of
training
data
to
61.
The
number
of
test
samples
is
121,
lying
in
the
same
range.
The
test
errors
in
T
able
4,
con
v
er
gence
curv
e
in
Figure
7
highlights
that
the
ISMA
algorithm
admit
the
higher
approximate
e
xactitude
in
addition
to
the
f
astest
con
v
er
gence
rate.
T
able
4.
Sigmoid
dataset
results
GA
GW
O
SCA
W
O
A
HHO
SMA
MV
O
MFO
ISMA
Min
8,9E-09
8,6E-09
1,3E-02
1,7E-03
3,9E-04
2,9E-04
3,7E-04
4,0E-04
5,0E-09
Max
5,8E-02
4,5E-02
1,4E-01
1,5E-01
7,8E-03
6,4E-02
6,5E-02
5,6E-03
2,9E-03
A
V
G
1,6E-02
3,6E-03
6,3E-02
4,6E-02
5,1E-03
1,2E-02
1,0E-02
2,5E-03
8,0E-04
Std
1,6E-02
1,0E-02
3,0E-02
4,7E-02
2,9E-03
1,9E-02
1,7E-02
1,4E-03
7,3E-04
Error
0,78
0,20
9,63
3,50
1,41
1,56
1,77
1,79
0,14
p-v
alue
8,60E-08
5,61E-01
6,80E-08
1,06E-07
2,60E-06
7,41E-09
4,60E-04
9,28E-09
N/A
Figure
7.
Con
v
er
gence
curv
es-sigmoid
dataset
5.2.
Cosine
function
The
cosine
dataset
belongs
to
the
interv
al
[1
:
25
;
2
:
75]
with
increases
of
0
:
05
,
therefore
the
amount
of
training
data
is
31.
The
number
of
test
samples
is
38,
lying
in
the
same
range.
The
test
errors
in
T
able
5,
con
v
er
gence
and
curv
e
in
Figure
8
highlights
that
the
ISMA
algorithm
admit
the
higher
approximate
e
xactitude
in
addition
to
the
f
astest
con
v
er
gence
rate.
T
able
5.
Cosine
dataset
results
GA
GW
O
SCA
W
O
A
HHO
SMA
MV
O
MFO
ISMA
Min
3,8E-04
2,1E-04
2,9E-03
3,1E-03
2,1E-03
1,7E-04
6,7E-04
1,3E-02
1,2E-04
Max
4,3E-03
2,0E-03
1,4E-02
6,8E-02
1,3E-01
2,5E-03
2,4E-03
1,3E-01
1,2E-03
A
V
G
1,4E-03
6,8E-04
6,6E-03
2,0E-02
4,4E-02
8,2E-04
1,6E-03
8,0E-02
6,0E-04
Std
8,8E-04
4,6E-04
3,1E-03
2,0E-02
4,9E-02
6,7E-04
4,9E-04
3,9E-02
3,3E-04
Error
0,79
0,94
1,43
1,81
1,42
0,65
0,92
3,56
0,44
p-v
alue
1,20E-01
1,58E-08
6,80E-06
6,80E-06
1,23E-07
2,22E-04
5,17E-08
6,80E-06
N/A
Artificial
neur
al
network
based
meta-heuristic
for
performance
impr
o
vement...
(Chouar
Abdelsamad)
Evaluation Warning : The document was created with Spire.PDF for Python.
1170
r
ISSN:
2502-4752
Figure
8.
Con
v
er
gence
curv
es-cosine
dataset
5.3.
Sine
function
The
sine
dataset
belongs
to
the
interv
al
[
2
;
2
]
with
increases
of
0
:
1
,
therefore
the
amount
of
training
data
is
126.
The
number
of
test
samples
is
256,
lying
in
the
same
range.
The
test
errors
in
T
able
6,
con
v
er
gence
and
curv
e
in
Figure
9
highlights
that
the
ISMA
algorithm
admit
the
higher
approximate
e
xactitude
in
addition
to
the
f
astest
con
v
er
gence
rate.
T
able
6.
Sine
dataset
results
GA
GW
O
SCA
W
O
A
HHO
SMA
MV
O
MFO
ISMA
Min
8,0E-02
6,1E-02
1,4E-01
1,1E-01
1,1E-01
4,9E-02
1,6E-02
1,1E-01
4,4E-02
Max
2,9E-01
1,2E-01
2,8E-01
2,9E-01
1,2E-01
2,8E-01
2,2E-01
1,2E-01
2,2E-01
A
V
G
1,5E-01
1,2E-01
2,0E-01
2,1E-01
1,2E-01
1,3E-01
1,2E-01
1,2E-01
1,2E-01
Std
5,9E-02
5,0E-02
3,6E-02
5,4E-02
2,3E-03
5,5E-02
6,3E-02
2,5E-03
2,4E-03
Error
112,50
71,50
175,80
168,80
177,80
147,30
136,54
178,12
28,90
p-v
alue
4,8E-02
1,6E-02
6,08E-06
1,20E-08
8,35E-03
5,61E-02
6,17E-03
4,16E-04
N/A
Figure
9.
Con
v
er
gence
curv
es-sine
dataset
Indonesian
J
Elec
Eng
&
Comp
Sci,
V
ol.
24,
No.
2,
No
v
ember
2021
:
1161
–
1172
Evaluation Warning : The document was created with Spire.PDF for Python.