Content uploaded by Danil Yurievich Pimenov
Author content
All content in this area was uploaded by Danil Yurievich Pimenov on Sep 30, 2020
Content may be subject to copyright.
polymers
Article
Mechanical Strength Enhancement of 3D Printed
Acrylonitrile Butadiene Styrene Polymer Components
Using Neural Network Optimization Algorithm
Jasgurpreet Singh Chohan 1, Nitin Mittal 1, Raman Kumar 1, Sandeep Singh 1,
Shubham Sharma 2, Jujhar Singh 2, Kalagadda Venkateswara Rao 3, Mozammel Mia 4, * ,
Danil Yurievich Pimenov 5and Shashi Prakash Dwivedi 6
1University Centre for Research and Development, Chandigarh University, Mohali-140413, India;
jaskhera@gmail.com (J.S.C.); mittal.nitin84@gmail.com (N.M.); ramankakkar@gmail.com (R.K.);
drsandeep1786@gmail.com (S.S.)
2Department of Mechanical Engineering, IKG Punjab Technical University, Kapurthala-144603, India;
shubham543sharma@gmail.com or shubhamsharmacsirclri@gmail.com (S.S.);
jujharsing2085@gmail.com (J.S.)
3Center for Nanoscience and Technology, Institute of Science and Technology, Jawaharlal Nehru
Technological University Hyderabad, Telangana State 500085, India; kalagadda2003@gmail.com
4Department of Mechanical Engineering, Imperial College London, Exhibition Rd., London SW7 2AZ, UK
5Department of Automated Mechanical Engineering, South Ural State University, Lenin Prosp. 76,
454080 Chelyabinsk, Russia; danil_u@rambler.ru
6Department of Mechanical Engineering, G.L. Bajaj Institute of Technology and Management,
Greater Noida 201308, India; spdglb@gmail.com
*Correspondence: m.mia19@imperial.ac.uk
Received: 2 September 2020; Accepted: 26 September 2020; Published: 30 September 2020
Abstract:
Fused filament fabrication (FFF), a portable, clean, low cost and flexible 3D printing
technique, finds enormous applications in different sectors. The process has the ability to create
ready to use tailor-made products within a few hours, and acrylonitrile butadiene styrene (ABS) is
extensively employed in FFF due to high impact resistance and toughness. However, this technology
has certain inherent process limitations, such as poor mechanical strength and surface finish, which can
be improved by optimizing the process parameters. As the results of optimization studies primarily
depend upon the efficiency of the mathematical tools, in this work, an attempt is made to investigate
a novel optimization tool. This paper illustrates an optimization study of process parameters of
FFF using neural network algorithm (NNA) based optimization to determine the tensile strength,
flexural strength and impact strength of ABS parts. The study also compares the efficacy of NNA
over conventional optimization tools. The advanced optimization successfully optimizes the process
parameters of FFF and predicts maximum mechanical properties at the suggested parameter settings.
Keywords:
optimization; neural network algorithm; fused filament fabrication; mechanical
strength; simulation
1. Introduction
Globalization has intensified the market scenario of manufacturing units due to rapidly changing
customer demands, competition among peers and requirements for high quality and reliable products.
The demand for low cost and customized products has led to a paradigm shift from traditional
manufacturing techniques to additive manufacturing technologies by industries [
1
]. Additive
manufacturing is a collection of non-conventional techniques that follow the principle of layer
Polymers 2020,12, 2250; doi:10.3390/polym12102250 www.mdpi.com/journal/polymers
Polymers 2020,12, 2250 2 of 18
by layer manufacturing in contrast to traditional subtractive and joining techniques [
2
]. The last
decade witnessed a marginal increase in the development and market share of various additive
manufacturing techniques due to their implementation in medical, aerospace, automobile, military
and ornamental industries [
3
]. Additive manufacturing enables direct fabrication of a product from
three-dimensional computer-aided design (CAD) data through successive layer stacking of suitable
material. These techniques are also popularly referred to as 3D printing, rapid prototyping, solid
freeform fabrication, e-manufacturing and digital fabrication. There are more than thirty different
additive manufacturing techniques available, which differ on fabrication principle, materials used,
accuracy, bed size, part strength and applicability; however, fused filament fabrication (FFF) is the
most recognized [4].
FFF has acquired considerable attention from researchers, material scientists, innovators and
medical practitioners due to the unique advantages of this technique, such as material flexibility,
minimum environmental degradation, low cost, portability and higher accuracy [
5
]. FFF uses CAD
data as input, which is transferred to slicing software for tool path generation. These tool paths are
coded instructions that control the three-dimensional motion of the nozzle head and build platforms to
create the product within a few hours. The raw material used is a thin wire of thermoplastic material
with a lower melting point and zero toxicity. This wire is pushed by rollers into the nozzle head, where
heaters convert it into semi-molten filament. Finally, the material is deposited by a nozzle moving in
X and Y direction on the build platform, as shown in Figure 1. As one layer is deposited, the build
platform moves downwards (in Z direction), and the next layer of material is deposited. The process is
repeated until the desired part is achieved. Sometimes, another filament of washable material is used
to support the overhanging part, which is easily washed away after fabrication [6].
Polymers 2020, 12, x FOR PEER REVIEW 2 of 19
layer by layer manufacturing in contrast to traditional subtractive and joining techniques [2]. The last
decade witnessed a marginal increase in the development and market share of various additive
manufacturing techniques due to their implementation in medical, aerospace, automobile, military
and ornamental industries [3]. Additive manufacturing enables direct fabrication of a product from
three-dimensional computer-aided design (CAD) data through successive layer stacking of suitable
material. These techniques are also popularly referred to as 3D printing, rapid prototyping, solid
freeform fabrication, e-manufacturing and digital fabrication. There are more than thirty different
additive manufacturing techniques available, which differ on fabrication principle, materials used,
accuracy, bed size, part strength and applicability; however, fused filament fabrication (FFF) is the
most recognized [4].
FFF has acquired considerable attention from researchers, material scientists, innovators and
medical practitioners due to the unique advantages of this technique, such as material flexibility,
minimum environmental degradation, low cost, portability and higher accuracy [5]. FFF uses CAD
data as input, which is transferred to slicing software for tool path generation. These tool paths are
coded instructions that control the three-dimensional motion of the nozzle head and build platforms
to create the product within a few hours. The raw material used is a thin wire of thermoplastic
material with a lower melting point and zero toxicity. This wire is pushed by rollers into the nozzle
head, where heaters convert it into semi-molten filament. Finally, the material is deposited by a
nozzle moving in X and Y direction on the build platform, as shown in Figure 1. As one layer is
deposited, the build platform moves downwards (in Z direction), and the next layer of material is
deposited. The process is repeated until the desired part is achieved. Sometimes, another filament of
washable material is used to support the overhanging part, which is easily washed away after
fabrication [6].
Figure 1. Schematic of the fused filament fabrication (FFF) process used for 3D printing of
thermoplastics.
FFF supplies customized products with the minimum lead time and manufacturing cost, but the
mechanical strength of the part is always a matter of interest for researchers as considerable variation
in mechanical properties is experienced due to variation in design [7]. Moreover, issues related to the
lower mechanical strength of FFF parts may hinder the usability of these products for certain
applications. Thus, there is always a requirement for intelligent optimization tools for the prediction
and maximization of the mechanical strength of FFF parts. There are several input parameters of FFF
technology, which have a significant impact on the tensile strength, compressive strength, flexural
and impact strength of FFF parts [5]. Although numerous studies have been conducted for
optimization of process parameters of FFF, recent studies have focused on the development of
Figure 1.
Schematic of the fused filament fabrication (FFF) process used for 3D printing of thermoplastics.
FFF supplies customized products with the minimum lead time and manufacturing cost, but the
mechanical strength of the part is always a matter of interest for researchers as considerable variation
in mechanical properties is experienced due to variation in design [
7
]. Moreover, issues related to
the lower mechanical strength of FFF parts may hinder the usability of these products for certain
applications. Thus, there is always a requirement for intelligent optimization tools for the prediction
and maximization of the mechanical strength of FFF parts. There are several input parameters
of FFF technology, which have a significant impact on the tensile strength, compressive strength,
flexural and impact strength of FFF parts [
5
]. Although numerous studies have been conducted
for optimization of process parameters of FFF, recent studies have focused on the development of
Polymers 2020,12, 2250 3 of 18
conventional mathematical tools and algorithms which can optimize and forecast the mechanical
strength of FFF parts.
Hambali et al. [
2
] tested the deformation behavior of acrylonitrile butadiene styrene (ABS) material
parts made by FFF technology. The parts were fabricated at different orientations, and it was found
that the maximum strength occurred at a 45
◦
angle. The study was validated by finite element
analysis, which predicted the mechanical strength with 95% accuracy. Other studies also indicated
the significant impact of orientation angle [
3
] and infill density [
8
] on the mechanical strength of FFF
parts. Ahn et al. [
7
] investigated the anisotropic behavior of FFF parts and found that the air gap and
raster orientation significantly affected the tensile strength of FFF parts. The cross raster structure
(0
◦
/90
◦
) yielded the maximum tensile strength due to its directional stability, and it was suggested
that a negative air gap be maintained for higher strength and stiffness. In addition to conventional
optimization studies, researchers have used mathematical models and algorithms for the analysis of
process parameters. Multi-criteria genetic algorithm was used for the optimization and prediction
of the surface finish and manufacturing time of FFF parts [
4
] and aluminum-based metal matrix
composites [
9
]. The teaching–learning based optimization tool was utilized by Rao and Rai [
1
] to
enhance the sliding wear resistance and strength of FFF parts; the experimental data was compared
with genetic algorithm and advanced quantum-behaved particle swarm optimization algorithm, which
found strong correlation between experimental and computational data. Rayegani and Onwubolu [
5
]
developed a relationship between different factors, such as part orientation, raster angle, raster width
and air gap, with tensile strength of FFF parts using differential evolution techniques along with the
group method of data handling (GMDH). It was deduced that deposition and raster angle defined
the FFF part strength. Moreover, the fine-tuning of input parameters was performed using advanced
tools to achieve maximum mechanical strength. Natarajan et al. [
10
] also implemented a modified
teaching–learning based optimization method (NSMTLBO), referred to as non-dominated sorting type,
to acquire maximum finish and minimum material removal rate.
In another study, a hybrid version of particle swarm technique was applied to FFF input parameters,
such as layer thickness, deposition angle, material type and infill strategy, and for improving the
surface finish, hardness, flexural strength and tensile strength in combination with bacterial foraging
optimization [
11
]. The tool yielded promising results as higher strength (more than 7%) was achieved
using the hybrid optimization technique as compared to conventional algorithms. Recent studies
have reported the impact of orientation angle and infill percentage in mechanical properties of ABS
samples [
12
]. Moreover, in the case of polylactic acid material, the anisotropy of samples had a
significant impact on tensile strength as compared to the orientation angle [
13
]. In addition to
optimization tools, some advanced post-processing techniques, such as annealing and ultrasound
treatment, have been recommended for strength enhancement [14].
Zhang et al. [
15
] found that residual stress and porosity were directly proportional to printing
speed during the fabrication of virgin and composite ABS structures. Moreover, the raster angle of
±
45
◦
manifested lesser shrinkage and porosity, which further influenced dimensional accuracy and
mechanical strength, respectively. Similarly, Rankouhi et al. [
16
] found a major impact of layer thickness
and raster orientation on the mechanical strength of FFF parts, with a reduction in layer thickness
and 0
◦
raster angle strengthening the ABS structures. Another study reported the maximum impact
strength of the ABS part at 0
◦
orientation angle [
17
]. Christiyan et al. [
18
] evaluated the mechanical
strength of magnesium silicate reinforced ABS composites and found maximum tensile and flexural
strength at minimum values of layer thickness and printing speed. The increase in infill density also
enhanced the tensile behavior of ABS test samples [
19
]. The flexural and impact strength of ABS
samples under standard conditions was maximum with thinner layer thickness and 0
◦
deposition
angle [20,21].
The previous studies reported the impact of different input parameters on the mechanical
properties of ABS parts made by FFF technology. Although smaller layer thickness is uniformly
recommended by previous literature, the recommended settings of the raster angle, orientation angle
Polymers 2020,12, 2250 4 of 18
and air gap are different for each study. These issues are due to conventional optimization algorithms
and mathematical modeling tools used for forecasting optimum parameters, which yield conflicting
results. Moreover, limited studies are performed where advanced optimization algorithms are used
for prediction of the best parametric settings for mechanical strength enhancement. In the present
work, the efficacy of neural network algorithm (NNA) is tested to solve the mechanical strength
issues of FFF parts. As the introduction of advanced optimization algorithms have yielded significant
improvements compared to previous studies performed by regular algorithms, investigating the
optimization problems using this optimization and simulation technique is necessary.
In the next section, a detailed methodology of the formulation and implementation of NNA is
elaborated, along with a selection of objective functions and process parameters. The third section
presents a comparative analysis of different algorithms and a discussion of the simulation results.
Finally, the fourth section includes confirmatory experiments that are conducted to validate the
predicted results.
2. Materials and Methods
2.1. Neural Network Optimization Algorithm
Sadollah et al. [
22
] developed a metaheuristics based on neural networks (NNs) named neural
network algorithm (NNA). The authors found that a metaheuristic optimization algorithm could be
used to model artificial NNs (ANNs) to solve optimization problems. NNA was developed using the
ANNs framework to solve optimization problems. NNA is a parameter-free optimization algorithm
where users do not require any algorithm parameters to be adjusted.
ANNs iteratively update the ANN’s weights
wij
to minimize the mean square error and map the
input information according to the target information required at its output. ANNs are designed to
produce new alternatives, where the population’s best search agent is considered as the target and all
searching agents seek the solution through algorithm processes.
NNA draws on the concept and structure of ANN. NNA begins within a search space with an
initial population of randomly generated solutions. Each individual in the population is referred to as
a “pattern solution”, which is a vector of 1 ×D, representing the input data of the NNA.
PatternSolutioni=[xi,1,xi,2 ,xi,3,. . . ,xi,D].
To start the NNA optimization algorithm, within the boundaries of the search space, a pattern
solution matrix Xwith size Npop ×Dis generated randomly, given by:
X=
X1
X2
.
.
.
XNpop
=
x1,1 x1,2 x1,D
x2,1 x2,2 x2,D
...
...
...
xNpop,1 xNpop ,2 xNpop,D
(1)
where:
xij =LBj+randUB j−LBj,i=1, 2, . . . ,Npop,j=1, 2, . . . ,D
where LB and UB represent the search space’s lower and upper limits.
Similar to ANNs, every pattern solution
Xi
in NNA will have its corresponding
Wi
weight, where:
Wi=hwi,1,wi,2 ,wi,3,. . . ,wi,Npop iT
Polymers 2020,12, 2250 5 of 18
The weights array Wis given by:
W=hW1,W2,. . . ,Wi,. . . ,WNpop i=
w11 wi1. . . wNpop1
w12 wi2. . . wNpop2
...
...
...
w1Npop wiNpop,2 . . . wNpop Npop
(2)
where
W
represents a matrix of a
Npop ×Npop
randomly distributed number in [0, 1], used to generate
new candidate solutions.
The initial weights in NNA are randomly generated and the network changes their weights
according to the network error propagation as the iteration increases. The weight values are limited,
as the overall weight of this pattern solution must not exceed one and the solution for the weight
pattern is defined as:
wij ∈ U(0, 1),i,j=1, 2, 3, . . . ,Npop (3)
Npop
X
j=1
wij =1, i=1, 2, 3, . . . ,Npop (4)
Such weight-value constraints are used to regulate bias movement and to generate new pattern
solutions. NNA will get trapped in the local optimum without these constraints. The fitness
fi
of
each solution is determined using the corresponding pattern solution
Xi
by evaluating the objective
function fobj.
fi=fobj(Xi) = fob j(xi1,xi2,xi3,. . . ,xiD ),i=1, 2, 3, . . . ,Npop (5)
After fitness calculation for all pattern solutions, the pattern solution with the best fitness is
considered as the target solution, with a target location
XTarget
, target fitness
FTarget
and target weight
WTarget
. The new pattern solution is created using the weight summation technique used in ANNs
as follows:
XNew
j(k+1)=
Npop
X
i=1
wij(k).Xi(k),j=1, 2, 3, . . . ,Npop (6)
Xi(k+1)=Xi(k)+XNew
i(k+1),i=1, 2, 3, . . . ,Npop (7)
where kis an iteration index.
After the generation of the new pattern solutions, the weight matrix is also modified using
the equation:
WUpdated
i(k+1)=Wi(k)+2.rand.WTarget (k)−Wi(k),,i=1, 2, 3, . . . ,Npop (8)
where the constraints (3) and (4) during the optimization process must be satisfied.
A bias operator is used to better explore the search space by adjusting a fixed range of pattern
solutions created in the new
Xi(k+1)
population as well as using the updated weight matrix
WUpdated
i(k+1)
. This operator helps the algorithm prevent premature convergence by changing the
few individuals in the population to investigate certain positions in the search space that were not
explored yet.
An adjustment factor
βNNA
is used, using the bias operator, to determine the proportion of pattern
solutions to be transformed. The value of
βNNA
is set to 1 initially, which means all the entities in the
Polymers 2020,12, 2250 6 of 18
population are biased. At each iteration, the
βNNA
value will be reduced adaptively using any possible
reduction technique, such as:
βNNA(k+1)=1− k
Max_iteration!,k=1, 2, 3, . . . ,Max_iteration (9)
βNNA(k+1)=βNNA(k).αNNA,k=1, 2, 3, . . . ,Max_iteration (10)
where
αNNA
is a positive number slightly smaller than 1. The flowchart of the NNA process is given in
Figure 2.
Polymers 2020, 12, x FOR PEER REVIEW 6 of 19
𝛽𝑁𝑁𝐴(𝑘+1)=1−𝑘
𝑀𝑎𝑥
_
𝑖𝑡𝑒𝑟𝑎𝑡𝑖𝑜𝑛,𝑘=1,2,3,…,𝑀𝑎𝑥
_
𝑖𝑡𝑒𝑟𝑎𝑡𝑖𝑜𝑛 (9)
𝛽𝑁𝑁𝐴(𝑘+1)=𝛽𝑁𝑁𝐴(𝑘).𝛼𝑁𝑁𝐴,𝑘=1,2,3,…,𝑀𝑎𝑥
_
𝑖𝑡𝑒𝑟𝑎𝑡𝑖𝑜𝑛 (10)
where 𝛼 is a positive number slightly smaller than 1. The flowchart of the NNA process is given
in Figure 2.
Figure 2. Flowchart adopted during implementation neural network algorithm (NNA) (NFE, number
of function evaluations; TF, transfer function).
Reduction in the value of 𝛽𝑁𝑁𝐴 is done to enhance the algorithm's exploitation during the final
iterations. The transfer function operator is used in NNA (unlike ANNs) to generate better-quality
solutions using the following equation:
𝑋
𝑖∗(𝑘+1)=𝑇𝐹
𝑋
𝑖(𝑘+1)=
𝑋
𝑖(𝑘+1)+2.𝑟𝑎𝑛𝑑.
𝑋
𝑇𝑎𝑟𝑔𝑒𝑡(𝑘)−
𝑋
𝑖(𝑘+1)
𝑖=1,2,3,…,𝑁 (11)
In NNA, the bias operator has more chances to produce a new pattern solution at early iterations,
meaning that there are more possibilities to find unvisited pattern solutions. As the number of
iterations increases, the probability of applying the bias operator decreases. The transfer function
(𝑇𝐹) operator has more chances of enhancing the exploitation, particularly at the final iterations.
The generation of a new updated solution in NNA does not depend solely on the preceding
value of that solution but also depends on all the mathematically defined population (known as a
dynamic optimization model), as follows:
Figure 2.
Flowchart adopted during implementation neural network algorithm (NNA) (NFE, number
of function evaluations; TF, transfer function).
Reduction in the value of
βNNA
is done to enhance the algorithm’s exploitation during the final
iterations. The transfer function operator is used in NNA (unlike ANNs) to generate better-quality
solutions using the following equation:
X∗
i(k+1)=TF(Xi(k+1)) =Xi(k+1)+2.rand.XTarget(k)−Xi(k+1)i=1, 2, 3, . . . ,Npop (11)
In NNA, the bias operator has more chances to produce a new pattern solution at early iterations,
meaning that there are more possibilities to find unvisited pattern solutions. As the number of iterations
increases, the probability of applying the bias operator decreases. The transfer function
(TF)
operator
has more chances of enhancing the exploitation, particularly at the final iterations.
Polymers 2020,12, 2250 7 of 18
The generation of a new updated solution in NNA does not depend solely on the preceding value
of that solution but also depends on all the mathematically defined population (known as a dynamic
optimization model), as follows:
Xi(k+1)=f(Xi(k),X(k)),i=1, 2, 3, . . . ,Npop (12)
2.2. Selection of Process Parameters
The materials selected for the present study were ABS commercial-grade P400 (Supplier: Stratasys
Ltd., Eden Prairie, Minnesota, Inc., USA), which was manufactured by the polymerization of styrene
(42–60%) and acrylonitrile (18–35%) in an atmosphere of butadiene (6–30%). The criss-cross bonding
of long-chained butadiene with shorter styrene-acrylonitrile chains yields excellent toughness and
heat resistance. The filament also contained mineral oil, tallow and wax in small concentrations
(0–2%), as reported in the manufacturer’s datasheet [
23
]. The output of the case study performed
by
Panda et al.
[
24
] was considered to identify the optimum parameter settings of the FFF process to
enhance the mechanical properties of the test samples. The five input parameters considered for the
present study and their units were as follows:
x1Layer thickness in mm.
x2Orientation in degrees.
x3Raster angle in degrees.
x4Raster width in mm.
x5Air gap in mm.
The major reason for the selection of the aforementioned process parameters was that previous
studies found a strong correlation of these parameters with the mechanical strength of FFF parts [
7
].
The response parameters used for the present study were tensile strength (TS) in MPa, flexural strength
(FS) in MPa and impact strength (IS) in MJ/m
2
. The primary motivation behind the selection of such
response parameters was that FFF products withstand different types of loading conditions when
used for automobile, aerospace and medical applications. Thus, it was obligatory to test each type of
mechanical strength using the advanced optimization tool. These output parameters were taken as
secondary data as reported by Panda et al. [
24
], and were designated as objective functions for the
optimization study.
The objective functions are expressed by Equations (13)–(15) below:
Maximize TS =13.5625 +0.7156x1−1.3123x2+0.9760x3+0.5183x5+1.1671x2
1
−1.3014x2
2−0.4363x1x3+0.4364x1x4−0.4364x1x5+0.4364x2x3+0.4898x2x5
−0.5389x3x4+0.5389x3x5−0.5389x4x5
(13)
Maximize FS =29.9178 +0.8719x1−4.8741x2+2.4251x3−0.9096x4+1.6626x5
−1.7199x1x3+1.7412x1x4−1.1275x1x5+1.0621x2x5+1.0621x3x5+1.0408x4x5
(14)
Maximize IS =0.401992 +0.034198x1+0.008356x2+0.013673x3+0.021383x2
1
+0.008077x2x4
(15)
The upper and lower limits of these parameters are defined as per machine constraints, and most
commercial FFF printers are capable of fabricating products within the following parameter limits [
24
].
The parameter bounds are expressed by Equations (16)–(20).
0.127 ≤x1≤0.254 (16)
0≤x2≤30 (17)
0≤x3≤60 (18)
Polymers 2020,12, 2250 8 of 18
0.4064 ≤x4≤0.5064 (19)
0≤x5≤0.008 (20)
3. Results and Discussion
NNA was implemented in this work to solve the optimization problem of the FFF process. Because
heuristic algorithms are stochastic optimization methods, to generate meaningful statistical results,
they must be run more than 10 times at minimum.
Each simulation was carried out 30 times for this purpose, with population size varying from 20
to 40, and the maximum amount of iterations ranging from 100 to 500. Grey wolf optimization (GWO),
novel bat algorithm (NBA), dragonfly algorithm (DA), salp swarm algorithm (SSA) and sine cosine
algorithm (SCA) [
25
–
29
] were selected to check and compare the efficiency of NNA. The algorithm
parameter settings used for comparison are shown in Table 1. The value of different parameters,
such as the number of particles (NP), dimension size (D), maximum number of iterations (Gmax) and
other algorithm variables (A, f
min
, f
max
, c1, c2, c3, w, s, c, e,
α
,
γ
and
β
) are shown in Table 1. It must be
noted that for each of the algorithms, 20–40 search agents and 100–500 iterations for different setups
were used.
Table 1. Parameter settings for different algorithms.
Algorithm Parameters
NBA
NP =20–40; D=5; G
max
=100–500;
A
=0.5;
r
=0.5;
α
=γ=0.9; fmin =0; fmax =1.5
GWO NP =20–40; D=5; Gmax =100–500; a=[0,1,2]
DA
SSA
SCA
NP =20–40; D=5; Gmax =100–500; w=[0.4–0.9], s=
0.1, a=0.1, c=0.7, f=1, e=1
NP =20–40; D=5; Gmax =100–500; c1, c2, c3 =[0,1]
NP =20–40; D=5; Gmax =100–500; a=2
NNA NP =20–40; D=5; Gmax =100–500; βNNA =[1–0.05];
αNNA =0.99
The optimum solutions obtained by simulated algorithms are given in Tables 2–4for TS, FS and IS
estimation, respectively. It is evident from these outcomes that the optimum NNA’s fitness values are
the same as that of competitive algorithms for TS, FS and IS fitness functions.
Table 2.
Optimum solutions obtained by optimization algorithms for tensile strength (TS) estimation
for 500 iterations with population size 40.
Process
Parameters Units NBA GWO DA SSA SCA NNA
x1mm 0.127 0.127 0.127 0.127 0.127 0.127
x2degrees
9.557223075 9.556302041 9.555264322 9.554816312 9.418607509 9.557224815
x3degrees 60 60 60 60 60 60
x4mm 0.4064 0.4064 0.4064 0.4064 0.4064 0.4064
x5mm 0.008 0.008 0.008 0.008 0.008 0.008
y—
1.605823622 1.605823622 1.605823622 1.605823622 1.605823622 1.605823622
Polymers 2020,12, 2250 9 of 18
Table 3.
Optimum solutions obtained by optimization algorithms for flexural strength (FS) estimation
for 500 iterations with population size 40.
Process
Parameters Units NBA GWO DA SSA SCA NNA
x1mm 0.127 0.127 0.127 0.127 0.127 0.127
x2degrees 0 0 0 0 0 0
x3degrees 60 60 60 60 60 60
x4mm 0.4064 0.4064 0.4064 0.4064 0.4064 0.4064
x5mm 0.008 0.008 0.008 0.008 0.008 0.008
y-
162.6744472 162.6744472 162.6744472 162.6744472 162.6744472 162.6744472
Table 4.
Optimum solutions obtained by optimization algorithms for impact strength (IS) estimation
for 500 iterations with population size 40.
Process
Parameters Units NBA GWO DA SSA SCA NNA
x1mm 0.254 0.254 0.254 0.254 0.254 0.254
x2degrees 30 30 30 30 30 30
x3degrees 60 60 60 60 60 60
x4mm 0.5064 0.5064 0.5064 0.5064 0.5064 0.5064
x5mm
0.007951741 0.007951741 0.007951741 0.007951741 0.007951741 0.007951741
y-
1.605823622 1.605823622 1.605823622 1.605823622 1.605823622 1.605823622
The performance of the simulated algorithms for FFF over 30 independent runs for 500 iterations
and with a population size of 40 is given in Tables 5–7for TS, FS and IS estimation, respectively.
The results are presented in terms of best, worst, mean and standard deviation values over 30 runs.
Table 5.
The performance of simulated algorithms for TS estimation over 30 independent runs for
500 iterations and population size 40.
Algorithm Worst Best Average Median Std. Dev.
NBA 174.6234301 174.9214992 174.9016279 174.9214992 7.56 ×10−2
GWO 174.6234298 174.9214992 174.911563 174.9214991 5.44 ×10−2
DA 174.6234301 174.9214992 174.8800297 174.9214992 9.72 ×10−2
SSA 174.6761253 174.9214992 174.8844652 174.9214992 7.32 ×10−2
SCA 174.6177085 174.9214213 174.7818994 174.8788781 1.44 ×10−1
NNA 174.9214992 174.9214992 174.9214992 174.9214992 1.89 ×10−10
Table 6.
The performance of simulated algorithms for FS estimation over 30 independent runs for
500 iterations and population size 40.
Algorithm Worst Best Average Median Std. Dev.
NBA 162.1491001 162.6744472 162.6044009 162.6744472 1.82 ×10−1
GWO 162.6744472 162.6744472 162.6744472 162.6744472 5.78 ×10−15
DA 162.6278193 162.6744472 162.6727806 162.6744472 8.51 ×10−3
SSA 162.6744472 162.6744472 162.6744472 162.6744472 5.78 ×10−14
SCA 162.6744472 162.6744472 162.6744472 162.6744472 5.78 ×10−14
NNA 162.6744472 162.6744472 162.6744472 162.6744472 5.78 ×10−14
Polymers 2020,12, 2250 10 of 18
Table 7.
The performance of simulated algorithms for IS estimation over 30 independent runs for
500 iterations and population size 40.
Algorithm Worst Best Average Median Std. Dev.
NBA 1.605823622 1.605823622 1.605823622 1.605823622 2.26 ×10−16
GWO 1.605823622 1.605823622 1.605823622 1.605823622 2.26 ×10−16
DA 1.605823622 1.605823622 1.605823622 1.605823622 2.26 ×10−16
SSA 1.605823622 1.605823622 1.605823622 1.605823622 2.26 ×10−16
SCA 1.605823622 1.605823622 1.605823622 1.605823622 2.26 ×10−16
NNA 1.605823622 1.605823622 1.605823622 1.605823622 2.26 ×10−16
The convergence rate of NNA, as shown in Figure 3, is also better than the competitive algorithms.
The convergence characteristics for TS, FS and IS estimation are shown in Figure 3. It is found that for
TS estimation, GWO, DA, SSA and NBA algorithms achieve optimum value, but overall, NNA has the
capability to identify the best value with the least standard deviation. For FS estimation, GWO, SSA,
SCA and NNA have the potential to reach global optimal solutions with the same standard deviation.
For IS estimation, all algorithms are able to reach a near global optimal solution with the same standard
deviation. Overall, the result demonstrates that NNA’s mean, median and standard deviation values
are much better compared to competitive algorithms, which proves the enhanced exploration and
exploitation capabilities of NNA for process parameter optimization of FFF, especially in TS estimation.
The box plots for TS, FS and IS evaluations are displayed in Figure 4a–c, respectively, for NBA,
GWO, DA, SSA, SCA and NNA. These box plots are an excellent medium to ascertain the fitness values
and compare the effectiveness of different algorithms. For TS estimation, it is clear that NNA yields
the best fitness values as mean and median, along with the least standard deviation. As compared
to other rival algorithms, the NNA performs better, and these results can be used for the fabrication
of commercial products using ABS. From the box plots of FS estimation, it is clear that GWO, SSA,
SCA and NNA have similar mean and median fitness values, and their standard deviation values are
better in comparison to NBA and DA. Thus, the overall performance of GWO, SSA, SCA and NNA is
found to be better for FS estimation compared to other algorithms. From the box plots of IS estimation,
it is clear that all optimization algorithms have similar mean and median fitness values, their standard
deviation values are almost the same, and the algorithms reach optimum values.
Further, the performance comparison of metaheuristic algorithms for FFF over 30 independent
runs for 100 iterations and population size 40 are given in Tables A1–A3 (see Appendix A) for TS,
FS and IS estimation, respectively. The effect of the reduced total number of iterations clearly shows
that NNA’s mean, median and standard deviation values for TS estimation are much better compared
to competitive algorithms, which proves that NNA is able to find an optimum solution with reduced
iterations for process parameter optimization of FFF. Similarly, for FS estimation, SSA, SCA and NNA
are able to achieve global optimum with equal authority. However, in IS estimation, each algorithm
shows a similar effect to achieve the optimum value.
The performance of optimization algorithms for FFF process parameter estimation was evaluated
over 30 independent runs for 100 iterations with population size 20. The results are given in
Tables A4–A6 (see Appendix A) for TS, FS and IS estimation, respectively, which demonstrate that
NNA’s mean, median and standard deviation values are much better compared to competitive
algorithms for TS and FS estimation. This proves the enhanced exploration and exploitation capabilities
of NNA for the process parameter optimization of FFF. However, each algorithm is able to achieve
the optimum value for IS estimation, independent of the population size of variables and the given
number of iterations. The maximum values of TS, FS and IS can be achieved by manufacturing FFF
parts using the process parameters predicted by the NNA algorithm.
Polymers 2020,12, 2250 11 of 18
Polymers 2020, 12, x FOR PEER REVIEW 11 of 19
Figure 3. The convergence graph of simulated algorithm estimations over 30 independent runs for
500 iterations and population size 40 for (a) TS (b) FS and (c) IS.
Figure 3.
The convergence graph of simulated algorithm estimations over 30 independent runs for
500 iterations and population size 40 for (a) TS (b) FS and (c) IS.
Polymers 2020,12, 2250 12 of 18
Polymers 2020, 12, x FOR PEER REVIEW 12 of 19
Figure 4. The box plot of simulated algorithm estimations over 30 independent runs for 500 iterations
and population size 40 for (a) TS (b) FS and (c) IS.
The performance of optimization algorithms for FFF process parameter estimation was
evaluated over 30 independent runs for 100 iterations with population size 20. The results are given
in Tables A4–A6 (see Appendix A) for TS, FS and IS estimation, respectively, which demonstrate that
NNA's mean, median and standard deviation values are much better compared to competitive
algorithms for TS and FS estimation. This proves the enhanced exploration and exploitation
capabilities of NNA for the process parameter optimization of FFF. However, each algorithm is able
to achieve the optimum value for IS estimation, independent of the population size of variables and
Figure 4.
The box plot of simulated algorithm estimations over 30 independent runs for 500 iterations
and population size 40 for (a) TS (b) FS and (c) IS.
The optimum parameter settings to achieve maximum tensile strength of FFF parts are layer
thickness of 0.127 mm, 9.55
◦
orientation angle, 60
◦
raster angle, 0.4064 mm raster width and 0.008 mm
air gap. On the other hand, flexural strength can be maximized at 0.127 mm layer thickness, 0
◦
orientation angle, 60
◦
raster angle, 0.4064 mm raster width and 0.008 mm air gap. In order to obtain
the maximum value of impact strength, the FFF process must be carried out at a layer thickness of
Polymers 2020,12, 2250 13 of 18
0.254 mm, 30
◦
orientation angle, 60
◦
raster angle, 0.5064 mm raster width and 0.0079 mm air gap.
It can be observed that a raster angle of 60
◦
results in the maximization of all three parameters of
mechanical strength, i.e., tensile, flexural and impact strength. Thus, it is recommended to use the
default setting of 60
◦
raster angle for the best mechanical stability of FFF parts. In the case of layer
thickness, a lower value results in better impact and tensile strength, while the opposite phenomenon
is predicted for flexural strength. The air gap is also found to be constant for mechanical stability.
In the case of orientation angle, the horizontal layer deposition (0
◦
) strategy is the most successful in
attaining maximum flexural strength, while 9.55
◦
and 30
◦
result in better tensile and impact strength,
respectively, as suggested by NNA.
4. Confirmatory Experiments
The optimum parameters for each output suggested by NNA must be validated before
recommendation; hence, confirmatory experiments were conducted. The ABS samples were prepared
using commercial P400 material (supplied by Stratasys Inc. Ltd., Eden Prairie, Minnesota, USA) and
an open-source FFF printer (supplied by Prusa Research, Prague, Czech Republic). The technical data
sheet [
23
] of thermoplastic materials was referred to when deciding printing parameters. The three
samples were prepared for tensile strength, flexural strength and impact strength using ASTM D638,
ASTM D790 and ASTM D256, respectively. The test samples were prepared at a constant printing speed,
infill method, extrusion temperature, bed temperature and environmental temperature, as shown in
Table 8.
Table 8. Fixed parameters used for confirmatory experiments.
S. No. Fixed Parameter Value
1 Extrusion temperature 230 ◦C
2 Bed temperature 80 ◦C
3 Ambient temperature 25 ◦C
4 Infill type Rectilinear
5 Printing speed 50 mm/s
Fixed values of temperature were used to eliminate error as the significant impact of temperature
on the bonding strength of ABS layers has been noticed. As the semi-molten thermoplastic beads
are laid down, excessive temperature at the nozzle may increase flowability and cause deformation.
On the other hand, faster cooling may lead to shrinkage, which would exhibit dimensional variation.
Thus, the optimum values of temperature were selected as the thermoplastic polymer layers must
be cooled slowly to avoid deformation and dimensional variability [
19
]. The printing and testing of
samples was performed under controlled environmental conditions and using three replications of
each experiment to avoid random errors (Figure 5).
The variable parameters used for fabrication and experimentation are shown in Table 9. The values
of each parameter are taken from predictions made by NNA for tensile strength, flexural strength
and impact strength. It can be observed that there is minimal variation between the predicted
and experimental value of each output. The maximum variation of 2.92% occurs in sample no. 3,
which undergoes impact testing, and the minimum variation (1.3%) occurs in sample no. 2 during
flexural testing. The average variation of three experiments is 1.94%, which is much less compared to
previous studies. Hence, the NNA predicted results are validated with high accuracy, meaning it is
suitable for solving optimization issues in manufacturing processes.
The NNA results achieved in the present study are compared with the percentage error
(experimental vs. predicted) of previous studies in Figure 6. The response parameter and prediction
tool used by each author is also indicated in the graph. It can be observed that the minimum variation
between experimental and predicted results is achieved in the present study as compared to previous
studies that implemented advanced optimization algorithms. The maximum variation was found for
Polymers 2020,12, 2250 14 of 18
finite element analysis (FEA) [
2
], while the average error was found using artificial neural networks
(ANN) [30] and response surface methodology (RSM) [31].
Polymers 2020, 12, x FOR PEER REVIEW 14 of 19
(a) (b)
Figure 5. (a) FFF printer used for experimentation (b) Universal Testing Machine used for mechanical
testing.
The variable parameters used for fabrication and experimentation are shown in Table 9. The
values of each parameter are taken from predictions made by NNA for tensile strength, flexural
strength and impact strength. It can be observed that there is minimal variation between the
predicted and experimental value of each output. The maximum variation of 2.92% occurs in sample
no. 3, which undergoes impact testing, and the minimum variation (1.3%) occurs in sample no. 2
during flexural testing. The average variation of three experiments is 1.94%, which is much less
compared to previous studies. Hence, the NNA predicted results are validated with high accuracy,
meaning it is suitable for solving optimization issues in manufacturing processes.
Table 9. Variable parameters and results.
Sample
No.
Laye
r
Thickness
(mm)
Orientation
Angle
(°)
Raste
r
Angle
(°)
Raste
r
Width
(mm)
Ai
r
Gap
(mm)
Predicted
Value
Experimental
Value
Error
(%)
1 0.127 9.55 60 0.4064 0.008 17.49 17.23 1.61
2 0.127 0 60 0.4064 0.008 16.26 16.05 1.3
3 0.254 30 60 0.5064 0.0079 2.46 2.39 2.92
The NNA results achieved in the present study are compared with the percentage error
(experimental vs. predicted) of previous studies in Figure 6. The response parameter and prediction
tool used by each author is also indicated in the graph. It can be observed that the minimum variation
between experimental and predicted results is achieved in the present study as compared to previous
studies that implemented advanced optimization algorithms. The maximum variation was found for
finite element analysis (FEA) [2], while the average error was found using artificial neural networks
(ANN) [30] and response surface methodology (RSM) [31].
The comparative analysis indicates the higher efficacy of NNA as compared to other
optimization algorithms and prediction tools. The predicted parameters can be recommended for
commercial production of functional prototypes and end-use components manufactured using FFF.
Moreover, the NNA must be implemented to solve surface roughness and dimensional variability
issues of FFF technology when used for complex designs.
Figure 5.
(
a
) FFF printer used for experimentation (
b
) Universal Testing Machine used for
mechanical testing.
Table 9. Variable parameters and results.
Sample
No.
Layer
Thickness (mm)
Orientation
Angle (◦)
Raster
Angle (◦)
Raster
Width (mm)
Air Gap
(mm)
Predicted
Value
Experimental
Value
Error
(%)
1 0.127 9.55 60 0.4064 0.008 17.49 17.23 1.61
2 0.127 0 60 0.4064 0.008 16.26 16.05 1.3
3 0.254 30 60 0.5064 0.0079 2.46 2.39 2.92
Polymers 2020, 12, x FOR PEER REVIEW 15 of 19
Figure 6. Comparison of percentage error of NNA results with previous studies.
5. Conclusions
Despite an efficient additive manufacturing technique, mechanical strength is one of the major
obstructions against the applicability of FFF polymer products for end-use components. Thus, the
selection of optimum parameter settings is required to obtain the best mechanical properties of ABS
parts. The optimization was conducted employing NBA, GWO, DA, SSA, SCA and NNA algorithms
for the maximization of mechanical strength (TS, FS and IS) of parts with varying population size
and number of iterations. From the statistical and convergence results, it was found that the NNA
algorithm was highly competitive with respect to NBA, GWO, DA, SSA and SCA algorithms and was
able to achieve optimum results for FFF products. The endorsed input parameters indicated the
manifestation of enhanced mechanical strength among the test parts. In the future, researchers can
also implement a hybrid metaheuristic algorithm for the enhancement of quality and accuracy along
with a reduction in convergence time.
Author Contributions: Conceptualization, J.S.C., N.M., R.K., S.S. (Sandeep Singh), S.S. (Shubham Sharma), J.S.,
K.V.R., M.M., D.Y.P.; methodology, J.S.C., N.M., R.K., S.S. (Sandeep Singh), S.S. (Shubham Sharma) and M.M.;
investigation, J.S.C., N.M., R.K., S.S. (Sandeep Singh), S.S. (Shubham Sharma); resources, J.S.C., N.M., R.K., S.S.
(Sandeep Singh), S.S. (Shubham Sharma), J.S., K.V.R., M.M., D.Y.P. and S.P.D; writing—original draft
preparation, J.S.C., N.M., R.K., S.S. (Sandeep Singh), S.S. (Shubham Sharma) and M.M.; writing—review and
editing, J.S.C., N.M., R.K., S.S. (Sandeep Singh), S.S. (Shubham Sharma); supervision, J.S.C., N.M., R.K., S.S.
(Sandeep Singh), S.S. (Shubham Sharma) and M.M.; project administration, J.S.C., N.M., R.K., S.S. (Sandeep
Singh), S.S. (Shubham Sharma), J.S., K.V.R., M.M., D.Y.P. and S.P.D. All authors have read and agreed to the
published version of the manuscript.
Acknowledgments: The authors wish to acknowledge the resources of IK Gujral Punjab Technical University,
Main Campus, Kapurthala and Chandigarh University, Mohali for carrying out the research work.
Funding: This research received no external funding.
Conflicts of Interest: The authors declare no conflict of interest.
Appendix A
Table A1. The performance of simulated algorithms for TS estimation over 30 independent runs for
100 iterations and population size 40.
Algorithm Worst Best Average Median Std. Dev.
Figure 6. Comparison of percentage error of NNA results with previous studies.
Polymers 2020,12, 2250 15 of 18
The comparative analysis indicates the higher efficacy of NNA as compared to other optimization
algorithms and prediction tools. The predicted parameters can be recommended for commercial
production of functional prototypes and end-use components manufactured using FFF. Moreover,
the NNA must be implemented to solve surface roughness and dimensional variability issues of FFF
technology when used for complex designs.
5. Conclusions
Despite an efficient additive manufacturing technique, mechanical strength is one of the major
obstructions against the applicability of FFF polymer products for end-use components. Thus,
the selection of optimum parameter settings is required to obtain the best mechanical properties of ABS
parts. The optimization was conducted employing NBA, GWO, DA, SSA, SCA and NNA algorithms
for the maximization of mechanical strength (TS, FS and IS) of parts with varying population size
and number of iterations. From the statistical and convergence results, it was found that the NNA
algorithm was highly competitive with respect to NBA, GWO, DA, SSA and SCA algorithms and
was able to achieve optimum results for FFF products. The endorsed input parameters indicated the
manifestation of enhanced mechanical strength among the test parts. In the future, researchers can
also implement a hybrid metaheuristic algorithm for the enhancement of quality and accuracy along
with a reduction in convergence time.
Author Contributions:
Conceptualization, J.S.C., N.M., R.K., S.S. (Sandeep Singh), S.S. (Shubham Sharma),
J.S., K.V.R., M.M., D.Y.P.; methodology, J.S.C., N.M., R.K., S.S. (Sandeep Singh), S.S. (Shubham Sharma) and
M.M.; investigation, J.S.C., N.M., R.K., S.S. (Sandeep Singh), S.S. (Shubham Sharma); resources, J.S.C., N.M.,
R.K., S.S. (Sandeep Singh), S.S. (Shubham Sharma), J.S., K.V.R., M.M., D.Y.P. and S.P.D.; writing—original draft
preparation, J.S.C., N.M., R.K., S.S. (Sandeep Singh), S.S. (Shubham Sharma) and M.M.; writing—review and
editing, J.S.C., N.M., R.K., S.S. (Sandeep Singh), S.S. (Shubham Sharma); supervision, J.S.C., N.M., R.K., S.S.
(Sandeep Singh), S.S. (Shubham Sharma) and M.M.; project administration, J.S.C., N.M., R.K., S.S. (Sandeep Singh),
S.S. (Shubham Sharma), J.S., K.V.R., M.M., D.Y.P. and S.P.D. All authors have read and agreed to the published
version of the manuscript.
Funding: This research received no external funding.
Acknowledgments:
The authors wish to acknowledge the resources of IK Gujral Punjab Technical University,
Main Campus, Kapurthala and Chandigarh University, Mohali for carrying out the research work.
Conflicts of Interest: The authors declare no conflict of interest.
Appendix A
Table A1.
The performance of simulated algorithms for TS estimation over 30 independent runs for
100 iterations and population size 40.
Algorithm Worst Best Average Median Std. Dev.
NBA 174.6234301 174.9214992 174.9011405 174.921458 7.52 ×10−2
GWO 174.623429 174.9214992 174.8620095 174.9214386 1.05 ×10−1
DA 174.6234301 174.9214992 174.8394289 174.9201719 1.18 ×10−1
SSA 174.6324965 174.9214992 174.8028863 174.8169921 9.99 ×10−2
SCA 174.4505185 174.9200412 174.6821489 174.6282199 1.24 ×10−1
NNA 174.8553077 174.9214939 174.9100097 174.9200154 1.98 ×10−2
Polymers 2020,12, 2250 16 of 18
Table A2.
The performance of simulated algorithms for FS estimation over 30 independent runs for
100 iterations and population size 40.
Algorithm Worst Best Average Median Std. Dev.
NBA 162.1491001 162.6744472 162.5693778 162.6744472 2.14 ×10−1
GWO 162.674447 162.6744472 162.6744472 162.6744472 3.38 ×10−8
DA 162.6627456 162.6744472 162.6740571 162.6744472 2.14 ×10−3
SSA 162.6744472 162.6744472 162.6744472 162.6744472 5.78 ×10−14
SCA 162.6744472 162.6744472 162.6744472 162.6744472 5.78 ×10−14
NNA 162.6744472 162.6744472 162.6744472 162.6744472 5.78 ×10−14
Table A3.
The performance of simulated algorithms for IS estimation over 30 independent runs for
100 iterations and population size 40.
Algorithm Worst Best Average Median Std. Dev.
NBA 1.605823622 1.605823622 1.605823622 1.605823622 2.26 ×10−16
GWO 1.605823622 1.605823622 1.605823622 1.605823622 2.26 ×10−16
DA 1.605823622 1.605823622 1.605823622 1.605823622 2.26 ×10−16
SSA 1.605823622 1.605823622 1.605823622 1.605823622 2.26 ×10−16
SCA 1.605823622 1.605823622 1.605823622 1.605823622 2.26 ×10−16
NNA 1.605823622 1.605823622 1.605823622 1.605823622 2.26 ×10−16
Table A4.
The performance of simulated algorithms for TS estimation over 30 independent runs for
100 iterations and population size 20.
Algorithm Worst Best Average Median Std. Dev.
NBA 174.6234263 174.9214936 174.8372247 174.9196852 1.27 ×10−1
GWO 174.6242344 174.921498 174.8359942 174.9200114 1.11 ×10−1
DA 171.631808 174.9214992 174.1513635 174.6316391 1.04
SSA 174.5267321 174.9214992 174.7720952 174.7517588 1.25 ×10−1
SCA 174.1631947 174.921241 174.5762605 174.5885636 2.10 ×10−1
NNA 174.6348368 174.9214885 174.8893958 174.9163291 6.93 ×10−2
Table A5.
The performance of simulated algorithms for FS estimation over 30 independent runs for
100 iterations and population size 20.
Algorithm Worst Best Average Median Std. Dev.
NBA 162.1491001 162.6744472 162.6044009 162.6744472 1.82 ×10−1
GWO 162.6734733 162.6744472 162.6743693 162.6744472 2.15 ×10−4
DA 162.4635226 162.6744472 162.6453716 162.6744472 4.66 ×10−2
SSA 162.6744472 162.6744472 162.6744472 162.6744472 5.78 ×10−14
SCA 162.1491001 162.6744472 162.6569356 162.6744472 9.59 ×10−2
NNA 162.6744472 162.6744472 162.6744472 162.6744472 5.78 ×10−14
Table A6.
The performance of simulated algorithms for IS estimation over 30 independent runs for
100 iterations and population size 20.
Algorithm Worst Best Average Median Std. Dev.
NBA 1.605823622 1.605823622 1.605823622 1.605823622 2.26 ×10−16
GWO 1.605823622 1.605823622 1.605823622 1.605823622 2.26 ×10−16
DA 1.605823622 1.605823622 1.605823622 1.605823622 2.26 ×10−16
SSA 1.605823622 1.605823622 1.605823622 1.605823622 2.26 ×10−16
SCA 1.605823622 1.605823622 1.605823622 1.605823622 2.26 ×10−16
NNA 1.605823622 1.605823622 1.605823622 1.605823622 2.26 ×10−16
Polymers 2020,12, 2250 17 of 18
References
1.
Rao, R.; Rai, D. Optimization of fused deposition modeling process using teaching-learning-based
optimization algorithm. Eng. Sci. Technol. Int. J. 2016,19, 587–603. [CrossRef]
2.
Hambali, R.; Smith, P.; Rennie, A. Determination of the effect of part orientation to the strength value on
additive manufacturing FFF for end-use parts by physical testing and validation via three-dimensional finite
element analysis. Int. J. Mat. Eng. Innov. 2012,3, 269–281. [CrossRef]
3.
Kim, G.; Oh, Y. A benchmark study on rapid prototyping processes and machines: Quantitative comparisons
of mechanical properties, accuracy, roughness, speed, and material cost. Proc. Inst. Mech. Eng. B J. Eng.
Manuf. 2008,222, 201–215. [CrossRef]
4.
Pandey, P.; Thrimurthulu, K.; Reddy, N. Optimal part deposition orientation in FFF by using a multicriteria
genetic algorithm. Int. J. Prod. Res. 2004,42, 4069–4089. [CrossRef]
5.
Rayegani, F.; Onwubolu, G. Fused deposition modelling (FFF) process parameter prediction and optimization
using group method for data handling (GMDH) and differential evolution (DE). Int. J. Adv. Manuf. Technol.
2014,73, 509–519. [CrossRef]
6.
Rane, R.; Kulkarni, A.; Prajapati, H.; Taylor, R.; Jain, A.; Chen, V. Post-process effects of isothermal annealing
and initially applied static uniaxial loading on the ultimate tensile strength of fused filament fabrication
parts. Materials 2020,13, 352. [CrossRef]
7.
Ahn, S.; Montero, M.; Odell, D.; Roundy, S.; Wright, P. Anisotropic material properties of fused deposition
modeling ABS. Rapid. Prototyp. J. 2002,8, 248–257. [CrossRef]
8.
Srinivasan, R.; Babu, B.; Annamalai, P.; Sivasankaran, S.; Tharaan, M. An experimental on the influence of
process parameters on the tensile properties of carbon fiber reinforced PLA FFF parts. TEST Eng. Manag.
2019,81, 4606–4611.
9.
Rao, V.; Geethika, V.; Krishnaveni, P. Multi-objective optimization of mechanical properties of aluminium
7075-based hybrid metal matrix composite using genetic algorithm. In Advances in 3D Printing and Additive
Manufacturing Technologies, 1st ed.; Kumar, L., Ed.; Springer: Singapore, 2017.
10.
Natarajan, E.; Kaviarasan, V.; Lim, W.; Tiang, S.; Parasuraman, S.; Elango, S. Non-dominated sorting modified
teaching–learning-based optimization for multi-objective machining of polytetrafluoroethylene (PTFE).
J. Intell. Manuf. 2020,31, 911–935. [CrossRef]
11.
Raju, M.; Gupta, M.; Bhanot, N.; Sharma, V. A hybrid PSO–BFO evolutionary algorithm for optimization of
fused deposition modelling process parameters. J. Intell. Manuf. 2019,30, 2743–2758. [CrossRef]
12.
Garc
í
a-Dom
í
nguez, A.; Claver, J.; Camacho, A.M.; Sebasti
á
n, M.A. Considerations on the applicability of
test methods for mechanical characterization of materials manufactured by FDM. Materials
2020
,13, 28.
[CrossRef] [PubMed]
13.
Yao, T.; Ye, J.; Deng, Z.; Zhang, K.; Ma, Y.; Ouyang, H. Tensile failure strength and separation angle of FDM
3D printing PLA material: Experimental and theoretical analyses. Compos. Part B Eng.
2020
,188, 107894.
[CrossRef]
14.
Wickramasinghe, S.; Do, T.; Tran, P. FDM-based 3D printing of polymer and associated composite: A review
on mechanical properties, defects and treatments. Polymers 2020,12, 1529. [CrossRef] [PubMed]
15.
Zhang, W.; Wu, A.S.; Sun, J.; Quan, Z.; Gu, B.; Sun, B.; Cotton, C.; Heider, D.; Chou, T.-W. Characterization
of residual stress and deformation in additively manufactured ABS polymer and composite specimens.
Comp. Sci. Technol. 2017,150, 102–110. [CrossRef]
16.
Rankouhi, B.; Javadpour, S.; Delfanian, F.; Letcher, T. Failure analysis and mechanical characterization of 3D
printed ABS with respect to layer thickness and orientation. J. Fail. Anal. Prev.
2016
,16, 467–481. [CrossRef]
17.
G
ó
rski, F.; Kuczko, W.; Wichniarek, R. Impact strength of ABS parts manufactured using Fused Deposition
Modeling technology. Arch. Mech. Technol. Autom. 2014,31, 3–12.
18.
Christiyan, K.J.; Chandrasekhar, U.; Venkateswarlu, K. A study on the influence of process parameters on the
Mechanical Properties of 3D printed ABS composite. IOP Conf. Mater. Sci. Eng. 2016,114, 1–8. [CrossRef]
19.
Rodr
í
guez-Panes, A.; Claver, J.; Camacho, A.M. The influence of manufacturing parameters on the mechanical
behaviour of PLA and ABS pieces manufactured by FDM: A comparative analysis. Materials
2018
,11, 1333.
[CrossRef]
20.
Shubham, P.; Sikidar, A.; Chand, T. The influence of layer thickness on mechanical properties of the 3D
printed ABS polymer by fused deposition modeling. Key Eng. Mater. 2016,706, 636–637. [CrossRef]
Polymers 2020,12, 2250 18 of 18
21.
Vidakis, N.; Petousis, M.; Vairis, A.; Savvakis, K.; Maniadi, A. A parametric determination of bending and
Charpy’s impact strength of ABS and ABS-plus fused deposition modeling specimens. Prog. Add. Manuf.
2019,4, 323–330. [CrossRef]
22.
Sadollah, A.; Sayyaadi, H.; Yadav, A. A dynamic metaheuristic optimization model inspired by biological
nervous systems: Neural network algorithm. Appl. Soft Comput. 2018,71, 747–782. [CrossRef]
23.
Available online: http://groups.csail.mit.edu/drl/wiki/images/3/3b/MSDS_P400ABSModel_1062730A.pdf
(accessed on 27 January 2020).
24.
Panda, S.; Padhee, S.; Anoop, S.; Mahapatra, S. Optimization of fused deposition modelling (FFF) process
parameters using bacterial foraging technique. Intell. Inf. Manag. 2009,1, 89.
25.
Meng, X.; Gao, X.; Liu, Y.; Zhang, H. A novel bat algorithm with habitat selection and Doppler effect in
echoes for optimization. Exp. Syst. Appl. 2015,42, 6350–6364. [CrossRef]
26. Mirjalili, S.; Mirjalili, S.; Lewis, A. Grey wolf optimizer. Adv. Eng. Soft 2014,69, 46–61. [CrossRef]
27.
Mirjalili, S. Dragonfly algorithm: A new meta-heuristic optimization technique for solving single-objective,
discrete, and multi-objective problems. Neural Comput. Appl. 2015,27, 1053–1073. [CrossRef]
28.
Mirjalili, S.; Gandom, A.; Mirjalili, S.; Saremi, S.; Faris, H.; Mirjalili, S. Salp Swarm Algorithm: A bio-inspired
optimizer for engineering design problems. Adv. Eng. Soft 2017,114, 163–191. [CrossRef]
29.
Mirjalili, S. SCA: A Sine cosine algorithm for solving optimization problems. Know Base Syst.
2016
,96, 120–133.
[CrossRef]
30.
Boschetto, A.; Giordano, V.; Veniali, F. Surface roughness prediction in fused deposition modelling by neural
networks. Int. J. Adv. Manuf. Technol. 2013,67, 2727–2742. [CrossRef]
31.
Samykano, M.; Selvamani, S.K.; Kadirgama, K.; Ngui, W.K.; Kanagaraj, G.; Sudhakar, K. Mechanical property
of FDM printed ABS: Influence of printing parameters. Int. J. Adv. Manuf. Technol.
2019
,102, 2779–2796.
[CrossRef]
©
2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons Attribution
(CC BY) license (http://creativecommons.org/licenses/by/4.0/).
