

Ci a ion: Rajend an, S.; N., G.; ˇ
Cep,
R.; R. C., N.; Pal, S.; Kali a, K. A
Concep ual Compa ison o Six
Na u e-Inspi ed Me aheu is ic
Algo i hms in P ocess Op imiza ion.
P ocesses 2022,10, 197. h ps://
doi.o g/10.3390/p 10020197
Academic Edi o : Blaž Likoza
Recei ed: 23 Decembe 2021
Accep ed: 13 Janua y 2022
Published: 20 Janua y 2022
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p ocesses
A icle
A Concep ual Compa ison o Six Na u e-Inspi ed Me aheu is ic
Algo i hms in P ocess Op imiza ion
Shanka Rajend an 1, Ganesh N. 2,* , Robe ˇ
Cep 3, Na ayanan R. C. 4, Subham Pal 5
and Kanak Kali a 6,*
1Depa men o Compu e Science and Enginee ing, Kone u Lakshmaiah Educa ion Founda ion,
Gun u 522 502, India; shanka ajend an75@kluni e si y.in
2Depa men o Compu e Science and Enginee ing, Vel Tech Mul i Tech D . Ranga ajan D . Sakun hala
Enginee ing College, Chennai 600 062, India
3Depa men o Machining, Assembly and Enginee ing Me ology, Facul y o Mechanical Enginee ing,
VSB-Technical Uni e si y o Os a a, 17. Lis opadu 2172/15, 708 00 Os a a, Czech Republic;
[email p o ec ed]
4Depa men o Compu e Science and Enginee ing, Sona College o Technology, Salem 636 005, India;
[email p o ec ed]
5Depa men o Ae ospace Enginee ing and Applied Mechanics, Indian Ins i u e o Enginee ing Science and
Technology, How ah 711 103, India; [email p o ec ed]
6Depa men o Mechanical Enginee ing, Vel Tech Ranga ajan D . Sagun hala R&D Ins i u e o Science and
Technology, A adi 600 062, India
*Co espondence: [email p o ec ed] (G.N.); [email p o ec ed] (K.K.)
Abs ac :
In ecen yea s, se e al high-pe o mance na u e-inspi ed me aheu is ic algo i hms ha e
been p oposed. I is impo an o s udy and compa e he con e gence, compu a ional bu den and
s a is ical signi icance o hese me aheu is ics o aid u u e de elopmen s. This s udy ocuses on six
ecen me aheu is ics, namely, an lion op imiza ion (ALO), a i hme ic op imiza ion algo i hm (AOA),
d agon ly algo i hm (DA), g ey wol op imize (GWO), salp swa m algo i hm (SSA) and whale
op imiza ion algo i hm (WOA). Op imiza ion o an indus ial machining applica ion is ackled in his
pape . The op imal machining pa ame e s (peak cu en , du y ac o , wi e ension and wa e p essu e)
o WEDM a e p edic ed using he six a o emen ioned me aheu is ics. The objec i e unc ions o he
op imiza ion s udy a e o maximize he ma e ial emo al a e (MRR) and minimize he wea a io
(WR) and su ace oughness (SR). All o he cu en algo i hms ha e been seen o su pass exis ing
esul s, he eby indica ing hei supe io i y o e con en ional op imiza ion algo i hms.
Keywo ds:
op imiza ion; non- adi ional algo i hms; p ocess op imiza ion; p ocess pa ame e s;
algo i hms
1. In oduc ion
Nowadays, non- adi ional machining p ocesses a e mos ly used in elec onic and
ae ospace indus ies, whe e machining wi h high accu acy is equi ed. Non- adi ional
machining p ocesses a e de ined as p ocesses ha emo e ma e ial by a ious echniques
like mechanical, he mal, elec ical, chemical ene gy o combina ions o hese ene gies.
Unlike adi ional machining p ocesses, non- adi ional machining p ocesses do no equi e
any sha p cu ing ools. Gene ally, ma e ials ha a e di icul o machine using con en ional
machining p ocesses a e machined using non- adi ional machining p ocesses. Elec ical
discha ge machining (EDM) is one o he mos widely used non- adi ional machining
p ocesses. In EDM, he ma e ial is emo ed by he he moelec ic p ocess. A se ies o
disc e e elec ical spa ks be ween he wo kpiece and he elec ode is gene a ed o e ode
he undesi ed ma e ials om he wo kpiece. The Wi e Elec ical Discha ge Machining
(WEDM) p ocess is widely used o pa e n ool s eel o die making. WEDM is mos ly used
o make dies and punches in he ae ospace and au omo i e indus ies [
1
]. In his p ocess,
P ocesses 2022,10, 197. h ps://doi.o g/10.3390/p 10020197 h ps://www.mdpi.com/jou nal/p ocesses
P ocesses 2022,10, 197 2 o 20
a slowly mo ing wi e a els along a p e-de ined pa h and emo es ma e ial om he
wo kpiece. Wi es in WEDM a e mos ly made wi h b ass, coppe , ungs en o molybdenum.
Some imes zinc- o b ass-coa ed wi es a e also used. The wi e in WEDM should ha e
high ensile s eng h and good elec ical conduc i i y. The su ace oughness (SR) and
ma e ial emo al a e (MRR) o he machined su ace by WEDM depends on di e en
machining pa ame e s, such as peak cu en (A), du y ac o , wi e ension (N), and wa e
p essu e (MPa). Thus, op imizing such p ocess pa ame e s is e y impo an o maximize
o minimize he esponse pa ame e s and educe machining ime.
In he las ew decades, many esea che s ha e p oposed se e al op imiza ion ech-
niques, such as gene ic algo i hm (GA) [
2
], pa icle swa m op imiza ion (PSO) [
3
], an
colony op imiza ion (ACO), a i icial bee colony (ABC) [
4
], cuckoo sea ch op imiza ion
(CO), g ey wol op imize (GWO) [
5
], a i hme ic op imiza ion algo i hm (AOA) [
6
], salp
swa m algo i hm (SSA) [
7
], an lion op imiza ion (ALO) [
8
], whale op imiza ion algo-
i hm (WOA) [
9
], mul i- e se op imiza ion (MVO), ba algo i hm [
10
], d agon ly algo i hm
(DA) [
11
]. These op imiza ion echniques a e called non- adi ional op imiza ion echniques
o me aheu is ic echniques. These op imize s ha e been used in many ields, like he
p oduc ion, p ojec scheduling, managemen ield, manu ac u ing ield and design ield.
Hewidy e al. [
12
] used an RSM-based me amodel o he WEDM p ocess o op imize
he p ocess pa ame e s. The objec i e o hei wo k was o ind he maximum MRR and
minimize SR and wea a io (WR). The expe imen was conduc ed on Inconel 601. Zhang
e al. [
13
] pe o med op imiza ion o p ocess pa ame e s o machining SKD11. They
used a back-p opaga ion neu al ne wo k in link wi h a gene ic algo i hm (BPNN-GA)
o maximize MRR and minimize SR. Shihab [
14
] examined he op imal condi ions o
machining pa ame e s using a Box-Behnken design (BBD). Chaudha y e al. [
15
] op imized
WEDM p ocess pa ame e s o machining o ASSAB’88 ool s eel wi h RSM. The main
objec i e was o calcula e he op imal condi ion o p ocess pa ame e s o maximize MRR
and minimize SR. Mahapa a and Pa naik [
16
] examined op imum p ocess pa ame e s o
WEDM using he Taguchi me hod. They conside ed discha ge cu en , pulse du a ion,
pulse equency, wi e-speed, wi e ension and dielec ic low a e as p ocess pa ame e s
and MRR,SR and cu ing wid h (ke ) esponse pa ame e s. Nayak and Mahapa a [
17
]
pe o med op imiza ion o machining pa ame e s o WEDM p ocess pa ame e s o a deep
c yo- ea ed Inconel 718 ma e ial. Mukhe jee e al. [
18
] pe o med a compa a i e s udy
o six di e en non-con en ional op imiza ion echniques (i.e., gene ic algo i hm (GA),
pa icle swa m op imiza ion (PSO), sheep lock algo i hm (SF), an colony op imiza ion
(ACO), a i icial bee colony (ABC) and biogeog aphy-based op imiza ion (BBO)). The
objec i e o hei s udy was o maximize he MRR and minimize he SR and WR alues o
he WEDM p ocess.
A li e a u e su ey e ealed ha many esea che s ha e used a ied echniques o
op imize he p ocess pa ame e s o machining p ocesses. Howe e , mos esea che s ha e
been limi ed o desi abili y analyses h ough RSM and he use o adi ional me aheu is ics
like GA and PSO. Fu he mo e, among he me aheu is ic echniques, no compa a i e s udy
has been ca ied ou in compa ison o ecen ly-p oposed op imiza ion echniques. The e
is e y li le li e a u e a ailable whe e ecen na u e-inspi ed op imiza ion echniques a e
used o op imize he p ocess pa ame e s o machining p ocesses. Thus, in his pape , a
compa ison o six newly p oposed me aheu is ic echniques, namely, an lion op imiza ion
(ALO), a i hme ic op imiza ion algo i hm (AOA), d agon ly algo i hm (DA), g ey wol
op imize (GWO), salp swa m algo i hm (SSA) and whale op imiza ion algo i hm (WOA),
is made, and he esul s a e compa ed wi h p e iously published esul s. The es o
he a icle is p esen ed as ollows: in he second sec ion, he heo e ical backg ound o
he six me aheu is ic algo i hms wi h hei pseudo code a e shown; in he hi d sec ion,
he p oblem desc ip ion is shown; in he ou h sec ion, he esul s and discussions a e
discussed, and a las , he conclusions a e made.
P ocesses 2022,10, 197 3 o 20
2. Na u e-Inspi ed Me aheu is ics
2.1. An Lion Op imiza ion
An lion op imiza ion (ALO) is a newly p oposed na u e-inspi ed op imiza ion ech-
nique p oposed by Mi jalili [
19
]. The an lion algo i hm is inspi ed by he hun ing mech-
anism o an lions in na u e [
8
]. The li e cycle o he an lion in ol es wo s ages: one is
he la ae s age wi h he an lion hun ing p ey (an s), while he o he s age is he adul
s age wi h he ep oduc ion o he an lion [
20
]. In na u e, an an lion digs a ap wi h a
cone shape. The size o he ap de ines he hunge le el o an an lion. A big cone ap
ep esen s an an lion ha is hung ie han one wi h a small cone ap. Gene ally, a big
hole is dug by an eli e an lion, which has a be e p obabili y o ca ching p ey. The an
lion hides a he bo om o he ap wai ing o an an , which mo es andomly a ound he
ap o all. Once he an lion ealizes ha he e is an an in he ap, i ca ches i . Once an
insec is caugh , he an lions pull i unde he cone ap and h ow he sand owa ds he
ou e edges o he hole, using i s big jaw so ha he p ey canno escape. Then, he an lion
consumes he p ey and digs ano he hole o he nex hun [
21
]. The i ness o an lions
and he quali y o he aps imp o e in e e y hun . Conside ing his hun ing mechanism,
he ALO algo i hm ollows he main p ocesses. Such as andom walks o an s, apping in
an an lion’s hole, es ablishing a ap, sliding an s owa ds an an lion, ca ching p ey and
econs uc ing he hole, and eli ism [22].
Random walks o an s:
X(k)=[0, cs(2 (k1)−1),cs(2 (k2)−1), . . . . . . ·,cs(2 (km)−1)] (1)
whe e
cs
is he cumula i e sum,
m
is he maximum numbe o i e a ions,
k
is he s op o
andom walk (i e a ion), (k)is a s ochas ic unc ion and is gi en by:
(k)=1i α>0.5
0i α≤0.5 ,C∈[0, 1](2)
whe e αis he andom numbe gene a ed wi h uni o m dis ibu ion.
To make he andom mo emen inside he sea ch space. The ollowing equa ion is
used [23]:
Xk
=Xk
−a dk
−ck

(b −a )+c (3)
whe e
a
and
b
indica e he minimum and maximum o he andom mo emen o he
h
a iables, espec i ely;
ck
and
dk
a e he minimum and maximum o he
h
a iable a k
h
i e a ion, espec i ely.
T apping in an an lion’s hole:
The ollowing equa ion is used o ma hema ically model he andom walks o an s
a ec ed by he an lion’s aps.
ck
=An lionk
+ckdk
=An lionk
+dk(4)
whe e
ck
and
dk
a e he minimum and maximum o all a iables a he k
h
i e a ion,
ck
and
dk
a e he minimum and maximum o all a iables o he
h
an and
An lionk
ep esen s
he posi ion o he selec ed h an lion and k h i e a ion.
Es ablishing ap:
The la ges ap belongs o he i es an lions. Thus, ca ching an an by an an lion
is p opo ional o he i ness o ha an lion (i.e., he an lion wi h he highe i ness has a
highe chance o ca ch an an ) and he i es an lion is selec ed by applying he oule e
wheel selec ion.
Sliding an s owa ds an an lion:
P ocesses 2022,10, 197 4 o 20
To model he sliding an s owa ds an lions, he scope o he andom mo emen should
be dec eased adap i ely.
ck=ck
Idk=dk
I(5)
whe e Iis a a io ha con ols he explo a ion/exploi a ion a e in he ALO algo i hm by
limi ing he andom walk ange o he an s and p ey. The pa ame e
I
in he abo e equa ion
is equal o 10
wk
K
,
k
indica es he cu en i e a ion,
K
is he i e a ion max and
w
ep esen s a
cons an and is ela ed o he accu acy o he explo a ion. The w alues a e p esen ed as:
w=










2i k >0.1K
3i k >0.5K
4i k >0.75K
5i k >0.9K
6i k >0.95K











(6)
Ca ching p ey and econs uc ing he hole:
I an an eaches he bo om o he pi , i will be caugh and consumed by he an lions.
A e his, he an lions wai o ca ch new p ey by upda ing hei posi ion. The ollowing
equa ion can exp ess he abo e-men ioned p ocess.
An lionk
j=An k
ii An k
i> An lionk
j(7)
whe e k ep esen s he cu en i e a ion,
An lionk
j
and
An k
i
ep esen he posi ion o he j
h
an lion and he i h an a he k h i e a ion.
Eli ism:
As a key ai o e olu iona y algo i hms, eli ism is u ilized o s o e he bes solu ions
du ing he op imiza ion p ocess. In his algo i hm, he bes an lion ob ained is ega ded as
an eli e, which should ha e an impac on he all he an s in e e y s age. Thus, a ec ed by
he oule e wheel and he eli e a he same ime, e e y an mo es owa ds a selec ed an
lion, which can be exp essed as ollows:
An k
i=Rk
A+Rk
E
2(8)
whe e
RA
and
RE
indica e he andom mo es owa ds he an lion selec ed by he oule e
wheel and he eli e, espec i ely. The en i e e olu iona y p ocess o an lion op imiza ion is
gi en in Algo i hm 1.
Algo i hm 1 Pseudocode o An Lion Op imiza ion
Inpu s:Popula ion size (N), max (Max. i e a ion numbe )
Ini ialize he i s popula ion o Nan and an lions andomly
Calcula e he i ness o an and an lion
Find he bes an lions and assume i is he eli e.
while ( < max)
o e e y an (i = 1, 2, 3 . . . . . . , N)
Find an an lion using Roule e wheel
Upda e c and d using Equa ion (5)
C ea e a andom walk using Equa ion (1) and no malized walk by Equa ion (3)
Upda e he posi ion o an by Equa ion (8)
end
Calcula e i ness alues o all upda ed an s
Replace an lion by an i (an ) > (an lion)
Replace he eli e wi h he i es solu ion
= +1
end
Re u n he eli e solu ion as bes solu ion
P ocesses 2022,10, 197 5 o 20
2.2. A i hme ic Op imiza ion Algo i hm
A i hme ic op imiza ion algo i hm (AOA) is a popula ion-based me a-heu is ic capa-
ble o sol ing op imiza ion p oblems wi hou calcula ing hei de i a i es [
6
]. The AOA
algo i hm ollows basic a i hme ic ope a o s in ma h (i.e., mul iplica ion (
×
), di ision (
÷
),
sub ac ion (
−
), and addi ion (+)). Me aheu is ic op imiza ion echniques ha e wo main
pa s, explo a ion and exploi a ion. In he explo a ion p ocess, he sea ch agen s sea ch o
he op imal alues a ound he sea ch space so ha he solu ion does no ge apped in local
op ima. In he exploi a ion phase, he op imize akes ad an age o explo a ion and inds
global op imal alues among he local op imal alues. In his AOA op imiza ion echnique,
he explo a ion and exploi a ion p ocess is achie ed by hose a i hme ic ope a ions.
In AOA, he op imiza ion ope a ion begins wi h andomly gene a ed solu ions known
as candida e solu ions (
×
), as shown in Equa ion (9). The bes candida e solu ion in each
i e a ion is known as an op imal o nea -op imal solu ion.
X=










x1,1 · · · · · · x1,jx1,n−1x1,n
x2,1 · · · · · · x2,j· · · x2,n
· · · · · · · · · · · · · · · · · ·
.
.
..
.
..
.
..
.
..
.
..
.
.
xN−1,1 · · · · · · xN−1,j· · · xN−1,n
xN,1 · · · · · · xN,jxN,n−1xN,n










(9)
Be o e i ge s s a ed, i selec s he sea ch phase (i.e., explo a ion and exploi a ion) by
calcula ing a coe icien , ma h op imize accele a ed (MOA) unc ion using Equa ion (10).
MOA( )=Min + ×Max – Min
max (10)
whe e,
MOA( )
is he unc ion alue a
he
h
i e a ion, is he cu en i e a ion,
max
is
he maximum i e a ion, and Max and Min a e he maximum and minimum alues o he
accele a ed unc ion, espec i ely.
Explo a ion phase:
The sea ch a ea is explo ed andomly in se e al egions o ind a be e solu ion in
he explo a ion phase. Two main sea ch s a egies, such as he di ision (D) sea ch s a egy
and he mul iplica ion (M) sea ch s a egy, as gi en in Equa ion (10). I he andom numbe
( 1) is g ea e han he ma h op imize accele a ed (MOA) unc ion ( 1 > MOA), hen his
explo a ion phase will ake place. The i s ope a o (D) o Equa ion (11) is applicable
when 2 < 0.5; a ha ime, he second ope a o (M) is neglec ed. The mul iplica ion sea ch
s a egy is done a e he complica ion o he di ision sea ch s a egy [6].
xi,j( +1)
=bes xj÷(MOP +e)×UBj−LBj×µ+LBj, 2<0.5
bes xj×MOP ×UBj−LBj×µ+LBj, o he wise
(11)
whe e
xi,j( +1)
deno es he j
h
posi ion o he i
h
solu ion a he nex i e a ion and bes
(xj) is he j
h
posi ion in he bes -ob ained solu ion so a ,
e
is a small in ege numbe , UBj
and LBj deno e he uppe limi and lowe limi alue o he j
h
posi ion, espec i ely.
µ
is a
con ol pa ame e used o adjus he sea ch p ocess. A µo 0.5 is aken in his algo i hm.
MOP(k)=1− 1/α
max 1/α(12)
whe e he ma h op imize p obabili y (MOP) is a p obabili y alue in he ange be ween
0 and 1. I is calcula ed using Equa ion (12). MOP(k) deno es he p obabili y alue a he
k
h
i e a ion, ep esen s he cu en i e a ion and (
max
) deno es he maximum numbe o

P ocesses 2022,10, 197 6 o 20
i e a ions.
α
is a sensi i i y pa ame e and is esponsible o exploi ing accu acy o e he
i e a ions. An α alue o 5 is aken in he p esen algo i hm.
Exploi a ion phase:
The exploi a ion phase akes place when he andomly gene a ed numbe ( 1) is less
han he ma h op imize accele a ed (MOA) unc ion ( 1 > MOA). In he exploi a ion o AOA
op imiza ion, he be e solu ion sea ch is based on wo main s a egies: he sub ac ion (S)
sea ch s a egy and he addi ion (A) sea ch s a egy. The sub ac ion (S) sea ch s a egy
and addi ion (A) sea ch s a egy a e modelled as ollows:
xi,j( +1)=bes xj−MOP ×UBj−LBj×µ+LBj, 3<0.5
bes xj+MOP ×UBj−LBj×µ+LBj, o he wise (13)
The sub ac ion (S) sea ch s a egy akes place when 3 < 0.5 a ha ime, he o he
ope a o (A) is neglec ed. The p ocedu es in his phase a e simila o explo a ion, bu
ope a o S and A is used ins ead o ope a o D and M.
The pseudocode o he AOA algo i hm is gi en below in Algo i hm 2.
Algo i hm 2 Pseudocode o A i hme ic Op imiza ion Algo i hm
Inpu s: Popula ion size (N), max (Max. i e a ion numbe )
Ini ialize he a i hme ic op imiza ion pa ame e s α,µ.
Ini ialize he solu ions posi ions andomly.
while( < max)
E alua e he i ness alue o he gi en solu ion
Xbes = Selec he bes solu ion ob ained so a .
Upda e he MOA using Equa ion (10)
Upda e he MOP using Equa ion (12)
o i =1 o Solu ions
o j =1 o Posi ions
Gene a e a andom alue be ween [0,1] o 1, 2, 3.
i 1> MOA
Explo a ion phase
i 2> 0.5
Apply he di ision ma h ope a o (D)
Upda e he i h solu ion posi ion using he i s equa ion o Equa ion (11)
else
Apply he mul iplica ion ma h ope a o (M)
Upda e he i h solu ion posi ion using he second equa ion o Equa ion (11)
end
else
Exploi a ion phase
i 3> 0.5
Apply he sub ac ion ma h ope a o (S)
Upda e he i h solu ion posi ion using he i s equa ion o Equa ion (13)
Else
Apply he addi ion ma h ope a o (A)
Upda e he i h solu ion posi ion using he second equa ion o Equa ion (13)
End
end
end
end
= +1
end
Re u n he op imal solu ions
P ocesses 2022,10, 197 7 o 20
2.3. D agon ly Algo i hm
The d agon ly algo i hm (DA) was p oposed by Mi jalili [
24
] in 2015. The d agon ly
algo i hm is inspi ed by he swa ming beha iou o d agon lies—hun ing and mig a ion.
The hun ing p ocess is known as a s a ic swa m, and mig a ion is known as a dynamic
swa m. In a s a ic swa m, d agon lies make small g oups and mo e back and o h
o e a small a ea o hun o he lying p ey, such as bu e lies and mosqui oes. Local
mo emen s and ab up changes in he lying pa h a e he main cha ac e is ics o a s a ic
swa m. Howe e , in dynamic swa ms, many d agon lies swa m in one di ec ion o e
long dis ances o mig a ion. These wo swa ming beha iou s a e e y simila o he
explo a ion and exploi a ion echniques in me aheu is ics. The main objec i e o any swa m
is su i al, so all indi iduals should be a ac ed owa ds ood sou ces and dis ac ing
ou wa d enemies. The ma hema ical model o swa ming beha iou is gi en as ollows [
24
].
The sepa a ion is o mula ed as ollows:
Si=−
N
∑
j=1
X−Xj(14)
whe e Xis he posi ion o he cu en indi idual,
Xj
shows he posi ion o he j
h
neigh-
bou ing indi idual and Nis he numbe o neighbou ing indi iduals.
Alignmen is o mula ed as ollows:
Ai=∑N
j=1Vj
N(15)
he e, Vjis he eloci y o he i h neighbou ing indi idual.
The cohesion is o mula ed as ollows:
Ci=∑N
j=1Xj
N−X(16)
A ac ion owa ds a ood sou ce is o mula ed as ollows:
Fi=X+−X(17)
whe e X+is he posi ion o he ood sou ce.
Dis ac ion ou wa ds owa ds an enemy is o mula ed as ollows:
Ei=X−+X(18)
whe e X−is he posi ion o he enemy.
These i e echniques a e combined o ep esen he beha iou o d agon lies ma h-
ema ically. To upda e he posi ion o a i icial d agon lies in a sea ch space and simula e
hei mo emen s, wo ec o s a e conside ed: s ep (
∆X
) and posi ion (
X
). The s ep ec o
shows he di ec ion o he mo emen o he d agon lies. The ma hema ical model o he
s ep ec o is shown as ollows:
∆X +1=(sSi+aAi+cCi+ Fi+eEi)+w∆X (19)
whe e
s
,
a
,
c
,
,
e
and
w
a e he sepa a ion weigh , alignmen weigh , cohesion weigh , ood
ac o , enemy ac o and ine ia weigh , espec i ely.
Si
,
Ai
,
Ci
,
Fi
and
Ei
a e he sepa a ion,
alignmen , cohesion, ood sou ce and posi ion o an enemy o he i h indi idual.
∆X
is he
s ep ec o o he h i e a ion.
The posi ion ec o s a e calcula ed as ollows:
X +1=X +∆X +1(20)
P ocesses 2022,10, 197 8 o 20
whe e
X +1
is he posi ion ec o o he
( +1) h
i e a ion,
∆X +1
is he s ep ec o o he
( +1) h
i e a ion,
X
is he posi ion ec o o he
h
i e a ion. The d agon ly algo i hm is
ealized by using he pseudocode in Algo i hm 3.
Algo i hm 3 Pseudocode o D agon ly Algo i hm
Inpu s: Popula ion size (N), max (Max. i e a ion numbe )
Ini ialize he d agon lies popula ion Xi(i = 1, 2, . . . ., n)
Ini ialize he s ep ec o s ∆Xi(i = 1, 2, . . . ., n)
while ( < max)
E alua e he i ness alue o all d agon lies.
Upda e he ood sou ce and enemy.
Upda e w,s,a,c, and e.
Calcula e S, A, C, F and Eusing Equa ions (14)–(18).
Upda e neighbou ing adius.
i a d agon ly has a leas one neighbou ing d agon ly
Upda e eloci y ec o using Equa ion (19).
Upda e posi ion ec o using Equa ion (20).
else
Upda e posi ion ec o using Equa ion (20).
end
Check and co ec he new posi ions based on he bounda ies o a iables.
= +1
end
2.4. G ey Wol Op imize
Acco ding o Mi jalili e al. [
25
], g ey wol es li e oge he and hun in a g oup.
The e o e, in he GWO algo i hm, he social leade ship and hun ing mechanisms o g ey
wol es a e mimicked. In all popula ion-based op imiza ion echniques, good explo a ion
and exploi a ion capabili ies a e equi ed. The compu a ional ime o any me aheu is ic
depends on how much ime i spends in explo a ion and how as i inds he global op imal
ha is exploi a ion. The e o e, he igh balance o explo a ion and exploi a ion is essen ial
o he as ed con e gence o he global op imal. In he o iginal GWO algo i hm, hal o he
i e a ions a e se o explo a ion, and he o he hal o he i e a ions a e se o exploi a ion.
In GWO, he solu ions a e di ided in o ou g oups, he i es solu ions a e named as alpha
(
α
), he second-bes solu ions a e called be a (
β
) and he hi d-bes solu ions a e quo ed as
del a (
δ
). All emaining solu ions a e e med as omega (
ω
). In he hie a chy o GWO, he
omega wol is con olled by he alpha, be a and del a wol es. The hun ing echnique o
g ey wol es is di ided mainly in o i e pa s [25].
Social hie a chy.
T acking, chasing and app oaching he p ey.
Pu suing, enci cling and ha assing he p ey un il i s ops mo ing.
A acking he p ey (Explo a ion).
Sea ching o p ey (Exploi a ion).
The ma hema ical model o enci cling he p ey is w i en as:
→
D=|→
C·→
Wp( )−→
W( )|(21)
→
W( +1)=→
Wp( )−→
A·→
D(22)
whe e ep esen s he cu en i e a ion,
→
Wp( )
ep esen s he posi ion ec o o p ey a
he
h
i e a ion,
→
W( )
ep esen s he posi ion ec o o a g ey wol a he
h
i e a ion and
P ocesses 2022,10, 197 9 o 20
→
W( +1)
is he upda ed posi ion o he g ey wol .
→
A
and
→
C
a e he coe icien ec o s.
These coe icien ec o s a e exp essed as ollows:
→
A=2→
a·→
1−→
a(23)
→
C=2→
2(24)
whe e
→
1
and
→
2
a e andom ec o s in [0,1]. Values o he
→
a
ec o linea ly dec eased om
2 o 0 wi h he p og ess in i e a ion, and i is gi en as:
→
a( )=2−2
max (25)
whe e is he cu en i e a ion and max ep esen s he maximum i e a ion numbe .
A e he enci cling ope a ion, a g ey wol s a s o hun he p ey (i.e., bes solu ions).
The bes candida es (i.e.,
α
,
β
,
δ
-wol es) ha e be e in o ma ion abou he loca ion o he
p ey. O he candida es (
ω
-wol es) change hei posi ions o he posi ion o he h ee bes
candida es. The hun ing mechanisms o he g ey wol a e ma hema ically ep esen ed as
ollows: →
Dα=|→
C1·→
Wα−→
W|→
Dβ=|→
C2·→
Wβ−→
W|→
Dδ=|→
C3·→
Wδ−→
W|(26)
→
W1=→
Wα−→
A1·(
→
Dα)→
Dβ=|→
C2·→
Wβ−→
W|→
W3=→
Wδ−→
A3·(
→
Dδ)(27)
→
W( +1)=
→
W1( )+→
W2( )+→
W3( )
3(28)
The g ey wol es end he hun ing by a acking a las when he p ey is no mo ing. To
ep esen his ma hema ically, we dec eased he alue o
→
a
. The luc ua ion ange o
→
A
is
also dec eased by
→
a
.
→
A
is a andom alue in he in e al [
−
a,a]. When andom alues o
→
A
a e in [−1,1], he nex posi ion o he sea ch agen can be any posi ion be ween i s cu en
posi ion and he posi ion o he p ey. The alues o
|A|<
1 o ced he wol es o a ack he
p ey and
|A|>
1 o ced he g ey wol es o di e ge om he p ey o hope ully ind i e
p ey. A e he hun ing o p ey, he g ey wol es sea ch o he p ey in he nex i e a ion.
This p ocess will con inue un il he e mina ion c i e ion is sa is ied. The pseudocode o
he GWO algo i hm is gi en in Algo i hm 4.
Algo i hm 4 Pseudocode o G ey Wol Op imiza ion
Inpu s:Fi ness unc ion, lowe bound, uppe bounds, numbe o sea ch agen s,
maximum i e a ion.
Ini ialize a andom popula ion o g ey wol es (Wi) (i=1,2,3. . . ., n).
Ini ialize A, C and a; se =0.
Calcula e he i ness alues o all sea ch agen s.
Selec α,β,δ-wol es. (Conside ing i es solu ion as α-wol es, second-bes
solu ion as β–wol es and hi d-bes solu ion as δ-wol es).
while( < max)
o each sea ch agen
Upda e he posi ion o he cu en sea ch agen using Equa ion (28)
end
Upda e A, C and a.
Calcula e he i ness alues o all sea ch agen s.
Upda e he posi ion o α,β,δ-wol es.
= +1
end while( = max)
epo he bes indi idual.
End.
P ocesses 2022,10, 197 16 o 20
Table 2. Compa ison o cu en esul s wi h solu ions om he li e a u e o MRR op imiza ion.
Algo i hm x1x2x3x4Op imum % Imp o emen
Hewidy e al. [12] 6 0.5 7 0.5 6.57 -
ALO 3 0.3288 9 0.418 8.765 33.41%
AOA 3.16 0.4349 8.835 0.477 8.188 24.63%
DA 3 0.3288 9 0.417 8.765 33.41%
GWO 3 0.3288 9 0.417 8.765 33.41%
SSA 3 0.3288 9 0.417 8.765 33.41%
WOA 3 0.3288 9 0.417 8.765 33.41%
Figu e 3shows he con e gence o he algo i hms while op imizing he WR. I was
obse ed ha excep o AOA, all o he algo i hms ha e a simila con e gence end.
Table 3con ains he s a is ical summa y o he 10 independen ials o WR op imiza ion.
Like MRR op imiza ion, in he case o WR, AOA was unable o loca e he bes -known
op ima. All he o he i e algo i hms epo ed he bes -known op ima o be 1.216, an
imp o emen o app oxima ely 25% o e he AOA esul s. As seen om Equa ion (42), he
WR model was linea wi h only wo p ocess pa ame e s. This may be he eason behind
he 100% success a e epo ed by all he o he i e algo i hms excep AOA.
P ocesses 2022, 10, x FOR PEER REVIEW 16 o 20
a lowe numbe o unc ion e alua ions wi h lowe alues, indica ing ha hey had mo e
apid con e gence owa ds he op imal zone.
The op imal p ocess pa ame e s and he MRR, as epo ed by he a ious me aheu-
is ics, a e p esen ed in Table 2. Wi h espec o he Hewidy e al. [12] solu ions, AOA
showed a 24.63% imp o emen . All he o he algo i hms epo ed a 33.41% imp o emen
o e he exis ing solu ions in he li e a u e.
Table 2. Compa ison o cu en esul s wi h solu ions om he li e a u e o MRR op imiza ion.
Algo i hm 𝒙𝟏 𝒙𝟐 𝒙𝟑 𝒙𝟒 Op imum % Imp o emen
Hewidy e al. [12] 6 0.5 7 0.5 6.57 -
ALO 3 0.3288 9 0.418 8.765 33.41%
AOA 3.16 0.4349 8.835 0.477 8.188 24.63%
DA 3 0.3288 9 0.417 8.765 33.41%
GWO 3 0.3288 9 0.417 8.765 33.41%
SSA 3 0.3288 9 0.417 8.765 33.41%
WOA 3 0.3288 9 0.417 8.765 33.41%
Figu e 3 shows he con e gence o he algo i hms while op imizing he WR. I was
obse ed ha excep o AOA, all o he algo i hms ha e a simila con e gence end. Ta-
ble 3 con ains he s a is ical summa y o he 10 independen ials o WR op imiza ion.
Like MRR op imiza ion, in he case o WR, AOA was unable o loca e he bes -known
op ima. All he o he i e algo i hms epo ed he bes -known op ima o be 1.216, an im-
p o emen o app oxima ely 25% o e he AOA esul s. As seen om Equa ion (42), he
WR model was linea wi h only wo p ocess pa ame e s. This may be he eason behind
he 100% success a e epo ed by all he o he i e algo i hms excep AOA.
Figu e 3. Con e gence o op imum WR wi h espec o i e a ions.
Table 3. S a is ical summa y o 10 ials in op imizing WR.
Algo i hm Mean S anda d De ia ion Median Bes Wo s Success Ra e
ALO 1.216 0 1.216 1.216 1.216 100%
AOA 1.433 0.108 1.423 1.268 1.611 0%
DA 1.216 0 1.216 1.216 1.216 100%
GWO 1.216 0 1.216 1.216 1.216 100%
SSA 1.216 0 1.216 1.216 1.216 100%
WOA 1.216 0 1.216 1.216 1.216 100%
Figu e 3. Con e gence o op imum WR wi h espec o i e a ions.
Table 3. S a is ical summa y o 10 ials in op imizing WR.
Algo i hm Mean S anda d De ia ion Median Bes Wo s Success Ra e
ALO 1.216 0 1.216 1.216 1.216 100%
AOA 1.433 0.108 1.423 1.268 1.611 0%
DA 1.216 0 1.216 1.216 1.216 100%
GWO 1.216 0 1.216 1.216 1.216 100%
SSA 1.216 0 1.216 1.216 1.216 100%
WOA 1.216 0 1.216 1.216 1.216 100%
Figu e 4shows he sp ead o he o al unc ion e alua ions du ing a ypical ial
while op imizing WR. The o e all pa e n o he sp ead and dis ibu ion o he unc ion
e alua ions in Figu e 4is e y simila o ha in Figu e 2. This indica es ha he
algo i hms a e una ec ed by whe he he op imiza ion p oblem is a minimiza ion o
maximiza ion ype. GWO was seen o ha e he highes median unc ion e alua ion
alue among he algo i hms. Mo eo e , he mean unc ion e alua ion alue o GWO
was e y close o i s median. This indica es ha a e y high pe cen age o GWO’s

P ocesses 2022,10, 197 17 o 20
e alua ed unc ions we e in he op imal zone. This is gene ally p e e ed as i may be
indica i e o a high con e gence a e.
P ocesses 2022, 10, x FOR PEER REVIEW 17 o 20
Figu e 4 shows he sp ead o he o al unc ion e alua ions du ing a ypical ial while
op imizing WR. The o e all pa e n o he sp ead and dis ibu ion o he unc ion e alua-
ions in Figu e 4 is e y simila o ha in Figu e 2. This indica es ha he algo i hms a e
una ec ed by whe he he op imiza ion p oblem is a minimiza ion o maximiza ion ype.
GWO was seen o ha e he highes median unc ion e alua ion alue among he algo-
i hms. Mo eo e , he mean unc ion e alua ion alue o GWO was e y close o i s me-
dian. This indica es ha a e y high pe cen age o GWO’s e alua ed unc ions we e in he
op imal zone. This is gene ally p e e ed as i may be indica i e o a high con e gence
a e.
Figu e 4. Box plo s deno ing he sp ead o all he unc ion e alua ions du ing WR op imiza ion in a
ypical independen un. The ho izon al blue line (and nume ic alue) and he ed line indica e he
median and mean o all he unc ion e alua ions.
The op imum p ocess pa ame e s o minimizing WR a e p esen ed in Table 4. Wi h
espec o Hewidy e al. [12], he cu en esul s a e 70% be e o AOA and 71.32% be e
o ALO, DA, GWO, SSA and WOA. Simila ly, he op imum p ocess pa ame e s o min-
imizing SR a e p esen ed in Table 5. In his case, he cu en ALO and AOA esul s a e
obse ed o be 47.68% be e han Hewidy e al. [12]. On he o he hand, DA and GWO
esul s we e 47.82% be e , while SSA and WOA we e 48.05% be e han Hewidy e al.
[12]. Howe e , i is impo an o poin ou ha all six algo i hms epo ed a ied in op i-
mized alues o he p ocess pa ame e s. This indica es ha he objec i e unc ion sea ch
space was, pe haps, mul imodal. The e o e, i is wo h men ioning ha Hewidy e al.[12]
used an RSM-based model o calcula e he op imum alues. The op imum alues o e-
sponses ob ained by Hewidy e al.[12] we e MRR = 6.57 mm3/min, WR = 4.24 and SR =
2.20µm. The bes -known op imum alues ob ained in his s udy we e MRR = 8.765
mm3/min, WR = 1.216 and SR = 1.143µm.
Table 4. Compa ison o cu en esul s wi h solu ions om li e a u e o WR op imiza ion.
Algo i hm 𝒙𝟏 𝒙𝟒 Op imum % Imp o emen
Hewidy e al. [12] 7 0.7 4.24 -
ALO 3 0.3 1.216 71.32%
AOA 3 0.321 1.268 70.09%
DA 3 0.3 1.216 71.32%
GWO 3 0.3 1.216 71.32%
SSA 3 0.3 1.216 71.32%
WOA 3 0.3 1.216 71.32%
Figu e 4. Box plo s deno ing he sp ead o all he unc ion e alua ions du ing WR op imiza ion in a
ypical independen un. The ho izon al blue line (and nume ic alue) and he ed line indica e he
median and mean o all he unc ion e alua ions.
The op imum p ocess pa ame e s o minimizing WR a e p esen ed in Table 4. Wi h
espec o Hewidy e al. [
12
], he cu en esul s a e 70% be e o AOA and 71.32%
be e o ALO, DA, GWO, SSA and WOA. Simila ly, he op imum p ocess pa ame e s o
minimizing SR a e p esen ed in Table 5. In his case, he cu en ALO and AOA esul s a e
obse ed o be 47.68% be e han Hewidy e al. [
12
]. On he o he hand, DA and GWO
esul s we e 47.82% be e , while SSA and WOA we e 48.05% be e han Hewidy e al. [
12
].
Howe e , i is impo an o poin ou ha all six algo i hms epo ed a ied in op imized
alues o he p ocess pa ame e s. This indica es ha he objec i e unc ion sea ch space
was, pe haps, mul imodal. The e o e, i is wo h men ioning ha Hewidy e al. [
12
] used
an RSM-based model o calcula e he op imum alues. The op imum alues o esponses
ob ained by Hewidy e al. [
12
] we e MRR = 6.57 mm
3
/min, WR = 4.24 and SR = 2.20
µ
m.
The bes -known op imum alues ob ained in his s udy we e MRR = 8.765 mm
3
/min,
WR = 1.216 and SR = 1.143 µm.
Table 4. Compa ison o cu en esul s wi h solu ions om li e a u e o WR op imiza ion.
Algo i hm x1x4Op imum % Imp o emen
Hewidy e al. [12] 7 0.7 4.24 -
ALO 3 0.3 1.216 71.32%
AOA 3 0.321 1.268 70.09%
DA 3 0.3 1.216 71.32%
GWO 3 0.3 1.216 71.32%
SSA 3 0.3 1.216 71.32%
WOA 3 0.3 1.216 71.32%
Though he same numbe o unc ion e alua ions (i.e., 30
×
100 = 3000) we e
ca ied ou by each algo i hm, some algo i hms we e expec ed o be as e han o he s.
Thus, he CPU ime o each algo i hm was no ed and a e aged o 10 independen
ials o each esponse. F om Figu e 5, i is obse ed ha ALO, DA and WOA we e
he h ee mos expensi e algo i hms, whe eas SSA, GWO and AOA we e he h ee leas
expensi e. Ne e heless, he s anda d de ia ion o compu a ional ime o WOA was
e y high, indica ing ha in some ins ances, i may ake a e y sho compu a ion ime.
P ocesses 2022,10, 197 18 o 20
Pe haps his is because op imizing WR was e y as in op imizing he linea p oblem
wi h only wo a iables.
Table 5. Compa ison o cu en esul s wi h solu ions om he li e a u e o SR op imiza ion.
Algo i hm x1x2x3x4Op imum % Imp o emen
Hewidy e al. [12] 5 0.75 9 0.5 2.2 -
ALO 4 0.623 8.2 0.62 1.151 47.68%
AOA 3.8 0.605 7.2 0.5 1.151 47.68%
DA 3.4 0.623 7.1 0.38 1.148 47.82%
GWO 4.6 0.678 7.3 0.54 1.148 47.82%
SSA 4.2 0.623 8.5 0.68 1.143 48.05%
WOA 5.2 0.568 9 0.6 1.143 48.05%
P ocesses 2022, 10, x FOR PEER REVIEW 18 o 20
Table 5. Compa ison o cu en esul s wi h solu ions om he li e a u e o SR op imiza ion.
Algo i hm 𝒙𝟏 𝒙𝟐 𝒙𝟑 𝒙𝟒 Op imum % Imp o emen
Hewidy e al. [12] 5 0.75 9 0.5 2.2 -
ALO 4 0.623 8.2 0.62 1.151 47.68%
AOA 3.8 0.605 7.2 0.5 1.151 47.68%
DA 3.4 0.623 7.1 0.38 1.148 47.82%
GWO 4.6 0.678 7.3 0.54 1.148 47.82%
SSA 4.2 0.623 8.5 0.68 1.143 48.05%
WOA 5.2 0.568 9 0.6 1.143 48.05%
Though he same numbe o unc ion e alua ions (i.e., 30 × 100 = 3000) we e ca ied
ou by each algo i hm, some algo i hms we e expec ed o be as e han o he s. Thus, he
CPU ime o each algo i hm was no ed and a e aged o 10 independen ials o each
esponse. F om Figu e 5, i is obse ed ha ALO, DA and WOA we e he h ee mos ex-
pensi e algo i hms, whe eas SSA, GWO and AOA we e he h ee leas expensi e. Ne e -
heless, he s anda d de ia ion o compu a ional ime o WOA was e y high, indica ing
ha in some ins ances, i may ake a e y sho compu a ion ime. Pe haps his is because
op imizing WR was e y as in op imizing he linea p oblem wi h only wo a iables.
Figu e 5. A e age ime aken by he algo i hms in he op imiza ion o he esponses. The ba s and
whiske s deno e he mean and s anda d de ia ion o 10 uns (3 esponses X 10 independen uns/ e-
sponse).
All six ecen algo i hms pe o med be e han he exis ing solu ions by Hewidy e
al. [12]. Hewidy e al. [12] used a desi abili y unc ion-based app oach, which is, in gen-
e al, incapable o loca ing he global op ima. The ecen me aheu is ics es ed in his pape
eco ded a leas 25%, 70% and 47% be e solu ions han Hewidy e al. [12] o MRR, WR
and SR esul s. This imp o emen is pe haps due o he ac ha he me aheu is ics ini ia e
a andom popula ion and algo i hmically imp o e i o e gene a ions by con inuously
e ol ing he solu ions. Based on he comp ehensi e e alua ions o he algo i hms on he
h ee machining- ela ed es unc ions, i can be summa ized ha despi e AOA being he
mos ecen algo i hm among he six es ed me aheu is ics, i is no necessa ily he bes in
loca ing he bes -known op ima. I is e iden ha he AOA is apped in he local op ima
egion, and o bo h he minimiza ion ype es unc ions, he solu ion o AOA was 1–2%
poo e han he bes -known op ima. Fo he maximiza ion- ype es unc ion, he bes -
known op ima we e obse ed o be oughly 9% be e han he AOA’s solu ion. Howe e ,
he compu a ional ime equi emen o AOA was qui e low, nea ly on pa wi h SSA and
Figu e 5.
A e age ime aken by he algo i hms in he op imiza ion o he esponses. The ba s
and whiske s deno e he mean and s anda d de ia ion o 10 uns (3 esponses X 10 independen
uns/ esponse).
All six ecen algo i hms pe o med be e han he exis ing solu ions by Hewidy
e al. [
12
]. Hewidy e al. [
12
] used a desi abili y unc ion-based app oach, which is, in
gene al, incapable o loca ing he global op ima. The ecen me aheu is ics es ed in his
pape eco ded a leas 25%, 70% and 47% be e solu ions han Hewidy e al. [
12
] o MRR,
WR and SR esul s. This imp o emen is pe haps due o he ac ha he me aheu is ics
ini ia e a andom popula ion and algo i hmically imp o e i o e gene a ions by con inu-
ously e ol ing he solu ions. Based on he comp ehensi e e alua ions o he algo i hms on
he h ee machining- ela ed es unc ions, i can be summa ized ha despi e AOA being
he mos ecen algo i hm among he six es ed me aheu is ics, i is no necessa ily he
bes in loca ing he bes -known op ima. I is e iden ha he AOA is apped in he local
op ima egion, and o bo h he minimiza ion ype es unc ions, he solu ion o AOA
was 1–2% poo e han he bes -known op ima. Fo he maximiza ion- ype es unc ion,
he bes -known op ima we e obse ed o be oughly 9% be e han he AOA’s solu ion.
Howe e , he compu a ional ime equi emen o AOA was qui e low, nea ly on pa wi h
SSA and GWO. In e ms o con e gence, he SSA was obse ed o be he as es . The
median e alua ed unc ion alue o SSA was seen o be qui e a bi lowe ( o minimiza-
ion p oblems) han i s mean e alua ed unc ion alue, indica ing as e na iga ion o he
op imal solu ion zone.
P ocesses 2022,10, 197 19 o 20
5. Conclusions
Machining p ocess op imiza ion is a necessa y ask o manu ac u ing indus ies and
can lead o signi ican sa ings in ma e ial was age, powe consump ion and ool wea and
can imp o e p oduc i i y and e iciency o he p ocess. Since a ple ho a o no el algo i hms
ha e been p oposed in he ecen pas , wi h each ha ing demons a ed capabili ies in
he li e a u e, i is impo an o comp ehensi ely compa e hem o hei po en ial use
in machining p ocess op imiza ion. In his a icle, six ecen ly p oposed na u e-inspi ed
algo i hms, namely, ALO, AOA, DA, GWO, SSA and WOA, a e comp ehensi ely assessed,
and he ollowing conclusions we e d awn.
•
Based on he abili y o na iga e and ind he op imal solu ion, he es ed algo i hms
may be anked as SSA > WOA > GWO > DA > ALO > AOA. Bo h SSA and WOA
we e able o loca e he bes solu ion o all h ee esponses. Howe e , SSA’s success
a e was 100% as opposed o 83% o WOA.
•
Based on he compu a ional ime, he es ed algo i hms may be anked as
SSA > GWO > AOA > WOA > DA > ALO. Bo h SSA and GWO had e y mini-
mal and simila compu a ional equi emen s. Howe e , SSA had a ma ginally lowe
s anda d de ia ion han GWO. As compa ed o ALO, SSA was obse ed o be abou
25 imes as e .
•
The con e gence o SSA was obse ed o be sligh ly be e han i s coun e pa s. GWO
also showed as con e gence. AOA was p one o be apped in local op ima.
•
As compa ed o he p e ious known bes solu ions, an a e age (on h ee esponses)
imp o emen o 50.8% and 47.47% was obse ed o ALO and AOA, espec i ely.
DA and GWO showed a 50.85% imp o emen , whe eas SSA and WOA eco ded a
50.93% imp o emen .
The limi a ions o his s udy a e ha he e a e se e al ad anced and hyb id a ian s
o he algo i hms, which we e no conside ed in his pape . The s udy is also limi ed o one
class o op imiza ion p oblems. Ne e heless, he cu en op imiza ion p oblems a e o
immense impo ance o indus ies. In he u u e, his s udy can be ex ended o inco po a e
an in-dep h analysis o hyb id me aheu is ics and he use o ad anced quan um and
chao ic enhancemen s o hese algo i hms. Op imiza ion unde unce ain y could also be
an in e es ing a ea o hei applica ion.
Au ho Con ibu ions:
Concep ualiza ion, S.R., G.N., R. ˇ
C., N.R.C. and K.K.; da a cu a ion, S.P.;
o mal analysis, S.P. and K.K.; me hodology, S.R., G.N., R. ˇ
C. and N.R.C.; p ojec adminis a ion,
R. ˇ
C.; esou ces, S.R., G.N., R. ˇ
C. and N.R.C.; so wa e, S.R., G.N. and N.R.C.; supe ision, R. ˇ
C.;
alida ion, S.P. and K.K.; isualiza ion, S.P. and K.K.; w i ing—o iginal d a , S.R., G.N., N.R.C. and
S.P.; w i ing— e iew and edi ing, R. ˇ
C. and K.K. All au ho s ha e ead and ag eed o he published
e sion o he manusc ip .
Funding: This esea ch ecei ed no ex e nal unding.
Ins i u ional Re iew Boa d S a emen : No applicable.
In o med Consen S a emen : No applicable.
Da a A ailabili y S a emen :
The da a p esen ed in his s udy a e a ailable h ough email upon
eques o he co esponding au ho .
Con lic s o In e es : The au ho s decla e no con lic o in e es .
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