Enginee ing Applica ions o A i icial In elligence 116 (2022) 105397
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Enginee ing Applica ions o A i icial In elligence
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A i icial in elligence in single sc ew polyme ex usion: Lea ning om
compu a ional da a
An ónio Gaspa -Cunhaa,∗,F ancisco Monacob,Janusz Siko ac,Alexand e Delbemb
aIns i u e o Polyme s and Composi es, Uni e si y o Minho, Campus o Azu ém, 4800-058 Guima ães, Po ugal
bIns i u e o Ma hema ics and Compu e Science, Uni e si y o São Paulo, 400 T abalhado São-Ca lense A enue, São Ca los, São Paulo 13566-590, B azil
cFacul y o Mechanical Enginee ing, Lublin Uni e si y o Technology, 38 Nadbys zyska S ., 20-618 Lublin, Poland
ARTICLE INFO
Keywo ds:
Polyme ex usion
Single sc ew
A i icial in elligence
Mul i-objec i e op imiza ion
Da a-mining
ABSTRACT
Single sc ew polyme ex usion can be seen as a mul i-objec i e op imiza ion p oblem whe e a se o design
a iables mus be de ined as a unc ion o objec i es and cons ain s ha a e o be sa is ied simul aneously.
The de elopmen o powe ul modelling ou ines based on he use o nume ical me hods allows linking hose
objec i es wi h he decision a iables. In eali y, only a single solu ion can be used in he p oblem unde
conside a ion. Howe e , he compu a ion imes become p ohibi i e when e ec i e op imiza ion algo i hms
dealing wi h mul i-objec i es and decision-making a e o be used, such as hose based on popula ions o
solu ions. I is p oposed he e he use o A i icial In elligence echniques o de e mine he in e ela ion be ween
he design a iables and he objec i es. Fo ha , a da a analysis echnique, named DAMICORE, was used o
de ine hese in e ela ions. Examples, in ol ing he design o a sc ew ex ude , a ba el g oo es sec ion, and
a o a ional ba el segmen , we e in es iga ed using he p oposed AI echniques. The esul s ob ained show a
good co espondence wi h he expec ed he momechanical beha iou o he p ocess. This cons i u es an ini ial
s ep in he applica ion o AI echniques in di e en ields o enginee ing in he way o accomplishing, in he
u u e, op imiza ion based on he use o a ailable da a.
1. In oduc ion
Single sc ew polyme ex usion is one o he mos impo an plas-
ics ans o ma ion echnologies allowing o he p oduc ion o a g ea
a ie y o p oduc s, including pipes, p o iles, ilm, and ib es. The
p ocess goes h ough se e al s ages: plas icizing, shaping, and ancilla y
ope a ions, which depend on he ype o p oduc o be p oduced.
Plas icizing is he mos impo an phase since i allows anspo o he
solid polyme , mel ing and mixing i , and c ea ing he equi ed p essu e
o he mel ed polyme o c oss he die ha ga e he inal shape o he
p oduc . This is a complex p ocess in which he aw ma e ial, in pelle s
o powde o m, is ed in o he ex ude whe e i mel s by he ac ion
o hea conduc ed om he ba el and hea gene a ed by ic ion and
iscous dissipa ion. This in ol es he low o he polyme in di e en
physical s a es, solid, mel , and he coexis ence o bo h. Also, he
ma e ial has e y speci ic p ope ies, such as low he mal conduc ion
and non-New onian beha iou , and he sys em is cha ac e ized by a
complex geome y (Rauwendaal,1986;Agassan e al.,2017).
Polyme enginee ing, like o he ields o enginee ing and science,
is aced equen ly wi h he challenge o imp o e p oduc p ope -
ies while dec easing he cos s and he quan i y o ma e ial needed.
∗Co esponding au ho .
E-mail add esses: [email p o ec ed] (A. Gaspa -Cunha), [email p o ec ed] (F. Monaco), [email p o ec ed] (J. Siko a), [email p o ec ed]
(A. Delbem).
T adi ionally, o pe o m he equi ed op imiza ion, ial-and-e o p o-
cedu es based on expe imen s we e adop ed, in ol ing a long and
expensi e e o . I is e y equen , e en nowadays, he use o Taguchi
me hods o de ine he se o expe imen s o do, as a unc ion o he
decision a iables, and, a e he expe imen al esul s a e ob ained,
some da a analysis and/o eg ession echniques a e applied o a ain a
simple equa ion o a esponse su ace ela ing he decision a iables
wi h he objec i e (usually a single objec i e) (Taguchi,1990;Fei
e al.,2013). The e o e, o ha e a good ep esen a ion o eali y, he
numbe o expe imen s o do inc eases conside ably wi h he numbe o
decision a iables needed and speci ic me hodologies mus be applied
o ake in o accoun mul iple objec i es.
Wi h he de elopmen o nume ical modelling so wa e, expe i-
men a ion was eplaced by compu e calcula ions allowing a as and
less expensi e design/op imiza ion p ocess (Meha and Kama uddin,
2012). Howe e , as wi h mos eal op imiza ion p oblems, plas icizing
ex usion is a ha d p oblem o sol e, in ol ing disc e e and con inu-
ous a iables, con ex and noncon ex sea ch spaces, a huge numbe
o decision a iables and cons ain s, and mul iple objec i es. Also,
he ex ude machine is exposed o he en i onmen , which implies
h ps://doi.o g/10.1016/j.engappai.2022.105397
Recei ed 2 Feb ua y 2022; Recei ed in e ised o m 28 July 2022; Accep ed 26 Augus 2022
A ailable online 22 Sep embe 2022
0952-1976/©2022 The Au ho (s). Published by Else ie L d. This is an open access a icle unde he CC BY-NC-ND license
(h p://c ea i ecommons.o g/licenses/by-nc-nd/4.0/).
A. Gaspa -Cunha, F. Monaco, J. Siko a e al. Enginee ing Applica ions o A i icial In elligence 116 (2022) 105397
Fig. 1. Single sc ew ex usion: sys em geome y, un olled channel, and plas icizing phases.
ha i is subjec o some signi ican unce ain ies, such as he en-
i onmen al empe a u e ha in luences ba el empe a u e and, as
a consequence, he polyme mel ing. This implies ha he solu ion
ob ained mus be obus agains changes in he en i onmen (Gaspa -
Cunha and Co as,2008;Denysiuk e al.,2018). An ex ensi e and e y
ecen e ision o op imiza ion o polyme p ocesses was p esen ed
elsewhe e (Gaspa -Cunha e al.,2022a,b).
Taking in o accoun he mul i-objec i e na u e o his p oblem,
Mul i-Objec i e E olu iona y Algo i hms (MOEAs) o o he popula ion-
based algo i hms, e.g., Mul i-Objec i e An Colony Op imiza ion
(MOACO), Mul i-Objec i e Pa icle Swa m Op imiza ion (MOPSO),
Mul i-Objec i e Simula ed Annealing (MOSA), and Mul i-Objec i e Di -
e en ial E olu ion (MODE), can be applied (Deb,2001;Leguizamón
and Coello,2011;Coello e al.,2004;Ag awal e al.,2008;Suman
and Kuma ,2006;Mezu a-Mon es e al.,2008). Ne e heless, he
pe o mance o an op imiza ion p ocedu e is s ongly dependen on
he modelling capaci y o cap u e he cha ac e is ics o he p ocess
unde s udy. Due o he complexi y o he plas icizing ex usion, he
di e en ial equa ions ha go e n he p ocess can be sol ed analy ically
o nume ically. While in he o me case he esul ing equa ions a e
no able o ake in o accoun all he pa ame e s and can be di icul
o link he di e en s ages o he p ocess due o hose simpli ica ions,
he second case in ol es high compu a ion imes o e alua e a single
solu ion. Also, some complex enginee ing p oblems equi e he use o
mo e han one nume ical modelling so wa e, such as, o example, i
he aim is o analyse he mechanical beha iou o a plas ic pa and,
simul aneously, i is necessa y o analyse he low o he polyme inside
he ools used in i s manu ac u e.
The e o e, he applica ion o AI echniques o deal wi h he e en ual
sca ci y o da a can be o p imal impo ance. Simply, he applica ion o
da a mining echniques can easily gene a e su oga es o me amodels
linking di ec ly he objec i es wi h he decision a iables, which can
be inco po a ed in he e alua ion phase o a Mul i-Objec i e Op i-
miza ion Algo i hm (MOOA) o op imize he p ocess (Pa elski e al.,
2016). Howe e , he na u e o hese complex p oblems equi es some
deg ee o in e ac ion wi h a Decision Make (DM), since i is necessa y
o de ine he ele an decision a iables, cons ain s, and objec i es.
Simul aneously, in a mul i-objec i e en i onmen , he inal solu ion o a
Mul i-Objec i e Op imiza ion P oblem (MOOP) is a se o Pa e o poin s
ha equi es he in e en ion o he DM o selec he single solu ion o
be used in he eal wo ld (Gaspa -Cunha e al.,2022b;Ai okoski e al.,
2009). In his con ex , Machine Lea ning (ML) can play an impo an
ole in educing hese in e ac ions by c ea ing an in elligen sys em ha
can gi e a good answe , o a leas a good app oxima ion, conce ning
he solu ion o he p oblem unde s udy (Jin e al.,2019;Ibañez e al.,
2020).
The main aim o his wo k is o apply a da a mining amewo k
named DAMICORE (Anon,2022) o cap u e he ela ions be ween he
decision a iables and he objec i es ega ding he da a o he ex usion
p ocess aking in o accoun new geome ical de ices de eloped wi hin
he NEWEX p ojec (Sanches e al.,2011a), namely: (i) special sc ews;
(ii) ac i e g oo ed eed sec ions and (iii) o a ional ba el segmen s.
The esul s we e calcula ed using nume ical modelling so wa e. The
decision a iables a e o wo di e en ca ego ies, he ones ha a e
di ec ly in ol ed in he calcula ions o he objec i es and o he s ha
a e no in ol ed in he calcula ions. The e o e, he aim is no o
op imize he p ocess bu only o cap u e hese in e ela ions.
The s udy will be pe o med using ou di e en g oups o da a: a
simple case, whe e only changes in he sc ew geome y and ope a ing
condi ions o he machine we e made; a case whe e he geome y o
g oo es was conside ed sepa a ely; a case whe e he geome y and
ope a ing condi ions o he o a ional ba el segmen a e conside ed;
and, inally, a case whe e all he p e ious da a is mixed oge he o
in e abou he in luence o ope a ing condi ions and sc ew, g oo es
and o a ional ba el segmen geome y.
This pape is o ganized as ollows: in sec ion wo he polyme ex u-
sion p ocess, he modelling so wa e, and he op imiza ion p oblem a e
explained; in sec ion h ee he s a e-o - he-a conce ning da a-d i en
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A. Gaspa -Cunha, F. Monaco, J. Siko a e al. Enginee ing Applica ions o A i icial In elligence 116 (2022) 105397
op imiza ion and DAMICORE a e p esen ed; in sec ion ou he cases
s udied will be p esen ed and he esul s ob ained will be p esen ed
and discussed, and in sec ion i e he conclusions will be s a ed.
2. Polyme ex usion
2.1. P oblem o sol e
In a single sc ew ex ude , an A chimedes ype sc ew o a es inside
a hea ed ba el a a cons an speed (N), as illus a ed in Fig. 1. This
igu e also shows he ans e sal cu s in he di e en s ages o he
p ocess, as indica ed by he black a ows. The solid polyme , in pelle s
o powde o m, is ed in he hoppe and a e mel ing and p essu ized
is o ced o pass h ough he die.
The ma hema ical modelling o plas icizing consis s o sol ing he
di e en ial momen um and ene gy equa ions o each one o he s ages
iden i ied aking in o accoun he bounda y condi ions and a con inu-
ous link be ween he di e en s ages, i.e., he esul s o one s ep a e he
s a ing poin o he subsequen . Fo example, he ollowing simpli ied
momen um and ene gy equa ions mus be sol ed o he mel low
zones o he p ocess (Gaspa -Cunha,2009):
𝜕𝑃
𝜕𝑥 =𝜕
𝜕𝑦 (𝜂𝜕𝑉𝑥
𝜕𝑦 )(1)
𝜕𝑃
𝜕𝑧 =𝜕
𝜕𝑦 (𝜂𝜕𝑉𝑧
𝜕𝑥 )+𝜕
𝜕𝑦 (𝜂𝜕𝑉𝑧
𝜕𝑦 )(2)
𝜌𝑚𝐶𝑚𝑉𝑧(𝑦)𝜕𝑇
𝜕𝑧 =𝑘𝑚(𝜕2𝑇
𝜕𝑥2+𝜕2𝑇
𝜕𝑦2)+𝜂 𝛾2(3)
whe e 𝑇is he mel empe a u e, P is he p essu e, 𝑉xand 𝑉za e he
mel eloci ies in he 𝑥and z di ec ions, espec i ely, 𝜌m,𝐶mand 𝑘ma e
he speci ic mass, speci ic hea and he mal conduc i i y o he mel ,
espec i ely, 𝛾 is he shea a e and 𝜂is he iscosi y. The p essu e
g adien in he 𝑦-di ec ion is nil (Gaspa -Cunha,2009).
Fo ha pu pose, he sc ew channel was un olled (as illus a ed
in Fig. 1) and is conside ed a ec angula channel whe e all he -
momechanical phenomena desc ibed occu and he calcula ions a e
pe o med in small inc emen s along he channel using nume ical
me hods.
The e o e, he pe o mance o he machine depends on he polyme
p ope ies (physical, he mal, and heological), ope a ing condi ions
(sc ew speed and ba el and die empe a u e p o iles), and sc ew
geome y, and can be measu ed by aking in o accoun he pu poses
o he ex ude , namely: ou pu , a e age mel empe a u e, leng h o
he sc ew equi ed o mel ing he polyme , mechanical powe con-
sump ion, mixing deg ee and iscous dissipa ion. Fig. 1 illus a es he
use o a con en ional sc ew, consis ing o h ee zones: (i) eed zone,
cha ac e ized by ha ing a cons an dep h (𝐻i1); (ii) comp ession zone,
whe e he dep h dec eases; and (iii) me e ing zone, wi h a cons an
dep h, bu smalle (𝐻i3). Wi hin his wo k, he aim is o s udy he
in luence o he use o a G oo ed Ba el Sec ion (GBS) in he eed zone
and a Ro a ional Ba el Segmen (RBS) in he me e ing zone, o imp o e
he p essu e gene a ed and he mixing induced, espec i ely.
Imp o ing he p ocess consis s in de ining he alue o he deci-
sion a iables, ope a ing condi ions and sys em geome y, ha op i-
mize he objec i es, i.e., maximiza ion o ou pu and mixing deg ee,
and minimiza ion o mel empe a u e a die exi , mechanical powe
consump ion, and he leng h equi ed o mel ing (Ca ano e al.,
2015).
2.2. Modelling o polyme ex usion
The gene al cha ac e is ics o he p og am used in he calcula ions
a e ela ed o he plas icizing phases, as illus a ed in Fig. 1 (Gaspa -
Cunha,2009):
a) Solids con eying in he hoppe (1D): analy ical equa ions,
whe e he p essu e is de e mined by a mass balance and he
o ce balance esul ing om ic ion be ween he polyme and
hoppe walls (ex e nal ic ion) and be ween polyme and poly-
me (in e nal ic ion) and by g a i y.
b) Solids con eying (1D+): a non-iso he mal low o a solid plug
wi h hea ic ion a all su aces. Ou pu is ob ained by aking
in o accoun he geome y and he eloci y p o ile in he ba el,
p essu e is ob ained by a balance o o ces and momen um and
empe a u e by sol ing he ene gy equa ion in di ec ion y, bu
wi h he calcula ions pe o med o small inc emen s in he
channel (z) di ec ion (1D+).
c) Delay (1D+): solid plug wi h a mel ilm nea he inne ba el
su ace. The solids a e modelled as in he solids con eying zone
and he mel ilm is sol ed by aking in o accoun he ene gy
equa ion in he 𝑦-di ec ion and he compu a ions made o small
inc emen s in he 𝑧-di ec ion.
d) Mel ing I (1D+ and 2D+): using he 5-Zone Lind model (Lind
and Elbi li,1985), whe e he mel pool inc eases i s dimensions
un il o al mel ing. The solid plug and he mel ilms a e mod-
elled as in he delay zone, while in he mel poll he equa ions
o ene gy and momen um a e sol ed simul aneously wi h mass
balances and bounda y condi ions using ini e di e ences in he
2D non-iso he mal low o a Non-New onian luid.
e) Mel con eying (2D+): 2D non-iso he mal low o a
non-New onian luid ob ained h ough he simul aneous es-
olu ion o he ene gy and momen um equa ions, being he
calcula ions pe o med in small inc emen s along 𝑧-di ec ion.
) Flow in he die (2D+): 2D non-iso he mal low o a Non-
New onian luid, equal o he mel con eying zone.
The de ails o he modelling, compu e implemen a ion, and ex-
pe imen al assessmen can be ound in Gaspa -Cunha (2009), excep
in wha conce ns he modelling o he ba el g oo ed sec ion and
o a ional ba el segmen , which is desc ibed nex .
In he las o y yea s, nume ous heo e ical and expe imen al s ud-
ies ha e been pe o med using ex ude s wi h g oo es in he ba el,
om which i can be e i ied ha he e a e wo main me hods o
app oaching he p oblem, he i s conside s ha he coe icien o
ic ion polyme -ba el wi h g oo es can be eplaced by an a e age
ic ion coe icien , he second conside s he exis ence o he low o
g anules h oughou he g oo es (Po en e,1985). The main objec i e
o he g oo es is o inc ease he coe icien o ic ion be ween he solid
polyme g anules and he inne wall o he cylinde , which is known o
inc ease he h oughpu capaci y o he ex ude . The g oo es can be
longi udinal o helical (Fig. 2).
Following he s udy p esen ed in Gaspa -Cunha (2009), in his wo k
he model o Po en e (1985) was adop ed o calcula e he a e age
ic ion coe icien . This me hod conside s ha he inc ease o ic ion
caused by he g oo es can be quan i ied by eplacing he coe icien
o ic ion polyme -cylinde wi h he a e age ic ion coe icien (𝑓e ).
The a e age e ec i e ic ion coe icien esul s om he ac ha when
he solids bed mo es along he sc ew channel, he ba el ic ion a ies
be ween he polyme -ba el ic ion (𝑓b) and he in e nal (polyme –
polyme ) ic ion (𝑓p−p), esul ing in he ollowing equa ion (Po en e,
1985;Gaspa -Cunha e al.,2018):
e =𝑓𝑏+(𝑓𝑝−𝑝−𝑓𝑏)𝐵
𝜋𝐷𝑏{1 − exp [−𝛼(ℎ𝑁
𝐵𝑁𝑁)𝛽]} (4)
whe e 𝛼and 𝛽a e empi ical cons an s, which o he condi ions used
should ha e he alues o and 0.9, espec i ely, 𝐷bis he in e nal ba el
diame e , 𝑁Nis he numbe o g oo es, and B is he o al wi h o
g oo es, gi en by:
B=b𝑁N𝑁(5)
Finally, he o a ional ba el segmen is loca ed in he me e ing
zone o he ex ude , i.e., when he polyme is comple ely mel ed. I
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A. Gaspa -Cunha, F. Monaco, J. Siko a e al. Enginee ing Applica ions o A i icial In elligence 116 (2022) 105397
Fig. 2. Longi udinal and helical g oo es in he ba el (𝑏𝑁is he g oo es wid h and ℎ𝑁is he heigh o he g oo es).
Fig. 3. De ini ion o he ela i e ba el eloci y (V’b).
can o a e in he same o opposi e di ec ion as he sc ew and is in
con ac wi h he mel ed polyme . This is an inno a i e de ice ha
was desc ibed by Siko a and Sasimowski (Siko a and Sasimowski,
2006b,a;Siko a and Siko a,1998;Sasimowski,2008;Sasimowski e al.,
2014) and modelled by Gaspa -Cunha (2019). The aim is o con ol
he he mal, heological, kinema ic, and dynamic condi ions in he
plas icizing sys em, and, as a consequence, o imp o e he quali y o
he p oduc s because enhancing he abo e p ocesses will esul in he
homogeniza ion o he he mal and mechanical p ope ies o ma e ials
and he s uc u e o he p oduc s, wi hou he need o use addi ional,
expensi e de ices such as he gea pump and s a ic mixe .
Fig. 3 shows he h ee di e en si ua ions ha can occu when an
RBS is implemen ed in an ex ude : (a) he eloci y o he RBS (𝑁b) is
nil; (b) he eloci y o he RBS has he same di ec ion as ha o he
sc ew (𝑁s) and (c) he eloci y o he RBS has a di e en di ec ion
han ha o he sc ew. In he i s case, he ela i e ba el eloci y
(𝑉b) esul s by ans o ming he o a ional sc ew speed (𝑁s) in a
linea eloci y nea he in e io ba el eloci y (see Re . (Gaspa -Cunha,
2009)), his is: 𝑉b=𝜋 𝑁sD (whe e D is he ex e nal sc ew diame e ).
In he second case, he esul ing (𝑉′b) eloci y is educed, while in
he hi d he esul ing eloci y inc eases. All hese h ee si ua ions a e
implemen ed in he global plas icizing compu e p og am.
3. Da a-d i en op imiza ion
3.1. S a e-o - he-a
Sol ing eal-wo ld op imiza ion p oblems equi es some in e ac ion
wi h he DM, usually he expe s in he ield. This is mo e pe inen
when dealing wi h a MOOP. Thus, he aim is, based on da a analysis,
o educe hese in e ac ions, c ea ing an in elligen sys em able o gi e
a good answe o he p oblem, o , a leas , a good app oxima ion
o he (single) inal solu ion. This is he ole o (unsupe ised and
semi-supe ised) machine lea ning, o being able o build a model
wi h a low quan i y o da a. Also, he e is a pa icula ype o ap-
plica ion ha occu s when he e is no di ec link be ween decision
a iables and objec i es, i.e., he absence o calcula ions, e.g., o link
he ope a ing condi ions o he machine (decision a iables) wi h i s
pe o mance (objec i es). This enables he use o AI echniques as a
p ocedu e o imp o ing p edic ion by linking op imiza ion p ocedu es
and acili a ing decision-making (Chines a e al.,2020).
The applica ion o da a-d i en algo i hms can be seen (a leas ) in
wo ways: (i) use o su oga es o me amodels ha eplace he o iginal
me hod o calcula ing he objec i es, making use o da a analysis
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A. Gaspa -Cunha, F. Monaco, J. Siko a e al. Enginee ing Applica ions o A i icial In elligence 116 (2022) 105397
p e iously made o de e mine he pa ame e s o he model chosen, such
as polynomial eg ession (Zhou e al.,2005), k iging (Chugh e al.,
2018), A i icial Neu al Ne wo ks (ANNs) (Jin and Sendho ,2004),
adial basis unc ion ne wo ks (Regis,2014), swa m op imiza ion (Sun
e al.,2017); and (ii) use o da a o help he compu e sys em in
deciding on he bes solu ion o use in he speci ic p oblem (Dimiduk
e al.,2018), i.e., au oma ic op imiza ion, in he h eshold o AI.
A da a-d i en op imiza ion s uc u e is based on ou main com-
ponen s: (i) da a gene a ion, expe imen al and/o compu a ional; (ii)
da a p e-p ocessing, such as so ing he da a by one o he objec i es o
educe he amoun o da a necessa y; (iii) machine lea ning o es ima e
he su oga e model; and (i ) an op imiza ion algo i hm, making use o
he su oga e model o ind he solu ion. The aim is o ex ac models
om he ela ion be ween inpu s and ou pu s o p edic he ou pu
om new inpu s using nume ical me hods able o ake in o accoun he
physical models p esen in he sys em. This is an al e na i e modelling
app oach o op imiza ion.
This cons i u es a da a-science ield called Enginee ing AI, which
in ol es mul idimensional da a isualiza ion, da a classi ica ion, mod-
elling h ough su oga e models, ex ac ing knowledge om da a, and
c ea ing da a-d i en applica ion sys ems (Ibañez e al.,2020).
The quali y and ype o da a play an impo an ole in he en i e
p ocess. Fi s , machine lea ning can be based on di ec o indi ec da a.
In he i s case, he da a is ob ained di ec ly om he p oblem, by
expe imen s, o by compu a ion. In his case, he su oga e is ob ained
by aining he da a o i in he model (Jin,2011;Chugh e al.,
2019). Indi ec da a is he occasional da a, and ha is no possible o
p edic he ype o da a ha can be gene a ed, e.g., he en i onmen al
empe a u e ha in luences he ex usion p ocess du ing he mel ing
phase.
Also, he da a can be collec ed online o o line. Da a collec ed o -
line means ha no new da a can be gene a ed du ing he op imiza ion.
Thus, he quali y o he su oga e model depends on he quali y and
quan i y o da a, namely in wha conce ns da a p e-p ocessing, da a
mining, and syn he ic da a gene a ion, since i is di icul o alida e
he model be o e he solu ion is ound o be applied in p ac ice. When
he da a is collec ed online means ha as he da a is collec ed he model
adap s o he esul s o he p ac ical p oblem (Jin,2011;Jin e al.,
2002;Hüsken e al.,2005).
Finally, du ing he op imiza ion p ocess, a he beginning he da a
is gene a ed andomly in he sea ch space (in he case o E olu iona y
Algo i hms (EAs), o example), in oducing some deg ee o unce ain y
in he model. As a consequence, he op imal solu ion can be a om he
ini ial solu ions p oposed by he algo i hm and he model can gene a e
w ong p edic ions when he solu ions app oach he op imum. Howe e ,
i some da a is ob ained as he op imiza ion e ol es, he su oga e will
be able o p o ide a be e app oxima ion a ound he op imum (Jin
e al.,2002). This co esponds o a balance be ween exploi a ion, in
he case o he ini ial da a, and explo a ion, in he case o da a ob ained
nea he op imum. Anyway, k iging models can p o ide con iden le el
in o ma ion, while ensemble machine lea ning can p o ide unce ain
in o ma ion. Bo h a e impo an o he op imiza ion p ocess.
Di e en AI-based me amodels, i.e., modelling me hods o ma-
chine lea ning echniques, we e desc ibed in he li e a u e, including
linea and nonlinea eg ession, Suppo Vec o Machines (SVM) (C is-
ianini and Taylo ,2000), Inc emen al dynamic model decomposi-
ion (Schmid,2010;Williams e al.,2015), ANNs (Good ellow e al.,
2016), decision ees, and Code2Vec (A ge ich e al.,2019). Howe e ,
a limi a ion o machine lea ning is he possibili y o he sys em be-
ing in luenced by o he a iables no conside ed when he model is
ob ained.
Kohonen ne wo ks, o example, a e ANNs ha can lea n how o
a ange da a in an unsupe ised way (Kohonen,2001;Sei e and Jain,
2002), i.e., i equi es no labelled samples. I places neu ons om a
bi-dimensional g id (neighbou neu ons communica e) o ind he bes
co e age o a se o n-dimensional ec o s (samples) by he neu ons.
The assignmen be ween neu ons and samples na u ally esul s in
da a clus e ing. The p ocess o choosing he neu on’s displacemen s
is sel -o ganized and he esul ing clus e ing is called a sel -o ganized
map. Cellula NN is ano he ype o bi-dimensional g id (wi h local
communica ion among neu ons) ha can lea n om a se o unlabelled
samples in a way ha a s imulus (inpu ) makes he ou pu s o he
neu ons oscilla e un il inding an equilib ium poin (ou pu ). Bo h o
hose g id-based NN, as well as o he unsupe ised echniques, equi e
inpu s in a s uc u e o n-dimensional ec o s o ea u es. They bo h
apply ein o cemen lea ning whose success usually equi es da a ha
possesses some locali y o a oid many spu ious eedbacks (which may
become c i ical when modelling a sys em subjec o exogenous ac o s
— a iables). Al hough he mapping o samples o ea u e ec o s
is a common p ac ice, i may cons ain he applicabili y o A i icial
In elligence in some ields since i may equi e expe s on he p oblem
domain, which is no easily a ailable on he on ie s o knowledge.
Kohonen and Cellula NN da e om he 1980s and hei applicabili y
o se e al a eas has been well mapped since hen. Ano he pe spec i e
eme ged in he i s decade o he cen u y ha enabled he es ima ion
o dis ances by comp ession algo i hms (called NCD), which means ha
no ea u e ec o o p io knowledge om da a is equi ed. I opened
new oppo uni ies o c ea e ways o ace he challenges o some eal-
wo ld p oblems. The in es iga ions o i s po en ial o unsupe ised
and semi-supe ised lea ning as well as op imiza ion s a ed in he las
decade. DAMICORE (p oposed in 2011) is a amewo k based on NCD
aiming a acili a ing in es iga ions and de elopmen s o solu ions in
challenging scena ios, such as hose whe e a small amoun o aw da a
is a ailable and he co esponding sys em is unshielded om exogenous
e ec s.
Mos o he eal op imiza ion p oblems a e cha ac e ized by a
high numbe o decision a iables, and high sea ch space, bu also by
high dimensionali y in he Pa e o su ace. In his way, da a mining
can be use ul in clus e ing he Pa e o on in such a way o enable
he de e mina ion o he decision a iables ha in luence a pa icula
clus e , i.e., each clus e has i s meaning – o he p oblem. The use
o a single op imiza ion me hodology does no allow o he comple e
cha ac e iza ion o he egion o op imali y by (da a mining) design
ules (Deb and S ini asan,2007;Deb e al.,2014).
In he scena io o mining complex da a (as hose in ol ing high
dimensional sea ch and objec i e spaces), DAMICORE can ind use ul
in o ma ion since i enables lea ning om aw da a in a comple e da a
agnos ic way (i equi es no p io s). In o he wo ds, he mapping om
decision space o objec i e space can be in es iga ed independen ly
om he dimensionali y o hem o he p oblem p ope ies. Sec ion 3.2
in oduces he a ionale o such a s a egy based on DAMICORE and
FS-OPA (Kha a e al.,2020;Soa es e al.,2017), a i s DAMICORE-
based me hod wi h p ac ical esul s o ea u e sensi i i y analysis o
objec i es o low-le el (o one) expe knowledge.
3.2. Fea u e sensi i i y analysis
A Fea u e Sensi i i y (FS) analysis aims a inding a se wi h he
p incipal ea u es o a p oblem, aking in o accoun a eal-wo ld con ex
(e.g., he da abase quali y and i s ele ance o a pu pose), i s ea u e
in e ac ions, and hei con ibu ion o a a ge o objec i e. Such a
scope di e s om hose ha he s anda d ea u e selec ion algo i hms
ha e succeeded in. This is, an FS s a egy is expec ed o bene i he
lea ning o a p oblem om sc a ch. Such lea ning can induce a model
o op imiza ion algo i hms (such as in Es ima ion o Dis ibu ion Al-
go i hms — EDAs). We use phylog am-based models since hey a e
adequa e o wo k wi h small da ase s and he e is an op imiza ion
app oach adequa e o use such models: he Op imiza ion based on
Phylog am Analysis (OPA).
Fig. 4 shows a diag am syn hesizing OPA wi hin he use o he FS
analysis by i ; ha combina ion is called FS-OPA. The wo p incipal FS
s eps in ol ed a e: (i) ‘‘Salien ing Samples (SS) acco ding o a c i e ion’’
5

A. Gaspa -Cunha, F. Monaco, J. Siko a e al. Enginee ing Applica ions o A i icial In elligence 116 (2022) 105397
Fig. 4. Diag am o he Op imiza ion-based on Phylog am Analysis — OPA.
Fig. 5. SS p ocedu e ha ob ains he selec ed samples as shown in Fig. 4.
and (ii) applying DAMICORE o cons uc a phylog am-based model.
SS anks he samples acco ding o each o he Mc i e ia (o non-
domina ed on s), p oducing he se s o selec ed samples (Fig. 5),
deno ed BC1 ( he Bes ound samples acco ding o C i e ion 1), BC2,
..., BCM. DAMICORE (Sec ion 3.3) cons uc s a phylog am (a model)
o each BCi,i = 1, ..., M, gene a ing Mmodels (BC1-based model,
..., BCM-based model). Then, a consensus s a egy p oduces a uni ied
phylog am-based model. Finally, OPA can gene a e new samples om
such a model.
This pape ins an ia es he p ocedu es om S eps iand ii o mod-
elling he polyme ex usion (Sec ion 3.4). The lea ned model is ex-
pec ed o bene i , la e , he op imiza ion p oblem associa ed wi h poly-
me ex usion. Howe e , he sampling om he uni ied model ( he las
OPA s ep) is no pe o med, hus, no a comple e op imiza ion cycle is
un.
Soa es e al. (2017) and Ma ins e al. (2014) show some expe i-
men al esul s and p oo s ela ed o OPA’s pe o mance o challenging
combina o ial and mul i-objec i e op imiza ion p oblems. The main
mechanisms o FS-OPA ha a e ele an o he scope o a da a-
d i en design o an ex ude concen a e on he DAMICORE me hod,
in oduced in Sec ion 3.3.
3.3. Main concep s in DAMICORE
DAMICORE, (DA a MIning o Code REposi o ies), i s in oduced by
Sanches e al. (2011b), builds on concep s bo ed om Theo y, Complex
Ne wo ks, and Phylogene ic In e ence, and is aimed a e ealing hie -
a chical ela ionships be ween uns uc u ed da a objec s. I s wo king
p inciples a e implemen ed h ough h ee s eps: (𝑆1) gi en a me ic o
simila i y, build a dis ance ma ix compa ing e e y wo objec s; (𝑆2)
con e he ma ix in o a phylogene ic ee by connec ing close objec s
acco ding o hie a chical le els o simila i y; (𝑆3) apply a communi y
de ec ion p ocess o g oup close sub ees in o clus e s.
In Fig. 6 he elemen s 𝑑𝑖𝑗 o he dis ance ma ix co espond o a
measu e o dissimila i ies be ween elemen s 𝑥𝑖and 𝑥𝑗,acco ding o
some gi en me ic. The ma ix is hen b oken down in o a ee whe e
he dis ance be ween any wo i ems (lea nodes) co esponds o he
sum o he leng hs o he b anches connec ing hose wo i ems. Finally,
he hi d s ep iden i ies g oups o i ems ha a e signi ican ly connec ed
in o dis inguishable simila i y clus e s.
The o iginal DAMICORE me hod selec s h ee speci ic algo i hms o
his pu pose, as shown in Fig. 7.
As o he simila i y measu e, he No malized Comp ession Dis-
ance, NCD, is a compu able app oxima ion o he Kolmogo o dis ance
be ween wo objec s (Li and Vi ányi,2019;Lui e al.,2015), which
explo es he ac ha , o simila objec s, i should be ela i ely easy o
desc ibe one in e ms o he o he . Fo mally, NCD is de ined as
𝐷𝑧(𝑎𝑏) = 𝐶𝑧(𝑎𝑏) − 𝑚𝑖𝑛 {𝐶𝑧(𝑎), 𝐶𝑧(𝑏)}
𝑚𝑎𝑥 {𝐶𝑧(𝑎), 𝐶𝑧(𝑏)}(6)
whe e aand ba e he wo da a objec s o be compa ed, ab is he
conca ena ion o bo h objec s, and 𝐶𝑧(x) is he size o he comp essed
e sion o objec x, as ob ained by applying a comp ession algo i hm
z. The a ionale o NCD lies in he obse a ion ha he conca ena ion
o wo e y simila objec s is mo e e icien han i he wo iles we e
e y dissimila . Eq. (6) implies ha o an ideal comp esso and wo
iden ical iles, 𝐶𝑧(ab) =C𝑧(a) =𝐶𝑧(b), hus yielding 𝐷𝑧(a,b) = 0;
whe eas o wo iles wi h no simila i ies a all, 𝐶𝑧(ab) = C𝑧(a)+C𝑧(b),
yielding 𝐷𝑧(a,b) = 1. Fo non-ideal comp esso s, NCD anges om 0
o 1. As o comp esso Z, con en ional da a comp ession algo i hms
implemen ed by s anda d so wa e u ili ies such as he popula ZIP
(PKZIP: h ps://www.pkwa e.com/pkzip; WinZip: h p://www.winzip.
6
A. Gaspa -Cunha, F. Monaco, J. Siko a e al. Enginee ing Applica ions o A i icial In elligence 116 (2022) 105397
Fig. 6. Th ee s eps o he DAMICORE me hod.
Fig. 7. DAMICORE algo i hm oolchain.
com/win/bp) and he RAR (h p://www. a lab.com) ile a chi e s may
be employed.
The second s ep o he oolchain elies on he Neighbou Joining
(NJ) algo i hm, widely employed in bioin o ma ics. F om he dis ance
ma ix, NJ de i es a ee wi h he minimum numbe o modi ica ions
needed o explain he di e ences among Taxon (a axonomic uni y in
a classi ica ion sys em) — while non-op imal, he algo i hm p o ides
a compu a ionally easible al e na i e o o he non-polynomial op imal
me hods. Basically, i wo ks by joining, a each s ep, he wo closes
sub ees no al eady joined (Fig. 8), and making hem descenden o a
new ances o node; he newly c ea ed ances o node eplaces he joined
ees in he ma ix, and so on ecu si ely as a as he las join.
The inal s ep o DAMICORE is he de ec ion o communi ies in
he phylogene ic g aph, i.e., g oups o nodes dis inguishably mo e
connec ed among each o he han wi h o he nodes in he g aph.
Fo mal a communi y s uc u e may be iden i ied h ough he concep
o modula i y (Newman,2006), which is a measu e o how much he
densi y o edges in subg aphs is highe han wha would be expec ed i
all nodes we e connec ed a andom. I is compu ed by compa ing he
numbe o inne edges in a p ospec i e communi y o he numbe o
edges ha would likely be ound i he subg aph we e a he comple ely
andom. The o mula ion o modula i y Qcan be exp essed as in he
ollowing equa ion:
𝑄=1
2𝑚
𝑛
∑
𝑖,𝑗 (𝐴𝑖𝑗 −𝑃𝑖𝑗 )𝛿(𝐶𝑖, 𝐶𝑗)(7)
whe e Ais he adjacency ma ix ep esen ing he g aph, 𝑃𝑖𝑗 is he
p obabili y ha he nodes 𝑣𝑖and 𝑣𝑗a e connec ed in a pu ely andom
g aph, nis he numbe o e ices, mis he numbe o edges, and 𝛿(𝐶i,
𝐶j) is 1i he nodes a e in he same communi y, and 0o he wise.
Based on modula i y, Fas Newman (FN) (Newman,2004) is an e icien
bo om-up cons uc i e algo i hm ha wo ks by pe o ming a g eedy
sea ch o a g aph pa i ion ha maximizes he g aph modula i y.
The combina ion o NCD, NJ and FN esul s in some ele an
DAMICORE p ope ies. NCD makes DAMICORE a da a- ype agnos ic
me hod capable o wo king wi h any kind o objec : ex s, images,
audio, o o he kinds o da a iles a e all p ocessed a he symbolic
ep esen a ion. NJ hen builds a phylogeny exposing common aspec s
and how sha ed ea u es a e ela ed hie a chically. Finally, FN hen
iden i ies communi ies in his phylogeny o clus e ela ed objec s
in o meaning ul simila i y g oups. As esul , DAMICORE can be used
wi hou any da a p e-p ocessing, such as il e ing, ou lie de ec ion, and
ea u e ex ac ion, among o he asks ha usually include con igu a ion
biases and equi e knowledge om expe s in he ield o he applica-
ion. DAMICORE equi es no pa ame e se up o un (al hough some
execu ion op ions may imp o e i s pe o mance), which is adequa e o
non-expe s in machine lea ning and da a mining, and o de eloping
cybe –physical solu ions.
3.4. FS-OPA o he da a-d i en design o an ex ude
The da a-d i en design based on op imiza ion uses candida e solu-
ions in he decision space as samples. Tha da a usually co esponds o
dozens o hund eds o samples a each op imiza ion i e a ion. Al hough
such an amoun is no a huge sampling ( o such a complex p oblem),
i may be enough o s a o disco e some aspec s o he mechanisms
ha make an ex ude e icien , o example. The i s ick o applying
FS-OPA o he ex usion p oblem is o sa e he da a assigned o each
a iable (i s alues sp ead among he samples) in a ile, composing an
objec o analysis. The co esponding phylog ams p o ide in o ma ion
ha can p o ide ou le els o lea ning om aw da a, named 4-Le el
FS based on OPA (4LFS-opa):
1. Fi s -le el lea ning. The p oposed lea ning app oach inds
clades, whe e each o hem is a clus e o a iables ha sha e
in o ma ion; while he sha ing is ela i ely poo be ween clades.
Fo op imiza ion pu poses, each clus e shows a se o a iables
wi h signi ican in e ac ions. Fo example, hey may co espond
o co ela ed co a ia es in eg ession echniques. The ou pu is
a able wi h a lis o a iables (a clus e ) pe ow.
2. Second-le el lea ning. 4LFS-opa es ima es he po en ial con i-
bu ion o each clade (o he a iables in i ) o he objec i es. I
uses he clades o objec i es (oclade) and measu es he dis ances
om hose clades o each a iable clade ( clade). The dis ance
om a clade o an oclade is he longes pa h (maximum o he
numbe o edges om all he pa hs in he ound phylog am)
be ween he nodes in he union o clade and oclade. Those
dis ances (also called cophene ic dis ances) es ima e he powe
o a clade o imp o e an objec i e, while each leng h o a pa h
p om a iable i in clade o objec i e o in oclade ha is
no malized by he la ges pa h ound ( om all clades and clades)
is a ough es ima e o he ela i e con ibu ion o i o o. No e
ha a clade may ha e bo h a iables and objec i es oge he .
The compu a ion o hose dis ances i s equi es he spli ing o
a mixed clade (mclade) in o a pu e clade ( he mclade wi hou
any objec i e) and a pu e oclade ( he mclade wi hou a iables).
The ou pu o he second le el o lea ning possesses wo ma i-
ces: one wi h he phylog am dis ances om clades o oclades
and ano he wi h he ela i e phylog am dis ances om each
a iable o each objec i e.
7
A. Gaspa -Cunha, F. Monaco, J. Siko a e al. Enginee ing Applica ions o A i icial In elligence 116 (2022) 105397
Fig. 8. Neighbou Joining scheme.
Fig. 9. Ex ude geome y.
3. Thi d-le el lea ning. The decomposi ion o a p oblem in o
subg oups ( om clades) ha has some equi alence, complemen-
a i y, a ce ain le el o independence, and hei ela i e powe
o imp o e an objec i e a e use ul componen s o compose a
su oga e model, o example, a simple linea eg ession model
o each objec i e. 4LFS-opa uses he esul s lea ned om le els
one and wo o cons uc M Bayesian Ne wo ks, one o each o
he M objec i es, used as a a ge a iable. Thus, he ou pu is
M Bayesian Ne wo ks.
4. Fou h-le el lea ning. A mul i a ia e p obabilis ic model can
be cons uc ed om he lis o in o ma ion (in he las abo e
i em) oge he wi h he equency dis ibu ion o a iable alues
in each clade (o a a ia ion o i ). Tha is exac ly he ype o
model equi ed by Es ima ion o Dis ibu ion Algo i hms (Soa es
e al.,2017) o wo k o ela i ely complex p oblems. No e
ha , EDAs compose a ype o op imiza ion me hod based on
e olu iona y heo y. In o he wo ds, he da a-d i en lea ning
enabled by DAMICORE can p oduce mul i a ia e p obabilis ic
models and, hus, an EDA, i.e., an en i e op imiza ion app oach,
ha can lea n om he aw and ela i ely-small amoun o da a
a each i e a ion and decide how o walk in he decision space
o imp o e each objec i e o a se o hem. Thus, he ou pu o
he ou h le el is a mul iobjec i e EDA ha can lea n om aw
da a aiming a bene i ing he op imiza ion p ocess.
The case s udy wi h eal da a p esen ed in Sec ion 4illus a es he
i s and second lea ning le els desc ibed abo e. O he le els will be
in es iga ed in u u e wo k.
4. Case s udy
Ex ude geome y
The ex ude used has a squa e pi ch sc ew wi h a diame e (D)
o 2 mm and a L/D a io equal o 2 (Fig. 9). I was i ed wi h a
con en ional sc ew wi h he leng hs o he eed, comp ession, and
me e ing zones equal o 8D, 8D, and 9D, espec i ely. The o al leng h
o he g oo es zone (Lg) is 100 mm and he o a ional ba el segmen
was loca ed a u n 16D wi h a leng h (L bs) o 1D and 3D. Di e en
sc ew geome ies we e es ed, using h ee di e en in e nal diame e s
in he me e ing zone (𝐷3), i.e., Sc ew 1 wi h 22 mm, Sc ew 2 wi h
21 mm, and Sc ew 3 wi h 20 mm. The sc ew speed was ixed a 120
pm. Sc ew 2 (22 mm) was also es ed o h ee di e en pi ches (Pi ch)
in all sc ew leng hs, 20, 25, and 30 mm, espec i ely.
G oo es geome y
In he machine, a g oo ed ba el sec ion was implemen ed allowing
o change in he geome y o he g oo es. Th ee di e en solu ions
(Model), pa en ed in he amewo k o he NEWEX p ojec , we e s ud-
ied (Gaspa -Cunha e al.,2018;Gaspa -Cunha,2019). In p e ious wo k,
ou models o compu e he a e age coe icien o ic ion we e s udied
o e i y hei sui abili y and hei sensi i i y o changes in he sys em
geome y (Gaspa -Cunha,2019). F om his s udy, i was concluded ha
he exis ence o g oo es in he solids con eying zone is an e ec i e way
o imp o ing he pe o mance o he ex ude , which depends on bo h
he dep h (hN) and he o al wid h (B) o he g oo es.
Solu ion Model 1, as illus a ed in Fig. 10. In his model he dep h
is dec easing om a maximum alue a he beginning o he sec ion
(hN1), o ze o a he end o he g oo es zone, subsequen ly, he polyme
will no accumula e in he g oo es. Simul aneously, i is possible by
simply mo ing he de ice shown o ge changes in bo h he dep h and
o al wid h o he g oo es. Fig. 10-A ep esen s he g oo es de ice
open, i.e., when he g oo es ha e he maximum alue o he ini ial
dep h (hN1), while Fig. 10-B is he case when his dep h is nil. The
changes in he o al wid h can be implemen ed by mo ing only wo
o ou o he exis ing g oo es de ices. In his case he possibili y o
including sec ions wi h di e en geome y o g oo es wi h he leng h
o 4D (100 mm) and whe e he dep h a ies linea ly om a maximum
alue a he beginning o he g oo es, un il i cancels ou .
Solu ion Model 2 is shown in Fig. 11. The mos impo an di e ence,
when compa ed wi h Solu ion Model 1, conce ns he a ia ion o he
dep h along he leng h o he g oo e. In he p esen case, o example
o Model 2b, along wi h he ini ial 25 mm (1D) he dep h is cons an
(hN1) and equal o 1 mm, while in he emaining leng h (hN2), 75 mm
(3D), is also cons an , bu equal o 6 mm. The di e en geome ies
es ed in his case a e desc ibed geome ically in Table A.2.
Solu ion Model 3 is shown in Fig. 12. In his case, he g oo ed
sec ion is cons i u ed by a sequence o in e connec ed ings ha can
be o a ed independen ly o change he angle o he g oo es exis ing
in each one o he ings, as shown in Fig. 12. In his way, he e is
he possibili y o s udy he in luence o he g oo es angle and com-
pa e he pe o mance o longi udinal and helical g oo es. The helical
8
A. Gaspa -Cunha, F. Monaco, J. Siko a e al. Enginee ing Applica ions o A i icial In elligence 116 (2022) 105397
Fig. 10. Solu ion Model 1a: (A) o ally open; (B) o ally closed.
Fig. 11. Solu ion Model 2: (A) o ally open; (B) o ally closed.
g oo es wi h a channel implemen ed in he di ec ion o he sc ew
channel enable he au o-cleaning o he g oo es wi hou de e io a ing
he pe o mance. This is indica ed in Table A.2 by a iable Type: L
— longi udinal; RH — igh -helical; and LH — le -helical.
Ro a ional ba el segmen geome y
In he p esen s udy he o a ional ba el segmen (shown in Fig. 13)
was loca ed a 16D. Two di e en leng hs 1D (25 mm) and 3D (75 mm)
and ou di e en o a ional ba el segmen eloci ies (𝑁b=−80, −120,
80 and 100 pm) we e es ed.
Ma e ial p ope ies
Table 1 shows he ele an p ope ies o he polyme used in he
calcula ions, a Low-Densi y Polye hylene, Malen E FGAN 18-D003 om
Basell. The iscosi y was ob ained expe imen ally using a capilla y
heome e being he da a i ed using he powe -law model, as ollows:
𝜂=𝜂0𝛾(𝑛−1)𝑒−𝑎(𝑇−𝑇0)(8)
Ope a ing condi ions
In all calcula ions, he ba el empe a u e (Tba el) was ixed a
170 ◦C, bu in he solids zone (T eed) a ies linea ly be ween 30 ◦C
and 70 ◦C. Sc ew speed only changes in he Sc ews da ase , in which
he alues o 40, 80, and 120 pm we e used.
Da ase s
Two ypes o s udies will be ca ied ou : a pa ial and global
analysis. In he i s case, h ee di e en se s will be conside ed: (i)
Sc ew Da ase — analysis o ope a ing condi ions and sc ew geome y;
(ii) G oo es Da ase — analysis o g oo es sec ion; and (iii) RBS
Da ase — analysis o o a ional ba el segmen . In he la e case,
ee s udies will be made: (i) global analysis wi h all da a; (ii) global
analysis wi h 50% o he bes da a o Ou pu , and (iii) global analysis
wi h 50% o he bes da a o WATS. Fo ha pu pose, Tables A1, A2,
A3, and A4, in Appendix, p esen he da a used, he decision a iables
alues in oduced in he modelling p og am, and he alues o he
objec i e esul ing om he calcula ion. The decision a iable’s alues
we e de ined as a unc ion o he s udy made.
In he Sc ews da ase (Table A.1) h ee di e en sc ews we e used
(Sc ew equal o 1, 2, and 3) co esponding o 𝐷3equal o 22, 21, and
20 mm, espec i ely. In his case, G oo es and RBS a iables alues
we e ixed as ze o (0), since hey we e no p esen . Also, as e e ed,
9
A. Gaspa -Cunha, F. Monaco, J. Siko a e al. Enginee ing Applica ions o A i icial In elligence 116 (2022) 105397
Fig. 18. Phylog am ob ained by 4LFS-opa om he Global da ase , bes 50% o Ou pu .
This analysis allows us o conclude ha he esul s p oduced by he
applica ion o le els one and wo o lea ning a e ollowing he knowl-
edge abou he ex usion p ocess and ha i cons i u es an impo an
s ep owa d he applica ion o he o he lea ning le els.
Fu u e wo k includes he applica ion o he same da a a wo
addi ional lea ning le els: hi d-le el lea ning whe e he aim will be
o ob ain a su oga e model ela ing o he da a, which can be used
oge he wi h an op imiza ion algo i hm; and ou h-le el lea ning,
which aims o ob ain mul i a ia e p obabilis ic models ha can be used
as an en i e op imiza ion app oach.
CRediT au ho ship con ibu ion s a emen
An ónio Gaspa -Cunha: Concep ualiza ion, Me hodology, W i ing
– o iginal d a , Supe ision, In es iga ion, Fo mal analysis, W i ing –
e iew & edi ing. F ancisco Monaco: So wa e, Da a cu a ion, In es-
iga ion, Fo mal analysis. Janusz Siko a: Supe ision, Visualiza ion,
In es iga ion, W i ing – e iew & edi ing. Alexand e Delbem: Supe -
ision, Resou ces, W i ing – e iew & edi ing, In es iga ion, Fo mal
analysis.
Decla a ion o compe ing in e es
The au ho s decla e ha hey ha e no known compe ing inan-
cial in e es s o pe sonal ela ionships ha could ha e appea ed o
in luence he wo k epo ed in his pape .
Da a a ailabili y
Da a will be made a ailable on eques .
Acknowledgemen s
This esea ch was pa ially unded by NAWA-Na odowa Agencja
Wymiany Akademickiej, unde g an PPN/ULM/2020/1/00125 and
Eu opean Union’s Ho izon 2020 esea ch and inno a ion p og amme
unde he Ma ie Skłodowska-Cu ie G an Ag eemen No 734205–H2020-
MSCA-RISE-2016. The au ho s also acknowledge he unding by FEDER
unds h ough he COMPETE 2020 P og amme and Na ional Funds
h ough FCT (Po uguese Founda ion o Science and Technology)
unde he p ojec s UID-B/05256/2020, and UID-P/05256/2020, he
Cen e o Ma hema ical Sciences Applied o Indus y (CeMEAI) and he
suppo om he São Paulo Resea ch Founda ion, B azil (FAPESP g an
No 2013/07375-0, he Cen e o A i icial In elligence (C4AI-USP), he
suppo om he São Paulo Resea ch Founda ion, B azil (FAPESP g an
No 2019/07665-4) and he IBM Co po a ion.
Appendix
See Tables A.1–A.4
16

A. Gaspa -Cunha, F. Monaco, J. Siko a e al. Enginee ing Applica ions o A i icial In elligence 116 (2022) 105397
Table A.1
Sc ew da ase .
Decision a iables Objec i es ERROR
Sc ew G oo es RBS Dex D1 D3 L eed L1 L2 L3 Pi ch T eed Tba el NOu pu 𝑇𝑚𝑒𝑙𝑡 Powe 𝐿𝑚𝑒𝑙𝑡𝑖𝑛𝑔 WATS ViscousD
1 0 0 25 16.6 22 100 200 200 225 25 70 170 40 1.8 175.3 995 6.2 315.5 1.04 0
1 0 0 25 16.6 22 100 200 200 225 25 70 170 80 3.5 182.1 1594 12.4 295.9 1.36 0
1 0 0 25 16.6 22 100 200 200 225 25 70 170 120 5.2 188.6 2460 13.2 298.9 1.25 0
1 0 0 25 16.6 22 100 200 200 225 20 70 170 80 2.8 182.1 1953 10.6 334 1.38 0
1 0 0 25 16.6 22 100 200 200 225 25 70 170 80 3.5 182.1 1594 12.4 295.9 1.36 0
1 0 0 25 16.6 22 100 200 200 225 30 70 170 80 4.3 182.4 1314 14.7 279.1 1.07 0
1 0 0 25 16.6 22 100 200 200 225 20 70 170 40 1.716 175.1 1063 6.676 319.6 1.19 0
1 0 0 25 16.6 22 100 200 200 225 25 70 170 40 1.764 175.3 995 6.15 315.5 1.04 0
1 0 0 25 16.6 22 100 200 200 225 30 70 170 40 1.754 175.4 918 6.69 305.9 1.04 0
1 0 0 25 16.6 22 100 200 200 225 20 70 170 120 5.112 188.1 2404 13.996 329 1.39 0
1 0 0 25 16.6 22 100 200 200 225 25 70 170 120 5.229 188.6 2460 13.16 298.9 1.25 0
1 0 0 25 16.6 22 100 200 200 225 30 70 170 120 5.394 189.7 2224 14.71 292.4 1.12 0
2 0 0 25 16.6 21 100 200 200 225 25 70 170 40 2.3 176.3 946 8.7 263.3 1.04 0
2 0 0 25 16.6 21 100 200 200 225 25 70 170 80 4.6 183.2 1487 15.4 245 1.08 0
2 0 0 25 16.6 21 100 200 200 225 25 70 170 120 7.1 188.8 2201 17.1 219.2 1.11 0
2 0 0 25 16.6 21 100 200 200 225 25 70 170 40 2.099 176.1 1157 6.816 294.6 1.04 0
2 0 0 25 16.6 21 100 200 200 225 25 70 170 40 2.329 176.3 946 8.67 263.3 1.04 0
2 0 0 25 16.6 21 100 200 200 225 25 70 170 40 2.25 176.4 966 6.76 272.4 1.04 0
2 0 0 25 16.6 21 100 200 200 225 25 70 170 120 6.378 187.7 2425 15.66 266.2 1.14 0
2 0 0 25 16.6 21 100 200 200 225 25 70 170 120 7.143 188.8 2201 17.14 219.2 1.11 0
2 0 0 25 16.6 21 100 200 200 225 25 70 170 120 7.571 190.6 2116 17.55 204.5 1.12 0
3 0 0 25 16.6 20 100 200 200 225 25 70 170 40 2.8 176.8 724 14.2 209.7 1.04 0
3 0 0 25 16.6 20 100 200 200 225 25 70 170 80 5.9 182.9 1371 17.8 156.9 1.08 0
3 0 0 25 16.6 20 100 200 200 225 25 70 170 120 10.2 185.2 1727 21.6 70.3 1.09 0
3 0 0 25 16.6 20 100 200 200 225 20 70 170 40 2.458 177 1233 5.824 295.4 1.04 0
3 0 0 25 16.6 20 100 200 200 225 25 70 170 40 2.766 176.8 724 14.22 209.7 1.04 0
3 0 0 25 16.6 20 100 200 200 225 30 70 170 40 2.872 177.1 668 14.96 193 1.04 0
3 0 0 25 16.6 20 100 200 200 225 20 70 170 120 7.246 185.7 2518 16.604 195.5 1.09 0
3 0 0 25 16.6 20 100 200 200 225 25 70 170 120 10.176 185.2 1727 21.64 70.3 1.09 0
3 0 0 25 16.6 20 100 200 200 225 30 70 170 120 53.947 224.5 2432 25 2 1.32 1
Table A.2
G oo es da ase .
Decision a iables Objec i es ERROR
Sc ew G oo es RBS Dex D1 D3 L eed L1 L2 L3 Pi ch T eed Tba el NModel bN hN1 hN2 NN Lg1 Lg2 B Type Ou pu 𝑇𝑚𝑒𝑙𝑡 Powe 𝐿𝑚𝑒𝑙𝑡𝑖𝑛𝑔 WATS ViscousD
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 1 6 6 6 4 100 0 24 L 5.43 188.5 2647 14.21 302.6 1.53 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 1 6 4 4 4 100 0 24 L 5.38 188.6 2597 14.17 303.1 1.54 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 1 6 2 2 4 100 0 24 L 5.38 188.6 2630 13.69 299.5 1.54 0
1 0 0 25 16.6 22 100 200 200 225 25 70 170 120 1 6 0 0 4 100 0 0 L 5.34 188.9 2278 14.64 308 1.46 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 1 6 6 6 5 100 0 30 L 5.47 188.3 2728 14.21 301.8 1.53 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 1 6 4 4 5 100 0 30 L 5.46 188.3 2669 13.83 299.2 1.51 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 1 6 2 2 5 100 0 30 L 5.35 188.3 2709 13.88 301.2 1.53 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 1 6 0 0 0 100 0 0 L 5.34 188.9 2278 14.64 308 1.46 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 6 6 4 100 0 24 L 5.48 189.2 2745 14.1 300.8 1.52 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 1 6 4 25 75 24 L 5.47 188.4 2741 14.23 301.9 1.53 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 1 6 4 50 50 24 L 5.47 188.4 2739 14.23 301.9 1.53 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 1 6 4 75 25 24 L 5.46 188.3 2737 14.22 301.9 1.53 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 1 1 4 100 0 24 L 5.46 188.3 2732 14.21 301.9 1.53 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 6 6 5 100 0 30 L 5.55 188.3 2768 13.97 298.8 1.52 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 1 6 5 25 75 30 L 5.48 188.2 2816 14.1 300.9 1.52 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 1 6 5 50 50 30 L 5.47 188.2 2745 14.21 300 1.52 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 1 6 5 75 25 30 L 5.47 188.3 2740 14.21 300 1.53 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 1 1 5 100 0 30 L 5.46 188.4 2739 14.22 301.9 1.53 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 6 6 4 100 0 24 L 5.43 188.5 2647 14.21 302.6 1.53 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 6 6 4 100 0 24 RH 5.39 188.5 2672 13.87 300.6 1.53 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 4 4 4 100 0 24 RH 5.37 188.5 2657 13.37 297.7 1.54 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 2 2 4 100 0 24 RH 5.36 188.5 2584 13.98 301.8 1.54 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 6 6 4 100 0 24 LH 5.35 188.3 2709 13.88 301.2 1.53 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 4 4 4 100 0 24 LH 5.36 188.4 2637 14.02 302.2 1.54 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 2 2 4 100 0 24 LH 5.38 188.6 2597 14.17 303.1 1.54 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 6 6 5 100 0 30 RH 5.47 188.3 2650 13.99 300.2 1.51 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 4 4 5 100 0 30 RH 5.45 188.3 2662 13.89 300.1 1.51 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 2 2 5 100 0 30 RH 5.44 188.3 2656 14.12 301.1 1.51 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 6 6 5 100 0 30 LH 5.46 188.4 2739 14.22 301.9 1.53 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 4 4 5 100 0 30 LH 5.47 188.2 2725 14.51 302.5 1.53 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 2 2 5 100 0 30 LH 5.47 188.1 2712 14.7 303.7 1.63 0
Table A.3
RBS da ase .
Decision a iables Objec i es ERROR
Sc ew G oo es RBS Dex D1 D3 L eed L1 L2 L3 Pi ch T eed Tba el N L bs L bs/L Nb Ou pu 𝑇𝑚𝑒𝑙𝑡 Powe 𝐿𝑚𝑒𝑙𝑡𝑖𝑛𝑔 WATS ViscousD
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 25 16 05.3 188.9 2278 14.6 308 1.46 0
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 25 16 −20 5.4 189 2295 14.8 334.2 1.46 0
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 25 16 −40 5.5 189.2 2331 14.8 328.4 1.46 0
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 25 16 −80 5.5 189.3 2383 14.8 317.3 1.46 0
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 25 16 −120 5.7 189.8 2397 15.1 307.9 1.44 0
(con inued on nex page)
17
A. Gaspa -Cunha, F. Monaco, J. Siko a e al. Enginee ing Applica ions o A i icial In elligence 116 (2022) 105397
Table A.3 (con inued).
Decision a iables Objec i es ERROR
Sc ew G oo es RBS Dex D1 D3 L eed L1 L2 L3 Pi ch T eed Tba el N L bs L bs/L Nb Ou pu 𝑇𝑚𝑒𝑙𝑡 Powe 𝐿𝑚𝑒𝑙𝑡𝑖𝑛𝑔 WATS ViscousD
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 25 16 20 5.3 188.8 2283 14.3 339.2 1.47 0
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 25 16 40 5.2 188.8 2238 14.4 347.5 1.47 0
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 25 16 80 4.9 188.8 2214 14.2 358 1.48 1
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 25 16 120 4.9 189 2185 14 366 1.48 1
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 75 16 0 5.3 188.9 2278 14.6 308 1.46 0
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 75 16 −20 5.5 189.3 2358 14.8 383.3 1.46 0
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 75 16 −40 5.8 190.1 2395 15.5 376.4 1.45 0
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 75 16 −80 6.1 191.1 2583 15.6 339.9 1.44 0
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 75 16 −120 6.4 192.2 2834 15.8 315.6 1.43 0
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 75 16 20 5.1 188.5 2241 14.1 405.1 1.47 0
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 75 16 40 4.8 188.2 2163 14 422.9 1.48 0
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 75 16 80 4 187.7 2195 12.8 451 1.5 1
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 75 16 120 3.7 187.8 2100 12.2 484.1 1.51 1
Table A.4
Global da ase ..
Decision a iables Objec i es ERROR
Sc ew G oo es RBS Dex D1 D3 L eed L1 L2 L3 Pi ch T eed Tba el NModel bN hN1 hN2 NN Lg1 Lg2 B Type L bs L bs/L Nb Ou pu 𝑇𝑚𝑒𝑙𝑡 Powe 𝐿𝑚𝑒𝑙𝑡𝑖𝑛𝑔 WATS ViscousD
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 25 16 05.3 188.9 2278 14.6 308 1.46 0
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 25 16 −20 5.4 189 2295 14.8 334.2 1.46 0
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 25 16 −40 5.5 189.2 2331 14.8 328.4 1.46 0
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 25 16 −80 5.5 189.3 2383 14.8 317.3 1.46 0
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 25 16 −120 5.7 189.8 2397 15.1 307.9 1.44 0
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 25 16 20 5.3 188.8 2283 14.3 339.2 1.47 0
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 25 16 40 5.2 188.8 2238 14.4 347.5 1.47 0
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 25 16 80 4.9 188.8 2214 14.2 358 1.48 1
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 25 16 120 4.9 189 2185 14 366 1.48 1
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 75 16 0 5.3 188.9 2278 14.6 308 1.46 0
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 75 16 −20 5.5 189.3 2358 14.8 383.3 1.46 0
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 75 16 −40 5.8 190.1 2395 15.5 376.4 1.45 0
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 75 16 −80 6.1 191.1 2583 15.6 339.9 1.44 0
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 75 16 −120 6.4 192.2 2834 15.8 315.6 1.43 0
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 75 16 20 5.1 188.5 2241 14.1 405.1 1.47 0
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 75 16 40 4.8 188.2 2163 14 422.9 1.48 0
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 75 16 80 4 187.7 2195 12.8 451 1.5 1
1 0 1 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 75 16 120 3.7 187.8 2100 12.2 484.1 1.51 1
1 1 1 25 16.6 22 100 200 200 225 25 70 170 120 2 6 6 6 4 100 0 24 L 75 16 0 5.3 188.9 2278 14.6 308 1.46 0
1 1 1 25 16.6 22 100 200 200 225 25 70 170 120 2 6 6 6 4 100 0 24 L 75 16 −20 5.7 188.4 2975 14.4 372.1 1.13 0
1 1 1 25 16.6 22 100 200 200 225 25 70 170 120 2 6 6 6 4 100 0 24 L 75 16 −40 5.8 188.9 3077 14.6 358 1.11 0
1 1 1 25 16.6 22 100 200 200 225 25 70 170 120 2 6 6 6 4 100 0 24 L 75 16 −80 6.1 189.7 3306 15 330.2 1.12 0
1 1 1 25 16.6 22 100 200 200 225 25 70 170 120 2 6 6 6 4 100 0 24 L 75 16 −120 6.4 191.1 3488 15 304.6 1.13 0
1 1 1 25 16.6 22 100 200 200 225 25 70 170 120 2 6 6 6 4 100 0 24 L 75 16 20 5.3 187.7 2798 14 398.4 1.1 0
1 1 1 25 16.6 22 100 200 200 225 25 70 170 120 2 6 6 6 4 100 0 24 L 75 16 40 5 187.6 2714 13.6 411.6 1.21 0
1 1 1 25 16.6 22 100 200 200 225 25 70 170 120 2 6 6 6 4 100 0 24 L 75 16 80 4.3 187.6 2767 11.7 430 1.3 0
1 1 1 25 16.6 22 100 200 200 225 25 70 170 120 2 6 6 6 4 100 0 24 L 75 16 120 3.9 188 2771 6.1 482.4 1.28 0
1 0 0 25 16.6 22 100 200 200 225 25 70 170 40 0 0 0 0 0 0 0 0 0 0 0 0 1.8 175.3 995 6.2 315.5 1.04 0
1 0 0 25 16.6 22 100 200 200 225 25 70 170 80 0 0 0 0 0 0 0 0 0 0 0 0 3.5 182.1 1594 12.4 295.9 1.36 0
1 0 0 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 0 0 0 5.2 188.6 2460 13.2 298.9 1.25 0
1 0 0 25 16.6 22 100 200 200 225 20 70 170 80 0 0 0 0 0 0 0 0 0 0 0 0 2.8 182.1 1953 10.6 334 1.38 0
1 0 0 25 16.6 22 100 200 200 225 25 70 170 80 0 0 0 0 0 0 0 0 0 0 0 0 3.5 182.1 1594 12.4 295.9 1.36 0
1 0 0 25 16.6 22 100 200 200 225 30 70 170 80 0 0 0 0 0 0 0 0 0 0 0 0 4.3 182.4 1314 14.7 279.1 1.07 0
1 0 0 25 16.6 22 100 200 200 225 20 70 170 40 0 0 0 0 0 0 0 0 0 0 0 0 1.716 175.1 1063 6.676 319.6 1.19 0
1 0 0 25 16.6 22 100 200 200 225 25 70 170 40 0 0 0 0 0 0 0 0 0 0 0 0 1.764 175.3 995 6.15 315.5 1.04 0
1 0 0 25 16.6 22 100 200 200 225 30 70 170 40 0 0 0 0 0 0 0 0 0 0 0 0 1.754 175.4 918 6.69 305.9 1.04 0
1 0 0 25 16.6 22 100 200 200 225 20 70 170 120 0 0 0 0 0 0 0 0 0 0 0 0 5.112 188.1 2404 13.996 329 1.39 0
1 0 0 25 16.6 22 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 0 0 0 5.229 188.6 2460 13.16 298.9 1.25 0
1 0 0 25 16.6 22 100 200 200 225 30 70 170 120 0 0 0 0 0 0 0 0 0 0 0 0 5.394 189.7 2224 14.71 292.4 1.12 0
2 0 0 25 16.6 21 100 200 200 225 25 70 170 40 0 0 0 0 0 0 0 0 0 0 0 0 2.3 176.3 946 8.7 263.3 1.04 0
2 0 0 25 16.6 21 100 200 200 225 25 70 170 80 0 0 0 0 0 0 0 0 0 0 0 0 4.6 183.2 1487 15.4 245 1.08 0
2 0 0 25 16.6 21 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 0 0 0 7.1 188.8 2201 17.1 219.2 1.11 0
2 0 0 25 16.6 21 100 200 200 225 25 70 170 40 0 0 0 0 0 0 0 0 0 0 0 0 2.099 176.1 1157 6.816 294.6 1.04 0
2 0 0 25 16.6 21 100 200 200 225 25 70 170 40 0 0 0 0 0 0 0 0 0 0 0 0 2.329 176.3 946 8.67 263.3 1.04 0
2 0 0 25 16.6 21 100 200 200 225 25 70 170 40 0 0 0 0 0 0 0 0 0 0 0 0 2.25 176.4 966 6.76 272.4 1.04 0
2 0 0 25 16.6 21 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 0 0 0 6.378 187.7 2425 15.66 266.2 1.14 0
2 0 0 25 16.6 21 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 0 0 0 7.143 188.8 2201 17.14 219.2 1.11 0
2 0 0 25 16.6 21 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 0 0 0 7.571 190.6 2116 17.55 204.5 1.12 0
3 0 0 25 16.6 20 100 200 200 225 25 70 170 40 0 0 0 0 0 0 0 0 0 0 0 0 2.8 176.8 724 14.2 209.7 1.04 0
3 0 0 25 16.6 20 100 200 200 225 25 70 170 80 0 0 0 0 0 0 0 0 0 0 0 0 5.9 182.9 1371 17.8 156.9 1.08 0
3 0 0 25 16.6 20 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 0 0 0 10.2 185.2 1727 21.6 70.3 1.09 0
3 0 0 25 16.6 20 100 200 200 225 20 70 170 40 0 0 0 0 0 0 0 0 0 0 0 0 2.458 177 1233 5.824 295.4 1.04 0
3 0 0 25 16.6 20 100 200 200 225 25 70 170 40 0 0 0 0 0 0 0 0 0 0 0 0 2.766 176.8 724 14.22 209.7 1.04 0
3 0 0 25 16.6 20 100 200 200 225 30 70 170 40 0 0 0 0 0 0 0 0 0 0 0 0 2.872 177.1 668 14.96 193 1.04 0
3 0 0 25 16.6 20 100 200 200 225 20 70 170 120 0 0 0 0 0 0 0 0 0 0 0 0 7.246 185.7 2518 16.604 195.5 1.09 0
3 0 0 25 16.6 20 100 200 200 225 25 70 170 120 0 0 0 0 0 0 0 0 0 0 0 0 10.176 185.2 1727 21.64 70.3 1.09 0
3 0 0 25 16.6 20 100 200 200 225 30 70 170 120 0 0 0 0 0 0 0 0 0 0 0 0 53.947 224.5 2432 25 2 1.32 1
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 1 6 6 6 4 100 0 24 L 0 0 0 5.43 188.5 2647 14.21 302.6 1.53 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 1 6 4 4 4 100 0 24 L 0 0 0 5.38 188.6 2597 14.17 303.1 1.54 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 1 6 2 2 4 100 0 24 L 0 0 0 5.38 188.6 2630 13.69 299.5 1.54 0
1 0 0 25 16.6 22 100 200 200 225 25 70 170 120 1 6 0 0 4 100 0 0 L 0 0 0 5.34 188.9 2278 14.64 308 1.46 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 1 6 6 6 5 100 0 30 L 0 0 0 5.47 188.3 2728 14.21 301.8 1.53 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 1 6 4 4 5 100 0 30 L 0 0 0 5.46 188.3 2669 13.83 299.2 1.51 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 1 6 2 2 5 100 0 30 L 0 0 0 5.35 188.3 2709 13.88 301.2 1.53 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 1 6 0 0 0 100 0 0 L 0 0 0 5.34 188.9 2278 14.64 308 1.46 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 6 6 4 100 0 24 L 0 0 0 5.48 189.2 2745 14.1 300.8 1.52 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 1 6 4 25 75 24 L 0 0 0 5.47 188.4 2741 14.23 301.9 1.53 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 1 6 4 50 50 24 L 0 0 0 5.47 188.4 2739 14.23 301.9 1.53 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 1 6 4 75 25 24 L 0 0 0 5.46 188.3 2737 14.22 301.9 1.53 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 1 1 4 100 0 24 L 0 0 0 5.46 188.3 2732 14.21 301.9 1.53 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 6 6 5 100 0 30 L 0 0 0 5.55 188.3 2768 13.97 298.8 1.52 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 1 6 5 25 75 30 L 0 0 0 5.48 188.2 2816 14.1 300.9 1.52 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 1 6 5 50 50 30 L 0 0 0 5.47 188.2 2745 14.21 300 1.52 0
(con inued on nex page)
18
A. Gaspa -Cunha, F. Monaco, J. Siko a e al. Enginee ing Applica ions o A i icial In elligence 116 (2022) 105397
Table A.4 (con inued).
Decision a iables Objec i es ERROR
Sc ew G oo es RBS Dex D1 D3 L eed L1 L2 L3 Pi ch T eed Tba el NModel bN hN1 hN2 NN Lg1 Lg2 B Type L bs L bs/L Nb Ou pu 𝑇𝑚𝑒𝑙𝑡 Powe 𝐿𝑚𝑒𝑙𝑡𝑖𝑛𝑔 WATS ViscousD
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 1 6 5 75 25 30 L 0 0 0 5.47 188.3 2740 14.21 300 1.53 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 2 6 1 1 5 100 0 30 L 0 0 0 5.46 188.4 2739 14.22 301.9 1.53 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 6 6 4 100 0 24 L 0 0 0 5.43 188.5 2647 14.21 302.6 1.53 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 6 6 4 100 0 24 RH 0 0 0 5.39 188.5 2672 13.87 300.6 1.53 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 4 4 4 100 0 24 RH 0 0 0 5.37 188.5 2657 13.37 297.7 1.54 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 2 2 4 100 0 24 RH 0 0 0 5.36 188.5 2584 13.98 301.8 1.54 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 6 6 4 100 0 24 LH 0 0 0 5.35 188.3 2709 13.88 301.2 1.53 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 4 4 4 100 0 24 LH 0 0 0 5.36 188.4 2637 14.02 302.2 1.54 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 2 2 4 100 0 24 LH 0 0 0 5.38 188.6 2597 14.17 303.1 1.54 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 6 6 5 100 0 30 RH 0 0 0 5.47 188.3 2650 13.99 300.2 1.51 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 4 4 5 100 0 30 RH 0 0 0 5.45 188.3 2662 13.89 300.1 1.51 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 2 2 5 100 0 30 RH 0 0 0 5.44 188.3 2656 14.12 301.1 1.51 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 6 6 5 100 0 30 LH 0 0 0 5.46 188.4 2739 14.22 301.9 1.53 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 4 4 5 100 0 30 LH 0 0 0 5.47 188.2 2725 14.51 302.5 1.53 0
1 1 0 25 16.6 22 100 200 200 225 25 70 170 120 3 6 2 2 5 100 0 30 LH 0 0 0 5.47 188.1 2712 14.7 303.7 1.63 0
Re e ences
Agassan , J.F., A enas, P., Ca eau, P.J., Ve gnes, B., Vincen , M., 2017. Polyme
P ocessing: P inciples and Modeling. Ca l Hanse Ve lag, Munich.
Ag awal, S., Dasho a, Y., Tiwa i, M.K., Son, Y.J., 2008. In e ac i e pa icle swa m:
a pa e o-adap i e me aheu is ic o mul iobjec i e op imiza ion. IEEE T ans. Sys .
Man. Cybe n. Pa A Sys . Hum. 38, 258–277. h p://dx.doi.o g/10.1109/TSMCA.
2007.914767.
Ai okoski, T., Äy ämö, S., Mie inen, K., 2009. Clus e ing aided app oach o decision
making in compu a ionally expensi e mul iobjec i e op imiza ion. Op im. Me hods
So w. 24, 157–174. h p://dx.doi.o g/10.1080/10556780802525331.
Anon, 2022. h p://newex.pollub.pl, NEWEX – In es iga ion and de elopmen o a
new gene a ion o machines o he p ocessing o composi e and nanocomposi e
ma e ials, 07.01.2022.
A ge ich, C., Ibanez, R., Ba asinski, A., Chines a, F., 2019. Code2 ec : An e icien
he e ogenous da a classi ie and nonlinea eg ession echnique. C. R. Mecanique
347, 754–761. h p://dx.doi.o g/10.1016/j.c me.2019.11.002.
Ca ano, E.G., Coelho, D.G., Gaspa -Cunha, A., Wanne , E.F., Takahashi, R.H., 2015.
Feedback-con ol ope a o s o imp o ed Pa e o-se desc ip ion: Applica ion o a
polyme ex usion p ocess. Eng. Appl. A i . In ell. 38, 147–167. h p://dx.doi.o g/
10.1016/j.engappai.2014.10.016.
Chines a, F., Cue o, E., Abisse -Cha anne, E., Du al, J.L., Khaldi, F.E., 2020. Vi ual,
digi al and hyb id wins: A new pa adigm in da a-based enginee ing and engi-
nee ed da a. A ch. Compu . Me hods Eng. 27, 105–134. h p://dx.doi.o g/10.1007/
s11831-018-9301-4.
Chugh, T., Jin, Y., Mie inen, K., Hakanen, J., Sindhya, K., 2018. Su oga e-assis ed
e e ence ec o guided e olu iona y algo i hm o compu a ionally expensi e
many-objec i e op imiza ion. IEEE T ans. E ol. Compu . 22, 129–142. h p://dx.
doi.o g/10.1109/TEVC.2016.2622301.
Chugh, T., Sindhya, K., Hakanen, J., Mie inen, K., 2019. A su ey on handling
compu a ionally expensi e mul iobjec i e op imiza ion p oblems wi h e olu iona y
algo i hms. So Compu . 23, 3137–3166. h p://dx.doi.o g/10.1007/s00500-017-
2965-0.
Coello, C.A.C., Pulido, G.T., Lechuga, M.S., 2004. Handling mul iple objec i es wi h
pa icle swa m op imiza ion. IEEE T ans. E ol. Compu . 8, 256–279. h p://dx.doi.
o g/10.1109/TEVC.2004.826067.
C is ianini, N., Taylo , J.S., 2000. An In oduc ion o Suppo Vec o Machines: In
Addi ion, O he Ke nel-Based Lea ning Me hods. Camb idge Uni e si y P ess, New
Yo k, NY.
Deb, K., 2001. Mul i-Objec i e Op imiza ion using E olu iona y Algo i hms. Wiley,
Chiches e .
Deb, K., Banda u, S., G eine , D., Gaspa -Cunha, A., Tu um, C.C., 2014. An in eg a ed
app oach o au oma ed inno iza ion o disco e ing use ul design p inciples: Case
s udies om enginee ing. Appl. So Compu . 15, 42–56. h p://dx.doi.o g/10.
1016/j.asoc.2013.10.011.
Deb, K., S ini asan, A., 2007. Inno iza ion: Disco e y o Inno a i e Design P inciples
Th ough Mul iobjec i e E olu iona y Op imiza ion, Mul iobjec i e P oblem Sol ing
om Na u e: F om Concep s o Applica ions, Na u e Compu ing Se ies. Sp inge ,
New Yo k, NY.
Denysiuk, R., Recio, G., Co as, J.A., Gaspa -Cunha, A., 2018. Using mul iobjec i e
op imiza ion algo i hms and decision making suppo o sol e polyme ex usion
p oblems. Polym. Eng. Sci. 58, 493–502. h p://dx.doi.o g/10.1002/pen.24732.
Dimiduk, D.M., Holm, E.A., Niezgoda, S.R., 2018. Pe spec i es on he impac o machine
lea ning, deep lea ning, and a i icial in elligence on ma e ials, p ocesses, and
s uc u es enginee ing. In eg . Ma e . Manu . Inno . 7, 157–172. h p://dx.doi.o g/
10.1007/s40192-018-0117-8.
Fei, N.C., Meha , N.M., Kama uddin, S., 2013. P ac ical applica ions o aguchi
me hod o op imiza ion o p ocessing pa ame e s o plas ic injec ion moulding:
A e ospec i e e iew. ISRN Ind. Eng. 2013, 462174. h p://dx.doi.o g/10.1155/
2013/462174.
Gaspa -Cunha, A., 2009. Modelling and Op imisa ion o Single Sc ew Ex usion using
Mul i-Objec i e E olu iona y Algo i hms. Lambe Academic Publishing, Koln.
Gaspa -Cunha, A., 2019. Global ex ude modelling: Ac i e g oo ed eed sec ion,
o a ional ba el segmen and special sc ews. In: Siko a, J., Dulebo a, L. (Eds.),
Lublin Uni e si y o Technology Publishing House: Technological and Design
Aspec s o he P ocessing o Composi es and Nanocomposi es: Volume II. pp.
97–111.
Gaspa -Cunha, A., Co as, J.A., 2008. Robus ness in mul i-objec i e op imiza ion using
e olu iona y algo i hms. Compu . Op im. Appl. 39, 75–96. h p://dx.doi.o g/10.
1007/s10589-007-9053-9.
Gaspa -Cunha, A., Co as, J.A., Siko a, J., 2018. Modelling he e ec o g oo ed ba els
on he pe o mance o single sc ew ex ude s. In: Siko a, J., Dulebo á, L. (Eds.),
Technical Uni e si y o Kosice: Technological and Design Aspec s o he P ocessing
o Composi es and Nanocomposi es: Volume I. pp. 22–42.
Gaspa -Cunha, A., Co as, J.A., Siko a, J., 2022a. Op imiza ion o polyme p ocessing: A
e iew (pa I—Ex usion). Ma e ials h p://dx.doi.o g/10.3390/ma15010384, 15,
384.
Gaspa -Cunha, A., Co as, J.A., Siko a, J., 2022b. Op imiza ion o polyme p ocess-
ing: A e iew (pa II-molding echnologies). Ma e ials h p://dx.doi.o g/10.3390/
ma15031138, 15, 1138.
Good ellow, I., Bengio, Y., Cou ille, A., 2016. Deep Lea ning. MIT P ess, Camb idge.
Hüsken, M., Jin, Y., Sendho , B., 2005. S uc u e op imiza ion o neu al ne wo ks
o e olu iona y design op imiza ion. So Compu . 9, 21–28. h p://dx.doi.o g/10.
1007/s00500-003-0330-y.
Ibañez, R., Cas e an, F., A ge ich, C., Ghna ios, C., Hascoe , N., Amma , A., Cassag-
nau, P., Chines a, F., 2020. On he da a-d i en modeling o eac i e ex usion.
Fluids 94, 5. h p://dx.doi.o g/10.3390/ luids5020094.
Jin, Y., 2011. Su oga e-assis ed e olu iona y compu a ion: Recen ad ances and u u e
challenges. Swa m E ol. Compu . 1, 61–70. h p://dx.doi.o g/10.1016/j.swe o.
2011.05.001.
Jin, Y., Olho e , M., Sendho , B., 2002. A amewo k o e olu iona y op imiza ion
wi h app oxima e i ness unc ions. IEEE T ans. E ol. Compu . 6, 481–494. h p:
//dx.doi.o g/10.1109/TEVC.2002.800884.
Jin, Y., Sendho , B., 2004. Reducing i ness e alua ions using clus e ing echniques and
neu al ne wo k ensembles. In: Deb, K. (Ed.), Gene ic and E olu iona y Compu a ion
– GECCO 2004. GECCO 2004, Lec u e No es in Compu e Science, Vol. 3102.
Sp inge , Be lin, Heidelbe g, 10.1007/978-3-540-24854-5_71.
Jin, Y., Wang, H., Chugh, T., Guo, D., Mie inen, K., 2019. Da a-d i en e olu iona y
op imiza ion: An o e iew and case s udies. IEEE T ans. E ol. Compu . 23,
442–458. h p://dx.doi.o g/10.1109/TEVC.2018.2869001.
Kha a , F.G.Z., Miyoshi, N.S.B., Cob e, J., Aze edo-Ma ques, J. Mazzoncini De,
de Aze edo-Ma ques, P. Mazzoncini, Delbem, A.C.B., 2020. Fea u e sensi i i y
c i e ion-based sampling s a egy om he op imiza ion based on phylog am
analysis (Fs-OPA) and cox eg ession applied o men al diso de da ase s. PLOS
ONE 15, h p://dx.doi.o g/10.1371/jou nal.pone.0235147, e0235147.
Kohonen, T., 2001. Sel -O ganizing Maps, Sp inge Se ies in In o ma ion Sciences. Vol.
30, Sp inge , Be lin.
Leguizamón, G., Coello, C.A.C., 2011. Mul i-objec i e an colony op imiza ion: A
axonomy and e iew o app oaches. In: Se ies in Machine Pe cep ion and A i icial
In elligence. pp. 67–94. h p://dx.doi.o g/10.1142/9789814280150_0003.
Li, M., Vi ányi, P., 2019. An In oduc ion o Kolmogo o Complexi y and I s
Applica ions. Sp inge Science Cham.
Lind , J.T., Elbi li, B., 1985. E ec o he c oss-channel low on he mel ing pe o mance
o a single-sc ew ex ude . Polym. Eng. Sci. 25, 412–418. h p://dx.doi.o g/10.
1002/PEN.760250706.
Lui, L.T., Te azas, G., Zenil, H., Alexande , C., K asnogo , N., 2015. Complexi y
measu emen based on in o ma ion heo y and Kolmogo o complexi y. A i . Li e
205–224. h p://dx.doi.o g/10.1162/ARTL_a_00157.
Ma ins, J.P., Fonseca, C.M., Delbem, A.C.B., 2014. On he pe o mance o linkage- ee
gene ic algo i hms o he mul idimensional knapsack p oblem. Neu ocompu ing
146, 17–29. h p://dx.doi.o g/10.1016/j.neucom.2014.04.069.
19
A. Gaspa -Cunha, F. Monaco, J. Siko a e al. Enginee ing Applica ions o A i icial In elligence 116 (2022) 105397
Meha , N.M., Kama uddin, S., 2012. Quali y con ol and design op imisa ion o plas ic
p oduc using Taguchi me hod: a comp ehensi e e iew. In . J. Plas . Technol. 16,
194–209. h p://dx.doi.o g/10.1007/s12588-012-9037-1.
Mezu a-Mon es, E., Reyes-Sie a, M., Coello, C.A.C., 2008. Mul i-objec i e op imiza ion
using di e en ial e olu ion: A su ey o he s a e-o - he-a . In: Chak abo y, U.K.
(Ed.), Ad ances in Di e en ial E olu ion. S udies in Compu a ional In elligence.
Sp inge -Ve lag, Heidelbe g, pp. 173–196. h p://dx.doi.o g/10.1007/978-3-540-
68830-3_7.
Newman, M.E.J., 2004. Fas algo i hm o de ec ing communi y s uc u e in ne wo ks.
Phys. Re . E 69, 066133. h p://dx.doi.o g/10.1103/phys e e.69.066133.
Newman, M.E., 2006. Modula i y and communi y s uc u e in ne wo ks. P oc. Na l.
Acad. Sci. 103, 8577–8582. h p://dx.doi.o g/10.1073/pnas.0601602103.
Pa elski, L.M., Delgado, M.R., Almeida, C.P., Gonçal es, R.A., Venske, S.M., 2016.
Ex eme lea ning su oga e models in mul i-objec i e op imiza ion based on decom-
posi ion. Neu ocompu ing 180, 55–67. h p://dx.doi.o g/10.1016/j.neucom.2015.
09.111.
Po en e, H., 1985. Me hods o calcula ing g oo ed ex ude eed sec ions. Kuns s o e
Ge m. Plas . 75, 439–441.
Rauwendaal, C., 1986. Polyme Ex usion. Hanse Publishe s, Munich.
Regis, R.G., 2014. E olu iona y p og amming o high-dimensional cons ained expen-
si e black-box op imiza ion using adial basis unc ions. IEEE T ans. E ol. Compu .
18, 326–347. h p://dx.doi.o g/10.1109/TEVC.2013.2262111.
Sanches, A., Ca doso, J.M.P., Delbem, A.C.B., 2011a. Iden i ying me ge-bene icial so -
wa e ke nels o ha dwa e implemen a ion. In: P oc. o he In e na ional Con e ence
on Recon igu able Compu ing and FPGAs. Cancun, Quin ana Roo Mexico, pp.
74–79. h p://dx.doi.o g/10.1109/ econFig.2011.51.
Sanches, A., Ca doso, J.M., Delbem, A.C., 2011b. Iden i ying me ge-bene icial so wa e
ke nels o ha dwa e implemen a ion. In: 2011 In e na ional Con e ence on Recon-
igu able Compu ing and FPGAs. pp. 74–79. h p://dx.doi.o g/10.1109/ReConFig.
2011.51.
Sasimowski, E., 2008. Cha ac e is ics o an ex usion p ocess wi h a o a ing slee e o
he ba el. Polime y 53, 47–54. h p://dx.doi.o g/10.14314/polime y.2007.047.
Sasimowski, E., Siko a, J.W., K ólikowski, B., 2014. E ec i eness o polye hylene
ex usion in a single-sc ew g oo ed eed ex ude . Polime y 59, 505–510. h p:
//dx.doi.o g/10.14314/polime y.2014.505.
Schmid, P.J., 2010. Dynamic mode decomposi ion o nume ical and expe imen al da a.
J. Fluid Mech. 656, 5–28. h p://dx.doi.o g/10.1017/S0022112010001217.
Sei e , U., Jain, L., 2002. Sel -O ganizing Neu al Ne wo ks. Recen Ad ances and
Applica ions. Sp inge -Ve lag, Heidelbe g.
Siko a, J.W., Sasimowski, E., 2006a. P ocessing uni wi h o a ing cylinde segmen .
Kuns s o e In . 96, 104–105.
Siko a, J.W., Sasimowski, E., 2006b. Ve ah enseinhei mi o ie endem Zylinde be eich.
Kuns s o e 96, 104.
Siko a, R., Siko a, J.W., 1998. Ba el o an ex ude . Polish Pa en No 185728.
Soa es, A., Râbelo, R., Delbem, A., 2017. Op imiza ion based on phylog am analysis.
Expe Sys . Appl. 78, 32–50. h p://dx.doi.o g/10.1016/j.eswa.2017.02.012.
Suman, B., Kuma , P., 2006. A su ey o simula ed annealing as a ool o single and
mul iobjec i e op imiza ion. J. Ope . Res. Soc. 57, 1143–1160. h p://dx.doi.o g/
10.1057/palg a e.jo s.2602068.S2CID18916703.
Sun, C., Jin, Y., Cheng, R., Ding, J., Zeng, J., 2017. Su oga e-assis ed coope a i e
swa m op imiza ion o high-dimensional expensi e p oblems. IEEE T ans. E ol.
Compu . 21, 644–660. h p://dx.doi.o g/10.1109/TEVC.2017.2675628.
Taguchi, G., 1990. In oduc ion o Quali y Enginee ing. Mc G aw-Hill, New Yo k, NY.
Williams, M.O., Ke ekidis, G., Rowley, C.W., 2015. A da a-d i en app oxima ion o
he Koopman ope a o : Ex ending dynamic mode decomposi ion. J. Nonlinea Sci.
25, 1307–1346. h p://dx.doi.o g/10.1007/s00332-015-9258-5.
Zhou, Z., Ong, Y.S., Nguyen, M.H., Lim, D., 2005. A s udy on polynomial eg ession
and Gaussian p ocess global su oga e model in hie a chical su oga e-assis ed
e olu iona y algo i hm. IEEE Cong. E ol. Compu . 3, 2832–2839. h p://dx.doi.
o g/10.1109/CEC.2005.1555050.
An onio Gaspa -Cunha ecei ed a Ph.D. deg ee in Op i-
miza ion and Modelling o Single Sc ew Ex usion om he
Uni e si y o Minho, Po ugal, in 2000. He is cu en ly an
Auxilia y P o esso o Polyme P ocessing a he Uni e si y
o Minho. The main a eas o scien i ic ac i i y a e he
modelling o polyme ex usion-based p ocesses and mul i-
objec i e op imiza ion. He is he au ho o co-au ho o
mo e han 170 wo ks, including books edi ed, book chap-
e s, pape s published in in e na ional e e eed jou nals, and
mo e published in p oceedings o in e na ional con e ences.
In 2015 was he gene al chai o he 8 h In e na ional
Con e ence on E olu iona y Mul i-C i e ion Op imiza ion
(EMO2015) and in 2019 was he gene al chai o he
EUROGEN 2019 in e na ional con e ence.
F ancisco José Monaco holds a Ph.D. deg ee in Elec ical
Enginee ing om he Uni e si y o São Paulo (USP) in 2002.
He is cu en ly an Assis an P o esso a he Depa men o
Compu e Sys ems a USP, whe e he conduc s esea ch in
compu a ional modelling and Simula ion, wi h emphasis on
e olu iona y mul iobjec i e op imiza ion and unsupe ised
machine lea ning. D . Monaco is he au ho o se e al scien-
i ic publica ions among jou nal pape s, con e ence a icles,
and book chap e s, se ing also on con e ences and jou nal
echnical commi ees, and in na ional and in e na ional
esea ch p ojec s.
Janusz Siko a - wo ks a he Lublin Uni e si y o Tech-
nology. He s a ed wo king in 1990, in 1995 he ob ained a
doc o al deg ee, in 2000 he i le o habili a ed doc o , since
2009 he has been a ull p o esso . His scien i ic in e es s
mainly include echnological issues o polyme p ocessing.
He is he c ea o o co-c ea o o o e 100 pa en s and
u ili y models. He is he au ho o co-au ho o o e 270
publica ions. He was a coo dina o o wo in e na ional
p ojec s wi h FP7 and Ho izon 2020. He is he au ho o
opinions and expe ise o indus y, and he is in ol ed in he
p ocess o e alua ing in es men and esea ch p ojec s o
en i ies om all o e Poland. He has ecei ed many medals
and awa ds a in e na ional exhibi ions o in en ions.
Alexand e Delbem is a Full P o esso a he Depa men
o Compu e Sys ems o he Ins i u e o Ma hema ical and
Compu e Sciences in he Uni e si y o São Paulo (ICMC-
USP) and Resea ch P oduc i i y Fellow 1C a CNPq (a
B azilian Resea ch Founda ion). He was chie o he De-
pa men om 2014 o 2018. Delbem in es iga es compu e -
based solu ions o wo k wi h eal-wo ld p oblems ha can
be modelled as cybe –physical sys ems. In es iga ions ocus
on mul idisciplina y applica ions in ields such as powe
es o a ion a e blackou s in la ge-scale elec ical ne wo ks,
popula ion dynamics and in eg a ed p ojec s o supply and
a ending ne wo ks in ol ing ag ibusiness, heal hca e, en-
i onmen and social assis ance. So wa e and ha dwa e
a e de eloped o deal wi h some challenges inhe en o
complex sys ems: la ge-scale (compu a ional complexi y and
es ima ion o dis ibu ion algo i hms), mul idimensionali y
(au oma ic cons uc ion o mul i a ia e models o di e en
da a ypes), mul ic i e ia decision making and op imiza-
ion (mul iobjec i e e olu iona y algo i hms) and eal- ime
esponse (pa alleliza ion using FPGAs).
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