Artificial intelligence in single screw polymer extrusion: Learning from computational data

Enginee ing Applica ions o A i icial In elligence 116 (2022) 105397 Con en s lis s a ailable a ScienceDi ec Enginee ing Applica ions o A i icial In elligence jou nal homepage: www.else ie .com/loca e/engappai 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 2 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 3 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 4 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. 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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). 20