C uz, Ya ens J.; Villalonga, Albe o; Cas año, Fe nando; Ri as, Ma celino; Habe ,
Rodol o E.
A icle
Au oma ed machine lea ning me hodology o op imizing
p oduc ion p ocesses in small and medium-sized
en e p ises
Ope a ions Resea ch Pe spec i es
P o ided in Coope a ion wi h:
Else ie
Sugges ed Ci a ion: C uz, Ya ens J.; Villalonga, Albe o; Cas año, Fe nando; Ri as, Ma celino; Habe ,
Rodol o E. (2024) : Au oma ed machine lea ning me hodology o op imizing p oduc ion p ocesses
in small and medium-sized en e p ises, Ope a ions Resea ch Pe spec i es, ISSN 2214-7160, Else ie ,
Ams e dam, Vol. 12, pp. 1-10,
h ps://doi.o g/10.1016/j.o p.2024.100308
This Ve sion is a ailable a :
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Au oma ed machine lea ning me hodology o op imizing p oduc ion
p ocesses in small and medium-sized en e p ises
Ya ens J. C uz
a
,
*
, Albe o Villalonga
a
, Fe nando Cas a˜
no
a
, Ma celino Ri as
b
, Rodol o
E. Habe
a
a
Cen o de Au om´
a ica y Rob´
o ica, CSIC-Uni e sidad Poli ´
ecnica de Mad id, Mad id 28500, Spain
b
Cen o de Es udios de Fab icaci´
on A anzada y Sos enible, Uni e sidad de Ma anzas, Ma anzas 40100, Cuba
ARTICLE INFO
Keywo ds:
Au oma ed machine lea ning
Au oml
Model selec ion
Hype pa ame e op imiza ion
R-NSGA-II
Mul i-objec i e op imiza ion
ABSTRACT
Machine lea ning can be e ec i ely used o gene a e models capable o ep esen ing he dynamic o p oduc ion
p ocesses o small and medium-sized en e p ises. These models enable he es ima ion o key pe o mance in-
dica o s, and a e o en used o op imizing p oduc ion p ocesses. Howe e , in mos indus ial applica ions,
modeling and op imiza ion o p oduc ion p ocesses a e cu en ly ca ied ou as sepa a e asks, manually in a e y
cos ly and ine icien way. Au oma ed machine lea ning ools and amewo ks acili a e he pa h o de i ing
models, educing modeling ime and cos . Howe e , op imiza ion by exploi ing p oduc ion models is s ill in
in ancy. This wo k p esen s a me hodology o in eg a ing a ully au oma ed p ocedu e ha emb aces au oma ed
machine lea ning pipelines and a mul i-objec i e op imiza ion algo i hm o imp o ing he p oduc ion p ocesses,
wi h special ocus on small and medium-sized en e p ises. This p ocedu e is suppo ed on embedding he
gene a ed models as objec i e unc ions o a e e ence poin based non-domina ed so ing gene ic algo i hm,
esul ing in p e e ence-based Pa e o-op imal pa ame iza ions o he co esponding p oduc ion p ocesses. The
me hodology was implemen ed and alida ed using da a om a manu ac u ing p oduc ion p ocess o a small
manu ac u ing en e p ise, gene a ing highly accu a e machine lea ning-based models o he analyzed in-
dica o s. Addi ionally, by applying he op imiza ion s ep o he p oposed me hodology i was possible o inc ease
he p oduc i i y o he manu ac u ing p ocess by 3.19 % and educe i s de ec a e by 2.15 %, ou pe o ming he
esul s ob ained wi h adi ional ial and e o me hod ocused on p oduc i i y alone.
1. In oduc ion
Nowadays, gene alized adop ion o he new manu ac u ing pa a-
digms in ol es he assimila ion o key echnologies such as in elligen
da a analysis and machine lea ning (ML), among o he s, aiming a he
digi al ans o ma ion o en e p ises [46,56]. This digi al ans o ma ion
is c ucial o keep up wi h he compe i ion, especially in he case o small
and medium-sized manu ac u ing en e p ises (SMEs). One con empo-
a y a ge is o c ea e a highly econ igu able, decen alized, dynamic,
sel -o ganizing, and eal- ime (o nea eal- ime) decision-making
in as uc u e enabling o analyze cus ome expec a ions and each hei
a ge s [20]. By applying hese ans o ma ions, SMEs should be capable
o moni o ing and imp o ing hei key pe o mance indica o s (KPIs)
[67]. Howe e , in p ac ice, SMEs ace se e al di icul ies in applying
hese echnologies, mos ly ela ed o he ansi ion and main enance
cos s, inno a ion complexi y, and pe sonnel aining [50]. Addi ionally,
due o limi ed human and compu a ional esou ces, ime cons ain s and
complexi y o he op imiza ion p ocesses, SMEs usually ocus hei e -
o s on a single p oduc i i y objec i e, despi e being mo e desi able o
conside and op imize mul iple objec i es, which leads no only o mo e
e icien bu also a mo e sus ainable and en i onmen ally iendly p o-
duc ion. Due o hese obs acles, a la ge numbe o SMEs don’ coun ye
wi h he necessa y ools o con inue wi h hei digi al ans o ma ion. In
his con ex , he de elopmen o ools o gene a ing use ul in o ma ion
and sma ecommenda ions o p oduc ion sys ems in SMEs is almos
manda o y in a high-compe i i e ma ke and has a la ge numbe o
po en ial adop e s [12,42].
The in e es o indus ial ML applica ions has g own signi ican ly in
ecen yea s. Howe e , he design and deploymen o ML-based solu-
ions la gely s ill ollow adi ional app oaches, leading o high de-
pendency o domain expe s and ime-consuming de elopmen
p ocesses [13,15,16]. Fo dealing wi h his si ua ion, au oma ed
* Co esponding au ho .
E-mail add ess: [email p o ec ed] (Y.J. C uz).
Con en s lis s a ailable a ScienceDi ec
Ope a ions Resea ch Pe spec i es
jou nal homepage: www.else ie .com/loca e/o p
h ps://doi.o g/10.1016/j.o p.2024.100308
Recei ed 14 No embe 2023; Recei ed in e ised o m 25 Ap il 2024; Accep ed 10 June 2024
Ope a ions Resea ch Pe spec i es 12 (2024) 100308
2
machine lea ning (Au oML) has eme ged o sa ing ime and e o on
epe i i e asks du ing he c ea ion o ML-based solu ions [55]. The
c ea ion o an ML p oduc usually in ol es ope a ions such as da a
p e-p ocessing, ea u e enginee ing, model aining, model selec ion,
and hype pa ame e op imiza ion [36]. A ypical Au oML wo k low is
depic ed in Fig. 1. By au oma ing hese asks, an ML solu ion can be
ob ained in a sho amoun o ime, and i has he added bene i ha i
allows non-expe s o use hese echnologies [59]. Speci ically,
manu ac u ing SMEs can bene i om ongoing esea ch and de-
elopmen s on Au oML gi en he cu en need o solu ions ha a e easy
o adop and minimize he pe sonnel quali ica ion equi emen s. In
con as o la ge companies, manu ac u ing SMEs ypically do no ha e
an in-house eam o ML expe s and, wi hou Au oML ools, hey would
be o ced o ely on cos ly ex e nal alen . Addi ionally, he e sa ili y o
Au oML ools allows o apply hem ac oss di e en domains o p o-
duc ion p ocesses wi hou he need o manually c ea e a solu ion om
sc a ch each ime, con ibu ing o accele a e he digi al ans o ma ion
o manu ac u ing SMEs.
Al hough some open sou ce and comme cial Au oML solu ions a e
a ailable such as au o-sklea n [23], Au o-Ke as [32], H2O Au oML [34],
Google Cloud Au oML, Mic oso Azu e Machine Lea ning, T ans-
mog i AI, among o he s, Au oML is s ill a e y ac i e esea ch ield [71].
A ecen s udy has p oposed he use o an e olu iona y algo i hm o
inding he bes classi ie ensemble and hype pa ame e se ing in an
Au oML wo k low [61]. Ano he epo ed s a egy in oduced a
me a- ea u e- ee me a-lea ning echnique using a bandi s a egy in
budge alloca ion o building a po olio o Au oML pipelines and ca y
ou a g eedy sea ch o selec he bes candida e depending on he da ase
[24]. A p e ious e sion o a ee-based Au oML so wa e has been
ex ended o include neu al ne wo k es ima o s [48]. Simila ly, an
Au oML pla o m has been de eloped o build ML models subjec o
mul iple objec i es, as well as esou ce and ha dwa e cons ain s [64].
An Au oML amewo k ocused on deep lea ning has been de eloped o
join ly op imize deep ne wo k a chi ec u es and aining pa ame e s
[70]. The use o e olu iona y algo i hms o he au oma ic design o
composi e ML pipelines has also been explo ed [40]. O he ecen
s udies ha e been mo e ocused on he explainabili y o he models
ob ained wi h Au oML ools on Big Indus ial Da a [26].
O e all, up- o-da e epo ed Au oML solu ions gene a e ML models
(o ensemble o models) wi h op imal hype pa ame e s i ed o he
p o ided da a wi h ce ain eliabili y and ha , in some cases, a e
explainable. The p oblem hey we e designed o sol e is commonly
known as combined algo i hm selec ion and hype pa ame e op imiza-
ion (CASH). In many indus ial cases, his does no ep esen a comple e
au oma ed solu ion o p ac ical si ua ions, since he yielded model
should be also used o op imize he p ocess ha gene a ed he da a, and
his ask is cu en ly pe o med manually. In o he wo ds, cu en ap-
p oaches o applying Au oML solu ions in manu ac u ing only allows o
au oma ically ob ain da a-d i en models wi h op imal hype pa ame e s.
In o de o use hem o op imizing he p oduc ion p ocesses is necessa y
he eliance on expe s in he ield o conduc op imiza ion s udies which
a e gene ally con igu ed and igge ed manually. This is a c i ical issue
o companies acing small ba ch manu ac u ing and/o agile
manu ac u ing s a egies, equi ing as decision-making since hey
should a oid ime-consuming manual in e en ion. Mo eo e , in mos
applica ions he p e e ences o he decision make a e no aken in o
conside a ion du ing he op imiza ion p ocess, which implies, o
example, ha a e op imiza ion he echnologis o plan manage
should sea ch o an app op ia e solu ion wi hin he en i e Pa e o se .
Ano he issue wi h he exis ing Au oML solu ions is ha al hough hey
simpli y he modeling asks, i is s ill equi ed quali ied pe sonnel o use
hem, whe he hey a e used as a cloud se ice o in local se e s.
Fu he mo e, in o de o mi o he mul i ace ed na u e o p oduc ion
en i onmen s, complex models a e gene ally used, which demands
signi ican compu a ional powe . Abo e men ioned issues, ul ima ely,
ep esen a uly bo leneck o he democ a iza ion o Au oML,
specially o SMEs. These companies, accoun ing o mo e han 90 % o
all businesses in many coun ies, ha e o ace challenges such as lack o
pe sonnel wi h skills in ML o da a analy ics, o limi ed access o
compu a ional esou ces [53].
To ace hese challenges, his wo k in oduces an end- o-end ully
Au oML me hodology ha includes an e olu iona y algo i hm o he
p e e ence-based mul i-objec i e op imiza ion o p oduc ion p ocesses.
The goal o his me hodology is no only o gene a e op imal ML-based
models o he p oduc ion p ocesses bu also using hese models o ob ain
and ecommend di e en se s o pa ame e s ha he use can use o
imp o e he pe o mance o he p oduc ion p ocess by se ing desi ed
op imal egimes acco ding o he Pa e o op imali y c i e ion, imp o ing
p oduc i i y and hus e iciency. The use o he p e e ence-based op i-
miza ion is especially bene icial because he esul s gene a ed ha e been
al eady e ined conside ing he decision make ’s in e es s, making hem
di ec ly exploi able in he p oduc ion p ocess, which is an ad an ageous
app oach o highly dynamic en i onmen s. This implies ha i is no
necessa y o manually explo e and assess op imiza ion esul s. Addi-
ionally, in o ma ion abou he mos ele an da a ea u es o modeling
is also p o ided. Fu he mo e, by simpli ying he way o in e ac ing wi h
his me hodology, i is gua an ee ha non-expe use s can easily use i .
This me hodology is applied and alida ed using da a om a
manu ac u ing case s udy.
The pape consis s o i e sec ions. A e his in oduc ion, all he
aspec s o he me hodology a e explained in Sec ion 2. Sec ion 3 in-
oduces a case s udy o alida ing he me hodology whe e he Au oML
pipeline is c ea ed and hen used o ca y ou a wo-objec i es op imi-
za ion. La e , Sec ion 4 discusses he ob ained esul s. Finally, Sec ion 5
shows he conclusions and ou lines u u e wo ks.
2. Ma e ials and me hods
2.1. Da ase p epa a ion, p ep ocessing and gene al desc ip ion o he
me hodology
The p oposed me hodology s a s by p ep ocessing a his o ical
da ase o a p oduc ion p ocess and hen pe o m h ee main s eps: (1)
de e mine which a e he ea u es wi h highe in luence on p ede ined
KPIs o a p oduc ion sys em, (2) c ea e eg ession models o each KPI o
he p oduc ion sys em, and (3) use hese models o gene a e pa ame-
iza ions ha imp o e he KPIs h ough a mul i-objec i e op imiza ion
algo i hm.
A necessa y s ep be o e applying his me hodology consis s o
c ea ing a his o ical da ase o he p oduc ion sys em con aining a i-
ables, ea u es and KPIs alues. Mos ML lib a ies ha implemen he
algo i hms included in he me hodology a e designed o wo k only wi h
nume ical ea u es. Since he me hodology will be buil on op o hese
lib a ies he da ase s should be p epa ed in ad ance o comply wi h his
equi emen . I he da a collec ed o iginally con ains ca ego ical
Fig. 1. Typical Au oML wo k low.
Y.J. C uz e al.
Ope a ions Resea ch Pe spec i es 12 (2024) 100308
3
ea u es hey mus be encoded using an o dinal codi ica ion scheme o a
one-ho codi ica ion scheme depending on i hey ha e inhe en o de o
no , espec i ely. Also, he KPIs included in he da ase should be
quan i a i e me ics ela ed o he p oduc ion p ocess, which implies
ha he models ha will be gene a ed using he me hodology a e
eg ession models. In addi ion o his o ical da a, an op imiza ion
objec i e (i.e., minimiza ion o maximiza ion) o each KPI, e e ence o
desi ed alues (e.g., KPIs alues ha ep esen desi ed p oduc i i y), a
easible ange o each ea u e, and any o he cons ain s, i any, should
be also de ined o be able o ca y ou he op imiza ion p ocess.
The e a e no limi s on he numbe o inpu ea u es o he numbe o
ou pu s (KPIs) o conside ; al hough, he me hodology is designed o
being applied o SMEs, he e o e he expec ed da a should no con ain as
much in o ma ion as he da a acqui ed in a massi e shop loo . Assessing
he pe o mance o he p oposed me hodology o big olumes o da a is
ou o he scope o his s udy.
The inpu s o he me hodology a e a his o ical da ase , and a ile
speci ying he KPIs’ objec i es, e e ence alues, ea u es ange, and
cons ain s. These wo iles a e he only equi emen s o in e ac ing
wi h he p oposed me hodology o e a pla o m designed o execu e all
he p ocessing and gene a e a ile wi h he op imiza ion esul s [4,41].
The idea behind his app oach is o make i possible o e en SMEs ha
do no ha e he equi ed compu a ional capaci y o s a wi h ML o
p og amming skills o bene i om his ype o echnology, in line wi h
he concep s ou lined o se ice-based pla o ms o he democ a iza-
ion o A i icial In elligence [21,27].
Once he da ase is ecei ed, he i s s ep ca ied ou by he me h-
odology is da a p ep ocessing. P ep ocessing is c ucial o p epa ing
da a o machine lea ning models. Fo example, aw da a is o en
inconsis en , con aining missing alues o e o s ha can a ec model
aining. Remo ing poo -quali y da a can enhance model obus ness and
pe o mance. The e o e, he ecei ed da a i is examined o de ec
missing da a and dele e he co esponding samples, i applicable. Then,
he in eg i y o he da ase is checked o comply wi h he speci ica ion o
only con aining nume ical alues. Once he da ase in eg i y has been
checked, i is spli using 60 % da a o aining, 20 % o alida ion, and
20 % o es ing. Then, he aining, alida ion, and es inpu ec o s o
each ea u e x a e no malized using he ollowing equa ion:
x s d = x−
μ
x,
σ
x, (1)
whe e x is a ec o con aining he ea u e alues,
μ
x, is he mean o he
ea u e alues in he aining se , and
σ
x, is he s anda d de ia ion o he
ea u e alues on he aining se .
No malizing he ea u es is a c i ical s ep in he me hodology
because la e he ea u es will be analyzed o de e mine which a e he
mos ele an ones o each KPI. A e da a no maliza ion, he me h-
odology p oposes a se ies o s eps o accomplish i s goals. Fig. 2 shows a
high-le el schema o he p oposed me hodology. The ollowing sub-
sec ions desc ibe he mos impo an ope a ions o he me hodology.
2.2. Fea u e selec ion
The ea u e enginee ing s ep is undamen al o c ea ing high-quali y
ML models, since hey depend, ul ima ely, on he da a used o aining.
The goal o ea u e enginee ing is o imp o e he quali y o he a ailable
da a o making he aining p ocess mo e e icien . Fea u e enginee ing
Fig. 2. High-le el schema o he p oposed me hodology.
Y.J. C uz e al.
Ope a ions Resea ch Pe spec i es 12 (2024) 100308
4
can include ope a ions such as ea u e gene a ion o ea u e selec ion.
Pa icula ly, he design o he p oposed me hodology does no conside
ea u e gene a ion since his ope a ion adds mo e ea u es o he da ase
inc easing he complexi y o he models and he compu a ional ime.
Addi ionally, he au oma ed gene a ion o new ea u es can esul in
non-in e p e able ea u es o edundan in o ma ion which can lead o
o e i ing o he models. Al e na i ely, ea u e selec ion is conside ed
in he p oposed me hodology o dealing wi h da ase s ha al eady
con ain i ele an o edundan ea u es, which impac in he compu-
a ional cos o esul in biased models. Fea u e selec ion allows o
choose he mos use ul ea u es o a da ase o building models,
esul ing no only in a educ ion o he dimensionali y o he da a; bu
also leads o mo e compac models wi h be e gene aliza ion abili y and
educed compu a ional ime [3,11,52]. Fea u e selec ion is also an
enable o explainabili y in ML since i helps iden i y which inpu s ha e
he s onges impac on he ou pu s.
Gi en ha he me hodology is designed o wo k wi h a wide ange o
da a and he e is no a p io i knowledge o how many ea u es and
samples will con ain he da ase , a me hod based on Pea son’s co ela-
ion coe icien was chosen o ea u e selec ion. This is a widely used
app oach when he da a analyzed consis s o nume ical inpu s and
ou pu s, which is he case in he p oposed me hodology [25]. Addi-
ionally, by using his app oach, compu a ional cos emains low, which
is necessa y o ob ain he desi ed in o ma ion in a ela i ely sho
pe iod, aking in o conside a ion ha he e a e o he asks in he
me hodology, besides ea u e selec ion, ha equi es mo e ime o
execu e.
2.3. Modeling
Once he ea u e selec ion p ocess is inished he nex s ep is he
modeling conside ing p ees ablished KPIs. The objec i e is o c ea e
models capable o ep esen ing he ela ionship among he p oduc ion
p ocess pa ame e s and a iables (inpu s) wi h KPIs as ou pu s. Among
he a ailable modeling app oaches, ML is widely used in many esea ch
ields, o en as an al e na i e app oach [17]. Speci ically, ML echniques
a e being used o p edic KPIs aking ad an age o he a ailabili y o
la ge amoun s o da a gene a ed by new digi al sys ems [54]. Typically,
hese s udies a e ocused on h ee main KPIs ca ego ies: economic, so-
cie al, and en i onmen al. Some o he mos simple, ye e y used ML
echniques o modeling KPIs a e Mul ilaye Pe cep on (MLP) [38,43,
49], Suppo Vec o Reg ession (SVR) [22,37,47], Ridge Reg ession
(RR) [29], Leas Absolu e Sh inkage and Selec ion Ope a o eg ession
(LASSO) [6], Random Fo es (RF) (T. [57]), k-Nea es Neighbo s (k-NN)
[28], Gaussian P ocess Reg ession (GPR) [44,51] and Con olu ional
Neu al Ne wo ks (CNNs) [14,66].
The p e iously men ioned echniques we e selec ed o he sake o
keeping ce ain le el o di e si y and acco ding o he s a e-o - he-a
echniques in sma manu ac u ing scena ios, which is c ucial o
de e mining he mos app op ia e model [15]. In he speci ic case o
GPR, i s inclusion in he se o modeling s a egies elies on he size o
he da ase . Speci ically, i he da ase con ains mo e han 1500 samples
his echnique is au oma ically disca ded because o he high compu-
a ional cos o GPR, which g ows cubically wi h espec o he numbe
o samples due o he need o calcula ing ma ix in e sions. Ne e he-
less, o he echniques can be included, bu adding mo e models implies
mo e aining e o , analysis and o e all inc easing o compu a ional
cos du ing execu ion ime o he Au oML p ocedu e.
2.4. Hype pa ame e op imiza ion
One o he key s eps o he me hodology consis s o op imizing he
hype pa ame e s o he models. Du ing he c ea ion o a model i s
hype pa ame e s mus be speci ied; howe e , i is ha d o know a p io i
which hype pa ame e s alues will yield a good- i ing model. Fo his
eason, ML p ac i ione s o en explo e he easible sea ch space looking
o he bes hype pa ame e combina ion. Typically, one o he
ollowing s a egies is used o his ask: g id sea ch [9,65], andom
sea ch [31,62], o Bayesian sea ch (J. [68]).
G id sea ch implies ca ying ou an exhaus i e sea ch including all
he possible combina ions o hype pa ame e s. Fo his s a egy, i is
necessa y o de ine a ange o limi he sea ch space o unbounded
hype pa ame e s and o disc e ize he con inuous hype pa ame e s.
Random sea ch explo es hype pa ame e combina ions a andom
wi hin he sea ch space and, in his case, con inuous hype pa ame e s
do no necessa ily ha e o be disc e ized. The main sho coming o g id
and andom sea ch is ha hey do no ake ad an age o p e ious
e alua ions o hype pa ame e combina ions. To deal wi h his,
Bayesian op imiza ion c ea es a p obabilis ic model o a unc ion ha
maps hype pa ame e s alues o a me ic o e alua ing he model
i ness. On e e y i e a ion, a new p omising hype pa ame e combina-
ion based on he p obabilis ic model is chosen and e alua ed; hen, he
p obabilis ic model is upda ed using his new in o ma ion. In p ac ice,
Bayesian op imiza ion has demons a ed o ob ain be e esul s in ewe
e alua ions han g id and andom sea ch ([69]). Fo his eason, i was
selec ed as he hype pa ame e op imiza ion s a egy in he p oposed
me hodology o all he algo i hms, excep in he case o GPR, which
only equi es e alua ing se e al ke nels.
Table 1 summa izes pa ame e s o he di e en ML-based models
conside ed in he me hodology.
2.5. Model selec ion c i e ion
The me hodology explo es di e en ypes o models o each KPI, bu
only one model o each KPI is used la e and he o he s a e disca ded. In
o de o selec he mos app op ia e model acco ding o he co e-
sponding KPI, a compa ison based on a p ede ined me ic is ca ied ou .
The pe o mance index o igu e o me i used o selec ing a model was
he mean squa ed e o (MSE). MSE is di e en iable and o his eason
is commonly used as he de aul loss unc ion in ML- ela ed amewo ks.
MSE is also widely used o e alua ing eg ession models in ML appli-
ca ions. This me ic is pa icula ly a o ed o i s abili y o penalize
Table 1
Hype pa ame e s/a chi ec u e o he models.
Model Hype pa ame e /a chi ec u e Range/op ions
MLP numbe o hidden laye s 1–4
numbe o uni s pe laye 16–256
ini ialize glo o (no mal), glo o (uni o m), he
(no mal), he (uni o m), lecun
(no mal), lecun (uni o m)
ac i a ion ReLU, sigmoid, anh, linea
SVR ke nel linea , polynomial, b , sigmoid
deg ee 2–5
C 0–10
ε
0.1–1
RR alpha 0.1–10
sol e s d, cholesky, lsq , spa se_cg, sag,
saga
LASSO alpha 0.1–10
maximum numbe o i e a ions 100–2000
ole ance 0.00001–0.0001
RF numbe o es ima o s 10–200
k-NN numbe o neighbo s 5–100
algo i hm ball ee, kd ee, b u e
GPR ke nel cons an , whi e, b , Ma ´
e n, a ional
quad a ic, exp-sine-squa ed, do -
p oduc
CNN numbe o con olu ional laye s 1–2
con olu ional
laye
numbe o
il e s
16–128
ac i a ion ReLU, sigmoid, anh
dense laye numbe o
uni s
16–128
ac i a ion ReLU, sigmoid, anh
d opou laye a e 0–0.5
Y.J. C uz e al.
Ope a ions Resea ch Pe spec i es 12 (2024) 100308
5
la ge e o s mo e se e ely han smalle ones [30]. This sensi i i y o
ou lie s is use ul o selec ing models ha pe o m well on a e age bu
also in p esence o ex eme alues.
2.6. P ocess op imiza ion
A e modeling conside ing KPIs, he nex s ep is he op imiza ion o
he p oduc ion p ocess pa ame e s. Many op imiza ion me hods a e
cu en ly being used in esea ch s udies o p ocess op imiza ion
including e olu iona y algo i hms [16,60], pa icle swa m op imiza ion
([5,58]), c oss-en opy me hod [7,8], among o he s. Fo op imizing he
p oduc ion p ocesses in he p oposed me hodology, i was selec ed he
e e ence poin based non-domina ed so ing gene ic algo i hm II
(R-NSGA-II) as op imiza ion p ocedu e, which is a modi ica ion o he
non-domina ed so ing gene ic algo i hm II (NSGA-II) o aking in o
conside a ion he desi ed esul s in he op imiza ion p ocess.
NSGA-II is a mul i-objec i e e olu iona y algo i hm o inding
Pa e o-op imal on s [18]. NSGA-II was c ea ed o deal wi h some
sho comings o p e ious mul i-objec i e op imiza ion algo i hms such
as high compu a ional complexi y and non-eli is s a egies. This algo-
i hm implemen s a as non-domina ed so ing app oach and a as
c owded dis ance compu a ion ha allows inding mo e e icien ly a
be e sp ead o solu ions and be e con e gence nea he ue
Pa e o-op imal on when compa ed o o he s a egies [63]. I s con-
enience o op imizing KPIs o indus ial p ocesses has been p o ed
h ough many p ac ical applica ions [35,39]. Howe e , he solu ions
ob ained by using NSGA-II can include non-desi able esul s, e en i
hey a e Pa e o-op imal. In his case, i is necessa y o selec om he
Pa e o se he adequa e solu ions. This ask can be au oma ed by using
he R-NSGA-II algo i hm.
R-NSGA-II modi ies NSGA-II o include a p e e ence-based op imi-
za ion s a egy ha allows o pa allelly ind a se o Pa e o-op imal so-
lu ions nea some e e ence poin s [19]. I s ou line is e y simila o
NSGA-II, bu i implemen s a modi ied su i al selec ion. The in-
di iduals a e i s selec ed on wise; howe e , no all o hem a e
allowed o su i e. A second selec ion using a ank based on he
no malized Euclidean dis ance o he e e ence poin s is ca ied ou . The
no malized dis ance d om an indi idual (x) o he e e ence poin z is
calcula ed using he ollowing equa ion:
d=
∑
M
i=1( i(x) − zi
max
i− min
i)2
√
√
√
√(2)
whe e M is he numbe o objec i es and max
i and min
i a e he popula ion
maximum and minimum unc ion alues o he i- h objec i e. Finally, R-
NSGA-II also implemen s he ϵ-based selec ion s a egy o ensu e a
sp ead o solu ions nea he p e e ed Pa e o-op imal egions.
A de ailed desc ip ion o he algo i hm can be ound in he docu-
men a ion o he Pymoo lib a y [10]. Table 2 summa izes he pa ame-
e s assigned o his algo i hm in he p oposed me hodology.
3. A manu ac u ing case s udy
Fo alida ing he p oposed me hodology, a p oduc ion p ocess o an
SME specialized in manu ac u ing ae ospace componen s is conside ed
as case s udy. The complexi y o ae ospace sys ems poses a unique
challenge in manu ac u ing due o hei high-pe o mance equi emen s
ela ed o sa e y conce ns. The analyzed company is cu en ly acing a
challenge ha ela es o ansi ioning owa ds small ba ch and agile
manu ac u ing pa adigms, which a e bo h c ucial s a egies o mode n
businesses. This shi equi es a high deg ee o lexibili y and espon-
si eness o accommoda e a ying cus ome demands and o manage
equen changes in p oduc designs and speci ica ions. The e o e, i is
necessa y he use o ools o gene a ing ac ionable insigh s, enabling a
as e and mo e in o med decision-making. In his con ex , da a-d i en
solu ions enable he c ea ion o p oac i e managemen ools o
enhancing he p ocess e iciency and mee p oduc ion equi emen s in a
imely manne . Speci ically, ML p esen s se e al ad an ages o e o he
app oaches o ep esen ing he complex ela ionships unde lying da a
om manu ac u ing p ocesses including i s capaci y o handling la ge
mul i-dimensional olumes o da a beyond human abili y, i s gene al-
iza ion capaci y, and scalabili y, among o he s. Howe e , his company
does no ha e pe sonnel wi h ML knowledge. Al hough exis ing Au oML
ools could be help ul in his case since hey simpli y he wo k low o
c ea ing models, he e would s ill be un esol ed challenges i hey we e
used. Fi s ly, once he models a e c ea ed hey mus be used o gene -
a ing op imal pa ame iza ions o he p oduc ion p ocess bu cu en
Au oML me hodologies lack his s age. In o he wo ds, hey allow o
c ea e he models and op imize hei hype pa ame e s bu do no
au oma ically exploi hese models. Secondly, while de eloping a
cus om solu ion o exploi ing he models gene a ed by exis ing Au oML
ools is possible, on he one hand, his implies a long de elopmen
pe iod, which would delay he ansi ion o he SME o he new
manu ac u ing pa adigms, and on he o he hand, an in-dep h knowl-
edge o ML and mul i-objec i e op imiza ion is equi ed, which he
company does no ha e. Unde hese ci cums ances, he p oposed
me hodology is a sui able candida e since i allow o c ea e he models
and au oma ically use hem o gene a e op imal pa ame iza ions o he
p oduc ion p ocess o suppo ing he decision-making and, addi ion-
ally, i only equi es minimal aining o he s a o each hem how o
s uc u e he da a and con igu a ion ile, how o send he in o ma ion o
he me hodology, and how o in e p e he esul s, a oiding ha ing o
ain hem in machine lea ning subjec s.
The p ocess s a s by machining an aluminum AL7075-T6 (UNS
A97075) wo kpiece in a Kondia HS1000 machining cen e equipped
wi h a Siemens 840D open-a chi ec u e CNC. The wo kpiece is
machined acco ding o ou pa ame e s: adial dep h o cu (ae), ool
diame e (Diam), eed a e ( z) and spindle o a ion speed (ssp). Du ing
he machining p ocess six signals a e measu ed: ib a ions in x axis
(AcelX), ib a ions in y axis (AcelY), esul ing ib a ions (AcelR), o ce in
x axis (Fx), o ce in y axis (Fy) and esul ing o ce (F ). Fo measu ing he
ib a ions, i was used a PCB Piezo onics WJT 352B senso , while a
Kis le 9257B dynamome e was used o measu ing he o ces. A e
machining, he quali y o he componen is assessed using a Ca l Zeiss
Su com 130 s ylus p o ilome e o measu ing i s oughness a e age,
which is he mos used index o cha ac e ize he su ace oughness [7].
Depending on he measu ed oughness, he ope a o classi ies he
componen in o non-de ec i e (complian ) o de ec i e (non-complian )
and places i in he co esponding s ack. Then, he p oduc ion cycle
s a s again. In addi ion o he machining pa ame e s and signals
measu ed, he ope a o ’s a igue ( g) is also moni o ed. E e y hou he
ope a o should indica e in a ques ionnai e he pe cei ed le el o a igue
in a ange om 1 o 8, being 1 he lowes le el and 8 he highes .
Two KPIs we e used o assess he beha io and pe o mance o he
manu ac u ing p ocess. The wo KPIs selec ed we e h oughpu ( p) ha
deno es he a e a which componen s a e p ocessed and sc ap (sc) ha
deno es he p opo ion o de ec i e componen s p oduced. Bo h KPIs
Table 2
R-NSGA-II pa ame e s.
Pa ame e Value
popula ion size 500
o sp ing size 500
sampling andom
c osso e ope a o simula ed bina y c osso e
p obabili y 0.9
dis ibu ion index 15
mu a ion ope a o polynomial mu a ion
p obabili y 1.0
dis ibu ion index 20
numbe o gene a ions 100
ϵ 0.00001
Y.J. C uz e al.
Ope a ions Resea ch Pe spec i es 12 (2024) 100308
6
we e eco ded hou ly. The ollowing equa ions shows how o calcula e
hese wo a iables:
p = c
l(3)
sc =dc
c(4)
whe e c is he o al numbe o componen s p oduced in a p ede ined
ime window, dc is he numbe o de ec i e componen s p oduced in he
same ime window, and l is he leng h o he ime window, whose alue
has been se a one hou o his s udy.
Da a comp ising 15 wo king days wi h di e en machining pa am-
e iza ions we e collec ed. Fo unning and implemen ing he p oposed
me hodology in a compu a ional p ocedu e, a pe sonal compu e
equipped wi h an In el Co e i7–10,750 H Cen al P ocessing Uni
ope a ing a 2.6 GHz, wi h 16 GB DDR4 Random Access Memo y and an
NVIDIA GeFo ce RTX 2060 G aphics P ocessing Uni wi h 6 GB GDDR6
o capaci y was used. The me hodology was implemen ed on op o
Sciki -lea n [45], Tenso Flow [1], Op una [2], and Pymoo [10] lib a ies.
4. Resul s and discussion
A e collec ing and condi ioning da a om he manu ac u ing p o-
cess desc ibed in Sec ion 3, he p oposed me hodology and he co e-
sponding compu a ional p ocedu e was applied. Fig. 3 shows he
dis ibu ion o ea u es alues be o e and a e da a no maliza ion,
whe e i can be seen how he di e ence in he scales is d as ically
educed.
The i s ou comes ob ained we e he selec ed ea u es o each KPI
which a e summa ized in Table 3 whe e he F- alues a e de i ed om
Pea son’s co ela ion coe icien . This measu e is implemen ed in Sciki -
lea n esul ing always in a non-nega i e alue and i is used o ank he
co ela ion o he ea u es wi h he a ge . The F- alue in eg ession is
he esul o a null hypo hesis es whe e he null hypo hesis is ha all
he eg ession coe icien s a e equal o ze o, excep he in e cep . An
F- es compa es his model wi h a model ha includes coe icien s
di e en han ze o and decides whe he hese imp o ed he p edic ions
o no . Then, i is assumed ha he la ge he alue ob ained o a
ea u e, he mo e ele an i is o he model i ing.
I is in ui i e ha o p he ea u e wi h he mos ele an one is he
eed a e ( z) which is di ec ly ela ed o he machining speed, ha ing,
consequen ly, a e y la ge F alue compa ed o he o he ea u es. The
selec ion o ool diame e (Diam) was also likely since i has a di ec
impac on he p ocess speed gi en ha a la ge ool diame e is aduced
in ewe ope a ions o co e he same su ace o a wo king piece. I is
also comp ehensible ha he ib a ion signals (AcelR, AcelX, and AcelY)
we e selec ed gi en ha a highe machining speed will be expec edly
e lec ed as an inc ease in ib a ions. As can be deduc ed om he
selec ion o a igue ( g), he human ac o is also ele an o p because
a a igued ope a o is mo e likely o slowe he wo k, which dec eases
he p oduc i i y o he p ocess. In he case o sc is ema kable ha he
ou pa ame e s o he machining p ocess (ssp, ae, z, and Diam) ha e
been selec ed, deno ing he impo ance o a good pa ame iza ion o
achie ing a good quali y p oduc . Also, wo p ocess signals (Fy and
AcelR) we e selec ed, indica ing ha machining e ec s a e p obably
be e e lec ed in hese wo signals han in he o he s.
A e selec ing he ea u es o each KPI, he nex s ep o he me h-
odology is o gene a e a se o models, op imize co esponding hype -
pa ame e s and hen e alua e hese models. Table 4 summa izes he
esul s o he bes ins ance o each model ype ob ained a e comple ing
he p e iously men ioned ope a ions. The alues shown o he coe i-
cien o de e mina ion (R
2
) we e compu ed using he mos gene al
de ini ion o R
2
, also e e ed o as pseudo-R
2
. In he case o GPR, his
model was no e alua ed due o he numbe o samples which exceeded
1500, as desc ibed in Sec ion 2.3. The model wi h he lowes MSE alue
was selec ed o each KPI, which in he case o p was an MLP and o sc
was a k-NN. The a chi ec u e/hype pa ame e s o hese models a e
summa ized in Table 5.
Fig. 3. Da a dis ibu ion. (a) be o e no maliza ion, (b) a e no maliza ion.
Table 3
Selec ed ea u es o each KPI.
Fea u es F- alues o
p
Selec ed o p
modeling
F- alues
o sc
Selec ed o sc
modeling
AcelR 424.005 x 294.846 x
AcelX 339.367 x 147.229
AcelY 286.907 x 234.186
ae 25.130 466.176 x
Diam 4449.780 x 278.234 x
g 30.591 x 8.124
F 1.017 103.049
Fx 2.860 13.034
Fy 0.221 449.584 x
z 14,850.700 x 291.062 x
ssp 15.777 885.122 x
Table 4
Tes esul s ob ained o he di e en models a e hype pa ame e
op imiza ion.
Algo i hm R
2
o p MSE o p R
2
o sc MSE o sc
SVR 0.985 5.192 0.567 1 ×10
−4
GPR - - - -
RF 0.981 5.319 0.625 9 ×10
−5
RR 0.956 6.943 0.397 1.2 ×10
−4
LR 0.949 8.136 0.201 1.5 ×10
−4
k-NN 0.979 6.737 0.735 6 ×10
−5
MLP 0.999 2.585 0.698 7 ×10
−5
CNN 0.998 3.189 0.731 6 ×10
−5
Y.J. C uz e al.
Ope a ions Resea ch Pe spec i es 12 (2024) 100308
7
In o de o analyze he e ec i eness o he p oposed me hodology
wi h ega d o o he s a e-o - he-a Au oML amewo ks, a compa ison
is conduc ed and esul s a e shown in Table 6. Fo bo h KPIs, he esul s
ob ained a e e y simila . I is impo an o ema k he complexi y o he
solu ions o e ed by some o hese amewo ks, o ins ance, he s acked
ensemble gene a ed by H2O o p including up o 74 base models o he
ensemble gene a ed by au o-sklea n o sc including up o se en base
models. In he cases o au o-sklea n, TPOT and H2O, he amewo ks
we e con igu ed o ha e an execu ion ime o app oxima ely 15 min,
simila o he execu ion ime o he compu a ional p ocedu e ha im-
plemen s he p oposed me hodology.
Finally, he las s ep o he p oposed me hodology consis s o using
he gene a ed models in a mul i-objec i e op imiza ion o he p oduc-
ion p ocess. In his s ep, only he adjus able pa ame e s a e op imized,
while non-modi iable pa ame e s a e cons ained o be equal o hei
mean alues in he aining se . I should be no iced ha he de ini ion o
he op imiza ion p oblem is one o he i s s eps o he me hodology;
which allows o ca y ou he p ocess op imiza ion au oma ically
wi hou any in e en ion a e selec ing he models o all he KPIs. The
ollowing equa ions desc ibe he op imiza ion p oblem o he case
s udy:
MaxM1(x[F1]) (5)
MinM2(x[F2]) (6)
subjec oAcelR =AcelR (7)
AcelX =AcelX (8)
AcelY =AcelY (9)
g = g (10)
F =F (11)
Fx =Fx (12)
Fy =Fy (13)
ae ∈ {1,2,3,4,5}mm (14)
Diam ∈ {8,10,12,16,20}mm (15)
0.025 m/min ≤ z ≤0.13 m/min (16)
15,000 pm ≤ssp ≤22,500 pm (17)
M1(x[F1]) ≥ 0 (18)
M2(x[F2]) ≥ 0 (19)
whe e M1 and M2 ep esen he models p e iously selec ed by he
me hodology o p and sc, espec i ely. In his case, x[F1]and x[F2]
ep esen he selec ed ea u es o each KPI. Eqs. (5) and (6) a e he
objec i es o he p oblem and he emaining Equa ions ep esen he
cons ain s. Eqs. (7)–(13) a e equali y cons ain s o he non-
con ollable pa ame e s o he p ocess, Eqs. (14)–(17) a e inequali y
cons ain s o he con ollable pa ame e s whe e hei easible ange is
speci ied, and Eqs. (18) and (19) a e inequali y cons ain s o he
models since he wo KPIs o he case s udy a e non-nega i e.
The Pa e o-op imal pa ame iza ions o he p oduc ion p ocess a e
gene a ed ia he R-NSGA-II algo i hm. The ob ained esul s a e shown
in Fig. 4. Fo illus a ion pu poses on con e gence, an op imiza ion o
he p oduc ion p ocess by means o he NSGA-II algo i hm was also
ca ied ou , using he same hype pa ame e s han R-NSGA-II, excep o
popula ion and o sp ing sizes, which we e se o 1000. Addi ionally, he
pe o mance o he p ocess unde he pa ame iza ion ecommended by
he plan manage be o e he de elopmen o his s udy was also
included as a baseline.
Table 5
Selec ed models hype pa ame e s.
KPI Algo i hm A chi ec u e/Hype pa ame e s
p MLP Numbe o hidden laye s:2
Numbe o uni s in he 1s hidden laye : 128
Ac i a ion unc ion o he 1s hidden laye : anh
Numbe o uni s o he 2nd hidden laye : 64
Ac i a ion unc ion o he 2nd hidden laye : anh
Numbe o uni s in he ou pu laye : 1
Ac i a ion unc ion o he ou pu laye : linea
Ini ialize : he (uni o m)
sc k-NN Numbe o neighbo s: 99
Algo i hm: kd ee
Table 6
Compa ison o he modeling ask.
Au oML
amewo k
Bes model ype o p R
2
o
p
MSE
o p
Bes model ype o sc R
2
o
sc
MSE
o sc
au o-sklea n [23] ensemble: 3 g adien boos ing eg esso s +1
au oma ic ele ance de e mina ion eg esso
0.989 5.036 ensemble: 2 g adien boos ing eg esso s +1 ex emely
andomized ees eg esso +1 adap i e boos ing eg esso +
1
k-NN eg esso +1 MLP model +1 au oma ic ele ance
de e mina ion eg esso
0.756 6 ×
10
−5
TPOT [33] ex eme g adien boos ing eg esso 0.995 2.609 ex emely andomized ees eg esso 0.727 6 ×
10
−5
H2O [34] s acked ensemble: (74 base models) 0.986 6.048 s acked ensemble: 1 g adien boos ing eg esso +1 ex eme
g adien boos ing eg esso +1 dis ibu ed RF eg esso
0.748 6 ×
10
−5
P oposed
me hodology
MLP model 0.999 2.585 k-NN eg esso 0.735 6 ×
10
−5
Fig. 4. Resul s o e e ence alues a (105, 0.005), (125, 0.02) and (147, 0.02).
Y.J. C uz e al.
Ope a ions Resea ch Pe spec i es 12 (2024) 100308
8
Based on he esul s achie ed, he p oduc ion p ocess could be
pa ame ized o wo k in desi ed egimes nea he e e ence poin s. The
solu ions associa ed o e e ence 1 in Fig. 4 educe sc by 3.36 % on
a e age compa ed o he baseline pe o mance, a he cos o dec easing
p by 22.69 % on a e age. In he case o he solu ions associa ed o
e e ence 2, hey enable educing sc by 2.46 % on a e age compa ed o
he baseline pe o mance, a he cos o dec easing p by 9.57 % on
a e age. Finally, i can be seen how he solu ions associa ed o e e ence
3 domina e he baseline pe o mance. In his case, sc is educed by 2.15
% on a e age compa ed o he baseline pe o mance, while inc easing p
by 3.19 % on a e age. Wi h hese esul s, a echnologis , plan manage
o any designa ed pe son in he SME can decide on whe he o adop a
solu ion ha imp o es bo h KPIs o , i educ ion o de ec s is c i ical, o
adop a solu ion ha implies dec ease he p oduc i i y bu minimize he
numbe o de ec i e componen s. Fo es ing pu poses, one o he pa-
ame iza ions o he Pa e o se associa ed o e e ence 3 was applied o
he p oduc ion p ocess, esul ing in he ollowing ope a ing condi ions:
p =144.6 componen p oduced/hou and sc =0.024. These esul s a e
in line wi h he alues p edic ed in he Pa e o on .
As can be seen in his case s udy, he p oposed me hodology allowed
an SME wi hou in-house ML expe ise o c ea e accu a e models o wo
KPIs o i s manu ac u ing p ocess and au oma ically use hem o ind
op imal pa ame iza ions o he p oduc ion.This was possible hanks o
he holis ic app oach o he me hodology ha ex ends he classic
Au oML wo k low o include an au oma ed op imiza ion s age whe e he
p e iously c ea ed models a e used as objec i e unc ions wi hou he
need o manual in e en ion. In addi ion, he capabili ies o he op i-
miza ion algo i hm allowed o conside he ope a o p e e ences du ing
he gene a ion o he op imal pa ame iza ions, s eamlining he
decision-making p ocess.
5. Conclusions
This wo k p esen s an au oma ed machine lea ning me hodology o
op imizing manu ac u ing p ocesses in SMEs by combining he s anda d
asks o Au oML ools, such as da a p ep ocessing, ea u e selec ion,
model aining, and hype pa ame e op imiza ion, wi h p e e ence-
based mul i-objec i e op imiza ion. Fo his pu pose, he basic
Au oML wo k low is used o gene a e models o each o he KPIs o he
p oduc ion p ocess and, hen, a new au oma ed op imiza ion s ep is
in oduced o using he gene a ed models as objec i e unc ions,
esul ing in op imal pa ame iza ions o he p oduc ion p ocess. By
simpli ying he way o in e ac ing wi h his me hodology, i is possible
ha manu ac u ing SMEs wi h low a ailabili y o highly-skilled
pe sonnel o limi ed compu ing powe can bene i om ad anced
echnologies making easie he digi aliza ion and applica ion o Indus y
4.0 pa adigm.
The me hodology was implemen ed and alida ed in a p oduc ion
p ocess whe e, i s ly, he mos ele an ea u es o modeling each key
pe o mance indica o we e au oma ically selec ed based on he Pea -
son’s co ela ion coe icien , allowing o educe he dimensionali y o
he da a. Then, models o key pe o mance indica o s we e gene a ed
and hei a chi ec u e/hype pa ame e s op imized. Gene a ed models
we e compa ed o models ob ained h ough o he Au oML amewo ks
o e ing simila esul s, wi h alues o MSE =2.585 and R
2
=0.999, and
MSE =6 ×10
−5
and R
2
=0.735, espec i ely. Finally, he models we e
used as objec i e unc ions in he R-NSGA-II algo i hm o inding
op imal pa ame iza ions o he p oduc ion p ocess, yielding an
imp o emen in bo h KPI, educing sc ap by 2.15 % and inc easing
h oughpu by 3.19 %, wi h ega d o he baseline o con en ional
pa ame iza ion conside ing only a single p oduc i i y a ge . These
imp o emen s con ibu e o a highe p oduc ion a e while, a he same
ime, he numbe o de ec i e componen s is educed, which unde sco e
he po en ial o he p oposed me hodology o signi ican ly boos o e all
e iciency and p o i abili y o SMEs by op imizing hei p oduc ion
p ocesses mo e holis ically.
In he u u e, he s udy will be ex ended by including a me a-
heu is ic algo i hm o ini ializing he a chi ec u e and hype -
pa ame e s o he models. By explo ing p omising hype pa ame e s and
a chi ec u es i s , de i ed om simila p oblems, he model selec ion
p ocess will be mo e e icien , hus posi i ely impac ing he pe o -
mance o he en i e Au oML wo k low.
Fu he mo e, we in end o apply he p oposed me hodology o o he
domains beyond manu ac u ing SMEs. Po en ial domains include bu
a e no limi ed o cons uc ion, in as uc u e se ices, logis ics,
heal hca e, and inance. Many p oblems in hese ields also equi e he
c ea ion o models and i s use o op imiza ion, which pa es he way o
applying he p oposed me hodology. Howe e , i s sui abili y o di e en
domains mus be ca e ully e alua ed, ecognizing ha each ield p esen
unique challenges and cons ain s.
Funding
This wo k has been unded by Eu opean Commission ough he
Ho izon Eu ope p ojec “Mul i-Modal and Mul i-Aspec Holis ic Human-
Robo In e ac ion (FORTIS)”, g an ID 101135707. This wo k was also
pa ially unded by Minis e io de Ciencia, Inno aci´
on y Uni e sidades
(MICIU) o Spain ough he p ojec "Sel - econ igu a ion o Indus ial
Cybe -Physical Sys ems based on digi al wins and A i icial In elli-
gence. Me hods and applica ion in Indus y 4.0 pilo line (SELFRECO)",
g an ID PID2021–127763OB-100”. This wo k was also suppo ed in
pa by he p ojec “Digi aliza ion o Powe Elec onic Applica ions
wi hin Key Technology Value Chains (Powe izeD)”, g an ID
101096387, unded by he Eu opean Union HORIZON F amewo k
P og amme and Chips JU.
CRediT au ho ship con ibu ion s a emen
Ya ens J. C uz: Concep ualiza ion, In es iga ion, Me hodology,
So wa e, W i ing – o iginal d a . Albe o Villalonga: Fo mal analysis,
So wa e, Valida ion, Visualiza ion. Fe nando Cas a˜
no: Concep uali-
za ion, Da a cu a ion, In es iga ion, Valida ion. Ma celino Ri as:
Concep ualiza ion, Fo mal analysis, W i ing – o iginal d a . Rodol o E.
Habe : Funding acquisi ion, Me hodology, P ojec adminis a ion,
W i ing – e iew & edi ing.
Decla a ion o compe ing in e es
The au ho s decla e ha hey ha e no known compe ing inancial
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
The da a ha has been used is con iden ial.
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