Bioinspi ed e olu iona y me aheu is ic based on COVID sp ead
o disco e ing nume ical associa ion ules.
C. He uzo-Lodei o
Depa men o Languages and Compu e Sys ems,
Uni e si y o Se ille
Se ille, Spain
[email p o ec ed]
F. Rod íguez-Díaz
Da a Science and Big Da a Lab, Pablo de Ola ide
Uni e si y
Se ille, Spain
[email p o ec ed]
A. T oncoso
Da a Science and Big Da a Lab, Pablo de Ola ide
Uni e si y
Se ille, Spain
[email p o ec ed]
M. Ma ínez-Balles e os∗
Depa men o Languages and Compu e Sys ems,
Uni e si y o Se ille
Se ille, Spain
[email p o ec ed]
Abs ac
The social impac and global heal h c isis caused by he co ona i us
since la e 2019 led o he de elopmen o a no el bio-inspi ed al-
go i hm. This algo i hm simula es he beha io and sp ead o he
i us, known as he Co ona i us Op imiza ion Algo i hm. I p o-
ides se e al ad an ages o e simila app oaches and se es as a
basis o gene alizing pa e n o associa ion iden i ica ion om nu-
me ical da ase s. In his s udy, essen ial upda es and modi ica ions
a e p oposed o adap he CVOA algo i hm o mining nume i-
cal associa ion ules. These changes in ol e adjus men s o he
encoding o indi iduals and he in ec ion/mu a ion p ocess. Addi-
ionally, pa ame e alues a e upda ed, and a new i ness unc ion
is p oposed o be maximized. The main objec i e is o ob ain high-
quali y nume ical associa ion ules o any da ase ega dless o he
numbe and ange o a ibu es in he da ase . The implemen ed
algo i hm is compa ed o o he s designed o mining quan i a i e
associa ion ules in o de o alida e he esul s. Fo his eason,
di e en da ase s om he BUFA eposi o y a e used, con i ming
ha Co ona i us Op imiza ion Algo i hm is a p omising op ion o
disco e ing in e es ing associa ion ules wi hin nume ical da ase s.
CCS Concep s
•In o ma ion sys ems
→
Associa ion ules;•Theo y o com-
pu a ion →E olu iona y algo i hms.
Keywo ds
E olu iona y algo i hms, nume ical associa ion ules, bioinspi ed
me aheu is ic, COVID
ACM Re e ence Fo ma :
C. He uzo-Lodei o, F. Rod íguez-Díaz, A. T oncoso, and M. Ma ínez-
Balles e os. 2025. Bioinspi ed e olu iona y me aheu is ic based on COVID
sp ead o disco e ing nume ical associa ion ules.. In The 40 h ACM/SIGAPP
∗Co esponding au ho
This wo k is licensed unde a C ea i e Commons A ibu ion 4.0 In e na ional License.
SAC ’25, Ma ch 31-Ap il 4, 2025, Ca ania, I aly
©2025 Copy igh held by he owne /au ho (s).
ACM ISBN 979-8-4007-0629-5/25/03
h ps://doi.o g/10.1145/3672608.3707787
Symposium on Applied Compu ing (SAC ’25), Ma ch 31-Ap il 4, 2025, Ca ania,
I aly. ACM, New Yo k, NY, USA, 8 pages. h ps://doi.o g/10.1145/3672608.
3707787
1 In oduc ion
A e mo e han 4 yea s since he Wo ld Heal h O ganiza ion (WHO)
decla ed co ona i us disease 2019 (COVID-19) a global pandemic,
new in ec ions and dea hs caused by he i us known as se e e
acu e espi a o y synd ome co ona i us 2 (SARS-CoV-2) a e s ill
being eco ded a ound he wo ld. Cu en ly, he numbe o con-
i med COVID-19 cases epo ed o he WHO is 768,237,788, in-
cluding 6,951,677 dea hs [
24
]. Al hough he WHO decla ed he end
o COVID-19 as an in e na ional public heal h eme gency on May
2023, his does no mean ha i has ceased o be a h ea o global
heal h o a global public heal h p io i y [
17
]. Fo his eason, i is
necessa y o con inue collec ing da ase s ha allow us o analyze
and unde s and he sp ead o his and po en ial u u e diseases.
Me aheu is ics a e app oxima ion algo i hms, high-le el s a e-
gies ha allow explo a ion o he solu ion space h ough a wide
a ie y o me hods. Popula ion-based me aheu is ics mimic he be-
ha io o li ing o ganisms in na u e and aim o sol e op imiza ion
p oblems by sea ching o he bes esul wi hin he solu ion space.
The sea ch p ocess in ol es, on one hand, measu ing each agen ’s
p oximi y o he bes solu ion h ough he i ness unc ion, and
on he o he hand, pe o ming he mechanisms o explo a ion, o
collec in o ma ion, and exploi a ion, which uses ha in o ma ion
o explo e a o able a eas o he sea ch space in de ail. Bio-inspi ed
me aheu is ics, d awing om biological phenomena and na u al
p ocesses, ha e been widely de eloped and s udied o e he pas
ew decades [4].
Due o he apid sp ead and he signi ican heal h c isis caused
by he SARS-CoV-2 i us, he Co ona i us Op imiza ion Algo i hm
(CVOA) [
13
] was de eloped as an op imiza ion algo i hm based
on he beha io and sp ead model o COVID-19. This algo i hm
o e s se e al ad an ages o e simila s a egies. One o hem is
ha , gi en he abundance o da a and s a is ics due o he global
impac and impo ance o he disease, he e is no need o a bi-
a y ini ializa ion o pa ame e s, as alues such as in ec ion and
mo ali y a es a e al eady known. Vi uses sp ead by in ec ing indi-
iduals, who can, in u n, in ec o he s, die, o eco e . The concep
138
SAC ’25, Ma ch 31-Ap il 4, 2025, Ca ania, I aly C. He uzo-Lodei o e al.
o “supe -sp eade s” also exis s, e e ing o indi iduals who in ec
a la ge numbe o people, he eby in ensi ying he sea ch space.
The numbe o ini ially in ec ed indi iduals inc eases exponen ially
o e se e al i e a ions bu e en ually s a s o decline un il no in-
di iduals emain, which is a key ad an age o he algo i hm as i
elimina es he need o de ine a s opping c i e ion.
The CVOA algo i hm can be combined wi h o he A i icial In-
elligence echniques, such as associa ion ules (AR), which aim o
ex ac co ela ions, pa e ns, o associa ions be ween he a ibu es
o a da ase . When associa ion ules a e de i ed om da ase s wi h
nume ical a ibu es, hey a e e e ed o as nume ical associa ion
ules (NAR) [
2
]. This wo k p oposes a new algo i hm based on
CVOA o ob ain NAR. Speci ically, his algo i hm, hence o h e-
e ed o as CVNAR, in oduces he necessa y modi ica ions o, on
one hand, ob ain high-quali y nume ical associa ion ules and, on
he o he , gene alize he solu ion and he sea ch o such ules o
any da ase , numbe o a ibu es, and ange o nume ical alues.
The pape is s uc u ed in o he ollowing sec ions. Sec ion 2
p esen s an analysis o he cu en s a e o he a o nume ical
associa ion ules. Sec ion 3 desc ibes he adjus men s made o he
CVOA algo i hm, adap ing i o use in NAR mining o achie e he
de ined objec i es. The esul s ob ained a e p esen ed and analyzed
in Sec ion 4. Finally, Sec ion 5 summa izes he key conclusions
d awn om he esul s and discusses he u u e wo k.
2 Rela ed wo ks
In 1993, Ag awal e al. [
1
] i s p oposed he use o AR o iden i y
ela ionships be ween a iables in da ase s. The mos popula AR
algo i hms a e Ap io i, Ecla , and FP-g ow h. These algo i hms
handle bina y and ca ego ical a ibu es, bu he eal wo ld also
consis s o nume ical a ibu es. To add ess hese challenges, NARs,
o quan i a i e associa ion ules, a e in oduced as a means o
handling nume ical da a mo e e ec i ely.
Ini ially, p oblem-sol ing wi h NAR elies on disc e iza ion, us-
ing pa i ioning and combina ion ou ines, clus e ing, and uzzy
logic. Addi ionally, o he me hods such as op imiza ion and dis-
ibu ion ha e been p oposed o u he enhance he p ocess [
23
].
These h ee main app oaches a e ex ensi ely discussed h ough-
ou he li e a u e, and a wide ange o NAR algo i hms ha e been
de eloped based on hem, as demons a ed in [7] and [8].
Al hough disc e iza ion me hods can esul in in o ma ion loss
and educe he quali y o he ules, hey emain one o he mos
popula app oaches o add essing nume ical associa ion ule min-
ing p oblems due o hei simplici y and lexibili y. Disc e iza ion
can be pe o med using echniques such as uzzi ica ion, clus e ing,
o pa i ioning and combina ion.
Clus e ing echniques g oup nume ical columns in o ca ego ies
based on alue simila i y, using me hods like hie a chical, densi y-
based, and g id-based clus e ing. Fo ins ance, ARCS [
9
] clus e s
associa ion ules wi h bi wise ope a ions, while MQAR [
26
] uses a
dense g id equen pa e n ee o gene a e non- edundan NARs
by clus e ing subspaces. Mo e ecen ly, GCQAR [
15
] combines
modula i y-based g aph clus e ing wi h NAR o unco e ela ion-
ships wi hin cohesi e subg aphs.
Simila ly, pa i ioning echniques a e widely used in disc e iza-
ion. Fo example, S ikan and Ag awal [
22
] p oposed an algo i hm
o handling nume ic a ibu es in NARM, using equi-dep h dis-
c e iza ion o pa i ion a ibu es and gene a e equen i emse s
based on minimum suppo . La e app oaches, such as Ras ogi’s al-
go i hm [
19
], le e age p ede ined in e als o disc e ize nume ical
a ibu es in o segmen s. Mo e ecen ly, Song and Ge [
21
] in o-
duced NAR-Disco e y, a di ide-and-conque algo i hm ha e i-
cien ly pa i ions a ibu es in o bucke s o mine NAR.
Finally, uzzi ica ion o e s a lexible disc e iza ion me hod whe e
in e al bounda ies a e no s ic ly de ined. Fo ins ance, OFARM
[
27
] op imized uzzy se pa i ion poin s by using mul iple objec i e
unc ions and a wo-le el i e a ion p ocess o gene a e equen
i emse s.
Many s udies ocus on op imiza ion me hods o sol ing p ob-
lems in he con ex o NAR o add ess he disad an ages o algo-
i hms based on disc e iza ion me hods. These me hods use heu is-
ic algo i hms inspi ed by na u al phenomena, such as animal be-
ha io and biological p ocesses. They a e pa icula ly no ewo hy
o hei abili y o de ec ela ionships and pa e ns wi hin la ge
da ase s, wi hou he need o de ine h esholds o pe o m dis-
c e iza ion s eps. These me hods can handle bo h nume ical and
ca ego ical da a and a e obus agains noise and missing in o -
ma ion. Howe e , disc e iza ion me hods can ace challenges wi h
con e gence, o en leading o he disco e y o local op ima, along
wi h high compu a ional complexi y and signi ican esou ce e-
qui emen s.
Op imiza ion me hods consis o wo phases: i s , all se s o
equen i ems a e iden i ied, and hen all ele an associa ion ules
a e ex ac ed. They a e di ided in o wo ca ego ies: bio-inspi ed
op imiza ion me hods and physics-based op imiza ion me hods. De-
pending on he op imiza ion objec i es, hey can also be classi ied
in o single-objec i e and mul i-objec i e app oaches.
Bio-inspi ed me hods can be ca ego ized as ollows:
•
E olu ion-based algo i hms: These algo i hms mimic he
abili y o li ing o ganisms o adap o hei en i onmen .
They le e age sea ch me hods inspi ed by na u al selec ion
and gene ics.
•
Swa m-in elligence-based algo i hms: These can be u he
di ided in o wo sub-op imiza ion me hods:
–
Pa icle Swa m Op imiza ion: An algo i hm based on an-
imal beha io s, such as he collec i e mo emen o bi d
locks o ish schools, and designed o popula ion-based
op imiza ion o non-linea unc ions.
–
Wol Sea ch Algo i hm: A bio-inspi ed heu is ic op imiza-
ion algo i hm ha eplica es how wol es sea ch o ood
and su i e by a oiding p eda o s.
Se e al e olu ion-based me hods ha e been de eloped o NARM.
GENAR [
14
], o example, le e ages gene ic algo i hms o disco e
ules wi h nume ical a ibu es, while Yan e al. p oposed EARMGA
[
25
], which inco po a es gene ic ope a o s and a i ness unc ion
ha elimina es he need o p ede ined suppo h esholds, handling
bo h ca ego ical and quan i a i e a ibu es e ec i ely.
In con as o e olu iona y app oaches, pa icle swa m op imiza-
ion o e s a di e en s a egy. Fo ins ance, Bei an and e al. in o-
duced MOPAR [
3
], a mul i-objec i e PSO algo i hm ha ex ac s
139
CVNAR: Cona i us Op imiza ion Algo i hm o disco e Nume ical Associa ion Rules SAC ’25, Ma ch 31-Ap il 4, 2025, Ca ania, I aly
NAR by op imizing h ee key objec i es: con idence, comp ehen-
sibili y, and in e es ingness. MOPAR also ede ines he adi ional
swa m componen s o mo e e ec i ely handle nume ical a ibu es.
Recen ly, Moleshi e al. p oposed HGP-QAR [
16
], a hyb id algo-
i hm combining gene ic algo i hms and pa icle swa m op imiza-
ion o enhance he e iciency o NARM. This algo i hm le e ages
GA’s selec ion, c osso e , and mu a ion wi h PSO’s eloci y and
posi ion upda es o mo e e icien explo a ion o he solu ion space.
The i ness unc ion is based on con idence, in e es ingness, and
comp ehensibili y.
On he o he hand, physics-based op imiza ion me hods simula e
he beha io and p ope ies o ma e o ollow he laws o physics.
One such me hod is he G a i a ional Sea ch Algo i hm (GSA),
an op imiza ion algo i hm inspi ed by he laws o g a i y [
18
]. In
his app oach, agen s beha e as objec s, and hei pe o mance is
measu ed by hei mass.
A e a ho ough e iew o he li e a u e, i is no ewo hy ha
he e a e s ill many challenges o be add essed in de eloping NAR
me hods o disco e pa e ns in eal-wo ld da ase s. In his pape ,
we p opose he CVNAR algo i hm, which le e ages op imiza ion
echniques and builds on he CVOA algo i hm o add ess com-
mon limi a ions, including in o ma ion loss, con e gence p oblems,
he equi emen o use -de ined h esholds, and alling in o local
minima. To add ess hese challenges, se e al no el ea u es a e
p oposed, which will be de ailed in he ollowing sec ions.
3 Desc ip ion o he CVNAR algo i hm
The CVNAR algo i hm aims o ind high-quali y NAR based on
he CVOA algo i hm. The goal is o disco e a gene alized op imal
solu ion o any nume ical da ase , ega dless o he numbe o
a ibu es o hei ange o alues.
The ollowing sec ions desc ibe and de ail he a ious phases
o he algo i hm’s me hodology. Fi s is he ini ializa ion phase,
which is esponsible o gene a ing he ini ial popula ion o indi-
iduals. In his case, he popula ion consis s o a single subjec ,
known as Pa ien Ze o (PZ). Simula ing he beha io o he co on-
a i us, PZ ep esen s he i s in ec ed indi idual and is gene a ed
andomly. Once he ini ial popula ion is c ea ed, he i e a i e e o-
lu ion phase begins. This phase in ol es applying a se ies o s eps
un il he s opping condi ion is me . In he CVNAR algo i hm, he
s opping condi ion is sa is ied when a maximum numbe o i e a-
ions is eached o when no in ec ed indi iduals emain. The s eps
co esponding o his phase a e:
S ep 1. Calcula e he i ness unc ion o each indi idual in he
in ec ed lis . I he i ness unc ion does no e u n a esul , ha is,
i e u ns an unde ined o un ep esen able alue, he indi idual is
emo ed om he in ec ed lis and mo ed o he deceased lis .
S ep 2. Main ain a global lis and upda e i in each i e a ion wi h
he en indi iduals ha ing he bes i ness unc ion. The numbe o
op solu ions o indi iduals s o ed by he algo i hm is a con igu able
pa ame e and can be adjus ed in each un.
S ep 3. Sp ead he disease. The e a e a ious scena ios ha can
occu depending on he indi idual, which di ec ly a ec he numbe
o new in ec ed indi iduals and, consequen ly, he sp ead o he
disease:
(1)
An in ec ed indi idual will die wi h a ce ain p obabili y
(
𝑃_𝐷𝐼𝐸
). In his case, he indi idual will no in ec new indi-
iduals.
(2)
Indi iduals who do no die may become o dina y sp eade s,
meaning hey in ec new indi iduals a a no mal sp ead
a e, o “supe -sp eade s”, who will p opaga e he disease
a a highe a e. The p obabili y o being a supe -sp eade
(𝑃_𝑆𝑈 𝑃𝐸𝑅𝑆𝑃𝑅𝐸𝐴𝐷𝐸𝑅) will de e mine he a e o sp ead.
(3)
Finally, he e is a p obabili y ha he indi idual will a el,
ep esen ed by
𝑃_𝑇𝑅𝐴𝑉 𝐸𝐿
, which causes he solu ions c e-
a ed h ough in ec ion o change based on he a el dis ance,
deno ed as
𝑇𝑅𝐴𝑉 𝐸𝐿_𝐷𝐼𝑆𝑇𝐴𝑁𝐶𝐸
. The same indi idual can
be bo h a “supe -sp eade” and a a ele .
S ep 4. Manage and upda e h ee indi idual lis s a each i e a ion
a e he p e ious s ep is comple ed:
(1)
Deceased. The indi iduals added o his lis will no longe
be used.
(2)
Reco e ed. Fo simplici y, in ec ed indi iduals will mo e
o he eco e ed lis i he isola ion p obabili y is sa is ied
(
𝑃_𝐼𝑆𝑂𝐿𝐴𝑇𝐼𝑂𝑁
). The e is a p obabili y o ein ec ion, which
means ha a eco e ed indi idual can e u n o he in ec ed
lis (𝑃_𝑅𝐸𝐼 𝑁 𝐹𝐸𝐶𝑇 𝐼𝑂𝑁 ).
(3)
Newly in ec ed. Re e s o he g oup o indi iduals in ec ed
in he p e ious s ep.
The goal o he CVNAR algo i hm is o iden i y he indi iduals
wi h he highes i ness unc ion alue in he en i e popula ion.
Ini ially, PZ is conside ed as he bes solu ion ound. The lis g ows
wi h each i e a ion as new indi iduals become in ec ed, un il he
p ede ined numbe o op solu ions is eached. F om ha poin
on, du ing each i e a ion whe e he disease sp eads, he algo i hm
checks whe he any in ec ed indi idual has a be e i ness alue
han he op imal s o ed solu ions, eplacing hem i necessa y. Fi-
nally, as p e iously men ioned, he size o he bes solu ions lis in
CVNAR is de e mined by an inpu pa ame e o he algo i hm.
3.1 Indi idual codi ica ion
Associa ion ules can be de ined as implica ions o he o m “i
𝑋
hen
𝑌
”, conside ing ha he occu ence o
𝑋
in a ansac ion
implies he occu ence o
𝑌
, whe e
𝑋
is de ined as he an eceden
and
𝑌
as he consequen [
1
]. In he popula ion, each indi idual
ep esen s a ule, and each o hese ules unde goes an e olu iona y
mu a ion p ocess. A he end o he p ocess, he indi idual wi h he
bes i ness unc ion is designa ed as he bes ule [10].
When he da ase is o be analyzed nume ical, i is necessa y
o pe o m a disc e iza ion o he a ibu e domain in o in e als,
de ining an uppe limi and a lowe limi o each o hem. This
can lead o a po en ial loss o in o ma ion; o his eason, he
CVOA algo i hm lea ns he wid h o he in e als in each i e a ion
[
20
]. This decision-making p ocess ega ding he in e al wid h is
explained in de ail in Sec ion 3.2.4.
The encoding employed o indi iduals ha a e candida es o be
solu ions o he CVNAR algo i hm is desc ibed below, conside ing
ha :
• he a ibu es o he da ase a e nume ical,
•
he ange o alues o each a ibu e belongs o he se o
eal numbe s,
140
SAC ’25, Ma ch 31-Ap il 4, 2025, Ca ania, I aly C. He uzo-Lodei o e al.
Figu e 1: Indi idual codi ica ion.
•
i is no ixed whe he each a ibu e belongs o he an-
eceden , he consequen , o does no belong o he ule.
The e o e, gi en a da ase wi h
𝑚
a ibu es and
𝑛
ins ances, an
indi idual consis s o 2
×𝑚
elemen s, whe e each elemen
𝑘
is an
in ege be ween
[
1
,𝑛 −
1
]
. Each a ibu e will ha e a lowe limi ,
co esponding o he odd posi ions in he lis , and an uppe limi ,
co esponding o he e en posi ions. The alue o bo h is an in ege ,
𝑘𝑖∈ [
1
,𝑛 −
1
]
o he lowe limi and
𝑘𝑠∈ [
1
,𝑛 −𝑘𝑖]
o he uppe
limi . The s uc u e o he indi idual consis s o h ee pa s:
•
Encoded alue o he limi s. This e e s o he andom alue
gene a ed be ween
[
1
,𝑛 −
1
]
o he lowe limi
𝑘𝑖
and he
andom alue gene a ed be ween
[
1
,𝑛 −𝑘𝑖]
o he uppe
limi 𝑘𝑠.
•
Decoded alue o he limi s. Fi s , all he alues om he
da ase o he a ibu e a e aken and so ed in ascending
o de . The decoded alue o he lowe limi co esponds o
he alue ound a posi ion
𝑘𝑖
, and he decoded alue o he
uppe limi co esponds o he alue ound a posi ion 𝑘𝑠.
•
A ibu e ype. Each a ibu e o he indi idual can be o one
ype:
–0 when he a ibu e does no belong o he ule,
–1 when he a ibu e belongs o he an eceden ,
–2 when he a ibu e belongs o he consequen .
Figu e 1 g aphically shows he encoding o an indi idual and an
example o a coded NAR.
In pa icula , he ule
𝑎1∈ [
98
,
98
.
5
] ∧ 𝑎2∈ [
1
,
1
]=⇒𝑎3∈
[
61
,
89
]
is ep esen ed. I can be obse ed ha he a ibu es
𝑎1
and
𝑎2
belong o he an eceden , as
𝑡1
and
𝑡2
ha e he alue 1. Simila ly,
he a ibu e
𝑎3
belongs o he consequen because
𝑡3
has he alue
2. Fo a ibu e 𝑎1, he decoded in e al alues a e 98 as he lowe
bound and 98.5 as he uppe bound. These alues co espond o he
posi ions
𝑘𝑖1=
110 and
𝑘𝑠1=
0in he da ase , whe e
𝑘𝑖1
and
𝑘𝑠1
ep esen he k- h indices o he a ibu e alues when so ed in
ascending o de . This o de ing ensu es ha he in e al bounda ies
a e accu a ely iden i ied wi hin he con ex o he da ase . Simila ly,
o a ibu e
𝑎2
, he decoded in e al alues a e bo h 1, meaning
he lowe and uppe bounds o he in e al coincide. These alues
co espond o he k- h posi ions
𝑘𝑖2=
44 and
𝑘𝑠2=
57, espec i ely,
when he alues o a ibu e
𝑎2
a e so ed om smalles o la ges .
Finally, o a ibu e
𝑎3
, he decoded in e al alues a e 61 o he
lowe bound and 89 o he uppe bound. These alues co espond
o he posi ions
𝑘𝑖3=
4and
𝑘𝑠3=
0in he da ase when a ibu e
𝑎3is o de ed in ascending o de .
3.2 Gene al p ocess o CVNAR
This sec ion desc ibes he phases o he CVNAR algo i hm, de ailing
he gene a ion o he ini ial popula ion and he execu ion o he
in ec ion p ocess, highligh ing he p oposed i ness unc ions, and
he selec ion o indi iduals based on he chosen i ness unc ion.
3.2.1 Gene a ion o he ini ial popula ion. The ini ial popula ion
o CVNAR algo i hm consis s o a single indi idual, gene a ed an-
domly. Randomness encompasses he numbe o a ibu es p esen
in he ule, he ype o each a ibu e, and hei espec i e in e als.
Rega ding he a ibu e limi s, a andom in ege
𝑘𝑖∈ [
1
,𝑛 −
1
]
is
gene a ed o he lowe limi , and ano he in ege
𝑘𝑠∈ [
1
,𝑛 −𝑘𝑖]
is gene a ed o he uppe limi . The alues om he en i e da ase
o each a ibu e a e so ed in ascending o de , and inally, he
alue a posi ion
𝑘𝑖
is selec ed o he lowe limi , while he alue
a posi ion
𝑘𝑠
is selec ed o he uppe limi . Fo he ype, a andom
numbe be ween 0, 1, and 2 is gene a ed o each a ibu e.
To ensu e ha he gene a ed indi idual ep esen s a obus ule,
he ollowing cons ain s a e conside ed:
•
The uppe limi mus be g ea e han he lowe limi . I
his condi ion is no me , he andom gene a ion p ocess
men ioned ea lie is epea ed.
•
The alue o he in e als o each a ibu e mus all wi hin
he ange o alues in he da ase .
•
The numbe o a ibu es belonging o he an eceden mus
be g ea e han o equal o 1.
•
The numbe o a ibu es belonging o he consequen mus
be g ea e han o equal o 1.
•
I he numbe o a ibu es is g ea e han 2, he numbe o
a ibu es co esponding o he an eceden mus be g ea e
han he numbe o a ibu es belonging o he consequen .
3.2.2 Fi ness unc ion. Associa ion ules ep esen quan i iable
pa e ns ha e eal dependencies be ween a ibu es in a da ase .
Typically, he numbe o ex ac ed associa ions is high, hen, i
becomes c ucial o so o il e hem based on speci ic measu es o
141
CVNAR: Cona i us Op imiza ion Algo i hm o disco e Nume ical Associa ion Rules SAC ’25, Ma ch 31-Ap il 4, 2025, Ca ania, I aly
ele ance [
12
]. Quali y measu es used in his pape a e desc ibed
as ollows:
•
Suppo (X
⇒
Y): Pe cen age o ins ances in he da ase ha
sa is y 𝑋and 𝑌.
𝑆𝑢𝑝(𝑋⇒𝑌)=(𝑃(𝑋∪𝑌))
(|𝐷|)
whe e
𝐷
is he o al numbe o ins ances o ansac ions o
he da ase .
•
Con idence(X
⇒
Y): P obabili y ha ins ances sa is ying
𝑋also sa is y 𝑌.
𝐶𝑜𝑛𝑓 (𝑋⇒𝑌)=𝑆𝑢𝑝 (𝑋⇒𝑌)
𝑆𝑢𝑝 (𝑋)
•
Accu acy(X
⇒
Y): Deg ee o coincidence o he da a ob-
ained wi h he eal da a.
𝐴𝑐𝑐(𝑋⇒𝑌)=𝑆𝑢𝑝 (𝑋⇒𝑌)
𝑆𝑢𝑝 (¬𝑋⇒¬𝑌)
•
Le e age(X
⇒
Y): P opo ion o cases co e ed by bo h
𝑋
and
𝑌
compa ed o wha would be expec ed i
𝑋
and
𝑌
we e
independen .
Le (X ⇒Y)=Sup(X ⇒Y)-Sup(X)Sup(Y)
•
Ce ain y Fac o (X
⇒
Y): P obabili y ha
𝑌
is p esen in
an ins ance when conside ing only hose ins ances whe e
𝑋
appea s.
Si Con (X ⇒Y) >Sup(Y):
FC(X⇒Y) = 𝐶𝑜𝑛𝑓 (𝑋⇒𝑌)−𝑆𝑢𝑝 (𝑌)
1−𝑆𝑢𝑝 (𝑌)
I Con (X⇒Y) ≤Sup(Y):
FC(X⇒Y) = 𝐶𝑜𝑛𝑓 (𝑋⇒𝑌)−𝑆𝑢𝑝 (𝑌)
𝑆𝑢𝑝 (𝑌)
The i ness unc ion is used o iden i y he bes indi iduals. Two
dis inc objec i e unc ions a e p oposed o maximiza ion. Bo h
unc ions a e composed o di e en measu es o in e es :
Func ion 1 =𝐴𝑐𝑐(𝑋⇒𝑌) + 𝐶𝑜𝑛𝑓 (𝑋⇒𝑌) + 𝐿𝑒𝑣(𝑋⇒𝑌)(1)
Func ion 2 =𝐹𝐶(𝑋⇒𝑌) + 𝐶𝑜𝑛𝑓 (𝑋⇒𝑌) + 𝑆𝑢𝑝(𝑋⇒𝑌)(2)
These unc ions aim o ob ain high-quali y nume ical associa ion
ules by combining measu es o in e es o add ess he disad an-
ages p esen ed by some o hem. Le e age and accu acy, in some
cases, a e insu icien , as hey only measu e co-occu ences and do
no conside implica ion. The e o e, i may be bene icial o combine
hem wi h con idence, which measu es he eliabili y o he ule. On
he o he hand, Ce ain y Fac o has he ad an age o aking in o
accoun he suppo o bo h he an eceden and he consequen , as
well as he implica ion. Gi en his con ex , a compa a i e analysis
is conduc ed o iden i y he mos e ec i e measu e o gene a ing
in e es ing nume ical associa ion ules.
3.2.3 Indi idual selec ion. As p e iously men ioned, he CVNAR
algo i hm gene a es a lis o he bes indi iduals, speci ically hose
wi h he highes i ness unc ion alues. Ini ially, he only s o ed
elemen is PZ, and he lis inc eases as new indi iduals become
in ec ed un il i eaches he de ined size.
In each i e a ion, i is checked whe he any o he indi iduals in
he in ec ed lis has a highe i ness alue han hose in he lis o
bes indi iduals. I so, he in ec ed indi idual eplaces he one wi h
he lowe i ness alue. The size o he lis o bes indi iduals is an
inpu pa ame e o he CVNAR algo i hm and can be adjus ed as
needed.
3.2.4 In ec ion/Mu a ion. The in ec ion p ocess o an indi idual
in ol es pe o ming a mu a ion on he in ec ed subjec , which
means ha he alues o he in e als and he ype o each a ibu e
encoding he indi idual a e modi ied.
On one hand, he numbe o new in ec ions will depend on
whe he he indi idual is a egula sp eade o a “supe -sp eade ”.
On he o he hand, he numbe o a ec ed in e als will depend on
𝑇𝑅𝐴𝑉 𝐸𝐿_𝐷𝐼𝑆𝑇𝐴𝑁𝐶𝐸
. The dis ance is a andom alue be ween 1
and he o al numbe o in e als.
When e e ing o in ec ing an indi idual, bo h he in e al and
he ype o a ibu e a e conside ed. As men ioned abo e, as many
in e als will be in ec ed, as indica ed by he andomly gene a ed
alue
𝑇𝑅𝐴𝑉 𝐸𝐿_𝐷𝐼𝑆𝑇𝐴𝑁𝐶𝐸
. A di e en index is main ained o
each ype o in ec ion, allowing o he mu a ion o he in e al o
he second a ibu e and he ype o he hi d o he same indi idual.
The mu a ed indexed o each ype a e s o ed and no eused. The
p ocess is as ollows:
•
In ec ion o an in e al a ibu e: I consis s o inc easing o
dec easing he ampli ude o he in e al by a ce ain pe cen -
age (25%, 50%, 75%). A a iable
𝑑=|𝑎𝑓−𝑎𝑖|
is de ined, which
ep esen s he di e ence be ween he new ampli ude and
he ini ial one, and a andom numbe
𝑃
is gene a ed be ween
0 and 2. I
𝑃
= 0,
𝑑
= 0.25 x
𝑎𝑖
; i
𝑃
= 1,
𝑑
= 0.5 x
𝑎𝑖
and i
𝑃
= 2;
𝑑
= 0.75 x
𝑎𝑖
. The decision o inc ease o dec ease he
in e al is also andom. In case o inc easing,
𝑟𝑜𝑢𝑛𝑑(𝑑)/
2
( ounded down) is sub ac ed om each limi o he in e al,
and in case o dec easing,
𝑟𝑜𝑢𝑛𝑑(𝑑)/
2( ounded up) is added.
I he esul ing alue is less han 0, i is assigned 0.
•
In ec ion o a ype a ibu e: I consis s o changing he ype
o an a ibu e om 0 o 1 o 2; om 1 o 0 o 2 and om 2
o 0 o 1. I he ype o he in ec ed a ibu e does no mee
he ollowing condi ions:
–
The numbe o a ibu es belonging o he an eceden mus
be g ea e han o equal o 1.
–
The numbe o a ibu es belonging o he consequen
mus be g ea e han o equal o 1.
–
I he o al numbe o a ibu es is g ea e han 2, he num-
be o a ibu es co esponding o he an eceden mus
be g ea e han he numbe o a ibu es belonging o he
consequen .
Then, he ypes o all a ibu es o he indi idual a e in ec ed
ollowing he same p ocedu e as du ing he gene a ion o
he ini ial popula ion.
3.3 Compu a ional complexi y o CVNAR
The compu a ional complexi y o CVNAR can be exp essed as
𝑂(𝐼·𝑃·𝐹(𝑁, 𝑀))
, whe e
𝐼
ep esen s he numbe o i e a ions,
𝑃
is he a e age popula ion size pe i e a ion, and
𝐹(𝑁, 𝑀)
is he
compu a ional cos o e alua ing he i ness unc ion o each in-
di idual in he popula ion. The i ness unc ion
𝐹(𝑁, 𝑀)
e alua es
he quali y o each indi idual, NAR in his case, de i ed om he
da ase . This in ol es compu ing quali y measu es such as sup-
po , con idence, which equi e scanning he da ase o e i y he
ule condi ions. Fo a da ase wi h
𝑁
ins ances and
𝑀
a ibu es,
142
SAC ’25, Ma ch 31-Ap il 4, 2025, Ca ania, I aly C. He uzo-Lodei o e al.
𝐹(𝑁, 𝑀)=𝑂(𝑁·𝑀)
, whe e
𝑁
and
𝑀
de e mine he linea com-
plexi y o encoding and e alua ing ule condi ions.
To op imize un ime and enhance he scalabili y o CVNAR o
la ge da ase s, pa allelizing he i ness e alua ions and dynami-
cally con olling he popula ion size (e.g., adjus ing in ec ion a es
o isola ion p obabili ies) can educe execu ion ime wi hou com-
p omising pe o mance [11].
4 Expe imen a ion and Resul s
This sec ion ou lines he esul s ob ained om he execu ion o he
CVNAR algo i hm, including he execu ion pa ame e s, da ase s,
and e alua ion me ics used.
4.1 Execu ion pa ame e s
The pa ame e s used in he CVNAR algo i hm and he alue o each
a e de ailed below. These pa ame e s a e ex ac ed om a ious
sou ces, one o he mos impo an being he WHO.
(1)
Mo ali y a e: This is he p obabili y ha an in ec ed indi-
idual will die. I is calcula ed by di iding he numbe o
con i med dea hs by he numbe o con i med cases. Acco d-
ing o he da a a ailable in [
6
], a alue o
𝑃_𝐷𝐼𝐸
= 0.06 is
assigned.
(2)
P obabili y o being supe -sp eade . I is he p obabili y ha
an indi idual sp eads he disease a a highe a e. I is con-
side ed ha 10% o he popula ion a e supe -sp eade indi-
iduals, he e o e, 𝑃_𝑆𝑈 𝑃𝐸𝑅𝑆𝑃𝑅𝐸𝐴𝐷𝐸𝑅 = 0.1.
Two addi ional pa ame e s ela ed o he disease’s p opa-
ga ion a e a e aken in o accoun ,
𝑂𝑅𝐷𝐼𝑁𝐴𝑅𝑌_𝑅𝐴𝑇 𝐸
and
𝑆𝑈 𝑃𝐸𝑅𝑆𝑃𝑅𝐸𝐴𝐷𝐸𝑅_𝑅𝐴𝑇𝐸
. Bo h a e andom numbe s and
e e o he numbe o people ha can in ec . An o dina y
sp eade will in ec be ween 0 and 5 people, while a supe -
sp eade will in ec be ween 6 and 15.
(3)
T a el p obabili y: Acco ding o [
5
], i is conside ed ha 10%
o he popula ion can a el o any loca ion du ing a week
and in ec o he people, he e o e, 𝑃_𝑇 𝑅𝐴𝑉 𝐸𝐿 = 0.1.
(4)
Re-in ec ion p obabili y: The likelihood o e-in ec ion wi h
SARS-CoV-2 is es ima ed o occu in less han 1% o p e-
iously con i med cases. The e o e,
𝑃_𝑅𝐸𝐼𝑁 𝐹𝐸𝐶𝑇𝐼𝑂𝑁
=
0.001.
(5)
Isola ion p obabili y: A high alue is assigned, as i helps
educe he exponen ial g ow h o in ec ion. The selec ed
alue is 𝑃_𝐼𝑆𝑂𝐿𝐴𝑇𝐼𝑂𝑁 = 0.7.
(6)
Algo i hm i e a ions: The o al numbe o i e a ions is ep e-
sen ed by
𝑃𝐴𝑁𝐷𝐸𝑀𝐼𝐶_𝐷𝑈 𝑅𝐴𝑇𝐼𝑂𝑁
, which is se o 20. The
numbe o i e a ions wi hou social dis ancing measu es is
indica ed by
𝑆𝑂𝐶𝐼𝐴𝐿_𝐷𝐼𝑆𝑇𝐴𝑁𝐶𝐼𝑁𝐺
, wi h alues anging
om 7 o 12, inclusi e.
Table 1 summa izes he key pa ame e s and hei alues used
in he CVNAR algo i hm, o ganized acco ding o he main phases
and s eps ou lined in Sec ion 3.2.
4.2 Da ase s
The da ase s used o alida e he pe o mance o he CVNAR algo-
i hm a e sou ced om he Bilken Uni e si y Func ion App oxi-
ma ion Reposi o y (BUFA) eposi o y. Table 2 shows he name, he
Table 1: Summa y o pa ame e s in he CVNAR algo i hm.
Phase (S ep)
Pa ame e Value
Sp ead he
disease:
In ec ion
/Mu a ion
(S ep 3)
𝑂𝑅𝐷𝐼𝑁𝐴𝑅𝑌_𝑅𝐴𝑇 𝐸 Random [0, 5]
𝑆𝑈 𝑃𝐸𝑅𝑆𝑃𝑅𝐸𝐴𝐷𝐸𝑅_𝑅𝐴𝑇𝐸 Random [6, 15]
𝑃_𝑆𝑈 𝑃𝐸𝑅𝑆𝑃𝑅𝐸𝐴𝐷𝐸𝑅 0.1
𝑃_𝑇𝑅𝐴𝑉 𝐸𝐿 0.1
𝑇𝑅𝐴𝑉 𝐸𝐿_𝐷𝐼𝑆𝑇𝐴𝑁𝐶𝐸
Random [1, o al
in e als]
Manage and
upda e lis s
(S ep 4)
𝑃_𝐷𝐼𝐸 0.06
𝑃_𝑅𝐸𝐼𝑁 𝐹𝐸𝐶𝑇𝐼𝑂𝑁 0.001
𝑃_𝐼𝑆𝑂𝐿𝐴𝑇𝐼𝑂𝑁 0.7
Global
i e a ions
𝑃𝐴𝑁𝐷𝐸𝑀𝐼𝐶_𝐷𝑈 𝑅𝐴𝑇𝐼𝑂𝑁 20 i e a ions
𝑆𝑂𝐶𝐼𝐴𝐿_𝐷𝐼𝑆𝑇𝐴𝑁𝐶𝐼𝑁𝐺 7-12 i e a ions
numbe o ins ances, and he numbe o ea u es o each o he 5
da ase s used in his pape .
Table 2: Da ase s om he BUFA eposi o y.
Da ase Ins ances Fea u es
Baske ball (BK) 96 5
Body a (FA) 252 18
Bol s (BL) 40 8
Pollu ion (PO) 60 16
Quake (QU) 2178 4
4.3 Quali y measu es
The me ics o measu emen s o in e es selec ed in his pape o
e alua e he esul s ob ained a e hose desc ibed in Sec ion 3.2.2.
Addi ionally, we include li as an addi ional me ic, which cap u es
he co ela ion be ween he an eceden and he consequen . A
li alue g ea e han 1 indica es ha he ule p o ides aluable
in o ma ion when 𝑋and 𝑌appea oge he .
Suppo , con idence and accu acy can ake alues be ween 0
and 1. The goal is o hese alues o be as high as possible, wi h 1
being he bes esul . Le e age can ake alues om -1 o 1, wi h
alues g ea e han 0 conside ed a o able; alues close o 1 indica e
high-quali y associa ion ules, while alues below 0 sugges s s ong
independence be ween
𝑋
and
𝑌
. Ce ain y ac o also anges om
-1 o 1, whe e 1 indica es ha he ule is comple ely ce ain and
p ecise.
4.4 Resul s
This sec ion p esen s in Sec ion 4.4.1 he esul s o applying he
CVNAR algo i hm o he da ase s om Sec ion 4.2, op imizing he
objec i e unc ions ou lined in Sec ion 3.2.2 o de e mine which
unc ion pe o ms be e . Then, he bes unc ion is compa ed wi h
o he exis ing algo i hm o ob ain NAR in Sec ions 4.4.2. The s op-
ping c i e ion is se o 20 i e a ions, and he 10 bes solu ions a e
being sa ed.
4.4.1 Objec i e unc ion compa ison. As desc ibed in Sec ion 3.2.2,
wo di e en objec i e unc ions a e de ined in Equa ions 1 and 2
espec i ely, o maximize and sol e he NAR op imiza ion p oblem.
143
CVNAR: Cona i us Op imiza ion Algo i hm o disco e Nume ical Associa ion Rules SAC ’25, Ma ch 31-Ap il 4, 2025, Ca ania, I aly
Table 3: Objec i e unc ion compa ison o da ase s om he
BUFA eposi o y.
A . Con (%) A . Li A . Le A . Acc (%) A . Sup (%) A . FC
BK Func ion 1100.00 96.00 0.0103 100.00 1.04 1.00
Func ion 2 100.00 1.01 0.0073 50.41 48.54 1.00
BL Func ion 1100.00 5.00 0.1600 100.00 20.00 1.00
Func ion 2 100.00 1.13 0.0472 55.00 43.50 1.00
FAFunc ion 1 100.00 173.52 0.0039 99.12 0.39 1.00
Func ion 2 100.00 1.45 0.0115 32.53 5.03 1.00
PO Func ion 133.33 7.16 0.0061 97.66 0.66 0.33
Func ion 2 100.00 1.38 0.0375 42.00 18.00 1.00
QU Func ion 1100.00 4.06 0.0003 81.67 19.49 0.80
Func ion 2 99.71 1.10 0.0138 23.48 13.82 0.96
To al A . Func ion 1 86.66 57.14 0.0361 95.69 8.32 0.83
Func ion 2 99.94 1.21 0.0235 44.36 25.78 0.99
Table 3 shows he alues o each quali y me ic o he di e en
da ase s and objec i e unc ions.
The analysis o he esul s shows ha o mos da ase s, he
measu emen alues o bo h objec i e unc ions a e wi hin he
quali y h eshold. Analyzing each me ic, i can be obse ed ha
he second objec i e unc ion achie es highe con idence han he
i s , al hough in bo h cases he alues a e high and close o 100 %.
Con idence is no sui able o de e mining which objec i e unc-
ion is mo e app op ia e, as i does no conside he suppo o
he consequen and, consequen ly, canno de ec nega i e depen-
dencies. Howe e , his is add essed by quali y measu es such as
li , le e age, o accu acy, which ake in o accoun he ela ionship
be ween he an eceden and he consequen . Al hough he alues
o hese measu es a e highe o objec i e unc ion 1, i canno be
concluded ha he associa ion ules ob ained a e mo e in e es ing
han hose om objec i e unc ion 2. This is because o he sec-
ond unc ion, he li is consis en ly g ea e han 1, he le e age is
always posi i e, and he accu acy alues a e close o 100 %. Fu -
he mo e, li , le e age, and accu acy a e no symme ic measu es,
and in some cases, his is insu icien as hey ail o accoun o he
di ec ion o he implica ion. Las ly, he ce ain y ac o conside s
no only he suppo o bo h he an eceden and consequen bu
also he di ec ion o he ule’s implica ion. In his case, he second
objec i e unc ion yields he bes esul s.
Conside ing he abo e, objec i e unc ion 2 is selec ed as he
i ness unc ion. This is suppo ed by i s consis en pe o mance
ac oss all da ase s, yielding posi i e le e age, li alues g ea e
han 1, and accu acy alues close o 100%. These esul s indica e
ha objec i e unc ion 2 p o ides mo e eliable and obus ules
compa ed o objec i e unc ion 1, pa icula ly when conside ing
he di ec ionali y and dependency ela ionships in he NAR.
4.4.2 Compa a i e wi h o he NAR algo i hms. A e selec ing he
second objec i e unc ion, we compa e he esul s ob ained wi h he
CVNAR algo i hm o hose o se e al exis ing op imiza ion me hods
p esen ed in Sec ion 2. This compa ison is based on he analyses
ou lined in [
16
]. The da ase s used o he compa a i e analysis a e:
Baske ball (BK), Body a (FA), Quake (QU), Bol s (BL) and Pollu ion
(PO). The me ics analyzed include suppo and con idence, as
shown in Tables 4, 5, 6, 7 and 8.
Conside ing he de ini ions o suppo and con idence, when
suppo is low and con idence is high, ules wi h a la ge numbe
o a ibu es a e gene a ed, exp essing e y speci ic pa e ns o
beha io in he da a. On he o he hand, when suppo is high,
Table 4: Compa ison be ween CVNAR and NAR algo i hms
o he BK da ase .
Algo i hm A . Sup (%) A . Con (%)
GENAR (Ma a e al. 2001) 30.82 96.52
EARMGA (Yan e al. 2009) 2.70 100.00
MOPAR (Bei an and e al. 2014) 30.76 95.00
HGP-QAR (Moleshi e al. 2019) 62.37 97.40
CVNAR (Func ion 2 in his pape ) 48.54 100.00
Table 5: Compa ison be ween CVNAR and o he NAR algo-
i hms o he FA da ase .
Algo i hm A . Sup (%) A . Con (%)
GENAR (Ma a e al. 2001) 41.52 96.52
EARMGA (Yan e al. 2009) 4.97 100.00
MOPAR (Bei an and e al. 2014) 22.95 81.00
HGP-QAR (Moleshi e al. 2019) 65.43 98.90
CVNAR (Func ion 2 in his pape ) 5.03 100.00
Table 6: Compa ison be ween CVNAR and o he NAR algo-
i hms o he QU da ase .
Algo i hm A . Sup (%) A . Con (%)
GENAR (Ma a e al. 2001) 35.17 64.40
EARMGA (Yan e al. 2009) 3.40 100.00
MOPAR (Bei an and e al. 2014) 31.97 89.00
HGP-QAR (Moleshi e al. 2019) 63.35 99.80
CVNAR (Func ion 2 in his pape ) 13.82 99.71
Table 7: Compa ison be ween CVNAR and o he NAR algo-
i hms o he BL da ase .
Algo i hm A . Sup (%) A . Con (%)
GENAR (Ma a e al. 2001) 30.82 96.52
EARMGA (Yan e al. 2009) 11.43 100.00
MOPAR (Bei an and e al. 2014) 10.72 88.91
HGP-QAR (Moleshi e al. 2019) 81.14 89.77
CVNAR (Func ion 2 in his pape ) 43.50 100.00
less signi ican ules a e ob ained, which may esul in he loss
o hese pa e ns. Fu he mo e, when a ule co e s all eco ds, i
does no p o ide any meaning ul in o ma ion. The e o e, a high o
low suppo alue is no enough o assess he e ec i eness o an
algo i hm.
I can be obse ed ha o he i e da ase s, he suppo o he
ules gene a ed by CVNAR is nei he he highes no he lowes
bu gene ally emains in he mid- ange. Howe e , he con idence
is consis en ly highe , eaching 100% in mos cases, excep o QU,
whe e i emains a 99.8%. No ably, EARMGA is he only algo i hm
ha achie es a simila le el o con idence, bu i s suppo is sig-
ni ican ly lowe in all da ase s. The e o e, i can be concluded ha
he CVNAR algo i hm allows us o ob ain mo e eliable associa ion
ules.
144
SAC ’25, Ma ch 31-Ap il 4, 2025, Ca ania, I aly C. He uzo-Lodei o e al.
Table 8: Compa ison be ween CVNAR and o he NAR algo-
i hms published o he PO da ase .
Algo i hm A . Sup (%) A . Con (%)
GENAR (Ma a e al. 2001) 22.64 99.72
EARMGA (Yan e al. 2009) 5.36 99.90
MOPAR (Bei an and e al. 2014) 52.14 23.02
HGP-QAR (Moleshi e al. 2019) 70.66 96.60
CVNAR (Func ion 2 in his pape ) 18.00 100.00
5 Conclusions and u u e wo ks
The objec i e o his wo k was o p opose a new algo i hm, based
on he CVOA algo i hm, o disco e ing NAR. This algo i hm is in-
ended o be a gene al pu pose algo i hm and can be applied o any
da a se . To achie e his, a new indi idual enconding is p oposed,
andomly de e mining whe he each a ibu e is included in he
ule and speci ying i s ype. Addi ionally, he in ec ion p ocess was
modi ied, and wo new objec i e unc ions we e de ined o enhance
he op imiza ion p oblem.
The esul s demons a e ha he CVNAR algo i hm can handle
any nume ic da ase by lea ning, in each i e a ion, bo h he in e -
als and he a ibu es assigned o he an eceden , consequen , o
excluded om he ule. This lea ning p ocess leads o he gene -
a ion o mo e p ecise and eliable associa ion ules. Fu he mo e,
he CVNAR algo i hm enables he ex ac ion o pa e ns ha can
p edic u u e beha io s om cu en da a ac oss a ious domains
and ields.
As u u e wo k, he de ini ion o a new objec i e unc ion can be
conside ed, combining o he ele an me ics o inc ease he alue
o he lowes me ics and add essing he op imiza ion p oblem om
a mul i-objec i e p espec i e. Addi ionally, i would be ad isable
o educe he algo i hm’s execu ion ime. This could be achie ed,
o ins ance, by adding a pe ce ange o in ec ei he he in e al o
he sp eade indi idual o he ype o a ibu e, a he han always
in ec ing bo h.
Acknowledgmen s
The esea ch is suppo ed by PID2020-117954RB-C22, PID2020-
117954RB-C21, PID2023-146037OB-C21, PID2023-146037OB-C22
unded by MICIU/AEI/10.13039/501100011033. I also is suppo ed
by TED2021-131311B-C21 and TED2021-131311B-C22 unded by
MICIU/AEI/10.13039/501100011033 and he Eu opean Union Nex Gen-
e a ionEU/PRTR.
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