Op imal da a ansmission and pa h inding o
WSN and decen alized IoT sys ems using I-GWO
and Ex-GWO algo i hms
Ami Seyyedabbasi
a
, Fa zad Kiani
a
, To igh Allah i anloo
a
,
Unai Fe nandez-Gamiz
b
, Samad Noeiaghdam
c,d,*
a
So wa e Enginee ing Depa men , Facul y o Enginee ing and Na u al Science, Is inye Uni e si y, Is anbul, Tu key
b
Nuclea Enginee ing and Fluid Mechanics Depa men , Uni e si y o he Basque Coun y UPV/EHU, Nie es Cano 12, 01006
Vi o ia-Gas eiz, Spain
c
Indus ial Ma hema ics Labo a o y, Baikal School o BRICS, I ku sk Na ional Resea ch Technical Uni e si y, I ku sk
664074, Russia
d
Depa men o Applied Ma hema ics and P og amming, Sou h U al S a e Uni e si y, Lenin p ospec 76, Chelyabinsk
454080, Russia
Recei ed 4 May 2022; e ised 13 July 2022; accep ed 7 Augus 2022
A ailable online 19 Augus 2022
KEYWORDS
WSN;
DIoT;
Pa hfinding;
Me aheu is ic algo i hm;
Swa m in elligence
Abs ac E ficien esou ce use is a e y impo an issue in wi eless senso ne wo ks and decen al-
ized IoT-based sys ems. In his con ex , a smoo h pa hfinding mechanism can achie e his goal.
Howe e , since his p oblem is a Non-de e minis ic Polynomial- ime (NP-ha d) p oblem ype,
me aheu is ic algo i hms can be used. This a icle p oposes wo new ene gy-e ficien ou ing me h-
ods based on Inc emen al G ey Wol Op imiza ion (I-GWO) and Expanded G ey Wol Op imiza-
ion (Ex-GWO) algo i hms o find op imal pa hs. Mo eo e , in his s udy, a gene al a chi ec u e
has been p oposed, making i possible o many di e en me aheu is ic algo i hms o wo k in an
adap i e manne as well as hese algo i hms. In he p oposed me hods, a new fi ness unc ion is
defined o de e mine he nex hop based on some pa ame e s such as esidual ene gy, a fic, dis-
ance, bu e size and hop size. These pa ame e s a e impo an measu emen s in subsequen node
selec ions. The main pu pose o hese me hods is o minimize a fic, imp o e aul ole ance in
ela ed sys ems, and inc ease eliabili y and li e ime. The wo me aheu is ic algo i hms men ioned
abo e a e used o find he bes alues o hese pa ame e s. The sugges ed me hods find he bes
pa h o any leng h o he pa h be ween any sou ce and des ina ion node. In his s udy, no eady
da ase was used, and he es ablished ne wo k and sys em we e un in he simula ion en i onmen .
As a esul , he op imal pa h has been disco e ed in e ms o he minimum cos o he bes pa hs
ob ained by he p oposed me hods. These me hods can be e y use ul in decen alized pee - o-
*Co esponding au ho a : Indus ial Ma hema ics Labo a o y, Baikal School o BRICS, I ku sk Na ional Resea ch Technical Uni e si y,
I ku sk 664074, Russia.
E-mail add esses: ami .seyyedabbasi@is inye.edu. (A. Seyyedabbasi), a zad.kian[email p o ec ed] (F. Kiani), ofigh.allah i a[email p o ec ed]
(T. Allah i anloo), unai. e nand[email p o ec ed] (U. Fe nandez-Gamiz), snoei@is u.edu,noiagdams@susu. u (S. Noeiaghdam).
Pee e iew unde esponsibili y o Facul y o Enginee ing, Alexand ia Uni e si y.
Alexand ia Enginee ing Jou nal (2023) 63, 339–357
HOSTED BY
Alexand ia Uni e si y
Alexand ia Enginee ing Jou nal
www.else ie .com/loca e/aej
www.sciencedi ec .com
h ps://doi.o g/10.1016/j.aej.2022.08.009
1110-0168 Ó2022 THE AUTHORS. Published by Else ie BV on behal o Facul y o Enginee ing, Alexand ia Uni e si y.
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/).
pee and dis ibu ed sys ems. The me ics o pe o mance e alua ion and compa isons a e i) ne -
wo k li e ime, ii) he ali e node a io in he ne wo k, iii) he packe deli e y a io and los da a pack-
e s, i ) ou ing o e head, ) h oughpu , and i) con e gence beha io . Acco ding o he esul s, he
p oposed me hods gene ally choose he mos sui able and e ficien ways wi h minimum cos . These
me hods a e compa ed wi h Gene ic Algo i hm Based Rou ing (GAR), A ificial Bee Colony Based
ou ing (ABCbased), Mul i-Agen P o ocol based on An Colony Op imiza ion (MAP-ACO), and
Wi eless Senso Ne wo ks based on G ey Wol op imize . (GWO-WSN) algo i hms. The simula-
ion esul s show ha he p oposed me hods ou pe o m he o he s.
Ó2022 THE AUTHORS. Published by Else ie BV on behal o Facul y o Enginee ing, Alexand ia
Uni e si y. 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/).
1. In oduc ion
Wi eless Senso Ne wo ks (WSNs) a e one o he subca e-
go ies o ad-hoc ne wo ks and consis o many dis ibu ed sen-
so nodes. These nodes can also be used in sys ems comp ising
o he In e ne o Things (IoT). One o he ad an ages o hese
nodes is hei ease o assembly in di ficul en i onmen s. WSNs
can be used in a as a ie y o applica ion a eas, such as a -
fic moni o ing [1,2], ag icul u e [3,4], au omobiles [5], heal h
moni o ing [6], e c. The e a e also many applica ion a eas in
IoT, such as he In e ne o D ones [7,8], In e ne o Food
[9], In e ne o Medical-Things [10], Indus ial IoT (IIoT)
[11], and au onomous ehicles [12]. Mo eo e , WSNs and
IoT sys ems can also collabo a e as a single sys em [13–17].
I can be used widely, especially in decen alized IoT a chi ec-
u es [18,19].
In scena ios, whe e he e a e in e ne a ailabili y issues, o
when low cos is desi able, p oblems can occu in an IoT sys-
em wi h classical cen alized a chi ec u es. Fu he mo e, in
his a chi ec u e, a la ge pa o he load alls on he se e -
side cloud sys em. Some me hods a e p oposed o his, such
as og/edge compu e nodes. Ano he ecommenda ion o ou-
bleshoo his a chi ec u e is blockchain echnology. A decen-
alized a chi ec u al design can be mo e e ficien and is used
ex ensi ely in applica ion a eas. The e o e, decen alized dis-
ibu ed a chi ec u es can be employed as a solu ion. We define
hese sys ems as Decen alized IoT (DIoT) sys ems. WSNs a e
gene ally designed in a decen alized o m. The e o e, DIoT
and WSN a e simila in a chi ec u al aspec s. One impo an
issue in hese s uc u es is finding a sui able, op imal, and e fi-
cien pa h o da a communica ion be ween nodes. To achie e
his goal, his s udy p oposes wo e ficien me hods ha a e
inspi ed by me aheu is ic algo i hms. The p oposed me hods
can, bo h, find he op imal pa hs wi h e ficien esou ce usage,
and p o ide ea u es such as scalabili y and aul ole ance. A
sample sys em wi h he hyb id a chi ec u e o DIoT and WSN
echnologies is shown in Fig. 1.
Each senso node o IoT de ice can send i s da a packe s o
Base S a ion (BS) ia single-hop o mul i-hop model. In a
decen alized dis ibu ed s uc u e, mul i-hop me hods a e e-
quen ly employed. The BS collec s all da a packe s and ans-
mi s hem o a se e (possibly a cloud) o da a analysis and
end-use access [20]. As senso nodes wo k in collabo a ion,
i is necessa y o ha e an e ficien da a ans e me hod. These
nodes su e om a limi ed powe ba e y, bandwid h, compu-
a ional capaci y, and memo y space. The e o e, pe o ming
he complex compu a ions, in each senso node, is a challeng-
ing ask. Fu he mo e, echa ging is mos ly impossible due o
physical cons ain s, such as he loca ion o he nodes. A he
same ime, changing he ba e ies is no possible, as hese sen-
so s use one- ime ba e ies. The main issue in WSN and IoT
sys ems is inc easing he ne wo k li e ime. I is wo h no ing
ha esou ce managemen and ne wo k opology has an
impo an ole o play in ne wo k li e ime and a ailabili y
[21]. Since ne wo k li e ime deals di ec ly wi h senso nodes’
emaining ba e y le el, ene gy consump ion is a i al ac o
in hese sys ems, making ene gy-one o he mos impo an
esou ces. Howe e , while ocusing on his goal, i is also
essen ial o e ficien ly consume he o he necessa y esou ces.
The e o e, he me hods p oposed uses he esou ces in a bal-
anced manne . Unsu p isingly, e ficien esou ce consump ion,
such as ha o ene gy, inc eases he li e o he ne wo k and, as
such, he sys em [22,23].
In WSN and DIoT sys ems, one o he mos impo an
challenges is e ficien esou ce consump ion such as ene gy
[24,25]. Techniques o find he op imal pa hs, in an ene gy-
e ficien manne , a e o i al impo ance. To ackle his p ob-
lem, nume ous mul i-pu pose ou ing solu ions ha e been
in oduced in he li e a u e bu finding and p oposing a gen-
e al ou ing echnique ha p ese es he in eg i y, connec i -
i y, and inclusi eness o he ne wo k is a e y cos ly and
complica ed p ocess. In addi ion, finding he mos e ficien
ou e among many possible pa hs, in a wide and complex ne -
wo k demands u he p ocessing. Mo eo e , i is no easy o
find app op ia e, e ec i e coe ficien s o he ele an ou ing
pa ame e s. In addi ion, analy ical solu ions o such p oblems
a e di ficul o find. In ac , hese p oblems a e ca ego ized
unde Non-de e minis ic Polynomial- ime (NP-ha d) p oblems
[26–28]. The e o e, i is fi ing o use me aheu is ic algo i hms
o sol e i . Howe e , when hese algo i hms a e implemen ed
in he en i e ou ing p ocess, hey end o cause addi ional
o e head in he sys em and esul in ine ficien usage o some
o he sys em’s esou ces.
In his s udy, a gene ic sys em a chi ec u e is p oposed, and
his a chi ec u e can easily pe o m ou ing wi hou incu ing
any addi ional cos , in eg a ing wi h many di e en me a-
heu is ic algo i hms. Since he p oposed model is comp ehen-
si e, i will be able o wo k well by including a ious
algo i hms o many pu poses. In his s udy, we discussed
ou pe o mance me ics as ollows. i) ne wo k li e ime, ii)
he ali e node a io in he ne wo k, iii) he packe deli e y a io
and los da a packe s, i ) ou ing o e head, ) h oughpu , and
i) con e gence beha io .
This pape p oposes wo new ene gy-e ficien me hods
based on he Inc emen al G ey Wol Op imiza ion (I-GWO)
and Expanded G ey Wol Op imiza ion (Ex-GWO) algo i hms
340 A. Seyyedabbasi e al.
o help find op imal pa hs in DIoT and WSN sys ems. In he
GWO algo i hm [29], swa ming is con olled by he leade o
he g oup, which helps o ge he op imum solu ion o a
defined p oblem. I can ou pe o m o he me aheu is ic algo-
i hms hanks o i s hie a chy g oup wo king mechanism and
balanced ansi ions be ween explo a ion and exploi a ion
phases. These wol es can exhibi a success ul mechanism
because hey ha e an ex emely dominan hie a chy. In addi-
ion, his algo i hm does no equi e addi ional cos in finding
he op imal solu ions in line wi h he simple wo king mecha-
nism and pa ame e s. In o he wo ds, he GWO algo i hm
wo ks simply wi h a small numbe o pa ame e s, p ese ing
he andom p inciple. Thanks o hese ea u es, i has sui able
beha io in he explo a ion and exploi a ion phases which a e
e ec i e in finding he op imal solu ion. Addi ionally, i only
equi es one ec o o posi ion, which dec eases he memo y
demand. On he o he hand, o he me aheu is ic me hods su -
e om compu a ional o e load and ime ine ficiency in hei
app oach o he op imum answe . The e o e, hanks o he
cha ac e is ics o he GWO algo i hm, i can be used o find
solu ions o di e en complex and eal p oblems. In his
ega d, he GWO algo i hm may be mo e likely o be success-
ul han o he me aheu is ic me hods in his ype o p oblem
on a ious pa ame e s due o i s wo king mechanism. The e-
o e, he GWO a ian s may be mo e likely o be success ul
han o he me aheu is ic me hods in his ype o p oblem on
a ious pa ame e s due o i s wo king mechanism.
The I-GWO finds solu ions much mo e quickly, owing o
i s exploi a ion ea u e and as con e gence a e in non-
complex en i onmen s, whe eas Ex-GWO, due o i s s uc u e,
is deemed success ul in complex and la ge-scale sys ems.
Hence, an app op ia e choice can be made o di e en needs
and sys ems. In his con ex , he ou ing me hods p oposed in
his pape sugges he mos app op ia e model o a ious ne -
wo ks using hese wo algo i hms. In hese algo i hms, swa m-
ing is con olled by he leade o he g oup, which helps o ge
he op imum solu ion o a defined p oblem. As a esul , hese
algo i hms a e use ul in dec easing ne wo k complexi y and
inc easing he e ficiency o esou ces used in pa hfinding.
Besides, hese algo i hms a e used o p esen low-cos pa hs
among he a ious p obable pa hs. The p oposed pa hfinding
me hods, which use he me aheu is ic algo i hms, a e named
ene gy-e ficien ou ing based on I-GWO (EERI
-GWO
) and
ene gy-e ficien ou ing based on Ex-GWO (EER
Ex-GWO
).
The p oposed me hods y o find pa hs ha a e mos sui able
and mos e ficien wi h minimum cos s. The o he ea u es and
con ibu ions o he p oposed me hods a e:
1) A gene ic sys em a chi ec u e is p oposed ha combines
he me aheu is ic and ne wo k model. Due o his, he
a chi ec u e is adap able in a ious sys ems and o
nume ous pu poses. Fu he mo e, many me aheu is ic
algo i hms can be eadily applied in hese sys ems.
2) In o de o inc ease he pa hfinding e ficiency, me a-
heu is ic algo i hms a e used o disco e he mos
app op ia e coe ficien s o each pa ame e o he
defined fi ness unc ion.
3) A no el and comp ehensi e fi ness unc ion is defined
wi h an emphasis on balancing ade-o s be ween
impo an pa ame e s. This unc ion conce ns wi h fi e
Fig. 1 Sample a chi ec u e o DIoT and WSN [19].
Op imal da a ansmission and pa hfinding o WSN and decen alized IoT sys ems using I-GWO and Ex-GWO 341
pa ame e s (dis ance be ween nodes, BS-hop, alid-
a fic, ene gy consump ion, and bu e capaci y), and
a adeo be ween ela ed pa ame e s.
4) Finding he bes ou es be ween he nodes means ha
less ene gy is consumed in he ne wo k. This esul s in
inc eased ne wo k esilience and li e ime.
5) The global knowledge and p ocessing o he ne wo k a e
pe o med a he BS, which ha e abundan esou ces.
The es o his pape is o ganized as ollows. In he nex
sec ion, esea ch ha deals wi h finding a ou e using me a-
heu is ic me hods, p esen in li e a u e, is desc ibed. In he
hi d sec ion, he p oposed me aheu is ic algo i hms a e b iefly
explained. In he ou h sec ion, he p oposed me hods a e
de ailed. In he fi h sec ion, simula ion esul s and analyses
a e p o ided. Conclusion and u u e wo ks a e gi en in he las
sec ion.
2. Rela ed wo ks
In gene al, me aheu is ic algo i hms can a i e a op imal solu-
ions o eal-wo ld p oblems a a low cos . In he li e a u e,
he e a e se e al widely used classifica ions o me aheu is ic-
based algo i hms [30]: na u e-inspi ed s non-na u e-inspi ed
algo i hms, popula ion-based s single poin sea ch algo-
i hms, dynamic s s a ic objec i e unc ions, single s a ious
neighbo hood s uc u es, and memo y-less s memo y-
independen algo i hms [30]. One o he mos popula discus-
sions and classifica ions is he popula ion-based and single-
poin sea ch ca ego y. The imp o emen o a single-based
solu ion is achie ed by i e a ions, while he op imiza ion o a
popula ion-based solu ion is achie ed h ough a se o solu-
ions. Ano he impo an a ea is na u e-and non-na u e-
inspi ed classifica ion. Recen esea ch shows ha na u e-
inspi ed algo i hms a e a end and pe o m qui e well a sol -
ing a wide a ie y o p oblems. Me hods in his ca ego y a e
defined in o ou main ca ego ies [29]. They a e e olu ion-
based, Swa m-In elligence (SI)-based, physics-based, and
human-based [31,32] app oaches.
This s udy ocuses on he p oblem o finding he bes ou e.
S udies in la ely yea s p e e SI me hods because hey gene ally
ou pe o m o he me hods in sol ing p oblems, pa icula ly in
pa hfinding p oblems. SI me hods a e gene ally na u e-
inspi ed and a e based on a he d o collec i e social beha io
and communi y mindse . The e a e many s udies in his ca e-
go y in he li e a u e [33–36] showcasing ha SI-based me h-
ods can sol e complex p oblems mo e e ficien ly. These
algo i hms consis o a g oup o simple pa icles and homoge-
neous membe s ha in e ac wi h each o he as well as hei
en i onmen . Thei agen s y o find he bes solu ions ha
coope a e in he local sea ch a ea and benefi om he collec-
i e e o o all he agen s in ol ed. In his s udy, he use o SI
me hods in WSN and IoT o find op imal pa hs is discussed
[37–39].
An Colony Op imiza ion (ACO) is one o he mos e-
quen me aheu is ic algo i hms ha is used in he sys ems dis-
cussed. Au ho s in [40] p oposed a ou ing me hod o a
dis ibu ed mul i hop-based sys em using he ACO algo i hm
o eliable da a communica ion. The nex hops on he pa h
a e based on senso nodes wi h high ene gy le els. Howe e ,
i is no conside ed e y success ul in ene gy e ficiency because
i does no wo k in a ai and balanced manne . The main ea-
son o his is ha he fi ness unc ion used does no use su fi-
cien pa ame e s. Resea che s in [41] in es iga ed a new
phe omone upda e mechanism in he ACO algo i hm and used
i o achie e ene gy e ficiency o WSNs. The au ho s discuss
wo ene gy measu es. In nex node selec ion o ou ing, senso
nodes close o he a ge a e mo e likely o be selec ed. They
also use ou con ol pa ame e s in he p obabilis ic decision
unc ion. Since i does no use memo y e ficien ly, i canno
be e y success ul in showing e ficien pe o mance in he gen-
e al analysis. Au ho s in [42] p oposed a new ou ing algo-
i hm based on ACO algo i hm o achie e balanced ene gy
consump ion on each ne wo k senso node beside he choice
o he pa h wi h minimal cos . In hei wo k, called IEMACO,
hey make ou e disco e y based on a numbe o ac o s: he
con e gence speed o he ou ing algo i hm, he p obabili y
o ansi ion, and he emaining li e o he nodes. Posi ion
and speed in o ma ion p edic s he emaining li e ime o he
link. The mos ob ious sho coming o his s udy is he usage
o he memo y me hod. In [43], he au ho s ha e p oposed a
dynamic ene gy h eshold s a egy di e en om he mul i-
pa h app oaches, so-called ACOHCM. I has some ad an ages
such as ne wo k opology, sea ching he op imal pa h, and ne -
wo k load balancing. In he ACOHCM, ini ially hop coun ing
mechanism is applied. The hop coun o he sink (BS) is 0.
The numbe o hops o o he nodes is inc emen ed by one
depending on hei neighbo s. When he opology o he ne -
wo k changes, he hop coun ing mechanism is un again. So,
he hop coun s should be upda ed a di e en ime in e als.
Finally, an ene gy h eshold s a egy is used ha is applied
o each node. The au ho s o [44] p oposed a dynamic
decision-making sys em based on ACO algo i hm o con-
nec ed ca s in IoT sys ems. They used a ificial an s o con ol
he dynamics o connec ed ehicles in a fic flow and o
au onomous calcula ions. An an colony op imiza ion-based
ou ing p o ocol o mul i-agen s is p esen ed in his pape
ha manages ne wo k esou ces e ec i ely in eal- ime [19].
In addi ion o finding he nex des ina ion o an s, he p o-
posed me hod is also used o manage phe omone upda es
and e apo a ion a es. Se e al key pa ame e s a e aken in o
accoun when de e mining he nex des ina ion unde a ious
condi ions, including ene gy emaining, bu e size, a fic a e,
and dis ance. In e ms o ne wo k li e ime and ene gy con-
sump ion, simula ion esul s o he p oposed me hod ha e
ema kable pe o mance. An an colony op imiza ion-based
ou ing p o ocol o mul i-agen s is p esen ed in his pape
ha manages ne wo k esou ces e ec i ely in eal- ime [45].
In addi ion o finding he nex des ina ion o an s, he p o-
posed me hod is also used o manage phe omone upda es
and e apo a ion a es. Se e al key pa ame e s a e aken in o
accoun when de e mining he nex des ina ion unde a ious
condi ions, including ene gy emaining, bu e size, a fic a e,
and dis ance. In e ms o ne wo k li e ime and ene gy con-
sump ion, simula ion esul s o he p oposed me hod ha e
ema kable pe o mance.
Apa om ACO, he Gene ic Algo i hm (GA) is ano he
echnique also ecommended in such sys ems. In [46], i was
p oposed o combine simula ed annealing wi h gene ic algo-
i hms in o de o achie e op imal pe o mance. The e has
been a compa ison o he obse ed esul s in e ms o he a e -
age esidual ene gy, he ne wo k li espan, and he packe ans-
po be ween he BS and sink, wi h ha o a GA-based
342 A. Seyyedabbasi e al.
app oach. Gup a e al [47] p oposed an ene gy-e ficien algo-
i hm o minimize he ene gy consump ion in each ound
based on GA. The p oposed me hod a emp s o educe he
o al dis ance a eled by da a in he sys em. In his s udy, a
Di ec ed Acyclic G aph (DAG) model was used and he ch o-
mosome ep esen a ion, as well as a c osso e me hod, we e
p oposed. In hei s a egy, hey also emphasized he mini-
miza ion o he o al pa h leng h. This s udy, which is ambi-
ious in e ms o ene gy e ficiency, is used in compa ison
wi h he p oposed me hods in ou s udy. IoT has been added
o Clus e ed-Based Rou ing (CBR) o In o ma ion-Cen ic
WSNs (ICWSNs) in a p o ocol known as CBR-ICWSN, which
enables CBR o hese ne wo ks [48]. The e a e wo phases o
his pape , which include he choice o a Clus e Head (CH)
and he de e mina ion o he op imal ou e. Thus, by employ-
ing a Black Widow Op imiza ion (BWO) me hod in o de o
choose an op imal se o CHs, an op imal se o CHs is
selec ed. I is in e es ing o no e ha he au ho s in his pape
used a di e en algo i hm o find he op imal ou e. CBR-
ICWSN is a ou ing p o ocol ha is based on Opposi ional
ABC (OABC) and can be used o selec ou ing ou es mo e
e ficien ly.
The a ificial Bee Colony (ABC) algo i hm is ye ano he
me aheu is ic me hod used in such sys ems. Au ho s in [49]
ha e p oposed a new clus e ing ou ing me hod based on
an ABC algo i hm o clus e o ma ion. Thei main goal
is o educe ene gy consump ion and exploi low-powe clus-
e s. They a e conce ned abou he ade-o be ween ene gy
consump ion and he quali y o he communica ion link
wi hin clus e s. Au ho s in [50] p opose a me hod based
on he G ey Wol Op imize (GWO) algo i hm o sol e
he ene gy p oblem in WSNs. They a emp o handle he
p oblem o finding he co ec posi ion o unknown nodes
in he ne wo k. Based on hei esul s, hei GWO-based
me hod is be e han Pa ial Swa m Op imiza ion (PSO)
and Modified Ba Algo i hm (MBA) algo i hms in he con-
e gence and success a e. In [51] esea che s ha e p oposed
a new ou ing algo i hm in a hie a chical s uc u e using he
GWO algo i hm. I a oids he ene gy hole by balancing he
load on he nodes nea e o BS and clus e head nodes. The
new fi ness unc ion, p oposed in hei wo k, akes in o
accoun he o al dis ance and he o al numbe o hops.
This fi ness unc ion is solely used o help he wol es. One
sho coming o his s udy is ha i does no ocus su fi-
cien ly enough on he e ec i e pa ame e . Wi hou aking
in o accoun necessa y and su ficien pa ame e s, he esul s
ob ained om he fi ness unc ion can be, a bes , o e y
limi ed use in eal-wo ld cases. In con as , he fi ness unc-
ion p oposed in ou s udy is gene al and mul i-pu pose and
can also be easily adap ed o many me aheu is ic algo i hms.
I is wo h men ioning ha he a chi ec u e p oposed is he
leading eason o his adap abili y.
In ano he s udy, he au ho s p oposed a me a-heu is ic
a ificial in elligence app oach based on g ey wol social
beha io o minimize he ene gy consump ion o WSNs om
he li es ock indus y [52]. In o de o de e mine an algo-
i hm’s pe o mance, ene gy le el, g id size, ansmission
ange, and di ec ion o ansmission we e used as ac o s. A
me aheu is ic-d i en, ene gy-awa e ou ing scheme (IMD-
EACBR) is p oposed in [53]. The IMD-EACBR model aims
o maximum ene gy usage and li e ime. IMD-EACBR
employs an imp o ed A chimedes op imiza ion algo i hm-
based clus e ing (IAOAC) echnique o clus e head selec ion.
Fu he mo e, he TLBO-MHR echnique is applied o op i-
mum ou e selec ion using eaching–lea ning-based op imiza-
ion (TLBO). Simula ed ou comes e eal imp o emen s in
dead node p opo ions, ne wo k li espan, ene gy consump ion,
packe deli e y a io (PDR), and la ency. A no el clus e ing
and ou ing me hod is p esen ed in his pape in an e o o
enhance sys em e ficiency [54]. In o de o op imize i , i elies
mos ly on gene ic algo i hms as well as equilib ium op imiza-
ion. Using gene ic algo i hms, a fi s phase is ca ied ou ha
clus e s he senso nodes based on hei ea u es. As a esul ,
he bes clus e heads a e selec ed o imp o e sys em s abili y.
The pu pose o his wo k is o educe he ene gy consump ion
o WSN ne wo ks by imp o ing he clus e ing algo i hm and
he equilib ium op imiza ion algo i hm used o selec ing he
op imal pa h be ween clus e heads and base s a ions. Conse-
quen ly, he p oposed me hod has been ob ained o be he
mos ene gy-e ficien , ha e a longe ne wo k li espan, and deli-
e mo e packages han o he me hods. This s udy aims o
de elop an ene gy-e ficien clus e ou ing p o ocol ha can
be applied o wi eless senso ne wo ks [55]. In he fi s s ep
o he clus e head selec ion p ocess, we used he Honey Bad-
ge Algo i hm o selec clus e heads. In o de o find he op i-
mal clus e head among all senso s, he Honey Badge
Algo i hm is used. This algo i hm akes in o accoun ac o s
including dis ance o he base s a ion, esidual ene gy, dis ance
o i s neighbo s, node deg ee, and cen ali y. I hen selec s he
op imal clus e head. A uzzy Fi ebug Swa m Op imiza ion
algo i hm is used o pe o m he ou ing be ween he clus e
heads and he base s a ions. This me hod o e s a educ ion
in he amoun o end- o-end delay, an inc ease in he numbe
o packe s ha a e deli e ed, a highe h oughpu , and a
educ ion in he numbe o packe s los , which a e all ac o s
ha a ec how much ene gy is consumed by he ne wo k.
In ano he s udy in he li e a u e, a hyb id op imiza ion
algo i hm is p oposed o p opose a new ene gy-awa e CH
selec ion amewo k in WSNs h ough hie a chical ou ing
[56]. As well as ene gy and dis ance, delay, and Quali y o Se -
ice (QoS) a e conside ed when selec ing he CH. I is p o-
posed o de elop a hyb id algo i hm ha combines he
p inciples o Sea Lion Op imiza ion (SLnO) and Pa icle
Swa m Op imiza ion (PSO) o selec he op imal CH. The pe -
o mance o he adop ed me hod is compa ed wi h o he adi-
ional models using a a ie y o me ics. Compa ed o o he
con en ional me hods, he p oposed algo i hm has highe no -
malized ene gy. In his pape , he chao ic uzzy g asshoppe is
applied o op imizing ou ing on he In e ne o Things, ocus-
ing in pa icula on he sleep-wake schedules o nodes, which
a e an essen ial pa o he ou ing [57]. Du ing he e alua ion
o he e ficiency o he p oposed me hod, he ollowing h ee
c i e ia we e u ilized: he emaining ene gy, he ne wo k li e,
and he co e age a e o he ne wo k. I has been de e mined
ha he esul s a e based on wo di e en scena ios ha ha e
been analyzed. Consequen ly, he p oposed me hod pe o ms
be e han he base me hod in all scena ios and is mo e e ec-
i e o all c i e ia o compa ison han he base me hod.
The use o me aheu is ic me hods has become e y popula
in IoT and WSN sys ems, especially in ecen yea s. In his
pape , wo me hods o find op imal pa hs in DIoT and WSN
applica ions a e p o ided using wo me aheu is ic algo i hms
(I-GWO and Ex-GWO). These me hods can be applied in bo h
DIoT and WSNs.
Op imal da a ansmission and pa hfinding o WSN and decen alized IoT sys ems using I-GWO and Ex-GWO 343
3. I-GWO and Ex-GWO algo i hms
This sec ion b iefly desc ibes wo me aheu is ic algo i hms
used in he me hods p oposed in his pape . The G ey wol
op imize (GWO) algo i hm is inspi ed by g ey wol es in hei
na u al habi a [29]. Alpha (a), be a (b), del a (d), and omega
(x) a e he ou ypes o wol es ound in a pack. These wol es
ha e di e en esponsibili ies in he pack. Alpha Wol is he
leade o he pack. Be a wol es a e he co-leade s o he alpha
wol . The hi d le el o hie a chy in he pack is ha o del a
wol es. The emaining wol es which a e no pa o he uppe
le el o he hie a chy a e omega wol es. Enci cling, hun ing,
and a acking a e he h ee main a ibu es o he wol es.
Inc emen al G ey Wol Op imize (I-GWO) algo i hm,
used in he fi s pa hfinding me hod o his pape , is an
upg aded e sion o he GWO [36]. In he I-GWO algo i hm,
he leade enci cles he p ey (Eq. (1)), hun s i and finally (Eq.
(2)), a acks he p ey based on he A
! alue. I |A|less han1, a
wol is a acking i s p ey, o he wise, i ’s busy finding o he
p ey. The second wol on he pack ollows he leade s’ posi ion
and upda es i s own posi ion o a ack he p ey. Gene ally, he
n
h
wol in he pack upda es i s own posi ion based on he n-1
wol be o e i (Eq. (3)). Eq. (4), 5, and 6 a e he con ol mech-
anisms o a oid apping in local op ima and o balance mo e-
men s be ween explo a ion and exploi a ion phases.
Da
!¼Ca
!Xa
!X
!
ð1Þ
X1
!¼X
!
aA1
!Da
!ð2Þ
Xn
! þ1ðÞ¼
1
n1Xn1
i¼1Xi ðÞ;n¼2;3; mð3Þ
A
!¼2a
! 1
!a
!ð4Þ
C
!¼2 2
!ð5Þ
a
!¼21 2
T2
ð6Þ
Addi ionally, in bo h I-GWO and Ex-GWO, a
!is linea ly
dec eased om 2 o 0 o e he cou se o i e a ions, and is
ob ained using Eq. (6) and (12), espec i ely. The e ec o a
!
is on he ange o mo ion, di ec ing he algo i hm in finding
he solu ion and is used o ge close o he solu ion ange.
Random ec o s 1
!and 2
!lie in he ange [0, 1]. A
!, and C
!
a e coe ficien ec o s ha lead o enci cling he p ey [29,33–
35]. These pa ame e s con ol he adeo be ween explo a ion
and exploi a ion phases. Due o his, wol es do no always go
in he same di ec ion. In all a ian s, whene e A
*
is less han 1,
he wol es in he pack a ack o hun , o he wise, hey y o
find he p ey. X
!is he posi ion ec o o he p ey, whe eas
Xi
!is he posi ion ec o o he g ey wol , and Di
!is a ec o
ha depends on he loca ion o he a ge . Whe e i{a,b,
d}. Mo eo e , is cu en i e a ion and Tis maximum i e a ion
numbe s.
The o he me aheu is ic algo i hm used in his pape is he
Expanded G ey Wol Op imize (Ex-GWO) [36] algo i hm.
The hun ing mechanism o he Ex-GWO is uses a echnique
dissimila o one used in I-GWO and GWO algo i hms. Enci -
cling o he p ey is pe o med using he fi s wol in he pack
(Eq. (7)). The ou h wol in he pack upda es i s posi ion
based on he fi s h ee wol es be o e i . Gene ally, he n
h
wol
in he pack upda es i s own posi ion based on he fi s wol in
he pack as well as he wol es be o e i (Eq. (8) and (9)). In Ex-
GWO he a acking mechanism ensu es ha he p ey does no
escape. The coe ficien s a, A, and Ca e calcula ed using Eq.
(10), 11, and 12.
Da
!¼Ca
!Xa
!X
!
Db
!¼Cb
!Xb
!X
!
Dd
!¼Cd
!Xd
!X
!
ð7Þ
X1
!¼X
!
aA1
!Da
!
X2
!¼X
!
bA2
!Db
!
X3
!¼X
!
dA3
!Dd
!ð8Þ
Xn
! þ1ðÞ¼
1
n1Xn1
i¼1Xi ðÞ;n¼4;5; mð9Þ
A
!¼2a
! 1
!a
!ð10Þ
C
!¼2 2
!ð11Þ
a
!¼21
T
ð12Þ
I-GWO algo i hm is based on he leade wol s’ beha io .
O he wol es in he pack upda e hei own posi ion based on
all he wol es selec ed a o e hemsel es. In he Ex-GWO algo-
i hm, he n
h
wol upda es i s own posi ion ele an o he
p ey acco ding o hei immedia e successo and he fi s h ee
wol es. In [36], i is p o ed ha he pe o mance o I-GWO
and Ex-GWO algo i hms is be e han GWO. On he o he
hand, I-GWO ies o find solu ions much quickly due o i s
exploi a ion ea u e and i s as con e gence a e, and Ex-
GWO, owing o i s s uc u e, is likely o be success ul in com-
plex and la ge-scale sys ems.
4. P oposed pa h inding me hods
The used me aheu is ic algo i hms a e a na u al ma ch o he
p oblem sui and exhibi a balanced beha io , as such, hey
ha e been used in his pape as he p oblem-sol ing me hodol-
ogy. As explained in he li e a u e sec ion, many me aheu is ic-
based algo i hms ha e been used o simila sys ems. I is
known ha me aheu is ic-based me hods do no gua an ee o
find op imal solu ions, bu hey y o find he solu ions close
o he op ima, p o iding mo e e ficien execu ion ime and
CPU powe consump ion in ime and space complexi ies. Each
o he p oposed me aheu is ic me hods in he li e a u e has i s
ad an ages along wi h i s sho comings. This s udy ocuses on
b oade pa ame e s in p oposing comp ehensi e and accu a e
me hods o be used in WSN and DIoT. Acco dingly, a new fi -
ness unc ion has been defined. The defined fi ness unc ion is
used o calcula e he cos o each pa h in he ne wo k and
344 A. Seyyedabbasi e al.
includes esidual ene gy, a fic s a us, bu e a e, BS-hop, and
neighbo lis o each node as o mula ed in Eq. (13). BS-hop
indica es he hop coun s o each node o BS. In his s udy,
BS is assumed o be he des ina ion node. The BS node does
no look only a he dis ance o numbe o hops o each node
ela i e o i sel o find he mos sui able pa h (be ween each
node and i sel ) bu also ocuses on o he e ec i e pa ame e s
ha a e defined in he new fi ness unc ion. I akes in o
accoun he dynamic esou ces o he nodes in he sys em and
he a iable pa ame e s o he ne wo k. Fo his pu pose, a
new fi ness unc ion is defined. The pa hs be ween he sou ce
and des ina ion nodes a e selec ed acco ding o hop alues
and passed h ough he fi ness unc ion. The sum o he bes fi -
ness alues o each hop will be he candida e o he bes ou e
(Eq.14.). Subsequen ly, he minimum alue among candida es
is chosen as he bes pa h be ween he wo ele an nodes o
each hop coun (Eq.15). A his s age, he lowes -cos pa h is
chosen o each hop coun (s ep 2). S ep 3 selec s he bes pa h
wi h he minimum cos among all hop sizes (Eq.16). A he
same ime, as men ioned be o e, one o he mos impo an
issues discussed in hese sys ems is ene gy sa ing. In his sec-
ion, he new ene gy-e ficien ou ing me hods based on he
wo me aheu is ic algo i hms, EER
I-GWO
and EER
Ex-GWO
,
a e in oduced. They can aid in modeling use ul solu ion mod-
els in he pa hfinding o wide and complex ne wo ks (especially
in decen alized a chi ec u e). These me hods ocus on he c i -
ical ea u es o senso nodes in pa hfinding. As a o emen ioned,
pa hfinding and ou ing a e NP-ha d p oblems in he complex
dis ibu ed and Pee - o-Pee (P2P) s uc u es such as WSN and
DIoT. The e o e, hese p oposed me hods can p o ide a good
solu ion o finding op imal pa hs in he en i e sea ch space. In
sho , hey find he op imal pa h om he se s o possible pa hs
in mul iple hops.
4.1. P oposed a chi ec u e
In his subsec ion, some defini ions and design ac o s o he
p oposed me hods ha e been summa ized along wi h he
desc ip ion o he p oposed me hods. Senso nodes (IoT
de ices) a e deployed andomly in he ne wo k, and di e en
pa hs a e c ea ed be ween any pai o sou ce and des ina ion
nodes. The me aheu is ic algo i hms used in his pape belong
o he SI ca ego y and a e popula ion-based. A gene al a chi-
ec u e is sugges ed o he ele an me aheu is ic algo i hms
o wo k ha moniously wi h he p oposed me hods. Thanks o
his a chi ec u e, he algo i hms used can be easily adap ed o
he ele an sys em. Fu he mo e, i should be no ed ha o he
me aheu is ic me hods a e also able o easily use such sys ems.
The concep ual schema o he p oposed a chi ec u e is p e-
sen ed in Fig. 2.
In his a chi ec u e, he sea ch space is conside ed as a
ma ix whe e he ows ep esen he numbe o sea ch agen s,
and he columns signi y he coe ficien numbe s. In he simula-
ion o I-GWO and Ex-GWO, he numbe o sea ch agen s is
assumed o be equal o he numbe o g ey wol es in he pack.
Mo eo e , he coe ficien numbe s, which a e used as he
dimension o he p oblem, a e assumed o be ou and hei
alues a e ob ained using Eq. (13). The fi ness unc ion,
defined ea lie , is used o calcula e he cos o each pa h. In
addi ion, all he coe ficien s used in he p oposed me hods
a e upda ed a e e y ound o he ne wo k based on me a-
heu is ic algo i hms. When he numbe o hops be ween wo
nodes is one, hey a e al eady single-hop and a e di ec neigh-
bo s, so he e is no need o speci y a ou e. The p oblem a ises
wi h mul i-hop s uc u es. In hese cases, he e may be pa hs o
a ious leng hs be ween he wo nodes. The e may be in e me-
dia e nodes be ween sou ce and des ina ion when he hop
coun s a e mo e han one. In he p oposed a chi ec u e, bes
ou e o any hops o pa hs is ound conside ing Eq. (14)
and (15), and he bes among hem is chosen using Eq. (16).
The e o e, he bes pa h be ween wo in e media e nodes is
ob ained, along wi h he calcula ion o he final bes pa h cos
be ween sou ce and des ina ion. The fi ness unc ion is gi en
by Eq. (13), which calcula es he cos be ween wo nodes i
and j.
Cos i;j¼c1di;j
þc2Hj
þc2
ValidT a ic
Ti;j
þc3
Eini ial
Ej
:
Bu e Capaci y
Bj
ð13Þ
Whe e d
i,j
is dis ance be ween nodes iand j.E
j
indica es he
esidual ene gy o he node j, and H
j
is hops coun o node j o
BS. T
i,j
is he a fic s a us be ween nodes iand j.B
j
indica es
he bu e a e o he nodes j.ValidT a fic,Bu e Capaci y, and
E
ini ial
a e common a iables ha a e used o each node. The
alues o hese h ee a iables a e hei maximum alues a
each node and hey a e ela ed o node ha dwa e p ope ies.
Fu he mo e, c
1
,c
2
,c
3
,c
4
a e h ee con ol pa ame e s, wi h
alues be ween 0 and 1 whe e c
1
+c
2
+c
3
+c
4
= 1 and
c
1
<c
2
<c
3
<c
4
. These con ol pa ame e s a e calcula ed
by me aheu is ic algo i hms (I-GWO and Ex-GWO). The coe -
ficien s upda es a e done a each ound o he ne wo k. I is
wo h men ioning ha he ne wo k ounds e m is di e en
wi h me aheu is ic i e a ions. This di e ence is desc ibed in
he subsequen subsec ion.
4.2. The ne wo k ounds and me aheu is ic i e a ions
In he ac ual applica ion o senso ne wo ks and IoT, he ne -
wo k ound and me aheu is ic algo i hms i e a ion wo k sepa-
a ely. In he ne wo k conside a ions, he ounds and
i e a ions should be handled sepa a ely. Each ound o he ne -
wo k occu s in ce ain ime pe iods. In he p oposed me hods,
a ime in e al be ween each ound o he ne wo k is consid-
e ed. I he ound and i e a ions wo k oge he , i causes an
o e load on he ne wo k. Me aheu is ic algo i hms y o find
he bes solu ions. A he same ime, he e is no specific ime o
each he solu ion, as such, he pa hfinding ope a ion is done
in he BS. A e ha , o e a pe iod o ime, da a packe ans-
e is comple ed be ween he a ge (des ina ion) and he
sou ce. The concep o i e a ion is an exp ession used widely
in me aheu is ic me hods. Each i e a ion ies o app oach
he solu ion based on he esul s ob ained in he p e ious i e -
a ion. Bo h he numbe o i e a ions and he numbe o ne -
wo k ounds depend on he sys em design. In his pape ,
hese pa ame e s a e defined and quan ified. Fu he mo e,
hey a e desc ibed in he simula ion sec ion.
4.3. Pa hfinding mechanism
In he p oposed me hods, he me aheu is ic algo i hms used
help in finding he bes pa h wi h a minimum cos be ween
Op imal da a ansmission and pa hfinding o WSN and decen alized IoT sys ems using I-GWO and Ex-GWO 345
he sou ce and des ina ion (BS) node. The e a e pa hs wi h
a ious numbe s o hops as seen in he fi s s ep o Fig. 2.In
his s ep, he cos o he pa h o all in e media e nodes
be ween he sou ce and des ina ion nodes is calcula ed u ilizing
Eq. (13). The mos op imized coe ficien alues o each pa am-
e e in his equa ion a e ob ained om me aheu is ic algo-
i hms, as desc ibed in he p e ious subsec ion. In he second
s ep, he algo i hm calcula es cos s o he candida e pa h
applying Eq. (14) and hen selec s he pa h wi h he minimum
cos as he bes pa h o each hop coun using Eq. (15). This
p ocedu e is applied o all hop coun s. Indeed, his p ocess
is pe o med o all pa hs wi h di e en sizes. Na u ally, he
bes candida e pa h is chosen among he pa hs o he same
leng h. In he end, as indica ed in s ep 3 o Fig. 2, he algo-
i hm selec s he minimum cos pa h om he ob ained candi-
da e pa hs, as an op imal solu ion be ween hese nodes (sou ce
and des ina ion) based on Eq. (16). In o he wo ds, he op imal
pa h is chosen among he bes pa hs o di e en leng hs. The
p oposed me hods a emp o selec he pa hs ha a e he mos
con enien and e ficien ou es wi h he minimum cos s.
Cos Condida e
S;D¼X
j¼n
i¼1
cos i;jð14Þ
Cos h
S;D¼MinðCos Condida e
S;DÞ8hHopCoun ð15Þ
Cos S;D¼Min Cos h
S;D
ð16Þ
Whe e Cos Condida e
S;Dis shows he o al cos be ween nodes i
and j. This p ocess is calcula ed sepa a ely o each hop coun .
The sho es pa h ound o each hop is conside ed Cos h
S;D.
A e finding he sho es pa h o all hops, one sho es pa h
among all is accep ed as he final answe and i is called
Cos S;D. This p ocess is desc ibed in Fig. 3 wi h a schema ic
example.
Fo ins ance, he hop size in he fi s ound o he ne wo k
may be di e en om hop sizes in subsequen ounds. A he
same ime, he hop sizes in di e en ounds may a y om
each o he . In his s udy, he des ina ion node is assumed o
be he BS, and he e o e, he cos s be ween each senso node
and BS a e calcula ed. He e, in he pa h, he packe is also
passed jus once om each senso node. In he end, BS chooses
he minimum cos pa h using Eq. (16). Finally, he BS b oad-
cas s selec ed op imal pa hs o sou ce nodes. Fo example, i
he candida e pa h be ween node 4 and BS is N4, N61, N98,
N43, and BS, hen, fi s o all, he cos o uples (N4, N61),
(N61, N98), (N98, N43), and (N43, BS) is calcula ed om
Eq.13. An example o candida e pa hs wi h sample cos s a e
ep esen ed in Table 1. The sum o each uple alue is calcu-
la ed h ough Eq.14, which is he cos o each indi idual pa h.
A e all candida e pa hs o each hop coun ha e been calcu-
Fig. 2 Concep ual schema o he p oposed a chi ec u e in finding op imal pa hs.
346 A. Seyyedabbasi e al.
la ed, hei minimum is selec ed as bes , by means o Eq.15. In
he end, only one o he bes pa hs o all hops is ob ained
acco ding o Eq.16. This example is schema ically ep esen ed
in Fig. 3.
A hand-shaking me hod o checking he a ailabili y o
nex -hop is pe o med. On a de aul ne wo k, each node’s
in o ma ion is conside ed o be eco ded in he BS, as ou lined
in Table 2. This in o ma ion is ob ained by a eques da a
packe ha is sen o senso nodes ia BS in he ini ializa ion
phase o he ne wo k. Residual ene gy, a fic s a us, bu e
size, dis ance o he BS, and neighbo lis a e s o ed in he
BS. The decisions in finding he op imum pa h a e made using
me aheu is ic algo i hms by BS, which ha e unlimi ed ene gy
sou ces. No e ha balanced beha io is equi ed be ween hese
fi e pa ame e s. The emaining ene gy le el and he emaining
bu e size a e desi ed o be high, whe eas he ne wo k a fic
and he dis ances a e desi ed o be low. The me hods p oposed
and de ailed ea lie , handle he balancing equi emen .
As men ioned, he op imal pa hs a e ob ained in he BS.
Fo his, as p e iously emphasized, I-GWO and Ex-GWO
me hods a e used o find he op imized coe ficien s o he
defined pa ame e s. The BS node has a able ega ding nodes’
in o ma ion. In his able, some basic in o ma ion such as
esidual ene gy, a fic s a us, bu e a e, BS-hop and neigh-
bo lis o each node is s o ed. Each senso node also holds
a able, which is called he ou ing able, ha includes a neigh-
bo s lis , dis ance o neighbo s, dis ance o BS, and BS-hop.
The ele an ou ing able is p esen ed in Table 3.
4.4. Defini ion o da a packe ames
Da a packe s a e used o communica ion be ween sys em
nodes. These packe s ha e a ious sui able o ma s ha a e
defined in hese de ices. Howe e , hey can be cus omized o
op imize he use o esou ces. E ficien sys em esou ce u iliza-
ion can be ensu ed wi h he defini ion o he app op ia e
packe empla e and dynamic s uc u e, acco ding o he sys-
em needs. The use o cus om da a packe s is also help ul in
finding pa hs. In his s udy, wo gene al ypes o da a packe
ames a e defined. As men ioned be o e, in he ini ializa ion
phase o he ne wo k, BS b oadcas s a message o eques glo-
bal in o ma ion abou he senso de ices. This in o ma ion is
ob ained by a eques da a packe b oadcas ed o nodes ia
BS, as depic ed in Fig. 4(a). In esponse, he senso nodes
ansmi he ele an in o ma ion ( esidual ene gy, a fic si u-
a ion, bu e a e, BS-hop, and neighbo lis ) o BS. The o -
ma s o he senso node’s esponse packe a e also shown in
Fig. 4(b) along wi h di e en fields defined in hese packe s.
The TTL field is in ended o p e en he occupa ion o ne -
wo k a fic. A deadline alue is defined o each packe . Each
node educes he TTL alue by one o each packe ecei ed.
The ini ial alue o his field a ies depending on he ype o
applica ion. Owing o he sou ce and des ina ion add esses
filed, each node can be applied o mul iple sou ces and des ina-
ion scena ios a he same ime as pa allel and concu en
models because i knows which nodes a e sou ce and which
is des ina ion. Due o he na u e o he p oposed me hods, pa -
allel and concu en models a e na u ally suppo ed. This ea-
u e is e y impo an in he p oposed me hods, and i o e s
he oppo uni y o wo k in many pa allel and concu en
applica ion a eas.
Fig. 3 A wo king mechanism o p oposed me hod in pa hfinding.
Table 1 Templa e candida e pa hs cos a he end o each
i e a ion.
Candida e pa hs Sample alues
Pa h 1 0.78
Pa h 2 1.36
.
.
..
.
.
Pa h n n
Op imal da a ansmission and pa hfinding o WSN and decen alized IoT sys ems using I-GWO and Ex-GWO 347
5.8. Gene al compa ison and discussion
In his s udy, simula ions we e in es iga ed on 6 di e en
pa ame e s and he esul s o each we e shown. In addi ion,
in line wi h he esul s ob ained, he me hods used in each
pa ame e ha e hei pe o mances anked om he bes o
he wo s (Table 6). As can be seen om he esul s ob ained,
bo h o he p oposed me hods pe o m be e . I-GWO ies o
find solu ions mo e quickly hanks o i s exploi a ion ea u e
and as con e gence a e, and Ex-GWO, due o i s s uc u e,
is likely o be success ul in complex and la ge-scale sys ems. In
hese algo i hms, swa ming is con olled by he leade o he
g oup, which helps o ge he op imum solu ion o a defined
p oblem. Besides, benefi ing om he defined fi ness unc ions
and comp ehensi e a chi ec u e, hese algo i hms we e made
easie o adap o he p oposed pa hfinding me hods and exhi-
bi e ficien beha io . The hi d place, MAP-ACO, has pe -
o med well, bu because o he use o a me aheu is ic
algo i hm in all ope a ions in i s me hod, he pe o mance in
he ne wo k, na u ally, was limi ed. The main eason o his
is ha he de ices used ha e limi ed esou ces. Howe e , in
he a chi ec u e o his s udy, me aheu is ic algo i hms used
we e un only in he fi s pa o he me hod and his causes
inc eased e ficiency. In ou h place, GWO-WSN is lis ed.
GWO-WSN has no been e y success ul due o i s non-
comp ehensi e fi ness unc ion. Howe e , his me hod could
ha e had a mo e s able wo king mechanism due o i s GWO
s uc u e. When he pe o mance analysis o he o he wo
me hods is done, i is seen ha hey a e no e y success ul.
6. Conclusion and u u e wo ks
This wo k sol ed one o he main challenges in wi eless senso
ne wo ks and decen alized IoT sys ems by imp o ing he
Fig. 12 Th oughpu analysis.
Fig. 13 Con e gence speed analysis.
354 A. Seyyedabbasi e al.
ene gy consump ion o he ne wo k. I finds he bes ou e by
examining all a ailable pa hs be ween any wo nodes wi h a
p oposed gene al a chi ec u e. Finding he bes ou es be ween
nodes esul s in less ene gy being consumed in he ne wo k,
hus e ficien use o esou ces and inc easing he o e all li e-
ime o he sys em. Thanks o his a chi ec u e, many me a-
heu is ic algo i hms can wo k in an adap i e way, so i akes
he ole o a mul i-pu pose gene al model and will p o ide con-
enience o esea che s wo king in his field. In his s udy,
EERI
-GWO
and EER
Ex-GWO
ou ing me hods a e p oposed
using I-GWO and Ex-GWO algo i hms as me aheu is ic algo-
i hms. These wo me hods a e ene gy e ficien ou ing me h-
ods ha y o find op imum pa hs. These me hods p o ide
mo e e ficien execu ion ime and CPU powe in ime and
space complexi ies. The sea ch space is conside ed as a ma ix,
whe e he ows ep esen he numbe o sea ch agen s, and he
column signifies he coe ficien numbe s. These coe ficien s a e
upda ed by he me aheu is ics used.
This s udy ocuses on b oade pa ame e s in p oposing
mo e comp ehensi e and accu a e me hods in WSN and
DIoT. Acco dingly, a new fi ness unc ion has been defined.
The defined fi ness unc ion is used o calcula e he cos o each
pa h in he ne wo k and includes esidual ene gy, a fic s a us,
bu e a e, BS-hop, and neighbo lis o each node. The pa hs
be ween he wo sou ce and des ina ion nodes a e selec ed
acco ding o hop alues and passed h ough he fi ness unc-
ion. The sum o he bes fi ness alues o each hop will be
he candida e o he bes ou e. Subsequen ly, he minimum
alue among candida es is chosen as he bes pa h be ween
he wo compe ing nodes. Each node acqui es i s bes neighbo
om i s ou ing able. Rela ed ne wo k equa ions we e
mapped in acco dance wi h me aheu is ic algo i hms. The pe -
o mances o wo me aheu is ic algo i hms used in he p o-
posed ou ing me hods we e e alua ed on a ious
pa ame e s. A e i e a ions o me aheu is ic algo i hms, he
bes solu ion is ound as an op imal pa h o he ne wo k in
he cu en ounds. The ou ing ope a ions a e pe o med in
he BS. The esul s ha e displayed hose p oposed me hods
ha e be e pe o mance han ABCbased, GAR, GWO-
WSN, and MAP-ACO me hods. Fu he mo e, esul s show
ha hese wo me hods a e mo e success ul in finding he mos
app op ia e pa hs in hese sys ems. Acco ding o he esul s o
his s udy, and o he s udies in he li e a u e, i can be said
wi h confidence ha swa m in elligence is s onge han pa i-
cle in elligence in simila sys ems. The p oposed me hods in
his pape may be mo e sui able o a ne wo k o any scale.
In hese me hods, he mos app op ia e and e ficien pa h
can be ound be ween mul iple sou ces and des ina ion nodes
concu en ly o in pa allel (depending on he needs o he
p oblem and applica ion a ea). In addi ion, he p oposed
me hods ha e be e pe o mance in e ms o obus ness and
aul ole ance ac o s. Apa om he p os and s eng hs o
he s udy, he sho comings can be summa ized as ollows.
The sho comings o his s udy a e planned o be con inued
and comple ed in u u e s udies. In his s udy, no es s we e
pe o med on a eal sys em co e ing big da a. In his s udy,
simula ions we e made using homogeneous senso nodes.
Howe e , he e ogeneous senso nodes we e no used. This
s udy did no ocus on he mul i-objec i e and Pa e o-based
p oblem. In u u e wo k, he p oposed me hods will be es ed
on eal es beds wi h a la ge densi y o a ious de ices o he
gene a ion and analysis o big da a. Simila ly, he p oposed
app oach can pe o m mo e e ficien ly in mul i-objec i e and
Pa e o-based p oblems. Especially in pa ame e s ha ha e
ade-o s wi h each o he (e.g., ne wo k connec i i y and
ene gy consump ion) can be applied. The p oposed me hods
will be used o sol ing many complex p oblems such as ea-
u e selec ion, complex elec ical ci cui s, 3D pa h planning
in mobile obo ics o connec ed ehicle ne wo ks, and op i-
mized node localiza ion in he sys ems. I should be no ed ha
wi h he g ow h in IoT echnology, mos o he p oposed pa h
planning me hods ocus on homogeneous senso ne wo ks, bu
IoT de ices can g ea ly benefi om he e ogeneous senso
nodes. In his way, his wo k can help use he e ogeneous sen-
so nodes o suppo di e en IoT de ices. Acco dingly, he
p oposed me hod can be easily applied o he wea able senso
ne wo k, which has become ex emely popula in he las
decade.
Funding
The wo k o U.F.-G. was suppo ed by he go e nmen o he
Basque Coun y o he ELKARTEK21/10 KK-2021/00014
and ELKARTEK22/85 esea ch p og ams, espec i ely.
Decla a ion o Compe ing In e es
The au ho s decla e ha hey ha e no known compe ing
financial in e es s o pe sonal ela ionships ha could ha e
appea ed o influence he wo k epo ed in his pape .
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Ne wo k Li e ime Ra e 2 13564
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