Expe Sys ems Wi h Applica ions 272 (2025) 126757
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0957-4174/© 2025 The Au ho s. Published by Else ie L d. This is an open access a icle unde he CC BY license (h p://c ea i ecommons.o g/licenses/by/4.0/).
T uck-mul id one same-day deli e y s a egies: On- oad esupply s
depo e u n
Da id Sanchez-Wells
a,*
, Jos´
e L. And ade-Pineda
b
, Ped o L. Gonzalez-R
a
a
Depa men o Indus ial Enginee ing and Managemen Science, School o Enginee ing, Uni e si y o Se ille, Camino de los Descub imien os, s/n., 41092 Se ille, Spain
b
Robo ics, Vision &Con ol G oup, School o Enginee ing, Uni e si y o Se ille, Camino de los Descub imien os, s/n., 41092 Se ille, Spain
ARTICLE INFO
Keywo ds:
T uck-Mul id one Logis ics
Gene ic Algo i hm
Makespan
T uck Mileage
Las -mile Deli e y
Resupply
ABSTRACT
This pape explo es an enhanced wo-wa ed same-day deli e y (SDD) sys em ha le e ages a mo he ship uck
equipped wi h mul iple d ones suppo ed by an auxilia y “ esupply” uck. Unde s anda d SDD ope a ions, his
mo he ship uck, also capable o pe o ming deli e ies, mus e u n o he depo o eload, incu ing ex a a el
ime and mileage. In con as , he p oposed esupply s a egy enables he second deli e y wa e by dispa ching a
seconda y ehicle o mee he mo he ship uck on- oad, eloading pa cels wi hou in e up ing ongoing de-
li e ies by he d ones. A single uni ied ou ing amewo k, he Gene ic Algo i hm wi h I e a ed Es ima ions o
Resupply (GAIER), is p esen ed o op imise bo h s a egies unde wo selec able c i e ia: minimising o al se ice
ime o o al uck mileage.
In es s wi h benchma k ne wo ks o di e en sizes (20, 50, and 75 nodes), inco po a ing a esupply uck
educed e e y selec ed c i e ion when compa ed o he s a egy whe e he mo he ship ehicle e u ns o he
depo . Subsequen compa a i e analysis poin s an a e age educ ion o 17 % in se ice ime and 21 % in uck
mileage while s a is ical analyses suppo he s a egy choice signi icancy, con i ming esupply s a egy’s po-
en ial o cos sa ings and educed en i onmen al impac . These indings bols e ou p oposi ion ha inco -
po a ing a esupply uck in o hyb id uck-mul id one sys ems enhances lexibili y in d one deli e y scheduling
and imp o es he sys em’s abili y o mee u ban demand.
1. In oduc ion
Las -mile deli e y is cu en ly unde g owing p essu e o commi o
he sho e deli e y ime equi emen s o inc easingly demanding cus-
ome s. In pa icula , he e is a ising demand o same-day deli e y
(SDD) se ices, o en e e ing o goods ha a i e o a cen al depo
o e ime—e.g., in make- o-o de ope a ions, such as pha maceu icals,
pe ishable goods, o online shopping o de s—and o be deli e ed in
u ban a eas. While asking cus ome s o e ch he pa cel is an al e na i e,
whe he lea ing he goods a p ede e mined collec ion cen es (Hong
e al., 2019) o a mobile pa cel locke s (Peppel e al., 2024), cus ome s
a e mo e willing o wai o a sui able home deli e y, e en in cases
whe e no speci ic deli e y ime slo has been explici ly ag eed upon.
Howe e , along wi h he implici claim o a sho deli e y ime,
cus ome s ha e a limi ed willingness o pay o ins an deli e ies, wha
has led he cou ie indus y o eo ganise hei SDD se ice in dispa ch
wa es (Klapp e al., 2018). When conside ing he s anda d sys em
conce ning deli e ies ha a e made wi h only ucks o ans, he key
issue is hence deciding when o e u n o he cen al depo o eload o
subsequen deli e ies, by seeking o he ade-o be ween wai ing o
addi ional p oduc s and dispa ching he ehicle as soon as possible
(Klapp e al., 2018). Howe e , while maximising load consolida ion
leads o lowe ing he numbe o ips, i can esul no only in g ea e
mileage, bu also in inc eased idle ime and delayed deli e ies. Fo ha
eason, mo e dis up i e a emp s a e appea ing e e y day, which ede-
sign exis ing deli e y p ocesses o be e adap o he new scena ios.
1.1. Eme gence o d one-based solu ions on SDD
One o he mos p omising a enues o inno a ion on same-day de-
li e y lies in he inco po a ion o d ones (o unmanned ae ial au ono-
mous ehicles, UAVs) ha despi e coming wi h hei own se o
limi a ions—e.g., payload and ba e y cons ain s (Tadi´
c e al., 2024; Bi
e al., 2024)—can ly back and o h in middle-sized ci ies wi hin 15 km
(Shankland, 2022). Lamb e al. (2022) compa ed he adi ional uck-
only deli e y wi h a UAV deli e y sys em used in combina ion wi h
* Co esponding au ho .
E-mail add esses: [email p o ec ed] (D. Sanchez-Wells), [email p o ec ed] (J.L. And ade-Pineda), [email p o ec ed] (P.L. Gonzalez-R).
Con en s lis s a ailable a ScienceDi ec
Expe Sys ems Wi h Applica ions
jou nal homepage: www.else ie .com/loca e/eswa
h ps://doi.o g/10.1016/j.eswa.2025.126757
Recei ed 22 Ma ch 2024; Recei ed in e ised o m 30 Janua y 2025; Accep ed 2 Feb ua y 2025
Expe Sys ems Wi h Applica ions 272 (2025) 126757
2
sho - o-medium e m capaci a ed in en o y s o age acili ies ( e e ed
o as mic o- ul ilmen cen es) o mi iga e he UAV ange limi a ions.
Recen ly, some wo ks (Ghias and e al., 2024; Li e al., 2024) ha e
conside ed ha an/ uck ole consis s o mo ing o de s om he
depo /s o a se o sa elli e, no-capaci a ed, ixed loca ions, om which
UAV ligh s a e scheduled o comple e he deli e y. Symme ic oles
ha e been applied in ecen li e a u e (Daya ian e al., 2020; Pina-Pa do
e al., 2021; McCunney &Cauwenbe ghe, 2019; Diens knech e al.,
2022; Pina-Pa do e al., 2024a; Pina-Pa do e al., 2024b). These au ho s
inno a e he SDD se ice by assuming ha pa cels a e uck-deli e ed-
only, whe eas d ones a e ese ed he ole-play o auxilia y ehicles
o “ esupply”whose ligh s a e scheduled o injec ing newly a i ed
o de s in o he ongoing uck dis ibu ion ou e. Dynamic collabo a i e
ou ing s a egies, such as en- ou e synch onisa ion be ween ucks and
d ones—which we name “on- oad” o highligh ha ou mo he ship
uck is eloaded while deli e ing—ha e shown signi ican po en ial in
op imising deli e y imes and esou ce u ilisa ion unde andom e-
ques s (Cui e al., 2024).
Thus, he ex en o which d ones in e ac wi h ucks di e s, whe eas
esupplying he uck di ec ly when mee ing i en- ou e a mee ing
poin s (Pina-Pa do e al., 2021; Pina-Pa do e al., 2024b) o lea ing i s
load a ansshipmen poin s om which he uck picks up he pa cels
(McCunney &Cauwenbe ghe, 2019). Acco ding o Mosh e -Ja adi e al.
(2023), his d one esupply concep can esul in a g ea e numbe o
packages deli e ed wi hin a speci ic ime window, since a oiding uck
e u ns o he depo o pick up newly a ailable o de s educes he de-
li e y uck down ime, he eby bene i ing he o e all ope a ional e i-
ciency (Mosh e -Ja adi e al., 2020a; Mu ay &Chu, 2015). On hei
ecen wo k, Alkaabneh &Su ha son (2024) conside ha he assess-
men o he esupply ope a ional mode should ake in o conside a ion
bo h he o al mileage o g ound ehicle/s as well as he o al ime ha
he la es g ound ehicle equi es o e u ning o he depo a e se ing
all he clien s.
In his pape , we conside ha he SDD se ice could gain in ope -
a ional e iciency wo old: (i) by ully exploi ing he lexibili y o d one
package deli e ies, and (ii) by using a g ound ehicle o execu ing
esupply asks. The esupply ole could he e o e be gi en o bo h a an
o a uck, g ound ehicles sui ed o ca y a g ea e quan i y o o de -
s—aligning wi h he cou ie indus y’s p ima y goals. Addi ionally, we
p opose inno a ing he SDD se ice by le e aging he d ones’abili y o
bypass g ound a ic and p o ide apid, lexible deli e y op ions in
pa icula , mul i-d op ligh missions. The la e is pe ec ly possible in
cu en d one echnology, as p esen ed in he las -mile hyb id deli e y
sys em by Masmoudi e al. (2022), e e ed o as he ehicle ou ing
p oblems wi h d ones equipped wi h mul i-package payload compa -
men s, which in ol es mul iple andems o uck-d one pai s and mul i-
isi d one ips. In ac , in con ex s o he han he SDD, u he opol-
ogies o hyb id uck-d one deli e y sys ems ha e conside ed he use o
d ones o deli e packages di ec ly o cus ome s; e.g., aking o om
ucks ac ing as mobile depo s (Mu ay &Chu, 2015; Mu ay &Raj,
2020) o om he depo i sel (Ham, 2018).
1.2. Resea ch gap and p oposed app oach
A ound he SDD p oblem, and on he assump ion ha he ac ual
demand o he nex day is unknown, Ghias and e al. (2024) ackle
unce ain y on cus ome demands h ough a ke nel-based machine
lea ning app oach o minimise he o al cus ome wai ing ime, while Li
e al. (2024) con igu es a as -deli e y s a egy o online g oce y
e ailing, i ing o he unce ain y o demands h ough a wo-s ep s o-
chas ic p ocedu e aimed a minimising he o al deli e y cos s. This is
achie ed i s ly by consolida ing a subse o uckloads o designa e he
sa elli e loca ions om which d ones will ake he goods o deli e o
cus ome s, and secondly by ma king he emaining g oce ies o be
ou ed along wi h u u e a i als. Ulme &Thomas (2018) ha e
conside ed an SDD sys em combining uck and d one deli e ies,
dis ibu ing he se ed a eas so ha d ones a e used o deli e y cus-
ome s in he ou e mos loca ions, whe eas ucks a e s ill p e e ed o
se ice he down own a eas close o he depo . Howe e , deploying
d ones o se e cus ome s only based on hei loca ion is no ully
exploi ing he lexibili y ha could be gained om conside ing a uck-
d one andem sys em whe e d ones can be dispa ched om he ca ying
uck o isi cus ome s. Daya ian e al. (2020) and Pina-Pa do e al.
(2021; 2024a) p oposed models o d one-suppo ing deli e y o he
SDD, whe e all cus ome s a e se ed by ucks while d ones solely
p o ide suppo o ucks wi h pa cel esupply. This mode sui s dy-
namic o de ing by p e en ing ucks om epea edly e u ning o he
depo o pick up newly a i ed o de s.
In ou esea ch, we p opose add essing one o such scena ios, bu
using combined uck and d one deli e y o pa cels wi h pa cel esupply
by means o a g ound ehicle. Speci ically, we p opose a no el s a egy
o he SDD ha explo es he syne gy be ween a simple esupply uck
(RT), and a mo e sophis ica ed d one-commanding uck (DCT). The
DCT manages a a ie y o d ones ha ake-o om and land om i
along wi h i s ou e—i.e., cus ome loca ions aken as he endez ous
poin s o synch onise wi h i — o pe o m mul i-d op d one missions,
while he RT is able o pe o m deli e ies o cus ome s while e u ning
o he depo a e eloading he DCT. This ea u e has been o me ly
add essed, al hough no always along he use o combined uck and
d one deli e y (Jeong &Lee, 2023; Poikonen &Golden, 2020). Poiko-
nen &Golden (2020) s a ed he k-mul i- isi d one ou ing p oblem (k-
MVDRP), whe e kd ones a e assigned o se e a se o cus ome s and he
uck ac s as a mobile pla o m o he d one o bo h eplenish i s ene gy
o o pick he packages up be o e lying o deli e o cus ome s. Jeong &
Lee (2023) add he lexible launching a loca ions sepa a e om
cus ome si es, al hough again unde he assump ion o ucks no
isi ing cus ome s bu mo ing be ween launch posi ions.
Di e en o he abo e-men ioned wo ks, ou s a egic app oach
holds on: (i) he ac i e deli e y ole o ucks and d ones, bo h wi h
capaci y cons ain s and (ii) he d one se ice ange limi . In he hyb id
uck-d one esea ch a ea, ou uck-based esupply s a egy is a no -
el y, which we p opose o a mo e ex ensi e use o a DCT libe a ed om
e u ning o depo . This allows us o design a SDD se ice ha combines
he s eng hs o bo h ucks while ensu ing pa cels a e eadily accessible
o d ones wi hou eloca ing hem om he su oundings o deli e y
zones. We ha e also ou lined a uni ied VRP-based ma hema ical
o mula ion in o de o decide be ween bo h s a egies—depo e u n
and on- oad esupply—by igo ously cap u ing he in e play be ween
di e en cons ain s and a iables, such as he capaci ies o each ype o
ehicle, as well as d one au onomy, among o he s.
1.3. Con ibu ion s a emen and o ganisa ion o his pape
This s udy assesses he e iciency gains achie able h ough he
in eg a ion o a esupply uck suppo ing a d one-commanding uck
equipped wi h a mul id one lee in a SDD scena io. While he ma he-
ma ical modelling o he explained assump ions—i.e., au onomy limi-
a ion o d ones while all ehicles a e capaci y-limi ed and pe o m he
same ype o deli e y—is conside ed in insic, in o de o e alua e such
e iciency gains we need o design and make use o a p oblem-sol ing
amewo k capable o minimising one objec i e a a ime: he du a ion
o he se ice— he ime elapsed un il inal ga he ing a he depo —o
he o al mileage o he ucks, ecognising he la e as a key en i on-
men al impac ac o . This mileage c i e ion is pe inen bo h o elec ic
ucks, whe e i se es as a d i e o elec ical ba e y li e cycle con-
sump ion, and o combus ion engine ucks, whe e i gauges he le el o
emissions. These ac o s will be in eg al o he design c i e ia o he
no el join deli e y s a egy p oposed he ein.
The esea ch ques ions a e as ollows:
D. Sanchez-Wells e al.
Expe Sys ems Wi h Applica ions 272 (2025) 126757
3
•How will he adop ion o an auxilia y “ esupply” uck a ec he
pe o mance o a SDD se ice based on a uck deploying a lee o
d ones?
•Do he ins ances in luence in he compa a i e pe o mance o he
s anda d and he esupply s a egy?
As p e iously s a ed, in o de o suppo he compa ison o bo h
s a egies, and ha ing in o accoun he compu a ional bu den om he
s a ed NP-ha d ma hema ical model, we ha e de ised a uni ied way o
gene a ing high-quali y solu ions wi hin a mul id one and capaci y-
limi ed con ex , he so-called GAIER (Gene ic Algo i hm wi h I e a ed
Es ima ions o Resupply). Impo an ly, he GAIER amewo k adhe es
o he es ablished o mula ions o he pu pose o acili a ing he
compa a i e assessmen o he s a egies a he han in oducing no el
ma hema ical cons uc s. GAIER is an op imisa ion amewo k ha
u ilises a unique blend o heu is ic solu ion e olu ion me hods,
combining a Gene ic Algo i hm (GA) and an I e a ed G eedy (IG) heu-
is ic (Ruiz &S ü zle, 2007), all unde he global guidance o Simula ed
Annealing (SA). GAIER also le e ages an e icien bina y-cus omised
encoding o minimise he combina o ial solu ion space and in oduces
a no el ec o -based coding e ol ed om p e ious wo ks (Gonzalez-R
e al., 2020; Gonzalez-R e al., 2024). The GAIER amewo k s ands ou
o i s inno a i e use o a hyb id op imisa ion echnique ha combines
he s eng hs o mul iple heu is ics, no only accele a ing he solu ion
p ocess bu also imp o ing he quali y o he solu ions ound. In sho ,
GAIER is pa icula ly e ec i e in handling he complex dynamics o a
mul i-modal deli e y sys em in ol ing bo h ucks and d ones.
In p o iding an o iginal and comp ehensi e app oach o op imising
las -mile deli e y ope a ions, his pape seeks o make a signi ican
con ibu ion o bo h schola ly discou se and p ac ical implemen a ion in
he apidly e ol ing landscape o same-day deli e y logis ics. In
pa icula , om he applica ion o ou GAIER ool we can claim ha he
SDD se ice can be edesigned wi h a suppo ing RT o a aining a mo e
dynamic ou e adjus men on he DCT by means o i s eplenishmen o
pa cels, which ul ima e leads o educing he DCT idle ime and
inc easing he numbe o deli e ies ha can be made wi hin a gi en ime
ame. Fu he mo e, he la e is a ained while ge ing a educ ion in
DCT uck mileage—le ’s ecall he e, cos s o a DCT mile is ypically
high, om i s mo e sophis ica ed ea u es—which di ec ly ansla es o
lowe emissions and uel consump ion, aligning wi h sus ainabili y goals
in logis ic indus ies ha equi e apid deli e y o pe ishable goods o
u gen medical supplies.
The emainde o he pape is s uc u ed as ollows. Sec ion 2 p o-
ides a comp ehensi e e iew o he exis ing li e a u e in he domains o
las -mile d one logis ics, esupply in las -mile deli e y sys ems, and
gene ic algo i hms, pinpoin ing he gaps ha his esea ch aims o ill.
Sec ion 3 del es in o he mechanics o he p oposed esupply s a egy,
and Sec ion 4 elucida es he GAIER amewo k. Sec ion 5 p esen s a
igo ous case s udy and a sensi i i y analysis o empi ically alida e he
e ec i eness o he esupply s a egy. Finally, Sec ion 6 p o ides a
syn hesis o he indings, ou lines he con ibu ions o academia and
indus y, and sugges s di ec ions o u u e esea ch.
2. Li e a u e e iew
This li e a u e e iew p o ides a comp ehensi e o e iew o ecen
esea ch ocusing on he ele an s udies ega ding he use o d ones on
SDD and las -mile deli e y, as well as how gene ic algo i hms a e
applied oday o he las -mile uck-d one deli e y p oblem. Table 1
epo s on he mo e di ec ly connec ed wo ks a isen om ou li e a u e
e iew.
2.1. Same-day deli e y and d ones
Nowadays, SDD se ice companies a e s uggling o decide how o
dispa ch o de s ha become eady du ing he day o wo k o be e mee
he inc eased cus ome expec a ions. In explo ing he ade-o be ween
deli e y cos and ime, a ious new d one-based ope a ional models
ha e eme ged.
Ulme &Thomas (2018) p esen ed a dynamic ehicle ou ing
p oblem ha combines con en ional ehicles and d ones o SDD,
deciding based on cus ome loca ion whe he he ehicle o he d one
will be he se icing ehicle. Speci ically, in his wo k, d ones a e
employed o make au onomous deli e ies om he depo o he cus-
ome s loca ed in a eas a om he depo , since hey can each hem in a
sho e ime (wi h he highe a el speed esul ing om he a oidance
o a ic). Howe e , in his wo k d one ange limi a ion is igno ed,
which is indeed a e y c ucial assump ion in d one ou ing.
The e a e o he ope a ional models ha a e based on exploi ing a
wo-echelon deli e y ne wo k: he d one anships i s load a ans-
shipmen loca ions which a e in u n collec ed by ucks o las -mile
deli e y. McCunney &Cauwenbe ghe (2019) applied his ocus in a
simula ion s udy, concluding ha he d one esupply policy ou pe o ms
he adi ional one, whe e ucks ha e o e u n o he depo o pick up
pa cels, bo h on deli e y ime and dis ance o se ing all cus ome s.
Mosh e -Ja adi e al. (2023) analysed wo case s udies o an u ban and
subu ban a ea upon he simula ion app oach by McCunney &Cau-
wenbe ghe (2019) bu ex ended o he conside a ion o mul i- ip ligh
missions o esupply d ones ha lea e hei load a he anshipmen
loca ions. Thei p oposal consis s o a hyb id uck and d one wo-
echelon loca ion ou ing p oblem whose objec i e is he minimisa ion
o he o al a el ime o ucks and d ones, decomposed in o wo
s ages: uck ou ing decisions and d one esupply e en s o occu a any
o he po en ial anshipmen loca ions.
As highligh ed in ecen sys ema ic e iews o d one deli e y sys-
ems, in eg a ing d one esupply mechanisms in o u ban logis ics can
e olu ionise las -mile deli e y solu ions (Jazai y e al., 2025). The
seminal wo k by Daya ian e al. (2020) in oduces he VRP wi h
esupply o s udy how a lee o deli e y ucks is dispa ched om a
ul ilmen cen e o pe o m home deli e ies o online o de s whe eas a
so o d ones wo king in andem wi h hem a e egula ly esupplying
he deli e y uck by mee ing wi h i a any loca ion a which he uck is
s a iona y o ans e he newly a i ed packages. Speci ically, he au-
ho s ocused on how bes o schedule uck-d one mee ings a any
cus ome loca ion along he uck’s ou e o maximise he pe cen age o
o de s se ed and minimise o al ope a ional cos s (including he
anspo a ion cos s due o bo h ypes o ehicles). The complexi y o he
p oblem ha a ises led esea che s o conside only he single deli e y
uck and a single d one case, concluding ha he d one esupply e-
duces bo h uck a el and deli e y imes compa ed o he uck-only
ope a ional model.
A guing ha he e is a limi ed capaci y o he uck, Diens knech
e al. (2022) conside ed ha only a subse o o de s can be loaded on he
uck when i depa s om he depo and ha he eminde s a e sub-
sequen ly esupplied by he d one o he uck. No iceably, hey assume
ha d ones can ca y only one package on each ip. They s a e he
T a elling Salesman P oblem (TSP) wi h d one esupply, whose eso-
lu ion is i s ocused on he d one esupply subp oblem (dynamic p o-
g amming o ind he op imal d one schedule o a gi en uck ou e)
and hen aimed a he explo a ion o di e en algo i hms o de e mine
e icien uck ou es (gene ic algo i hms and a ious cons uc ion
heu is ics). Howe e , he epo ed nume ical expe imen s indica e ha
uck e u ns a e s ill needed.
The impossibili y o ca ying he en i e se o packages in he de-
li e y uck can also be due o a deli e y ime o he o de a he
ul ilmen cen e o depo . Pina-Pa do e al. (2021) s udied an SDD
scena io whe e hey assume ha he elease imes and due da es o o -
de s a e known in ad ance. They p o ide a MILP o mula ion ha is
sol ed h oughou a wo-s age decomposi ion heu is ic, i s ly de e -
mining he uck ou e and secondly de ining he occu ence o esupply
e en s a cus ome loca ions. The same SDD scena io is u he s udied
by Pina-Pa do e al. (2024a), bu ex ended o mul iple ucks and
D. Sanchez-Wells e al.
Expe Sys ems Wi h Applica ions 272 (2025) 126757
4
Table 1
Li e a u e classi ica ion (own elabo a ion).
Rela ed li e a u e Vehicles In e ac ion Capaci y limi s D one ope a ion ea u es Modelling &Sol ing Fea u es
Numbe
o
T ucks
Numbe
o
D ones
D one-
T uck
di ec
in e ac ion
T uck
ca ying
d ones o
se ice
a ea
T uck
can se e
any
cus ome
D one
se ing
any
cus ome
Limi ed
uck
capaci y
Limi ed
d one
capaci y
Mul i-
d op
ligh s
Launch
e ie al
D one
ligh
ange/
ime
a ies
Flexible
docking
Modelling
app oach
Minimised
objec i e
Sol ing me hods
&algo i hms
Ins ances
size
Gonzalez-R e al.
(2020)
1 1 ✓ ✓ ✓ ✓✓ ✓ MILP Time IG +SA 250
Ma a e al. (2022) 1 1 ✓ ✓ ✓ ✓ ✓ ✓ ✓ MILP Time COTS +ALNS 200
Mu ay &Raj
(2020)
1 m ✓ ✓ ✓ ✓ ✓ ✓ MILP Time 3-PH-HEUR 8 o 100
Leon-Blanco e al.
(2022)
1 m ✓ ✓ ✓ ✓✓ ✓ Agen s Time AGENTS 500
Gu e al. (2022) m m ✓ ✓ ✓ ✓✓ ✓ ✓ MILP Time, Cos ILS +VNS 200
Jiang e al. (2024) m m ✓ ✓ ✓ ✓ ✓✓MILP Cos COTS +ALNS 100
Masmoudi e al.
(2022)
m m ✓ ✓ ✓✓ ✓ ✓P o i
(Max)
TS +SA 200
Ki jacha oenchai
e al. (2020)
m m ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ MILP Time LNS 76
Ki jacha oenchai
e al. (2019)
m m ✓ ✓ ✓ ✓ ✓✓MILP Time ADAP. HEUR 100
Luo e al. (2021) 1 m ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ MILP Time TS +NEIGH 100
Poikonen &
Golden (2020)
1 m ✓ ✓ ✓ ✓ ✓ Rou eT ans o m
Sho es
50
Poikonen &
Golden (2020)
1 m ✓ ✓ ✓ ✓ ✓ ✓ B&B+GREEDY
HEUR
Mosh e -Ja adi
e al. (2020a)
1 m ✓ ✓ ✓ ✓ ✓ Time TS +SA 100
Mosh e -Ja adi
e al. (2020b)
1 m ✓ ✓ ✓ ✓ ✓ ✓ ✓ Time 100
Sac amen o e al.
(2019)
m m ✓ ✓ ✓ ✓ ✓ ✓ Cos 200
Daya ian e al.
(2020)
1 1 ✓✓ ✓ Dyn. Op . Cus ome s HEUR 60
Diens knech
e al. (2022)
1 1 ✓✓✓ ✓ Dyn. P og.
+Sim.
Cos DYN OPT
++CONSTR.
HEUR
350
Pina-Pa do e al.
(2021)
1 m ✓✓ ✓ MILP Time 2-STEP-HEUR 50
Li e al. (2024) m m ✓ ✓ S och. Cos PSO +Rein o .
Lea ning
25
Ghias and e al.
(2024)
m m ✓✓ MILP +
MDP
Time Da a-D i en-Op <100
Pina-Pa do e al.
(2024b)
m m ✓✓✓ ✓ MILP +
MDP
Time 100
Pina-Pa do e al.
(2024a)
m m ✓✓✓ ✓ MILP Time MATHEUR 100
Gao e al. (2023) m m ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ MILP Cos COL
GEN+BENDERS
<35
Kuo e al. (2022) m m ✓ ✓ ✓ MILP VNS 200
D. Sanchez-Wells e al.
Expe Sys ems Wi h Applica ions 272 (2025) 126757
5
mul iple d ones, whe e newly eleased o de s can be collec ed by ucks
a he depo o esupplied en- ou e ia d ones. The assump ion in ecen
wo ks (Pina-Pa do e al., 2021; Pina-Pa do e al., 2024a) is ha all
cus ome in o ma ion—i.e., deli e y loca ions and o de a i al ime-
s—is known be o e he ope a ion s a s, and hence hey conce n a s a ic
ou ing p oblem. Going u he in he same SDD con ex , Pina-Pa do
e al. (2024b) claim ha in iew ha he dispa che mus immedia ely
decide whe he o accep o ejec a cus ome eques o same-day
deli e y o an o de , dynamic decision conce ning o o de accep ance
unde unce ain o de elease can be a ained using a ou e-based
Ma ko Decision P ocess and an e icien online policy o dynamically
ou e a uck ha can ecei e newly a i ed o de s along i s ou e ia
d ones dispa ched om a depo . In hese h ee e e ed wo ks, bo h
ypes o ehicles a e allowed o pe o m se e al ou es—i.e., e u n o
he depo —du ing he deli e y ho izon, synch onising hese ehicles
spa ially and empo ally o en- ou e esupply ope a ions. Howe e , as
ega ds as he mul i- ip ea u e ha we a e applying in he p esen
pape , we mus poin ou ha he mul i- ip ea u e ha he au ho s
endo se o hei ope a ional model is unclea as ega ds he d ones: he
common meaning o mul i- ip ega ds as mul i-d op capabili y, and his
is no assumed in (Pina-Pa do e al., 2021; Pina-Pa do e al., 2024a;
Pina-Pa do e al., 2024b). In e e y synch onised mee ing, he d one has
aken o om he depo and le all i s load on he co esponding uck
and hen p oceeded o ly back o he depo .
2.2. D ones o las -mile deli e y
The e is a esea ch s eam ha o yea s has been conside ing ha
d one echnology allows o ans o ming he las -mile deli e y by dis-
pa ching d ones om ucks o deli e packages o cus ome s. Wi hin
he scope o las -mile deli e y in ol ing hyb id uck-d one logis ics, he
schola ly li e a u e shows wo p edominan iewpoin s on he ole o
g ound ehicles o ucks. One school o hough posi s ucks mainly as
mobile depo s o aid d ones in ope a ions such as ba e y eplacemen
(Ka ak &Abdelghany, 2019; Fe andez e al., 2016). Ano he pe spec-
i e a ibu es a mo e ac i e ole o ucks whe e, in addi ion o se ing
as launch and eco e y pla o ms o d ones, hey also pa icipa e in he
deli e y o packages o cus ome s (de F ei as &Penna, 2020; Dell’Amico
e al., 2022; Ha e al., 2018; Mu ay &Chu, 2015).
The e has been a p oli e a ion o esea ch ha explo es he in e -
ac ion be ween a single uck and mul iple d ones. Fo ins ance, Chang
&Lee (2018) and Mosh e -Ja adi e al. (2020b) ocus on scena ios
whe e d ones a e deployed and hen collec ed by he same uck bu
po en ially a a di e en loca ion om ha i was launched, which ap-
poin s o he synch onisa ion o uck-d one mee ings as c ucial de-
cisions (Mosh e -Ja adi e al., 2020a; Yoon, 2018). O he wo ks such as
Mu ay &Raj (2020) and Raj &Mu ay (2020) ex end he seminal
FSTSP o he case o an ac i e deli e y uck equipped wi h mul iple
d ones (mFSTSP) and model he ene gy consump ion o d ones as a non-
linea unc ion o pa cel weigh , speed and ope a ion ime. Mo e
ecen ly, d one launch/ e ie al in ou e has been add essed in Ma inelli
e al. (2018), Sche me e al. (2019) and Li e al. (2022), al hough hey
all a e limi ed o he case o one d one ou e co e ing exac ly one
cus ome . Con e sely, he cu en pape ollows Gonzalez-R e al. (2020)
and Gonzalez-R e al. (2024) assump ion o mul i-d op missions, whe e
d ones se e mul iple cus ome s pe ligh and synch onisa ion e en s
occu always a cus ome loca ions in a so-called T uck-mul iple D ones
Tandem Logis ics (TmDTL) sys em.
I is no ewo hy ha o he esea che s such as Poikonen &Golden
(2020; 2020), Luo e al. (2021), Leon-Blanco e al. (2022), and Gu e al.
(2022) ha e also explo ed he mul icus ome pe ly case. Poikonen &
Golden (2020) conside mul i- ip d one missions in andem wi h a
single uck ha can also deli e o cus ome s, while Poikonen &Golden
(2020) p esen ed an in e es ing TSP-D wi h mul iple d ones conside ing
adjus able speeds and ba e y consump ion a e as a unc ion o he
payload, d ones ha can be launched and e ie ed by a uck a any
poin in i s way be ween wo loca ions, al hough hey assumed he uck
se es solely as a mobile depo (d one p ima y) which does no deli e
packages o cus ome s. Mul i-d op d one deli e ies a e conside ed by
Jeong &Lee (2023), adding he lexible launching a loca ions sepa a e
om cus ome si es, al hough again unde he assump ion o ucks no
isi ing cus ome s bu mo ing be ween launch posi ions. Luo e al.
(2021), which ha e add essed a sys em simila o TmDTL, al hough hei
compu a ional expe ience is se e ely limi ed by he numbe o d ones in
he lee (solely wo d ones pe uck). The connec ion is di ec wi h
Leon-Blanco e al. (2022) and Gonzalez-R e al. (2024). The o me used
an agen -based heu is ic sol ed la ge TmDTL ins ances wi h he make-
span minimisa ion as he single objec i e c i e ion, while he la e
adop ed a mul iobjec i e app oach o he TmDTL based on a bi ec o
coding scheme and a simula ed annealing algo i hm o gene a e
app oxima e Pa e o on s o a biobjec i e p oblem, wi h uck mileage
and se ice comple ion ime as key pe o mance indica o s. Di e en ly
o he abo e-men ioned wo ks, we a e conce ned by he ac i e deli e y
ole o ucks and d ones, bo h wi h capaci y cons ain s.
In iew o he conduc ed e iew, we ound ha he e is a p omising
new ope a ional model o ans o ming he SDD, which, o he bes o
ou knowledge, has ne e been s udied. Why no using a g ound
esupply ehicle ha coo dina es wi h he deli e y uck? Simila o
Pina-Pa do e al. (2021) and Pina-Pa do e al. (2024a), we aim a s a ic
ou ing o de ining he esupply mee ings, ha in ou case in ol e an
auxilia y uck and no esupply d ones. Since we know i could
ou pe o m he adi ional uck-only sys em, why no ully exploi ing a
las -mile deli e y based on a mul id one lee dispa ched om he de-
li e y uck? Ou pape deepens in o his issue by add essing a uni ied
CTmDTL o mula ion o iden i y which is he bes s a egy. Like in ou
o me wo k (Gonzalez-R e al., 2024), in his esea ch we also app oach
he ope a ional model, aiming a an e icien esolu ion me hod o
a aining he holis ic op imisa ion o ou no el logis ical sys em i ing
o ins ances acco ding o single depo in a se ice a ea wi h om 25 o
75 loca ions o se e (Li e al., 2024; Pina-Pa do e al., 2021; Poikonen &
Golden, 2020; Daya ian e al., 2020; Ki jacha oenchai e al., 2020).
2.3. Gene ic algo i hms use in he las -mile uck-d one deli e y p oblem
The esupply concep in las -mile logis ics is p omising. Howe e ,
he compu a ional complexi y o sol ing hese p oblems canno be
o e looked, no he need o de elop e icien algo i hms o sol e d one
esupply p oblems igno ed. Fo example, Ponza (2016) used a simula ed
annealing algo i hm o sol e he Flying Sidekick T a elling Salesman
P oblem (FSTSP), a p oblem ela ed o d one and uck logis ics ha
se es up o 200 cus ome s. Gu e al. (2022) de eloped I e a i e Local
Sea ch and Va iable Neighbou hood Descen algo i hm in hei VRPD
wi h mul i- isi s model in which a lee o uck-d one andems o se e
up o 200 cus ome s is sol ed in less han 250 s. Ma a e al. (2022) ha e
designed an adap i e la ge neighbou hood sea ch (Ropke &Pisinge ,
2006), abb e ia ed as ALNS, heu is ic o add essing he same p oblem
in Gonzalez-R e al. (2020), which hey call he mul i-d op FSTSP. Al-
go i hms based on ALNS ha e also been de eloped o sol e mul iple
a ian s o esupply p oblems, demons a ing scalabili y and e iciency
(Mosh e -Ja adi e al., 2020b; Sac amen o e al., 2019). Mosh e -Ja adi
e al. (2020b) p oposed an in eg a ed Tabu Sea ch and Simula ed
Annealing (TS-SA) showing ha hei hyb id solu ion (single uck
deploying mul iple d ones e u ning o he uck a a loca ion di e en
om whe e hey a e o iginally launched) could achie e signi ican ime
sa ings in wai ing, as compa ed o he uck-only model. Sac amen o
e al. (2019) p oposed an ALNS wi h se e al des oy and epai ope a-
o s o sol ing a VRPD gene alisa ion om he FSTSP ha , like us used
capaci a ed uck and d one, bu hey conside ha some loca ions a e o
be se ed by he uck owing o he weigh o he load, limi s he syn-
ch onisa ion a uck s ops among a p eselec ed subse o candida e lo-
ca ions and u he , ha d one can only isi one cus ome pe ip. Tha
was he case also in Ki jacha oenchai e al. (2019) which ha e used an
D. Sanchez-Wells e al.
Expe Sys ems Wi h Applica ions 272 (2025) 126757
6
Adap i e Inse ion algo i hm along wi h se e al mTSP cons uc ion
heu is ics (one o hem based on GAs) o sol ing a benchma k o
Solomon-like ins ances sized up o 100 cus ome s o be se ed by a lee
o uck-d one andems, each d one wi h uni a y payload and wi h he
chance o be e ie ed a a di e en uck o ha om i ook o . This
ea u e, e e ed o as lexible docking has been epo ed along wi h
mul i-d op capabili y in d one deli e y in ecen mul id one li e a u e
(Masmoudi e al., 2022; Jiang e al., 2024). Masmoudi e al. (2022) ha e
applied a mul i-s a TS wi h SA heu is ic o sol ing ins ances wi h up o
200 cus ome s o maximising he p o i om espec ing hei due da e
wi h a mul i- uck dis ibu ion sys em using a lee o suppo i e (no
deli e y) uck equipped wi h a d one o se e cus ome s and hen
allowed o e u n o a di e en uck. Jiang e al. (2024) ha e de eloped
an ALNS heu is ic o sol e ins ances o up o 100 loca ions o se ed,
a isen om he ich VRPD he au ho s o mula ed o model how a uck
and d one lee a e deployed aking ad an age o he d one lexible
docking ea u e o ul il pickup and deli e y in u al a eas a minimal
o al ou ing cos s.
In his con ex , i is wo h no ing ha GAs a e inc easingly used in
he con ex o uck-d one deli e y, such as Lu e al. (2022), in con as
wi h o he op imisa ion me hods such as G a i a ional Sea ch Algo-
i hms (GSA) by Rashedi e al. (2009), Pa icle Swa m Op imisa ion
(PSO) as explained in Rasouli (2024), o he Inclined Planes Sys em (IPS)
me hod p oposed by Moza a i e al. (2016). The main eason o his is
he combina o ial na u e o he p oblem o be sol ed. Unlike GSA and
PSO, which excel in con inuous op imisa ion bu ace signi ican chal-
lenges when adap ed o disc e e p oblems, GAs o e a lexible ame-
wo k ha na u ally handles he disc e e na u e o combina o ial asks
(Nhu e al., 2023; Rau e al., 2024). While IPS op imisa ion in oduces
inno a i e heu is ic s a egies, i also equi es ex ensi e cus omisa ion
o main ain e iciency in combina o ial con ex s (Yang e al., 2024).
S udies ha e demons a ed ha GAs consis en ly ou pe o m GSA,
IPS, and PSO in e ms o solu ion quali y and compu a ional e iciency in
combina o ial se ings (Rau e al., 2024; Le e al., 2024). Addi ionally,
in he case o Ka aoka e al. (2022), he au ho s e e o he GA me h-
odology desc ibed by Hazama e al. (2022). Fu he mo e, while none o
he e iewed documen s di ec ly add esses a p oblem iden ical o he
single-c i e ion uck-d one deli e y p oblem we a e conce ned wi h,
wo o hem p o ide aluable insigh in o he applica ion o GAs in
sol ing d one ou ing p oblems. Consecu i ely, we ocus on highligh ing
he mos ele an and impac ul s udies o build a solid case o he
applica ion o GAs, p o iding a comp ehensi e o e iew o how GAs can
e ec i ely add ess he unique challenges posed by his p oblem.
Zhang e al. (2022) p oposed an e olu ion o he Non-domina ed
So ing Gene ic Algo i hm II o NGSA-II (Deb e al., 2002) known as
ENSGA-II. This app oach is designed o handle mul iobjec i e p oblems
ela ed o uck-d one deli e y. In ENSGA-II, solu ions a e ep esen ed
by a single ec o ( e e ed o as he “gian ou e”), which is subse-
quen ly p ocessed by wo dis inc algo i hms: a uck ou e spli algo-
i hm and a d one ou e cons uc ion algo i hm. The c osso e ope a ion
in ENSGA-II inco po a es bo h pa ially ma ching c osso e (PMX) and
o de c osso e (OX) ope a o s in a andom manne o p omo e di e si y
wi hin he popula ion. Fu he mo e, a mul idimensional local sea ch is
applied o he Pa e o on gene a ed a each GA i e a ion o enhance
solu ion quali y and di e si y.
Fu he mo e, Cai &Qian (2022) add ess he No-wai D one Sched-
uling T a elling Salesman P oblem (NW-DSTSP) using a hyb id
app oach ha combines Adap i e Pa icle Swa m Op imisa ion (APSO)
wi h Gene ic Algo i hms (GAs). Thei solu ion me hodology in ol es a
h ee-s ep p ocess, beginning wi h he o mula ion o he p oblem as a
Mixed In ege Linea P oblem (MILP). A G eedy s a egy is employed o
gene a e an ini ial solu ion o a simpli ied e sion o he p oblem.
Subsequen ly, a GA c osso e ope a o is applied o e ine he solu ion.
An adap i e adjus men o he lea ning ac o and ine ia ac o weigh s
is also pe o med o imp o e he con e gence beha iou . Un o una ely,
speci ic implemen a ion de ails a e no a ailable.
Adding o exis ing s udies, Ka ak¨
ose (2024) in oduces an inno a i e
app oach o he hyb id uck-mul id one p oblem. This esea ch ex-
pands on he use o mo e gene ic GAs by de eloping a me hod ha
op imises deli e y ime in scena ios in ol ing single and mul iple
d ones in conjunc ion wi h a uck, c ea ing a ious deli e y scena ios
whe e d ones can only deli e one single clien . The esul s o his s udy
show a no able in e se ela ionship be ween he numbe o d ones and
deli e y ime, a inding ha complemen s he app oaches o Zhang e al.
(2022) and Cai &Qian (2022).
As a conclusion, we p opose o pu GAs in he cen e o ou esolu ion
amewo k, no ing ha he applica ion o GAs in add essing he uck-
d one deli e y p oblem is an ac i e ye s ill unde de eloped a ea o
esea ch. Zhang e al. (2022) ENSGA-II, Cai &Qian (2022) hyb id APSO-
GA, and Ka ak¨
ose (2024) gene ic GA app oaches demons a e he po-
en ial o GAs o op imise complex uck-d one deli e y ope a ions bo h
o single and mul iple c i e ia op imisa ions. While u he esea ch is
needed o e ine hese me hodologies and adap hem o speci ic eal-
wo ld scena ios, ul ima ely con ibu ing o he ad ancemen o las -
mile logis ics using d ones, GAs we e deemed he mos sui able o
ou op imisa ion amewo k, p o iding a balanced app oach o explo-
a ion and exploi a ion, c ucial o sol ing he complex combina o ial
op imisa ion p oblem p esen ed in his esea ch (Wen e al., 2024).
In summa y, he decision o use GAs in ou op imisa ion amewo k
is based on hei p o en abili y o balance explo a ion and exploi a ion,
which is c ucial o sol ing complex combina o ial op imisa ion p ob-
lems. This app oach aligns wi h he me hodologies success ully applied
in o he logis ics and deli e y op imisa ion s udies. While i is ue ha
some s udies a e no di ec ly compa able o ou speci ic p oblem, he
gene al success and adap abili y o GAs in ela ed scena ios s ongly
suppo hei use in ou esea ch.
2.4. Add essing main esea ch gaps
Ou model in eg a es he esupply uck (RT), he d one-
commanding uck (DCT), and d ones in o a cohesi e sys em ha
dynamically adap s o di e en demands. This in eg a ion allows o
mo e e icien coo dina ion and u ilisa ion o esou ces, add essing he
limi a ions o p e ious hyb id models ha ea ed hese componen s
mo e independen ly.
Fi s ly, a he han jus se ing as esupply ehicles (Daya ian e al.,
2020; Pina-Pa do e al., 2021; McCunney &Cauwenbe ghe, 2019;
Diens knech e al., 2022; Pina-Pa do e al., 2024a; Pina-Pa do e al.,
2024b), ou goal is ully exploi ing he capabili ies o d ones by allowing
hem o pe o m di ec deli e ies o cus ome s. This app oach maxi-
mises he lexibili y and speed ad an ages o d ones, especially in u ban
a eas wi h high a ic conges ion. In his manne , he mul i-modal SDD
model p oposed aims o con ol cos s by op imising he lee size and
usage, ul ima ely c ea ing economic alue by enhancing deli e y
esponsi eness and e iciency while keeping ope a ional expenses in
check. We ake he s anda d DCT e u n- o-depo s a egy as a baseline
o compa e wi h, while we explici ly decide no accoun ing o o he
models ha we judge would d aw a scena io wi h complexi ies beyond
wha is being o widesp ead adop ion in cu en las -mile hyb id de-
li e y ope a ion. Fo ins ance, we a e awa e o models such as ha by
Gao e al. (2023), whe e d ones add ess bo h picking and deli e y and
a e deployed om se e al ucks, o ha in S odola &Ku ˇ
ej (2024),
whe e ucks a e ope a ed om di e en ia ed (decen alised) depo s,
each uck in andem wi h one d one.
Secondly, we ound ha he impac o he uck capaci y is somehow
o e looked in mos o he s udies on d one- uck combined ope a ions,
excep o Sac amen o e al. (2019) and Ki jacha oenchai e al. (2020).
Sac amen o e al. (2019) s udied a VRPD gene alisa ion om he FSTSP
ha , like us used capaci a ed uck and d one, bu hey conside ha
some loca ions a e o be se ed by he uck owing o he weigh o he
load, limi s he synch onisa ion a uck s ops among a p eselec ed
subse o candida e loca ions and u he , ha d one can only isi one
D. Sanchez-Wells e al.
Expe Sys ems Wi h Applica ions 272 (2025) 126757
7
cus ome pe ip. Kuo e al. (2022) p oposed a VRPTWD model by
conside ing he p esence o cus ome ime windows wi hin he VRPD
model o Sac amen o e al. (2019), he eby adding capaci y cons ain s
o uck bu no conside ing he mul i-d op d one missions ha a e
wi hin he scope o ou in es iga ion. Ki jacha oenchai e al. (2020)
conside ed bo h ucks and d ones’capaci ies when s a ing a a ia ion
o he classic CVRP which, deno ed as wo-echelon ehicle ou ing
p oblem wi h d ones (2EVRPD), deploys mul iple ucks and d ones
wi h he capabili y o mul iple isi s. They aimed hei esolu ion a
inding op imal ou es o bo h ucks and d ones o minimise he a i al
a depo o all he ehicles a e comple ing he deli e ies. Hence, in ou
s udy we explici ly inco po a e he capaci y limi a ions o bo h ucks
and d ones he eby p o iding a mo e ealis ic and p ac ical amewo k
o e alua ing he e iciency o he deli e y ope a ions.
Finally, we poin ou ha he esea ch in uck-d one deli e y op-
e a ions o en p io i ises op imisa ion o an only objec i e, such as
minimising ei he deli e y ime o ope a ional cos . The e is a need o
s udies whe e algo i hms show lexibili y o op imise aiming o di e en
objec i es in a lexible manne by choice o he use . Exis ing wo ks like
hose by Leon-Blanco e al. (2022) and Poikonen &Golden (2020) end
o ocus on singula op imisa ion goals, which does no p o ide a holis ic
iew o ope a ional e iciency. While ou algo i hm op imises ei he
makespan o uck mileage in sepa a e uns, i can sol e bo h s anda d
and esupply s a egies wi hou modi ica ions. This lexibili y allows
decision make s o choose he op imisa ion c i e ion ha bes aligns
wi h hei ope a ional goals. The capabili y o swi ch be ween objec i es
wi hou changing he algo i hm unde sco es i s obus ness and adap -
abili y, being highly bene icial o he case s udy and analysis conduc ed
in Sec ion 4 o demons a e he esupply s a egy’s supe io pe o -
mance in educing deli e y imes and uck mileage compa ed o he
s anda d s a egy: a DCT e u ning o he depo o eloading and hen
mo ing again o he deli e y a ea. O e all, he p oposed esupply
s a egy no only enhances ope a ional e iciency and educes cos s bu
also con ibu es o en i onmen al sus ainabili y. These imp o emen s
p o ide a compe i i e edge o logis ics companies in he apidly
e ol ing landscape o same-day deli e y se ices.
3. Capaci a ed uck-mul iple d ones andem logis ics
Capaci a ed T uck-mul iple D ones Tandem Logis ics (CTmDTL) is a
deli e y sys em based on he TmDTL sys em de ailed in Gonzalez-R e al.
(2024) wi h he addi ion o capaci y cons ain s. As in he ci ed wo k,
he CTmDTL sys em aims o se e pa cels o a se o cus ome s by means
o a DCT and a lee o au onomy-limi ed d ones ha wo k collabo a-
i ely, bu on his occasion, all g ound and ae ial ehicles a e capaci y-
cons ained. The e o e, d ones do no only e ill hei au onomy bu also
he necessa y load o hei nex mul i-d op mission when synch onising
wi h he uck. This is wha we call he “s anda d”DCT e u n- o-depo
s a egy, as ep esen ed in Fig. 1.
Hence, in he con ex o TmDTL, ucks and d ones, despi e bo h
se ing cus ome s, di e signi ican ly in e ms o au onomy, a el
speed, and, acco ding o he ecen es ic ion, deli e y capaci y. Con-
s an a el speeds o d ones and ucks ha e been assumed, simila o
o he s udies (Gonzalez-R e al., 2020). We assume d one speed is always
highe han uck speed a he ope a ional le el, as usual in his ype o
app oach a a planning decision le el (Luo e al., 2021; Mosh e -Ja adi
e al., 2020b). The impac o accele a ion and i s implica ions on ake-o
and landing, as well as he e ec o wind on d one ene gy consump ion,
is beyond he scope o his s udy.
3.1. Ou p oposal: A esupply s a egy
On i s side, he “ esupply”s a egy p oposed in his pape wo ks
unde he assump ion ha an auxilia y g ound ehicle (wi h he same
capaci y limi a ion as he DCT uck) is included in he men ioned sys-
em o help con ey o he deli e y a ea hose pa cels beyond he
capaci y o he DCT (o ha a i ed la e a he depo ) in wo di e en
ways: (i) synch onisa ion wi h he DCT a any cus ome loca ion o
eload i s capaci y and (ii) di ec deli e y o cus ome s on i s way back o
he depo .
The eason o his las poin is wo old: i s ly, aiming o op imise
e iciency by ensu ing ha he DCT and he d one lee ope a e a o nea
ull capaci y o mos o hei ou es, educing he numbe o ips
equi ed, and op imising uel usage; and secondly, by e illing he DCT’s
capaci y, he ope a ion can minimise he ime spen e u ning o he
depo o addi ional ca go. This can lead o as e deli e y imes,
imp o ing cus ome sa is ac ion, and allowing o mo e deli e ies
wi hin a gi en pe iod. This s a egy is isually ep esen ed in Fig. 2.
As a esul , while he DCT and i s accompanying d ones synch onise
o o e pass d one au onomy and capaci y limi a ions, he e is a pa allel
need o he DCT o synch onise wi h he esupply ehicle o add ess i s
own capaci y cons ain . This assumes ha he ehicle ha a i es i s
will need o wai o he o he , ensu ing a cohesi e ope a ional low.
Despi e he added complexi y in oduced by his new synch onisa ion,
he inco po a ion o he auxilia y ca go ehicle is iden i ied as ha ing
he po en ial o dec ease he o al se ice ime (makespan) and/o
minimise he o al mileage co e ed by he ucks in he logis ics sys em.
A ele an de ail is ha , as in TmDTL, d ones ha e he op ion o
emain pa ked on he DCT. Upon eaching he nex node, hey can ake-
o o a new se ice ou e o s ay pa ked on he DCT o mul iple ips.
Consequen ly, a no ewo hy conside a ion is ha a po ion o he d one
lee in he DCT may emain unused, emphasising he impo ance o
accu a ely sizing he lee .
Ou s udy ocuses on assessing he impac o esupply in wo-wa ed
SDD scena ios, whe e he s anda d me hod equi es only one e u n o
he depo o capaci y eplenishmen . On he con a y, in he esupply
s a egy, a single synch onisa ion be ween he DCT and he esupply
uck is su icien o adhe e o he capaci y cons ain s o he DCT.
Fig. 1. CTmDTL s anda d s a egy ou ing diag am.
D. Sanchez-Wells e al.
Expe Sys ems Wi h Applica ions 272 (2025) 126757
8
3.2. Visi assump ions
To summa ise he p e iously men ioned condi ions in a s aigh o -
wa d and in e p e able manne , we es ablish wo se s o ules, each
ou lining he beha iou o he s anda d and esupply s a egies. Based
on he e minology in oduced by Gonzalez-R e al. (2024), he ules
con ained in his lis will be called “ isi assump ions”. The isi as-
sump ions o he s anda d s a egy a e s a ed as ollows:
1) All ehicles mee a he depo , as i is assumed ha i is he necessa y
s a ing and end node o a comple e se ice.
2) Any ehicle can se e any node, and all nodes mus be se ed.
3) I a node is no isi ed by he DCT, only a single d one can isi and
se e i .
4) I a node is isi ed by he DCT, any numbe o d ones can mee i a
ha node, ully eco e ing au onomy and eloading capaci y. F om
his poin on, he e a e wo possibili ies o any d one:
a. Res a again o con inue o se e he nodes.
b. Land in he DCT wi hou consuming any au onomy un il he DCT
eaches i s nex node.
5) The synch onisa ion ime is conside ed negligible when compa ed o
he mission ime, and, as such, i has been dis ega ded.
6) Mee ing a a node necessa ily in ol es wai ing ime, as all ehicles in
need o synch onising will ha e o wai un il he es each ha node.
These wai ing imes do no consume any au onomy o he d ones.
The e o e, ho e ing is no conside ed.
7) The uck echnology allows i o na iga e any po en ial ou e among
he se o loca ions, i espec i e o i s leng h. The e o e, he au on-
omy o he uck is assumed o be unlimi ed.
8) The capaci y o d ones is limi ed and homogeneous, wi h he only
me hod o eplenishing hei capaci y h ough synch onisa ion wi h
he DCT.
9) The capaci y o he DCT is limi ed, and he only me hod o eplen-
ishing i is isi ing he depo . In his s udy, he numbe o isi s o he
depo is es ic ed o one.
As expec ed, when s a ing he isi assump ions o he esupply
s a egy, many o he p e ious emain. On he o he hand, we mus make
some adjus men s. Speci ically, all ules o he s anda d s a egy can be
kep excep isi assump ion 9, which e e s o uck capaci y, and an
addi ional one ( isi assump ion 10) mus be added. The e o e, o he
esupply s a egy, he las wo ules would be s a ed as ollows.
10) The capaci y o he DCT is limi ed, and he only me hod o
eplenishing i is by synch onising wi h he esupply uck.
Numbe o synch onisa ions is limi ed o one in his s udy.
11) The esupply uck can only se e o he nodes han he syn-
ch onisa ion one a e i has synch onised wi h he DCT, he e-
o e, on i s way back o he depo .
3.3. Ma hema ical ou line: A uni ied modelling app oach
In his sec ion, we p esen a comp ehensi e ma hema ical o mula-
ion o he CTmDTL p oblem, in eg a ing bo h he s anda d depo e u n
and on- oad esupply s a egies unde a single uni ied amewo k. The
objec i e is o c ea e a model lexible enough o handle a ange o
ope a ional cons ain s—ba e y au onomy, ehicle capaci ies, and
ou e synch onisa ions—while allowing us o op imise o ei he
makespan o uck mileage. This o malisa ion is essen ial o unde -
s anding how we la e design and implemen an e ec i e, heu is ic-
based esolu ion me hod.
Since he model gene alises he Vehicle Rou ing P oblem—al eady
known o be NP-ha d— he CTmDTL o mula ion inhe i s his
complexi y. The e o e, we do no aim o ob ain exac solu ions o la ge
ins ances ia classical b anch-and-bound echniques. Ins ead, we p o-
ide a obus ma hema ical ep esen a ion ha can be ackled by spe-
cialised algo i hms o heu is ics. The model cap u es he iming,
capaci y usage, d one au onomy, and synch onisa ion equi ed o
mul i- ehicle, mul i-d one ou es. I also accommoda es wo al e na i e
objec i es (minimising he makespan o minimising o al uck a el) o
be chosen by he decision make s, which allows o align he op imisa ion
goal wi h hei speci ic ope a ional p io i ies.
By embedding bo h s a egies—depo e u n and on- oad esupply-
—in o a single o mula ion, we enable he s a egy o be chosen by he
sol e i sel wi h he same me hodological ool. In p ac ice, he p oblem
can be app oached wi h heu is ic o ma heu is ic me hods ha inco -
po a e he ele an load- ans e and synch onisa ion cons ain s. These
cons ain s ex end ea lie capaci y es ic ions inspi ed by Ka a e al.
(2007) and d one ba e y models adap ed om Gonzalez-R e al. (2020).
Ou emphasis is on demons a ing how each s a egy pe o ms unde a
consis en se o assump ions, a he han compe ing on sol e imple-
men a ions o exhaus i e algo i hmic benchma ks. In wha ollows we
p esen he modelling choices and no a ion used (e.g., bina y ou ing
a iables, load ans e a iables, and ime acking a iables) be o e
add essing ou design o he GAIER solu ion amewo k in Sec ion 4.
3.3.1. Se s and pa ame e s
Se s
•N: Se o nodes N= {0,1,2,⋯,n}, whe e 0 is he depo and {1,⋯,n}
cus ome s.
•Λ: Se o a cs Λ= {(i,j)|i,j∈N,i∕= j}.
•V: Se o g ound ehicles V= { 1, 2},whe e 1deno es he single
D one-Commanding T uck (DCT) and 2(only ac i e in he esupply
s a egy) deno es he esupply uck (RT).
•D: Se o d ones D= {d1,⋯,dm}, whe e each d one h∈Dexhibi s
homogeneous au onomy and load capaci y ea u es.
Pa ame e s
•qi: Load demand a cus ome i.
•Q(g)
1: Maximum load capaci y o DCT.
Fig. 2. CTmDTL esupply s a egy ou ing diag am.
D. Sanchez-Wells e al.
Expe Sys ems Wi h Applica ions 272 (2025) 126757
9
•Q(g)
2: Maximum load capaci y o RT (i used).
•Q(a)
h: Maximum capaci y o any d one.
•
α
: Maximum unin e up ed ligh ime (o dis ance budge ) be o e
needing o esynch onise wi h he DCT, also de ined as au onomy o
e e y d one in he homogenous lee .
•
τ
(a)
i,j: Time ha any ae ial ehicle (d one) needs o mo ing om node
i o node j.
•
τ
(g)
i,j: Time ha any g ound ehicle (DCT o RT) needs o a el om
node i o node j.
•dis i,j: Dis ance o a ehicle a eling om i o j.
•M: Su icien ly la ge posi i e cons an used in cons ain s o enable
o disable speci ic condi ions based on he alues o associa ed bi-
na y a iables.
3.3.2. Decision a iables
Bina y a iables
•β: S a egy selec ion lag, whe e β=0 indica es ha he s anda d
depo e u n s a egy is chosen, and β=1 indica es ha he on- oad
esupply s a egy is chosen.
•Ri: RT o DCT esupply node lag, whe e Ri=1 indica es ha he
DCT 1mee s and ecei es load om he RT 2a node i, ze o
o he wise.
•Zi,h: DCT and D one mee ing node lag, whe e Zi,h=1 indica es ha
he d one hmee s he DCT 1a node i, ze o o he wise. This mee ing
needs o happen o d one landing, d one ake-o , d one au onomy
eplenishmen and/o d one capaci y eload.
•Xi,j, : T uck a c lag, whe e Xi,j, =1 indica es i uck a els
di ec ly om node i o node j, ze o o he wise.
•Yi,j,h: D one a c lag, whe e Yi,j,h=1 indica es i d one h lies di ec ly
om node i o node j, ze o o he wise.
•S(g)i, : T uck se ice lag, whe e S(g)i, =1 indica es i uck se es
node i, ze o o he wise.
•S(a)i,h: D one se ice lag, whe e S(a)i,h=1 indica es i d one hse es
node i, ze o o he wise.
Con inuous a iables
•L(g)i,j, : weigh loaded in ehicle i i goes om i o j, ze o o he wise.
L(g)i,j, ≥0,L(g)i,j, ≤Q(g)
,∀(i,j) ∈ Λ, ∈V.
•L(a)i,j,h: weigh loaded in d one hi i goes om i o j, ze o o he wise.
L(a)i,j,h≥0,L(a)i,j,h≤Q(a)
h,∀(i,j) ∈ Λ,h∈D.
•Δi: amoun o load ans e ed om 2( he RT) o 1( he DCT) a
node i.
Δ0=0,Δi≥0,∀i∈N,
•θi,h: amoun o load ans e ed om 1( he DCT) o d one ha node
i.
θ0,h=0,θi,h≥0,∀i∈N,h∈D,
•T: o al se ice ime (makespan) by which all deli e ies a e
comple ed, and all ehicles ha e comple ed hei ou es and e u ned
o he depo .
•Ai, : a i al ime o ehicle a node i.
•Di, : depa u e ime o ehicle om node i.
•Ai,h: a i al ime o d one ha node i.
•Di,h: depa u e ime o d one h om node i.
•b+i,h: emaining au onomy o d one hon i s a i al o node i.
b+i,h≥0,b+i,h≤
α
,∀i∈N,h∈D,
•b−i,h: emaining au onomy o d one hon i s depa u e om node i.
b−i,h≥0,b−i,h≤
α
,∀i∈N,h∈D.
3.3.3. Objec i e unc ions
Minimise To al Se ice Time (Makespan)
min T.(1)
This objec i e ocuses on comple ing all deli e ies as ea ly as possible,
measu ed by he ime Ta which he las ehicle ( uck o d one) inally
e u ns o he depo .
Minimise To al T uck Dis ance
min(∑(i,j)∈Λdis i,j⋅Xi,j, 1+∑(i,j)∈Λdis i,j⋅Xi,j, 2).(2)
This al e na i e objec i e ocuses on educing g ound ehicle mileage by
penalising e e y dis ance uni a elled by any o he ucks. In se ings
whe e uel cos s, ehicle wea , o ca bon emissions a e he p ima y
conce n, minimising o al uck dis ance helps shi deli e ies o d ones
o sho e uck ips, e en i i does no necessa ily minimise he o e all
comple ion ime.
3.3.4. Key cons ain s
A Single Se icing Vehicle pe Cus ome
∑ ∈VS(g)i, +∑h∈DS(a)i,h=1,∀i∈ {1,⋯,n}.(3)
Se icing Vehicle Mus Visi he Cus ome
S(g)i, ≤∑j:(j,i)∈ΛXj,i, ,∀i∈ {1,⋯,n}, ∈V,(4)
S(a)i,h≤∑j:(j,i)∈ΛYj,i,h,∀i∈ {1,⋯,n},h∈D.(5)
Vehicles Flow Con inui y
∑j:(i,j)∈AXi,j, =∑k:(k,i)∈AXk,i, ,∀i∈ {1,⋯,n}, ∈V,(6)
∑j:(i,j)∈AYi,j,h=∑k:(k,i)∈AYk,i,h,∀i∈ {1,⋯,n},h∈D.(7)
Quan i y o Vehicles Depa u es F om he Depo Depending on he
S a egy
∑(0,j)∈ΛX0,j, 1=2−β,∑(j,0)∈ΛXj,0, 1=2−β,(8)
∑(0,j)∈ΛX0,j, 2=β,∑(j,0)∈ΛXj,0, 2=β,(9)
∑(0,j)∈ΛY0,j,h=1,∑(j,0)∈ΛYj,0,h=1,∀h∈D.(10)
Ac i a ion o Mee ing Flags in ol ing DCT
Zi,h≤∑k:(k,i)∈ΛXk,i, 1,Zi,h≤∑k:(k,i)∈ΛYk,i,h,∀i∈N,h∈D,(11)
Ri≤∑k:(k,i)∈ΛXk,i, 1,Ri≤∑k:(k,i)∈ΛXk,i, 2,∀i∈ {1,⋯,n}.(12)
RT o DCT Load T ans e is Limi ed o Resupply E en Node
Δi≤Q(g)
2⋅Ri,∀i∈ {1,⋯,n}.(13)
RT o DCT Load T ans e Mus be Pe o med a he Fi s Node Visi ed by
RT
Δi+∑j∈{1,⋯,n}L(g)i,j, 2≤Q(g)
2⋅X0,i, 2,∀i∈ {1,⋯,n},(14)
D. Sanchez-Wells e al.
Expe Sys ems Wi h Applica ions 272 (2025) 126757
16
di e en Two-Fac o ANOVAs (one o each esponse a iable) ha e
been pe o med. This o m o s a is ical analysis allows us o examine
he e ec o wo di e en ac o s (S a egy and Ins ance Numbe ) on
each ou come simul aneously, ideally by ejec ing he null hypo hesis
( he e is no signi ican di e ence among he a e age esponse alues o
he s a egies) and suppo ing he al e na i e hypo hesis ( he e is
signi ican di e ence among he s a egies).
Fac o s and ac o in e ac ions ha ha e a signi ican impac a e
deno ed wi h an as e isk (*) and a e u he emphasised h ough hei p-
alues. Acco ding o he me hodology adop ed and he p ede e mined
signi icance le el o 5 % o his s udy, ac o s o in e ac ions ha
exhibi a p- alue less han 0.05 a e conside ed signi ican . Fu he mo e,
he F- a io alues a e indica i e o he ela i e signi icance and impac o
hese ac o s o in e ac ions on he o e all pe o mance o he sys em. In
his case, he esul s o he ANOVAs ejec he null hypo hesis and
p o ide suppo o he al e na i e hypo hesis. Now, we can execu e
pos -hoc checks o gain u he insigh s and d aw conclusions.
Fu he mo e, Fig. 5 shows he ma ginal means plo s, which acili a e he
indica ion o an a e age e ec o each le el on e e y ac o . I is
impo an o no e ha , acco ding o he e alua ed esponse, smalle
alues mean be e pe o mance.
A as isual analysis o he igu e allows o easily iden i y ha in all
cases he applica ion o he esupply s a egy o CTmDTL p o ides be e
esul s, bo h when looking a he makespan o uck mileage esponse
a iables. The es o he ac o s’beha iou , while no s a is ically
s udied, is as expec ed: ega ding he ins ance size ac o , bigge size
means also g ea e makespan and uck mileage alues. The beha iou
o he op imisa ion c i e ion ac o is also logical: op imising o a spe-
ci ic esponse a iable lowe s he esul ing alues o he a iable and
p o ides wo se esul s o he o he esponse a iable.
A las , we e e he eade o Fig. 6 o an example o a GAIER
execu ion as an example o GASGA con e gence and he e olu ion o he
algo i hm’s pe o mance. No iceably, while he esul is highly uns able
in he ini ial i e a ions o he algo i hm, i ends o s abilise a e a
ce ain numbe o i e a ions. No u he imp o emen was iden i ied
a e he shown alue o his execu ion.
6. Discussion o he esul s
When examining he conclusions d awn om he abo e ANOVA
analysis, we mus in e p e he indings wi h ca e ul a en ion o he
ope a ional implica ions while ocused speci ically on he s a egy ac-
o , as i is he main con ibu ion o his pape . I is impo an o no e
ha he selec ion o con ol pa ame e s in ou s udy was made acco ding
o p elimina y pilo expe imen a ion. This expe imen a ion helped us
iden i y sui able pa ame e alues ha op imise he pe o mance o ou
p oposed sys em wi hin he gi en cons ain s. While we acknowledge
ha a comp ehensi e sensi i i y analysis o hese pa ame e s could
p o ide deepe insigh s o a speci ic case s udy, such an analysis alls
ou side he scope o he cu en wo k due o space limi a ions and he
speci ic ocus o ou s udy. Fu u e esea ch could ex end ou indings by
explo ing he sensi i i y o he sys em o a wide ange o pa ame e
a ia ions.
Table 8
DOE con igu a ion.
Fac o Desc ip ion Le els
INIns ance Numbe {61,62,⋯,90}
OcOp imisa ion C i e ion {Makespan,Mileage}
SS a egy {S anda d,Resupply}
Response a iables Desc ip ion
MMakespan
TT uck Mileage
DOE con igu a ion O de o da a collec ion Random
Design 120- un Full Fac o ial
Replica ions 5
To al ials 600
Alpha le el 0.05
Table 9
A e age me ics o s a egies esul o 5 eplica ions o each ins ance.
S a egy Nodes Op imising A e age
makespan
A e age uck
mileage
S anda d 20 Makespan 401 1216
T uck
Mileage
530 608
50 Makespan 659 3823
T uck
Mileage
851 1785
75 Makespan 851 6775
T uck
Mileage
1093 2868
Resupply 20 Makespan 245 1001
T uck
Mileage
337 517
50 Makespan 516 2931
T uck
Mileage
788 1266
75 Makespan 783 5369
T uck
Mileage
1188 1924
Table 10
Makespan and T uck Mileage esponse a iables Two-Fac o ANOVA analyses.
Response Va iable M
Sou ce SS DF MS F p- alue F c i
S579,703 1 579,703 236.1 * <0.001 3.9
IN18,428,655 29 635,471 258.8 * <0.001 1.5
S×IN507,420 29 17,497 7.1 * <0.001 1.5
Wi hin (e o ) 589,398 240 2456
TOTAL 20,105,175 299
Response Va iable T
Sou ce SS DF MS F p- alue F c i
S34,456,138 1 34,456,138 295.4 * <0.001 3.9
IN583,097,627 29 20,106,815 172.4 * <0.001 1.5
S×IN17,675,021 29 609,483 5.2 * <0.001 1.5
Wi hin (e o ) 27,992,719 240 116,636
TOTAL 663,221,505 299
D. Sanchez-Wells e al.
Expe Sys ems Wi h Applica ions 272 (2025) 126757
17
Conce ning he makespan esponse a iable (Table 10), s a egy
signi icance is p onounced wi h a p- alue less han 0.001, indica ing
ha changes in s a egy a ec comple ion ime (namely, a ea u e o
s eadiness no ma e ha he impac is no he la ges ). The in e ac ion
o he s a egy wi h he chosen ins ance is also s a is ically signi ican :
signi ican F- a ios and low p- alues indica e ha he syne gis ic e ec s
o hese ac o s should no be igno ed. In p ac ical e ms, his implies
ha he e ec i eness o selec ing a esupply s a egy is con ex -
dependen and can be enhanced o diminished by he le els o o he
ac o s in he ope a ional se ing.
Tu ning o he uck mileage esponse a iable (Table 10), he
s a egy ac o emains s a is ically signi ican wi h a p- alue less han
0.001. This ein o ces he no ion ha selec ing an op imal s a egy has
signi ican , in luence on uck mileage. The ins ance ac o in e ac ion
e ec s a e also s a is ically signi ican in his case, sugges ing ha he
impac o he s a egy on uck mileage does a y wi h di e en in-
s ances as well. This can be qui e insigh ul o ope a ional decisions, as
i sugges s ha he p oposed s a egy may no ha e a p edic able
s andalone e ec on uck mileage.
In a b oade las -mile logis ics con ex , he consis en signi icance o
s a egy selec ion ac oss di e en esponse a iables deno es he po-
en ial o he esupply s a egy as a le e o ope a ional imp o emen .
Fu he mo e, o ope a ional esea ch and logis ics planning, he ind-
ings could be ans o ma i e, as hey sugges ha decision make s
should also conside how he s a egy in e ac s wi h o he ope a ional
elemen s o maximise i s ull po en ial. A las , he uni o mi y o he
e ec o he s a egy ac o ac oss di e en pe o mance me ics implies
ha i could be a s able building block in he complex s uc u e o las -
mile logis ics op imisa ion.
6.1. Di ec compa ison be ween s a egies
The me ics used o he quali y assessmen in his sec ion, Makespan
Imp o emen and T uck Mileage Imp o emen , bo h measu ed in pe -
cen age, a e e en compa ison me ics o bo h s a egies. The alues a e
calcula ed by di iding each o he esupply s a egy me ic alues by he
s anda d s a egy me ic alues o Makespan and T uck Mileage op i-
misa ion ials ha co espond o he same demand pa e n. In ui i ely,
bo h pe cen ages a e c ucial in e alua ing any possible ad an ages in
ope a ional e iciency and en i onmen al impac when compa ing
s a egies.
The analysis o he same se o a o al o 600 expe imen s used o
gene a ing Table 9 as well as in he DOE d aws he esul s ha can be
Fig. 5. Makespan and Mileage esponse a iables. Ma ginal means esponse a e ages plo .
Fig. 6. T uck mileage e olu ion in 75 nodes size ins ance op imised using
GASGA and esupply s a egy.
D. Sanchez-Wells e al.
Expe Sys ems Wi h Applica ions 272 (2025) 126757
18
seen in Fig. 7. The high makespan imp o emen a lowe node coun s
(38 % o 20 nodes) sugges s ha , o smalle deli e y ne wo ks, he use
o a esupply uck signi ican ly educes deli e y imes. This is likely due
o he educed need o he mo he ship uck o e u n o he depo ,
which can be ime-consuming. As he numbe o nodes inc eases, he
makespan imp o emen dec eases un il s abilising a app oxima ely 20
% o bo h 50 and 75 nodes. This could be due o he inc eased
complexi y in coo dina ing deli e y and esupplying as he size o he
ne wo k inc eases.
On he o he hand, he imp o emen in mileage is s eadie be ween
di e en node sizes. In pa icula , o 75 nodes, mileage imp o emen is
he highes (30 %), sugges ing ha , in dense ne wo ks, op imising o
mileage can subs an ially educe o al uck a el dis ances, po en ially
leading o cos sa ings in uel and ehicle main enance. The nega i e
imp o emen o makespan a 75 nodes when op imising o mileage
(−10 %) implies ha ocusing solely on educing mileage can lead o
ine iciencies in ime, possibly due o a mo e ex ensi e use o he d ones
o pe o ming deli e ies, which di ec ly implies mo e bu also longe
wai ing imes o he synch onisa ions.
Finally, he in e ac ion be ween he numbe o nodes and he applied
op imisa ion s a egy is complex. A lowe node coun s, makespan
imp o emen is dominan , bu as he numbe o cus ome s g ows, he
ad an age shi s owa ds mileage imp o emen . This change may be
in luenced by ac o s such as ou ing complexi y and logis ical chal-
lenges o coo dina ing mul iple deli e ies in he same a ea while
espec ing all cons ain s.
6.2. Manage ial lessons
Ce ainly, he p e ious compa ison analysis o e s aluable insigh s
ha can be ansla ed in o ac ionable manage ial lessons ha a e p e-
sen ed hence o h.
6.2.1. E iciency in small-scale ope a ions
Fo ope a ions wi h ewe deli e y nodes (e.g., 20 nodes), he sig-
ni ican inc eases in he makespan (38 %) indica e he oppo uni y o
g ea ly educe deli e y imes by inco po a ing a esupply uck. In ime-
sensi i e scena ios (e.g., pe ishable goods), using a esupply uck o
a oid depo e u ns signi ican ly inc eases e iciency.
Addi ionally, he minimisa ion o mileage is also an imp o emen
sou ce when coping wi h low numbe o cus ome s, as i also leads o
sa ings in ope a ional cos s.
6.2.2. S a egies o la ge ne wo ks
As he numbe o cus ome s inc eases (e.g., 75 nodes), he bigge
oppo uni y o imp o emen g adually shi s owa ds op imising uck
mileage, whe e we see he highes imp o emen (30 %). This app oach
can subs an ially educe a el dis ances, leading o lowe uel cos s and
educed ehicle wea and ea .
Howe e , he nega i e e ec on makespan a highe node coun s
when ocusing solely on mileage unde sco es he need o a balanced
s a egy. Manage s a e ad ised o app oach op imisa ion wi h a holis ic
pe spec i e, ensu ing ha emphasis on one ope a ional aspec does no
inad e en ly comp omise he o e all balance and e icacy o o gan-
isa ional pe o mance. I is impo an o p oceed wi h cau ion, ecog-
nising he in ica e in e play be ween di e en ope a ional dimensions,
o achie e a ha monious ou come.
6.2.3. Adap i e planning and ou e op imisa ion
The esul s sugges ha he op imal s a egy migh a y depending
on he size o he deli e y ne wo k. Manage s should employ adap i e
ou e planning ools ha can adjus s a egies based on daily deli e y
olume and ne wo k size. De ini ely, using ad anced ou ing algo i hms
like he GAIER we ha e applied in ou esea ch will be help ul in
dynamically disco e ing ou ing planning wi h easible alues o bo h,
makespan and uck mileage.
6.2.4. Economic impac
The applica ion o he esupply s a egy demons a es subs an ial
imp o emen s in bo h makespan and uck mileage ac oss a ious sce-
na ios. This ansla es o economic gains by educing he numbe o ips
equi ed, op imising ucks usage, and inc easing he numbe o de-
li e ies wi hin a gi en pe iod. These imp o emen s a e indica i e o he
esupply s a egy’s po en ial o signi ican ly educe ope a ional cos s
and enhance he o e all alue c ea ed in he deli e y p ocess, which
aligns wi h indings by Xiao e al. (2024), who demons a ed he
impo ance o dynamic d one esupply in enhancing he e iciency and
esponsi eness o same-day deli e y sys ems.
Fig. 7. Resupply Imp o emen s. Numbe o Nodes and Op imisa ion Ta ge .
D. Sanchez-Wells e al.
Expe Sys ems Wi h Applica ions 272 (2025) 126757
19
6.2.5. B oade implica ions o p ac ical applica ions
The indings om ou s udy ha e signi ican implica ions o p ac-
ical applica ions in uck ou ing op imisa ion. Ou mul i-modal de-
li e y model, which includes a esupply uck, demons a es clea
bene i s in educing deli e y imes while con olling cos s. This s a egy
is pa icula ly ad an ageous in indus ies whe e same-day deli e y is
c i ical, such as pha maceu icals and pe ishable goods, as hese in-
dus ies o en ace igh deli e y windows and hea y a ic, whe e
d ones can bypass conges ion and imp o e e iciency. By educing he
need o ucks o e u n o he depo , he s a egy enables as e , mo e
lexible deli e ies, making i a iable solu ion in dense, high-demand
a eas.
By limi ing he lee size o ucks equipped wi h d ones and in o-
ducing a simple esupply an, ou model enhances deli e y e iciency
wi h a modes inc ease in ope a ional cos s. This app oach no only
op imises esou ce u ilisa ion bu also p o ides a scalable solu ion
adap able o a ious deli e y con ex s, p omising imp o ed se ice
le els and cus ome sa is ac ion. Addi ionally, he 17 % educ ion in
makespan and 21 % dec ease in uck mileage demons a e ha he
p oposed s a egy can po en ially lead o eal-wo ld bene i s, including
as e deli e ies, educed uel consump ion, and lowe ope a ional cos s.
These imp o emen s also suppo sus ainabili y goals by cu ing emis-
sions and ex ending ehicle li espan. O e all, he esupply s a egy en-
hances bo h economic e iciency and en i onmen al impac , p o iding a
clea ad an age o logis ics companies.
7. Conclusions and u u e esea ch
In an age in which he sho e deli e y ime is mo e and mo e
becoming a c i ical ac o in as -paced same-day deli e y scena ios—e.
g., deli e y o meals and pe ishable goods—we p opose exploi ing a
hyb id uck-d one sys em bu adding an auxilia y esupply uck o
p e en he p ima y uck’s de ou back o he depo . Di e en o o he
ecen app oaches elega ing he esupply ole only o d ones, we
ese e i o a g ound ehicle ha se es he pu pose o p o iding he
main uck (mo he ship uck o launching and e ie ing o he d ones
unde i s con ol) wi h he newly a i ed o de s.
Building on he CTmDTL o mula ion, we ha e de eloped a uni ied
amewo k o iden i y he op imal s a egy while adhe ing o capaci y
cons ain s, d one au onomy, and ou e synch onisa ion unde wo
dis inc s a egies o gene a ing solu ions ha educe makespan o
uck mileage in ealis ic same-day deli e y ne wo ks.
We ha e compa ed he s anda d and he esupply s a egies h ough
de ailed analyses, b inging o ligh he signi ican imp o emen s in bo h
e iciency and en i onmen al sus ainabili y ha can be achie ed by
in eg a ing a esupply uck in o a uck-mul id one logis ics sys em.
The use o a esupply uck allows o a conside able dec ease in he
makespan wi hin small-scale deli e y ne wo ks, which also a ises when
add essing bigge deli e y scena ios bu wi h lowe in ensi y. In he
la e , he ope a ional gaining shi owa ds he sa ings in uck a el
o al dis ance, uel usage, and ehicle main enance eme ging om he
lowe uck mileage a ained.
Thus, ou s udy aims o p o ide ac ionable insigh s o decision
make s h ough an in-dep h sensi i i y analysis. The economic analysis
o ou app oach indica es ha he esupply s a egy no only imp o es
deli e y e iciency bu also esul s in no able cos sa ings. By minimising
he numbe o depo e u ns and op imising he use o deli e y e-
sou ces, his s a egy enhances he c ea ion o alue o logis ics com-
panies, o e ing a clea pa hway o inc eased p o i abili y and
compe i i e ad an age. In his sec o whe e imely and eliable deli e y
is key, he enhancemen s b ough o h by he esupply s a egy can
signi ican ly imp o e cus ome expe ience, he e o e o e ing businesses
a compe i i e edge ha can become a key di e en ia o .
This s udy also con ibu es o he ields o logis ics and supply chain
managemen by alida ing he heo e ical p oposi ion ha in eg a ing
esupply s a egies enhances ope a ional e iciency in small-scale
deli e y ne wo ks. The indings suppo dynamic ou ing and eal- ime
adap i e logis ics s a egies, demons a ing signi ican imp o emen s in
makespan and uck mileage. Addi ionally, he esea ch highligh s he
need o balanced op imisa ion in la ge ne wo ks, con ibu ing o
heo e ical models ha add ess ade-o s be ween ope a ional me ics
such as makespan and mileage. The applica ion o ad anced ou ing
algo i hms, speci ically he GAIER algo i hm, ein o ces he heo e ical
amewo ks ad oca ing o sophis ica ed compu a ional echniques o
op imise deli e y ou es dynamically.
Mo eo e , ou s udy o e s a ounda ion o economic impac and
cos -bene i analysis in logis ics aiming o quan i y cos sa ings and e -
iciency gains om esupply s a egies in pa icula cases. The insigh s
in o mul i-modal deli e y models, pa icula ly hose inco po a ing
esupply ucks and d ones, con ibu e o eme ging discussions on
hyb id deli e y sys ems and hei scalabili y. By p o iding a ounda ion
o analysing he scalabili y and adap abili y o di e en logis ical
s a egies, ou esea ch b idges a gap and opens new possibili ies o he
inco po a ion o esupply-based s a egies, enhancing bo h academic
knowledge and p ac ical ou comes in logis ics op imisa ion. In his di-
ec ion, u u e esea ch could build on ou indings by explo ing speci ic
cases, long- e m impac s and c oss-indus y applica ions.
In he ealm o u u e esea ch, eme ging app oaches, such as
Gene a i e A i icial In elligence (GAI), also p esen exci ing a enues
o explo a ion. While GAI has shown ema kable capabili ies in da a
gene a ion and p edic i e asks, i s applica ion in sol ing complex
combina o ial op imisa ion p oblems, such as he uck-d one deli e y
p oblem, emains unde explo ed. Fu u e wo k could in es iga e how
GAI could complemen exis ing me hods like GAIER by gene a ing dy-
namic deli e y scena ios o c ea ing hyb id op imisa ion amewo ks
possibly based on enhanced ma hema ical models— o example, om
adding mul iple auxilia y ucks o pa ial, mul i-node esupply ules.
Al hough GAI is no ye widely adop ed o hese speci ic p oblems, i
may o e no el insigh s o add essing la ge , mo e complex ne wo ks
o eal- ime adap i e logis ics en i onmen s. Besides, ou analysis
u he suppo s he need o adap i e planning and dynamic ou e
op imisa ion, ca e ing o he apidly e ol ing las -mile logis ics land-
scape. As he las -mile logis ics business landscape is apidly e ol ing,
he abili y o modi y s a egies based on luc ua ing deli e y olumes
and ne wo k sizes is c i ical.
While no di ec empi ical compa a ion be ween GAIER and o he
me hods is p o ided in his s udy, i is c ucial o no e ha he e ec-
i eness o GAs in sol ing combina o ial op imisa ion p oblems simila
o he uck-d one deli e y p oblem has been ex ensi ely documen ed in
he li e a u e, whe e hei use showed signi ican imp o emen s in so-
lu ion quali y and compu a ional e iciency. Fu u e esea ch could
explo e u he economic implica ions, isk s udies, compa a i e ana-
lyses o be e ini ialisa ion alues o algo i hm pa ame e s, as well as
he in eg a ion o mul iple esupply ucks o u he enhance sys em
e iciency and lexibili y. This app oach may o e inc eased scalabili y
o la ge o mo e dynamic deli e y egions, po en ially imp o ing
ope a ional dynamics and en i onmen al sus ainabili y. Such de-
elopmen s could u he e ine ou s a egy, p omising e en g ea e
imp o emen s in deli e y pe o mance and cus ome sa is ac ion.
In conclusion, ou esupply s a egy o uck-wi h-mul id one sys-
em o e s a p omising app oach o op imising las -mile deli e y ope -
a ions. This model subs an ially imp o es deli e y imes and lowe s
cos s, making i highly applicable o a ious deli e y con ex s while
inc easing logis ics pe o mance and cus ome sa is ac ion. This
esea ch makes a signi ican con ibu ion o he ield o las -mile logis-
ics, p oposing he esupply s a egy as an e ec i e me hod o imp o e
ope a ional e iciency and en i onmen al sus ainabili y which ca ies
p ac ical implica ions o he logis ics indus y. These indings se he
s age o u he esea ch and de elopmen o s a egies o op imise las -
mile deli e y in he inc easingly complex logis ics en i onmen .
D. Sanchez-Wells e al.
Expe Sys ems Wi h Applica ions 272 (2025) 126757
20
Decla a ion o Gene a i e AI and AI-assis ed echnologies in he
w i ing p ocess
Du ing he p epa a ion o his wo k he au ho s used Gene a i e P e-
ained T ans o me 4 (GPT-4) in o de o imp o e language and ead-
abili y. A e using his ool, he au ho s e iewed and edi ed he con en
as needed and ake ull esponsibili y o he con en o he publica ion.
CRediT au ho ship con ibu ion s a emen
Ped o L. Gonzalez-R: Concep ualiza ion, Fo mal analysis,
Visualiza ion, Supe ision. Da id Sanchez-Wells: Me hodology, So -
wa e, Valida ion, Compu a ional E alua ion, W i ing –o iginal d a .
Jos´
e L. And ade-Pineda: Concep ualiza ion, Fo mal analysis, In es i-
ga ion, Resou ces, Da a cu 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 .
Appendix A. . Design o GASGA gene ic algo i hm
The Gene ic Algo i hm Sanchez-Gonzalez-And ade (GASGA) is designed o add ess complex op imisa ion p oblems by le e aging a dual- ec o
indi idual ep esen a ion, specialised gene ic ope a o s, and adap i e mechanisms. GASGA, which lowcha is ep esen ed in Fig. 8, is pa icu-
la ly e ec i e o p oblems whe e solu ion componen s can be na u ally di ided in o dis inc ec o s, such as sequence and modes ec o s. This annex
p o ides a comp ehensi e and code-ex ensi e ead o he GASGA algo i hm, de ailing i s implemen a ion and unique ea u es.
A.1 GASGA key insigh s
GASGA adop s a no el app oach o he adi ional single- ec o indi idual ep esen a ion by u ilising wo dis inc ec o s: a sequence ec o
(nodes ec o ) and a modes ec o . The nodes ec o ep esen s a pe mu a ion sequence whe e each elemen is unique, e lec ing a sequence o
loca ions. In con as , he modes ec o allows epe i ions, ep esen ing a se o isi modes.
A.1.1 Dual-Vec o ep esen a ion
•Nodes Vec o : The nodes ec o is always a pe mu a ion ec o whe e no epe i ion is allowed, ensu ing a unique sequence o loca ions. This
uniqueness is c ucial o main aining he in eg i y o he sequence, which is ypically equi ed in ou ing p oblems and o he combina o ial
op imisa ion challenges.
•Modes Vec o : The modes ec o does no equi e uniqueness, allowing o epea ed isi modes ac oss he ec o . This lexibili y enables he
algo i hm o ep esen scena ios whe e mul iple isi s o he same mode o s a e a e possible, which can be c i ical in scheduling and alloca ion
p oblems.
D. Sanchez-Wells e al.
Expe Sys ems Wi h Applica ions 272 (2025) 126757
21
Fig. 8. GASGA Algo i hm Flowcha .
A.1.2 Specialised gene ic ope a o s
•Ope a o s o Nodes Vec o : C osso e ope a o s such as Uni o m Pa ially Ma ched, Pa ially Ma ched, and O de ed a e chosen o p ese e he
pe mu a ion p ope y. These ope a o s ensu e ha he o sp ing main ain he necessa y cons ain s o he nodes ec o , acili a ing e ec i e
explo a ion o he solu ion space wi hou iola ing he p oblem’s cons ain s.
•Ope a o s o Modes Vec o : C osso e ope a o s like Two Poin and Uni o m a e selec ed o hei abili y o e ec i ely combine ec o s wi hou
a oiding epe i ions. These ope a o s allow o he lexible ecombina ion o modes, which is essen ial o explo ing di e en combina ions and
con igu a ions in he solu ion space.
D. Sanchez-Wells e al.
Expe Sys ems Wi h Applica ions 272 (2025) 126757
22
A.2 De ailed GASGA implemen a ion
This sec ion p o ides an ex ensi e, de ailed p esen a ion o he GASGA algo i hm.
A.2.1 Popula ion ini ialisa ion
The ini ialisa ion o he popula ion in ol es gene a ing a se o andom indi iduals ha se e as he s a ing poin o he e olu iona y p ocess.
Each indi idual in he popula ion is composed o a sequence ec o and a modes ec o , adhe ing o he p oblem’s speci ic cons ain s and e-
qui emen s. This ini ial popula ion o ms he basis o he subsequen e olu iona y ope a ions. I is gene a ed andomly, ha ing in o accoun he
cons ain s o bo h he nodes and modes ec o s.
A.2.2 E alua ion unc ion
The e alua ion unc ion assesses he i ness o each indi idual in he popula ion. This unc ion is c ucial as i de e mines how well an indi idual
sol es he p oblem a hand. The i ness e alua ion conside s bo h he nodes ec o and he modes ec o , ensu ing ha he solu ion espec s he unique
cons ain s o each ec o . The p ocess in ol es gene a ing ou es, esol ing he ou es o compu e objec i es and penal ies, and summa ising he
o e all i ness sco e. Highe i ness alues indica e be e solu ions, guiding he selec ion p ocess o u u e gene a ions.
Algo i hm 3 GASGA E alua ion Func ion
1: Recei e indi idual
2: Copy nodes and modes ec o s om he indi idual
3: Inse s a ing and ending poin s in o he ec o s
4: Gene a e ou es o he ehicles using he nodes and modes ec o s
5: Resol e he ou es o compu e he objec i e alue and penal ies
6: Compu e he o e all i ness sco e based on objec i e and penal ies
7: Assign he i ness sco e o he indi idual
8: end unc ion
A.2.3 Hall o ame ini ialisa ion
The hall o ame is ini ialised o keep ack o he bes indi iduals encoun e ed du ing he e olu iona y p ocess. This mechanism ensu es ha he
highes quali y solu ions a e p ese ed and a ailable o compa ison agains cu en popula ion membe s. The hall o ame p o ides a way o moni o
he p og ess o he algo i hm and gua an ees ha he bes solu ion ound can be e u ned a he end o he p ocess. I s ini ialisa ion is as s aigh -
o wa d as c ea ing an emp y lis .
A.2.4 Main e olu ion loop
The main e olu ion loop is he co e o he GASGA algo i hm, whe e he e olu iona y p ocess i e a es h ough gene a ions. In each i e a ion,
pa en s a e selec ed using a s ochas ic selec ion me hod, and o sp ing a e gene a ed h ough c osso e and mu a ion ope a ions. The new o sp ing
a e hen e alua ed, and he popula ion is upda ed. The hall o ame is also upda ed wi h he bes indi iduals om he cu en gene a ion. This loop
con inues un il a e mina ion condi ion is me .
Algo i hm 4. GASGA Main E olu ion Loop
1:while elapsed_ ime < ime_limi do
2: Selec pa en s om popula ion using s ochas ic selec ion me hod
3: Ini ialise o sp ing as an emp y lis
4: o each pai o pa en s do
5: De e mine ec o ype (nodes o modes) o c osso e and mu a ion
6: Selec app op ia e c osso e ope a o based on ec o ype
7: Apply c osso e o p oduce child en wi h p obabili y cxpb
8: Selec app op ia e mu a ion ope a o based on ec o ype
9: Apply mu a ion o child en wi h p obabili y mu pb
10: Add modi ied child en o o sp ing
11: end o
12: E alua e o sp ing
13: Upda e popula ion wi h o sp ing
14: Upda e hall o ame wi h bes indi iduals om cu en gene a ion
15: Adjus c osso e _p ob and mu a ion_p ob based on pe o mance
16:end while
A.2.5 Adap i e mechanism
The adap i e mechanism dynamically adjus s he p obabili ies o c osso e and mu a ion based on he e olu iona y con ex . I he algo i hm
de ec s s agna ion o insu icien p og ess, i inc eases hese p obabili ies o injec mo e di e si y in o he popula ion and encou age b oade
explo a ion. Con e sely, i imp o emen s a e consis en ly being made, i educes hese p obabili ies o allow o mo e in ensi e exploi a ion o
p omising a eas o he solu ion space. This sel - uning capabili y ensu es a balanced app oach o explo a ion and exploi a ion h oughou he
e olu iona y p ocess.
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Expe Sys ems Wi h Applica ions 272 (2025) 126757
23
Algo i hm 5. GASGA Adap i e Mechanism
1:i s agna ion_de ec ed o insu icien _p og ess hen
2: Inc ease c osso e _p ob and mu a ion_p ob
3:else i consis en _imp o emen hen
4: Dec ease c osso e _p ob and mu a ion_p ob
5:end i
A.3 Randomised deep sea ch in eg a ion
An in-dep h look a he Randomised Deep Sea ch heu is ic and i s in eg a ion in o GASGA.
A.3.1 Randomised deep sea ch
The Randomised Deep Sea ch heu is ic is a sophis ica ed sea ch s a egy designed o enhance he GASGA algo i hm’s e iciency. I in oduces
p oblem-speci ic knowledge and s a egies in o he e olu iona y p ocess, enabling mo e e ec i e na iga ion h ough challenging egions o he sea ch
space. This heu is ic is condi ionally applied, depending on speci ic c i e ia wi hin he e olu iona y loop, ensu ing ha i complemen s he gene ic
ope a ions wi hou domina ing hem. Check Algo i hm 2 in he pape o he Randomised Deep Sea ch pseudocode.
A.3.2 Condi ional applica ion
The condi ional applica ion o he Randomised Deep Sea ch heu is ic ensu es ha i is used judiciously wi hin he main GASGA loop. The heu is ic
is igge ed based on ce ain condi ions, such as s agna ion in he e olu iona y p og ess, speci ic pe o mance h esholds o wi h a ce ain p obabili y.
This s a egic applica ion helps he algo i hm escape local op ima and explo e mo e di e se solu ion spaces, imp o ing he o e all quali y o he
solu ions ound.
A.4 C osso e and mu a ion ope a o s
De ail o he a ious ailo ed c osso e and mu a ion ope a o s used in GASGA.
A.4.1 Tailo ed O de ed c osso e (OX)
Used o he nodes ec o o ensu e ha he pe mu a ion p ope y is main ained. This ope a o swaps sub sequences be ween wo pa en in-
di iduals, p oducing o sp ing ha inhe i he sequence s uc u e while p ese ing uniqueness.
The ailo ed OX main ains he co e idea o selec ing wo c osso e poin s and copying he segmen be ween hem om one pa en o he o sp ing.
Addi ionally, i uses a unc ion o ensu e he es o he posi ions a e illed wi h genes om he o he pa en while p ese ing he o de and a oiding
duplica es.
This ailo ed app oach emphasises main aining he pe mu a ion p ope ies and handles he complexi y o illing he emaining posi ions explici ly.
A.4.2 Tailo ed Pa ially Ma ched c osso e (PMX)
Ano he ope a o o he nodes ec o ha ensu es pe mu a ions a e p ese ed. I swaps segmen s be ween pa en s and maps emaining elemen s
o main ain he sequence’s alidi y.
The ailo ed PMX ollows he same ini ial s eps o selec ing wo c osso e poin s and copying he segmen . I includes an explici unc ion o handle
he mapping o alues be ween he pa en s, ensu ing ha con lic s a e esol ed, and no duplica es a e p esen in he o sp ing.
The ailo ed e sion places a clea emphasis on he p ocess o swapping alues o main ain pe mu a ion p ope ies, p o iding a s uc u ed way o
manage con lic s.
A.4.3 Tailo ed uni o m pa ially ma ched c osso e (UPMX)
This c osso e ope a o andomly selec s elemen s o swap be ween pa en s, p ese ing he pe mu a ion p ope y and c ea ing di e se o sp ing.
The ailo ed UPMX applies a p obabili y o decide whe he o swap each gene.
I also includes an explici unc ion o manage he swapping p ocess, ensu ing ha he pe mu a ion p ope ies a e p ese ed, and no duplica es a e
in oduced. This ailo ed app oach emphasises main aining he in eg i y o he sequence by using s uc u ed swapping o alues, p o iding cla i y and
consis ency.
A.4.4 Non- ailo ed wo poin mu a ion
Applied o he modes ec o , allowing changes a wo andomly selec ed posi ions. This ope a o in oduces a iabili y wi hou iola ing he
ec o ’s epe i ion cons ain s.
A.4.5 Non- ailo ed uni o m mu a ion
Randomly al e s elemen s in he modes ec o , in oducing new alues while espec ing he ec o ’s cha ac e is ics. This mu a ion helps explo e
di e en combina ions o modes.
A.5 Summa y and conclusion
The Gene ic Algo i hm Sanchez-Gonzalez-And ade (GASGA) ep esen s a signi ican ad ancemen in he ield o gene ic algo i hms, pa icula ly
o complex op imisa ion p oblems ha bene i om a dual- ec o ep esen a ion. This annex has de ailed he a ious componen s and inno a i e
ea u es o he GASGA algo i hm, p o iding a comp ehensi e unde s anding o i s implemen a ion and unc ionali y. Key poin s o he GASGA al-
go i hm include:
D. Sanchez-Wells e al.
Expe Sys ems Wi h Applica ions 272 (2025) 126757
24
•Dual-Vec o Rep esen a ion
•Specialised Gene ic Ope a o s
•Dynamic C osso e and Mu a ion S a egies
•Adap i e Mechanism
•Randomised Deep Sea ch In eg a ion
In conclusion, GASGA’s inno a i e aspec s— om i s dual- ec o indi idual ep esen a ion and dynamic ope a o selec ion o i s adap i e gene ic
ope a ions and he in eg a ion o deep sea ch heu is ics—collec i ely con ibu e o a highly adap able and e icien algo i hm. GASGA is adep a
ackling complex op imisa ion p oblems by balancing nuanced solu ion space explo a ion wi h a ge ed exploi a ion and p oblem-speci ic in-
e en ions. These ea u es enhance he algo i hm’s abili y o deli e high-quali y solu ions, making i an in aluable ool in gene ic algo i hm esea ch
and op imisa ion.
By p o iding a de ailed code-based explana ion o GASGA, his annex ensu es ha eade s can ully unde s and and implemen he algo i hm,
app ecia ing i s sophis ica ed design and p ac ical applica ions. The de ailed explana ions and examples se e as a comp ehensi e guide, acili a ing a
deepe g asp o GASGA’s mechanisms and bene i s.
Da a a ailabili y
Da a has been sha ed in a link in he Expe imen a ion sec ion.
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