Electric vehicle charge optimization using ant colony optimization

MÁSTER UNIVERSITARIO EN
In eg ación de las Ene gías Reno ables en el Sis ema Eléc ico
TRABAJO FIN DE MÁSTER
Elec ic Vehicle cha ge op imiza ion using An Colony
Op imiza ion
Es udian e A ano, Muñoz, Jokin
Di ec o /di ec o a Aba a egi Rane o, Oihane
Depa amen o Ingenie ía Eléc ica
Cu so académico 2022-2023
Bilbao, 12, 07, 2023
Table o con en s
1 In oducción ........................................................................................................... 1
2 Con ex ................................................................................................................... 1
3 Objec i es and Scope o Wo k ............................................................................... 2
4 Bene i s o he wo k ............................................................................................... 3
5 S a e o a .............................................................................................................. 3
5.1 De e minis ic Algo i hms ................................................................................ 4
5.1.1 Linea op imiza ion .................................................................................. 5
5.1.2 Non-linea op imiza ion ........................................................................... 6
5.1.3 G adien based algo i hms........................................................................ 7
5.1.4 De i a i e ee algo i hms ........................................................................ 7
5.2 S ochas ic Algo i hms ..................................................................................... 7
5.2.1 Heu is ic algo i hms ................................................................................. 8
5.2.2 Me a-heu is ic algo i hms ...................................................................... 10
6 Desc ip ion o he solu ion .................................................................................... 23
6.1 P oblem de ini ion ........................................................................................ 23
6.2 Benchma k de ini ion .................................................................................... 27
6.3 Adap ed ACO algo i hm o EV cha ging ..................................................... 31
6.3.1 Ge in o ma ion o each ca .................................................................... 33
6.3.2 Ini ialize ACO pa ame e s and phe omone and i ness ma ices ............. 34
6.3.3 Loca e an s andomly ............................................................................. 34
6.3.4 An Colony Op imiza ion: S a e T ansi ion Rule and Global Phe omone
Upda ing Rule. ..................................................................................................... 35
7 Resul s .................................................................................................................. 36
7.1 In luence o q0 .............................................................................................. 38
7.2 In luence o ρ ................................................................................................ 41
7.3 In luence o β / α ........................................................................................... 45
7.4 Bes Solu ion pa ame e s............................................................................... 46
8 Conclusions & u u e wo k ................................................................................... 47
9 Bibliog aphy ......................................................................................................... 49
Lis o illus a ions
Figu e 1. Classi ica ion o op imiza ion algo i hms [10] ................................................ 4
Figu e 2. Rep esen a ion o a lineal op imiza ion. [13] .................................................. 6
Figu e 3. Rep esen a ion o a non-linea op imiza ion [14] ............................................ 6
Figu e 4. Heu is ic p ocedu e [36] ................................................................................. 9
Figu e 5. Admissible and non-admissible heu is ic unc ions ........................................ 9
Figu e 6. Ini ial posi ion o he pa icle [20] ................................................................ 13
Figu e 7. Posi ion upda ed.[20] ................................................................................... 13
Figu e 8.P ocess low o pa icle swa m op imiza ion [28] .......................................... 14
Figu e 9. Gene ic algo i hm p ocess ............................................................................ 15
Figu e 10. Desc ip ion o BCO [23] ............................................................................ 16
Figu e 11. P ocedu e BCO algo i hms [37] ................................................................. 17
Figu e 12. ACO algo i hm example 1 [22] .................................................................. 20
Figu e 13. ACO algo i hm example 2 [22] .................................................................. 20
Figu e 14. ACO algo i hm example 3 [22] .................................................................. 20
Figu e 15. ASD 17 Goals [30] .................................................................................... 23
Figu e 16. New egis a ions o elec ic ca s in eu ma ke [34] .................................... 24
Figu e 17. A gene al s uc u e o a cha ging s a ion wi h h ee lines and mul iple
cha ging poin s (o pa king slo s). [3] .......................................................................... 27
Figu e 18 G aphical diag am EVs a i al ime ............................................................ 29
Figu e 19 G aphical diag am o he able 2 .................................................................. 30
Figu e 20 G aphical diag am o he able 3 .................................................................. 31
Figu e 21. Pseudocode o ACO algo i hm ................................................................... 32
Figu e 23. New dis ibu ion o due da e....................................................................... 33
Figu e 24. cumula i e equency o exploi a ion and explo a ion ................................. 36
Figu e 24. In luence o q0 in he esul s ...................................................................... 40
Figu e 25. Final phe omone ma ixes. ......................................................................... 41
Figu e 26. In luence o ρ in he esul s ........................................................................ 43
Figu e 27. Final phe omone ma ixes .......................................................................... 44
Figu e 28. In luence o β / α in he esul s ................................................................... 46
Lis o ables
Table 1 a i al ime dis ibu ion .................................................................................. 29
Table 2 ini ial cha ge dis ibu ion ................................................................................ 29
Table 3 Due da es dis ibu ion ..................................................................................... 30
Table 4. In o ma ion o each ca a i ing a he cha ging s a ion ................................. 37
Table 5. S anda d alues o ACO. .............................................................................. 38
Table 6. In luence o q0 in he esul s .......................................................................... 38
Table 7. In luence o ρ in he esul s............................................................................ 42
Table 8. In luence o β / α in he esul s....................................................................... 45
Table 9. Pa ame e s alue which GIVES he bes solu ion........................................... 47
Lis o Equa ion
(1) ............................................................................................................................... 13
(2) ............................................................................................................................... 17
(3) ............................................................................................................................... 18
(4) ............................................................................................................................... 18
(5) ............................................................................................................................... 18
(6) ............................................................................................................................... 22
(7) ............................................................................................................................... 22
(8) ............................................................................................................................... 22
(9) ............................................................................................................................... 22
(10) ............................................................................................................................. 22
(11) ............................................................................................................................. 27
(12) ............................................................................................................................. 28
(13) ............................................................................................................................. 28
(14) ............................................................................................................................. 28
(15) ............................................................................................................................. 28
(16) ............................................................................................................................. 34
1
1 In oducción
In his p ojec , we a e going o in es iga e a opic ha will be o g ea impo ance in he
coming yea s, such as he managemen o he cha ging o elec ic ca s. I is no hing new
ha he end in he au omo i e sec o is owa ds a u u e in which elec ic ehicles will
p edomina e, which can be a p oblem o he cu en elec ici y g id due o he inc ease
in ene gy demand p oduced by he cha ging o hese ca s. The e o e, i is necessa y o
in es iga e di e en cha ging me hods in o de no o sa u a e he g id.
In his wo k, esea ch has been ca ied ou abou he p oblem men ioned abo e, p oposing
an op imiza ion algo i hm which is able o manage he cha ging p ocess o a lee o ca s
in a cha ging ca pa k o elec ic ca s, based on he pape " Elec ic ehicle cha ging
unde powe and balance cons ain s as dynamic scheduling" [7].
In he i s pa o he wo k, an ex ensi e s a e o he a abou he mos impo an
op imisa ion algo i hms in use oday is made, explaining wha hey a e based on and
gi ing a b ie explana ion o how hey wo k.
Then, he p oblem ha has been in es iga ed wi h his wo k is desc ibed, he op imisa ion
o he elec ic ca cha ging using he an colony algo i hm (ACO). In addi ion, he esul s
ob ained a e analysed and he pa s o he wo k ha can be imp o ed in u u e p ojec s
ela ed o his opic a e de ailed. Finally, he conclusions ob ained a e gi en.
2 Con ex
In ecen yea s, he e has been a signi ican inc ease in he use o elec ic ca s, d i en
mainly by g owing conce n abou clima e change and he need o educe g eenhouse gas
emissions p oduced by in e nal combus ion ehicles.
The anspo sec o in one o he la ges con ibu o s o global g eenhouse gas emission.
Acco ding o EEA (Eu opean En i onmen Agency), “ he ecen ly p oposed legisla ion
(Fi o 55) se s a ge s o cu CO2 emissions om ca s by 55% and ans by 50% by
2030 (EU, 2021). I also p oposes o comple ely cu emissions om ca s and ans by
2035.
Elec ic ca s (EVs) a e a mo e sus ainable and en i onmen ally iendly al e na i e o
pe ol o diesel-powe ed ehicles, as hey do no emi ha m ul exhaus gases and a e mo e
ene gy e icien . In addi ion, ba e y echnology has imp o ed signi ican ly in ecen
yea s, making elec ic ca s inc easingly longe ange and mo e a o dable. Thus, “a
signi ican inc ease in he up ake o EVs will be needed o achie e hese goals” [1]. Fo
his eason, he numbe o cha ging poin s o elec ic ca s will inc ease d as ically in he
nex ew yea s, c ea ing a p oblem when i comes o managing he ne wo k o cha ging
hem.
Howe e , he in eg a ion o elec ic ca s in o he elec ici y g id poses some challenges.
In pa icula , cha ging elec ic ehicles can signi ican ly inc ease elec ici y demand a

2
peak imes, such as du ing peak hou s, which can o e load he g id and cause powe
ou ages. In addi ion, cha ging many elec ic ehicles in a concen a ed a ea can equi e
cos ly upg ades o he local g id in as uc u e o handle he addi ional load.
In o de o igh his issue, new echnology is equi ed, such as inc easing he capaci y
and li e ime o elec ic ca ba e ies and inc easing he speed o cha ging hem. Besides,
echnical solu ions a e being implemen ed, such as sma cha ging, which allows cha ging
speed o be adjus ed based on he capaci y o he elec ici y g id a he ime. In addi ion
o imp o ing he elec onics ha make up elec ic ca s and hei espec i e cha ge s, i is
necessa y o con ol he cha ging p ocess. “Se e al s udies ha e shown ha when he
EVs’ cha ging p ocess is no p ope ly coo dina ed in a cha ging s a ion, se e al p oblems
may occu , such as inc ease in he peak load pe iod, dec ease in se ice quali y,
deg ada ion o he ol age p o ile, o e load o ci cui s, and inc ease in ene gy losses” [5].
So, in o de o a oid he p oblems men ioned abo e, scheduling he cha ging o EV`s in
an e icien way is c ucial.
In his p ojec , he p oblem o coo dina ing he cha ging p ocess o elec ic ca s in a
pa king lo will be add essed.
3 Objec i es and Scope o Wo k
The main objec i e o his wo k is o add ess a opic ha is cu en ly gi ing a lo o alk
abou , such as he cha ging o elec ic ehicles. In o de o achie e his, he ollowing
objec i es a e es ablished:
The i s objec i e is o ho oughly analyse and unde s and he con ex and cha ac e is ics
ela ed o he di e en op imisa ion algo i hms ha ac ually exis . This in ol es a de ailed
e iew o he exis ing scien i ic and echnical li e a u e, as well as he iden i ica ion o
cu en ends, de elopmen s and challenges in he ield.
Fu he mo e, ano he objec i e is o ocus on he implemen a ion and ope a ionalisa ion
o he p oposed me hodology. This will in ol e he use o ele an ools, echniques o
expe imen s o ob ain conc e e da a and esul s ha con ibu e o knowledge and add
alue in he ield o EV cha ging.
The scope o his wo k is limi ed o, on he one hand, analysing he di e en op imisa ion
algo i hms ha exis , and, on he o he hand, using one o hem o op imise he p oblem
se ou in he p ojec .
3
4 Bene i s o he wo k
This Mas e 's hesis p o ides a numbe o signi ican bene i s and con ibu ions in he
ield o EV cha ging.
Fi s ly, his wo k con ibu es o he ad ancemen o knowledge in he ield o EV load
op imisa ion. By comp ehensi ely e iewing he exis ing li e a u e and conduc ing
empi ical esea ch, i is hoped o gain a be e unde s anding o he di e en al e na i es
ha exis o sol e p oblems in he ield, p o iding a solid basis o u u e esea ch and
de elopmen .
In addi ion, he me hodology de eloped in his wo k has an impo an p ac ical
applica ion, so ha he algo i hm could be implemen ed in a eal p oblem.
In e ms o social and economic impac , he indings and conclusions o his wo k a e
expec ed o gene a e bene i s in he ansi ion o EV. These bene i s can be economic,
social and en i onmen al, and will con ibu e o imp o ing people's quali y o li e and
sus ainable de elopmen .
Finally, he esul s and conclusions o his wo k will p o ide a solid basis o in o med
decision making in he ield o EV load op imisa ion. I will enable key s akeholde s o
use he in o ma ion and ecommenda ions de i ed om his wo k o mo e e ec i ely
add ess u u e EV load op imisa ion p ojec s.
5 S a e o a
This sec ion p o ides a comp ehensi e e iew o esea ch dealing wi h he elec ic
ehicle cha ging scheduling using di e en op imiza ion algo i hms. In o de o highligh
he lack o in o ma ion ega ding he di e en ypes o op imisa ion algo i hms used o
sol e his ask, a compila ion will be made o wha ype o algo i hms ha e been used so
a in he di e en s udies ca ied ou .
Op imiza ion algo i hms a e used in all kinds o ields such as enginee ing, medicine,
economics... in o de o ind he bes solu ion o a gi en p oblem. So, depending on he
p oblem o be sol ed, di e en ypes o hem can be used. Figu e 1 shows he
classi ica ion o he di e en ypes o algo i hms ha a e used oday o sol e di e en
4
p oblems, and al hough in he s udy o he elec ic ca cha ging p oblem only one will be
used, his wo k will make a b ie desc ip ion o each o hem.
FIGURE 1. CLASSIFICATION OF OPTIMIZATION ALGORITHMS [10]
As can be seen in Figu e 1, he op imiza ion algo i hms can be clea ly classi ied in o
wo ca ego ies. On one side, he de e minis ic algo i hms and on he o he , he
s ochas ic algo i hms. In sho , de e minis ic algo i hms allow a u u e e en o be
calcula ed p ecisely, wi hou he in ol emen o andomness. Howe e , a s ochas ic
algo i hm can handle unce ain ies in he inpu s applied [11]. In o he wo ds, i
some hing is de e minis ic, you ha e all o he da a necessa y o p edic (de e mine) he
ou come wi h ce ain y whils S ochas ic models possess some inhe en andomness -
he same se o pa ame e alues and ini ial condi ions will lead o an ensemble o
di e en ou pu s. A e wa ds, each one has di e en ypes, which will be b ie ly
explained below.
5.1 De e minis ic Algo i hms
De e minis ic algo i hms a e he classical b anch o op imisa ion algo i hms in
ma hema ics. They a e usually based la gely on linea algeb a, ei he based on g adien
compu a ion o in some cases on hessian calculus. Compa ed o s ochas ic algo i hms,
hey ha e he ad an age o con e ging as e , namely hey equi e ewe i e a ions han
s ochas ic algo i hms o each a solu ion.
These ypes o op imiza ion models a e based, as men ioned abo e, in igo ous
ma hema ical o mula ion wi hou in ol ing s ochas ic elemen s. Tha is why he esul s
achie ed a e eplicable and unequi ocal. Ne e heless, his does no mean ha s ochas ic
models canno p o ide same quali y solu ions. In e ms o me hod o ope a ion,
5
de e minis ic algo i hms ocus on inding s a iona y poin s in he esponse a iable,
hence, he bes solu ion ound could be he local bes and no he global bes . Besides,
hese algo i hms a e usually single objec i e. [12]
In an op imisa ion p ocess, elemen s mus be es ablished in o de o ind he igh solu ion.
I is necessa y o choose a sample o a g oup o samples om which o s a , as well as a
s opping c i e ion. By easible sample we mean an assignmen o each inpu a iable so
ha all he cons ain s o he p oblem a e sa is ied and as a s opping c i e ion we e e o
a condi ion ha once ul illed, leads o he co ec solu ion.
In he ollowing sec ions, di e en ypes o de e minis ic algo i hms will be explained.
5.1.1 Linea op imiza ion
Linea op imiza ion, also known as linea p og amming (LP) is a ma hema ical p ocedu e
o algo i hm used o sol e an inde e mina e p oblem, o mula ed h ough a sys em o
linea inequali ies, op imising he objec i e unc ion, which is also linea . I consis s o
op imising (minimising o maximising) a linea unc ion, called he objec i e unc ion, in
such a way ha he a iables o his unc ion a e subjec o a se ies o es ic ions ha we
exp ess by means o a sys em o linea inequali ies.
Any LP p oblem consis s o an objec i e unc ion and a se o cons ain s. In mos cases,
he cons ain s come om he en i onmen in which you objec i e is loca ed. I.e., when
an objec i e wan s o be achie ed, some cons ain will be se by he en i onmen o
achie e he goal.
In o de o a be e unde s anding, an example is gi en below. Imagine a ca pen e who
sells ables and chai s and wan s o maximise his income. In his case, i he sells each
chai (x2) o 3 eu os and each able (x1) o 5 eu os, he objec i e unc ion would be as
shown equa ion (1). The cons ain s a e se by ex e nal ac o s such as wo king ime and
aw ma e ial limi a ions (equa ions (2) and (3) espec i ely). The p oduc ion ime o a
able is 2 hou s and o he chai s 1 hou . Besides, he aw ma e ial equi ed o build a
able and a chai a e 1 uni and 2 uni s espec i ely. Besides, i is assumed ha X1 and
X2 a e bo h posi i e alues.
𝑂𝑏𝑗𝑒𝑡𝑖𝑣𝑒 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛: 5 ∙𝑥1 +3 ∙𝑥2 (1)
𝐶𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡 1→ 2 ∙𝑥1 +𝑥2≤40 (2)
𝐶𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡 2→ 𝑥1 + 2 ∙ 𝑥2≤50 (3)
One’s equa ions (1), (2) and (3) a e de ined, i is possible o ind op imal solu ion o he
p oblem. In he ollowing Figu e 2 a g aphical ep esen a ion o he p oblem can be seen.
12
5.2.2.1.1 PSO p og amming
E en i he e a e a ia ions, he s uc u e o a PSO algo i hm o op imise (maximise o
minimise) a unc ion wi h one o mul iple a iables ollows hese s eps:
1. C ea e an ini ial swa m o n andom pa icles. Each pa icle consis s o 4 elemen s:
a posi ion ep esen ing a ce ain combina ion o alues o he a iables, he alue
o he objec i e unc ion a he posi ion whe e he pa icle is loca ed, a eloci y
indica ing how and whe e he pa icle is mo ing, and a eco d o he bes posi ion
he pa icle has been in so a .
Each pa icle is de ined by a posi ion, eloci y and alue ha change as he
pa icle mo es. In addi ion, i also s o es he bes posi ion i has been in so a .
When a new pa icle is c ea ed, only in o ma ion abou i s posi ion and eloci y
(usually ini ialised as ze o) is known, all o he alues a e no known un il he
pa icle is e alua ed.
2. E alua e each pa icle wi h he objec i e unc ion.
E alua ing a pa icle consis s o calcula ing he alue o he objec i e unc ion a
he pa icle's cu en posi ion. Each pa icle also s o es he bes - alued posi ion i
has been in so a . In o de o iden i y whe he a new posi ion is be e han he
p e ious ones, i is necessa y o know whe he i is a minimisa ion o
maximisa ion p oblem.
3. Upda e he posi ion and eloci y o each pa icle
Mo ing a pa icle in ol es upda ing i s eloci y and posi ion. This s ep is he mos
impo an as i gi es he algo i hm he abili y o op imise.
4. I a s op c i e ion is no me , e u n o s ep 2
Each pa icle (indi idual) has a posi ion 𝑝, and a eloci y 𝑣 which de e mines i
mo emen h ough he space. In addi ion, as eal-wo ld physical pa icles, hey ha e an
amoun o ine ia, which keeps hem in he same di ec ion in which hey we e mo ing, as
well as an accele a ion (change in eloci y), which depends mainly on wo cha ac e is ics:
• Each pa icle is a ac ed o he bes loca ion ha i , pe sonally, has ound in i s
his o y (pe sonal bes ).
• Each pa icle is a ac ed o he bes loca ion ha has been ound by he se o
pa icles in he sea ch space (global bes ).

13
FIGURE 6. INITIAL POSITION OF THE PARTICLE [20]
The o ce wi h which he pa icles a e pushed in each o hese di ec ions depends on wo
pa ame e s ha can be adjus ed (a ac ion- o-bes -pe sonal and a ac ion- o-bes -global)
so ha , as he pa icles mo e away om hese bes loca ions, he o ce o a ac ion is
g ea e . Once he eloci ies a e upda ed, hei posi ions also upda e ollowing he nex
equa ion (1).
pi( +1)=pi( )+ i( )
(1)
FIGURE 7. POSITION UPDATED.[20]
Once he heo y o his algo i hm is explained, o ge a be e iew o how he algo i hm
wo ks and wha sequence i ollows, he ollowing block diag am has been used.
14
FIGURE 8.PROCESS FLOW OF PARTICLE SWARM OPTIMIZATION [28]
5.2.2.2 Gene ic algo i hms
Gene ic algo i hms (GA )we e de eloped in he 1960s and became popula h ough he
wo k o Holland and his s uden Goldbe g. GAs ep esen s a di e en app oach o
e olu iona y compu a ion in which he e olu ion o a popula ion is mainly due o he
e ec o a c oss-o e ope a o . In gene al, he inpu a iables a e encoded in o bina y
s ings, al hough GAs using eal- alued inpu a iables also exis [12].
Gi en a speci ic p oblem o be sol ed, he inpu s o he GA a e a se o po en ial solu ions
o ha p oblem, coded in some way, and a me ic called i ness unc ion, which allows
each candida e solu ion o be quan i a i ely e alua ed. These candida es can be solu ions
ha a e al eady known o wo k, wi h he goal o being imp o ed by he GA, bu hey a e
usually gene a ed andomly.
F om he e, GA e alua es each candida e acco ding o he i ness unc ion. O cou se, i
should be no ed ha hese i s andomly gene a ed candida es will ha e minimal
e iciency by he ime o sol e he p oblem, and mos will no wo k a all. Howe e ,
casually, a ew may be p omising, and may show some cha ac e is ics ha show, e en i
only in a weak and impe ec way, some abili y o sol e he p oblem.
These p omising candida es a e e ained and allowed o ep oduce. Mul iple copies o
hem a e made, bu hese copies a e no pe ec . Ins ead, some andom changes a e
in oduced du ing he copying p ocess, like he mu a ions ha can occu in he o sp ing
o a popula ion. These digi al o sp ing a e hen passed on o he nex gene a ion, o ming
15
a new se o candida e solu ions, and a e again subjec ed o a ound o i ness e alua ion.
Candida es ha ha e wo sened o no imp o ed wi h changes in hei code a e elimina ed
again; bu again, by pu e chance, andom a ia ions in oduced in o he popula ion may
ha e imp o ed some indi iduals, making hem be e , mo e comple e o mo e e icien
solu ions o he p oblem. The p ocess is epea ed as many i e a ions as necessa y, un il
we ge solu ions good enough o ou pu poses [20]. The p ocess has been schema ized
in he ollowing Figu e 9.
FIGURE 9. GENETIC ALGORITHM PROCESS
5.2.2.3 Bee colony op imiza ion
The a i icial bee colony (BCO) algo i hm is one o he mos ecen algo i hms in he
domain o collec i e in elligence. I was p oposed by De is Ka aboga in 2005, and i is
based on he beha iou o he bees when hey a e looking o ood sou ces. I is a
popula ion-inspi ed op imisa ion algo i hm, whe e he solu ions o he op imisa ion
p oblem a e he ood sou ces. The goal o hese bees is o disco e he ood sou ces wi h
he mos amoun o nec a .
5.2.2.3.1 BCO heo y
The p ocess o nec a o aging by bees is an op imisa ion p ocess, and he beha iou o
bees was modelled as a heu is ic op imisa ion based on he biological model consis ing
o he ollowing elemen s [23]:
• Food sou ce: he alue o a ood sou ce depends on many ac o s, such as
p oximi y o he hi e, ichness o concen a ion o ene gy and ease o ex ac ion
o his ene gy. I is summa ised in a nume ical alue ha indica es he po en ial
o he ood sou ce.
• Employed o age bees: a e associa ed wi h a ood sou ce. They ca y wi h hem
in o ma ion abou ha pa icula sou ce, i s dis ance, loca ion and p o i abili y o
sha e wi h he obse e bees.
16
• Unemployed o age bees: hese bees a e looking o ood sou ces o exploi .
The e a e wo ypes:
o Explo e s: hey a e esponsible o sea ching o new ood sou ces in he
en i onmen su ounding he hi e. Tha is, hey ca y in o ma ion abou a
speci ic sou ce and sha e i wi h o he bees wai ing in he hi e. The
in o ma ion includes he dis ance, di ec ion and nec a o he ood sou ce.
o Obse e s: Wi h in o ma ion sha ed by employees o o he scou s in he
nes , hey sea ch o a ood sou ce.
The employed bees communica e he in o ma ion abou he ood sou ce hey a e
exploi ing o he obse e bees by means o a dance, whe e he angle o he sun indica es
he di ec ion o he sou ce and a zigzag indica es he dis ance. The dances wi h he longes
du a ion desc ibe he mos p o i able ood sou ces mos likely o be chosen by he
obse e bees. Once ood sou ces ha e been deple ed, hey a e abandoned and eplaced
by new sou ces ound by scou bees.
FIGURE 10. DESCRIPTION OF BCO [23]
Figu e 10 shows he used bees assigned o a ood sou ce (1). Then (2) shows he
communica ion o ood sou ce in o ma ion by means o a dance, and he obse e bees
isi he mos p omising ood sou ces (3). And inally, he scou bees sea ch o new
sou ces (4).
17
5.2.2.3.2 BCO P og amming
Simila o o he me aheu is ic app oaches, he BCO algo i hm pe o ms an i e a i e
p ocess which is epea ed o a ce ain numbe o i e a ions (NG). I s a s wi h a
popula ion o solu ion o ood sou ces, which a e andomly gene a ed. Then, he nex
h ee ope a ions a e applied un il a s opping c i e ion is eached.
1. Send ou employed bees
2. Selec ion o ood sou ces by onlooke bees
3. De e mine which bees will be scou bees
No mally, hese algo i hms ollow he p ocedu e o he Figu e 11. Howe e , he
p og amming o he algo i hm is explained below. [27]
FIGURE 11. PROCEDURE BCO ALGORITHMS [37]
• Ini ializa ion phase.
The algo i hm s a s by ini ializing Np ood sou ces. Each ood sou ce, is
cha ac e ised by a ec o o D elemen s, which ep esen he decision a iables.
These a iables a e andomly gene a ed be ween he lowe 𝑥𝑗𝑙𝑜𝑤 and uppe
𝑥𝑗ℎ𝑖𝑔ℎ limi s, p e iously de ined. (2)
𝑥𝑗,𝑖= 𝑥𝑗𝑙𝑜𝑤+𝑟𝑎𝑛𝑑(0,1)∗(𝑥𝑗ℎ𝑖𝑔ℎ−𝑥𝑗𝑙𝑜𝑤)
(2)
𝑗=1,2…𝐷
𝑖=1,2…Np
Whe e j and i a e he indices o he pa ame e and popula ion espec i ely.
The e o e, 𝑥𝑗,𝑖 is he j- h pa ame e o he i- h indi idual.

18
• Send employed bees.
In his phase, each employed bee sea ches o a new ood sou ce, as ollows:
𝑣𝑗,𝑖= 𝑥𝑗,𝑖+ 𝜙𝑗,𝑖∗(𝑥𝑗,𝑖−𝑥𝑗,𝑘)
𝑘=1,2…Np
𝑗=1,2…𝐷
(3)
Whe e 𝑥𝑗,𝑖 is a pa ame e j andomly selec ed om he i- h indi idual and k is one
o he Np ood sou ces, sa is ying he condi ion i≠k. I a gi en pa ame e o he
candida e solu ion 𝑣𝑗,𝑖 exceeds i s p ede e mined bounds, ha pa ame e mus be
adjus ed so ha i is in he de ined ange. 𝜙𝑗,𝑖 is a andom numbe wi hing he
ange [-1,1]. Once a new solu ion has been gene a ed, i s quali y is calcula ed
using an objec i e unc ion. The quali y i i o a candida e solu ion 𝑣𝑗,𝑖 is assigned
by he ollowing exp ession:
𝑓𝑖𝑡𝑖={1
1 + 𝐽(𝑉𝑖) 𝑖𝑓 𝐽(𝑉𝑖)≥0
1+ 𝐽(𝑉𝑖) 𝑖𝑓 𝐽(𝑉𝑖)<0
(4)
Whe e J is he objec i e unc ion o be minimized and 𝐽(𝑉𝑖) is he objec i e
unc ion alue o solu ion 𝑉𝑖.
• Food sou ce selec ion by onlooke bees.
The e a e wo di e en g oups wi hin he unemployed bees, onlooke and scou
bees. The i s ones, sha e hei ood sou ce in o ma ion wi h he onlooke bees,
which a e wai ing in he hi e. Then, each onlooke bee selec s one o he p oposed
ood sou ces depending on i s quali y. The p obabili y o a ood sou ce being
selec ed is ob ained om he ollowing equa ion:
𝑃𝑟𝑜𝑏𝑖=𝑓𝑖𝑡𝑖
∑𝑓𝑖𝑡𝑖
𝑁𝑝
𝑖=1
(5)
Whe e i i is he quali y alue o he i- ood sou ce. The p obabili y o a ood sou ce
being selec ed by an onlooke bee inc eases wi h an inc ease in he quali y alue
o he ood sou ce. A e he ood sou ce is chosen, he onlooke bees will go o
he selec ed posi ion and will de e mine a new candida e ood sou ce wi hin he
neighbou hood o he selec ed ood sou ce. Such posi ion is calcula ed by (3). In
19
case he quali y o he new solu ion is wo se han he p e ious one, i s posi ion is
main ained; o he wise, he las solu ion is eplaced.
• De e mine new scou bees
I a ood sou ce i (candida e solu ion) canno be pe o med wi hin a ce ain
numbe o L ials, he ood o sou ce is abandoned and he co esponding bee
become a scou bee. In o de o e i y i a candida e solu ion has eached he limi
L o ials, a coun e Ai is assigned o each ood sou ce i. This coun e is inc eased
as a consequence o a bee ope a ion ailing o imp o e he quali y o a solu ion.
In summa y he BCO algo i hm:
a) is inspi ed by he o aging beha iou o honeybees,
b) is a global op imiza ion algo i hm,
c) has been ini ially p oposed o nume ical op imiza ion
d) can be also used o combina o ial op imiza ion p oblems
e) can be used o uncons ained and cons ained op imiza ion p oblems
) employs only h ee con ol pa ame e s (popula ion size, maximum cycle numbe
and limi ) ha a e o be p ede e mined by he use . [26]
5.2.2.4 An colony op imiza ion
An Colony Op imiza ion (ACO) heo y was in oduced by Ma co Do igo in he ea ly
1990s as a ool o he solu ion o complex op imisa ion p oblems. The ACO belongs o
he class o heu is ic me hods, which a e app oxima e algo i hms used o ob ain good
solu ions o complex p oblems in a easonable amoun o compu ing ime. [21]
The sou ce o inspi a ion o ACO is he ac ual beha iou o an s. These insec s when
sea ching o ood ini ially explo e he a ea a ound hei nes in a andom way. As soon
as hey ind ood sou ces, hey assess hei quan i y and quali y, and ca y some o his
ood back o hei nes . On he way back o he nes , he an s deposi a chemical subs ance
called phe omone on he pa h, which will se e as a u u e guide o o he s o ind he
ood. The amoun o phe omone deposi ed will depend on he quan i y and quali y o
ood. This will help o ind he sho es ou es be ween hei nes and ood sou ces.
5.2.2.4.1 ACOs heo y.
In o de o unde s and how an s, use he pa h wi h he mos phe omones ( he sho es ) o
ind hei ood, he ollowing example i s desc ibed.
Conside he example illus a ed in Figu e 12, in which an s each a poin whe e hey
ha e o decide whe he o u n igh o le . As he e is ini ially no phe omone p esen on
20
he wo al e na i e pa hs, he choice is made andomly. I is es ima ed ha on a e age
hal o he an s u n le and he o he hal decide o u n igh . The c i e ium o name he
an s is by a le e (R o L) ollowed by a numbe . So, i an an u ned o he igh in he
i s o k, i will be named R1. [21]
FIGURE 12. ACO ALGORITHM EXAMPLE 1 [22]
Figu es 13 and 14 show wha happens in he ollowing ins an s, assuming ha all he an s
walk a he same speed. The numbe o do ed lines is p opo ional o he numbe o
phe omones he insec s ha e deposi ed on he g ound.
FIGURE 13. ACO ALGORITHM EXAMPLE 2 [22]
FIGURE 14. ACO ALGORITHM EXAMPLE 3 [22]
21
As he lowe pa h is sho e han he uppe pa h, many mo e an s will ansi he lowe
pa h du ing he same pe iod o ime. This implies ha he sho e pa h accumula es mo e
phe omone much as e . A e a ce ain ime, he di e ence in he amoun o phe omone
in he wo pa hs is la ge enough o in luence he decision o new an s o en e hese pa hs.
Gi en he abo e, new an s en e ing he sys em will p e e o choose he lowe pa h due
o hey pe cei e a highe amoun o phe omone he e.
5.2.2.4.2 ACO p og amming
Ha ing explained he beha iou o he an s in inding he sho es ou e o he ood sou ce,
i is ime o analyse how he algo i hm wo ks. Tha is why in his sec ion, he
p og amming code will be examined.
Fi s o all, he di e en pa ame e s o be used in he algo i hm will be de ined. They a e
he ollowing:
• Pk( ): The pa h ollowed by he an k. I is ime-dependen because i changes wi h
each i e a ion.
• G = (V, E): weigh ed g aph
• Ni: nodes a ailable om node i
• k=1,2 …N: Numbe o he an
• τ ij: Numbe o phe omones be ween pa hs i and j
• α: is a pa ame e o con ol he in luence o τ ij
• β: is a pa ame e o con ol he in luence o nij
• i,j: i is he ac ual node and j he ollowing node.
• dij: dis ance be ween nodes i and j.
• nij: is he desi abili y o edge i, j. Typically 1/ dij
• ρ: is he a e o phe omone e apo a ion
• ∆ τ ij: is he amoun o phe omone deposi ed by each an in he pa h i-j.
The ime ( ) inc eases once all he an s ind ood and e u n o he o igin ( → +1).
The algo i hm ollows he ollowing sequences:
1. =0, ini ialize he phe omones σij o e e y pa h a ailable wi h andomly gene a ed
small alues.
2. Loca e N an s a he sou ce node.
3. Repea
3.1. Fo each an k=1,2 …N
3.1.1. Pk( )=0. A he i s ins an , he pa h ollowed by each an is 0, because
he an has no ye mo ed.
3.1.2. Repea
28
j
(
|∑𝑥𝑗𝑖−∑𝑥𝑞𝑙
𝑃𝑖
𝑞=1
𝑃𝑖
𝑗=1 |
𝑁≤∆,i,l={1,...,L},i ≠ l
(12)
𝑥𝑗𝑖={1,i cha ging poin j on line i is ac i e;
0,o he wise;
(13)
Eq. (11) ensu es ha each line can only ha e N cha ging poin s ac i e o cha ge N EVs
a he same ime, Eq. (12) con ols he maximum imbalance be ween lines (∆ ∈ [0, 1])
be ween he lines, and Eq. (13) de ines a decision bina y a iable [7]. j is he numbe o
pa ks using he pa king lo .
To pu sue he p oblem u he , i is necessa y o analyse how he luc ua ion o ca s will
a y o e ime, i.e. o p opose a scena io desc ibing he beha iou o ca s using he ca
pa k o cha ge EV ba e ies. Fo each ca a i ing a he ca pa k, i is necessa y o know
he ollowing da a:
• A i al ime: Desc ibes he a i al ime o he ca a he ca pa k in minu es.
Cha ging ime le : Desc ibe how much cha ging ime is needed o each ca o
each 100% cha ge o i s ba e ies, aking in o accoun ha he cha ging poin has
2.3 kW o cha ging powe and he ba e ies ha e a capaci y o 23kW.
• Due da e. Desc ibe he ime when he ca has o lea e he ca pa k.
The h ee pa ame e s shown abo e ollow he ollowing no mal o uni o m dis ibu ions
as shown in he ables below (Table 1 Table 2 Table 3). The i s column o he ables
shows he pe cen age o ca s a i ing a he ca pa k and he second column shows he
dis ibu ion ha ollow each g oup o ca s.
I can be seen ha Table 2 does no di ec ly show he emaining cha ging ime o cha ge
he ba e y o he ca s a i ing a he ca pa k o 100% (N(C,D)). In o de o calcula e his
da a, he ollowing equa ions ha e been used (14) (15).
𝑐=(100−𝐴)∗0.01∗60∗𝐵𝑎𝑡𝑡𝑒𝑟𝑖𝑒𝑠𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦
𝐶ℎ𝑎𝑟𝑔𝑖𝑛𝑔𝑃𝑜𝑤𝑒𝑟
(14)
𝐷=𝐵∗0.01∗60∗𝐵𝑎𝑡𝑡𝑒𝑟𝑖𝑒𝑠𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦
𝐶ℎ𝑎𝑟𝑔𝑖𝑛𝑔𝑃𝑜𝑤𝑒𝑟
(15)
The da a shown in he ables (Table 1 Table 2 Table 3) has been plo ed o ge a be e
unde s anding o wha he di e en p obabili y dis ibu ions mean.

29
% VEHICLES
ARRIVAL TIME (MINUTES)
10
U (0,1440)
20
N (510,15)
10
N (720,15)
50
N (1170,15)
10
N (1350,15)
TABLE 1 ARRIVAL TIME DISTRIBUTION
FIGURE 18 GRAPHICAL DIAGRAM EVS ARRIVAL TIME
% VEHICLES
INITIAL CHARGE (%)
10
N (80,10) -> N(A,B)
30
N (50,15)
30
N (35,7.5)
30
N (12,6)
TABLE 2 INITIAL CHARGE DISTRIBUTION
30
FIGURE 19 GRAPHICAL DIAGRAM OF THE TABLE 2
% VEHICLES
DUE DATE (MINUTES)
10
N (240,120)
30
N (360,120)
30
N (480,120)
30
N (660,120)
TABLE 3 DUE DATES DISTRIBUTION
31
FIGURE 20 GRAPHICAL DIAGRAM OF THE TABLE 3
I should be no ed ha hese dis ibu ions ha e been ob ained by means o a simple model
gene a o based on he s a is ical dis ibu ions, by means o which he da a necessa y o
pose he p oblem a e ob ained. Now, ha ing desc ibed he scena io on which he p ojec
is based, i is ime o explain how do he algo i hm c ea ed o sol e he p oblem wo ks.
6.3 Adap ed ACO algo i hm o EV cha ging
Ha ing desc ibed he scena io in which he p ojec will be ca ied ou , a de ailed
desc ip ion o he algo i hm ha I ha e p og ammed o op imise he cha ging o he EVs
ha come o he a o emen ioned ca pa k will be gi en. Fo his, he i s hing o do is o
show he pseudocode o he algo i hm (Figu e 21). I se es o ep esen he logical and
de ailed p ocess o an algo i hm in a clea and concise way, and acili a es he
unde s anding o he algo i hm by p og amme s and de elope s who can wo k on he
ac ual implemen a ion o he algo i hm in di e en p og amming languages.
32
FIGURE 21. PSEUDOCODE OF ACO ALGORITHM
33
Each block shown in he pseudocode is explained in mo e de ail below.
6.3.1 Ge in o ma ion o each ca
In his pa o he algo i hm he objec i e is o ob ain an a ay called "sample" which
s o es he ollowing in o ma ion:
• Ca iden i ica o y
• A i al ime
• Cha ging ime le
• Due da e
This in o ma ion is essen ial o he algo i hm o ind he bes sequence o op imise he
cha ging o he 30 EVs a i ing a he ca pa k.
I should be no ed ha he scena io desc ibed in sec ion X has been sligh ly modi ied. In
he case o "due da e", 1440 minu es ha e been added o he dis ibu ion, he equi alen
o 1 day, in case one o he ca s has o lea e he day a e a i al. This makes he new
dis ibu ion he same as he p e ious one bu shi ed 1440 minu es o he igh . The
dis ibu ion used is as ollows (Figu e 22):
FIGURE 22. NEW DISTRIBUTION OF DUE DATE

34
6.3.2 Ini ialize ACO pa ame e s and phe omone and i ness ma ices
These blocks a e al eady pa o he ACO algo i hm. The i s hing o do is o ini ialise
he main pa ame e s, which a e as ollows:
• MaxI : Maximum Numbe o I e a ions
• nAn : Numbe o An s (Popula ion Size)
• q0: ha con ols he explo a ion o he decision ule
• au0: Ini ial Phe omone alue
• alpha: Phe omone Exponen ial Weigh , pa ame e ha con ols he
in luence o he phe omone ails
• be a: Pa ame e ha con ols he in luence o he heu is ic in o ma ion
• ho: Phe omone e apo a ion Ra e
• ksi: Pa ame e ha con ols he in luence o he local phe omone upda e
• N: Numbe o EVs a i ing.
Then, he phe omone (Tauij) and i ness (e a) ma ices a e ini ialised. Tauij is he ma ix
ha s o es he numbe o phe omones in each pa h, which will be upda ed as he an s ind
a be e solu ion. I is a ma ix o NxN dimensions. When i is ini ialised, he same numbe
o phe omones is deposi ed in all he pa hs, au0. Gi en ha he p obabili y o going om
poin A o he same poin A is 0, he main diagonal o his ma ix is all 0.
E a is he ma ix ha s o es he i ness o each ca , which is calcula ed by he equa ion
15. I has been mul iplied by 1000 because o o he wise i s alue is e y low, causing
compu ing p oblems in he algo i hm. This ma ix is also o NxN dimensions.
𝑒𝑡𝑎= 1
𝐷𝑢𝑒 𝐷𝑎𝑡𝑒 ∗1000
(16)
6.3.3 Loca e an s andomly
Each an is andomly assigned he alue o a ca , which will be he ehicle ha s a s he
cha ge i s , hus se ing he ime ame o calcula e he a diness. This means ha each
an will s a c ea ing a solu ion om a andom ca . In his way di e en an s will explo e
di e en pa hs, i.e. di e en loading sequences o all ca s. Thus, he sequence wi h he
sho es o al loading ime, i.e. minimum a diness will be he bes solu ion o he p oblem,
and mo e phe omones will be deposi ed on he pa hs made by he an s in ha sequence.
35
6.3.4 An Colony Op imiza ion: S a e T ansi ion Rule and Global Phe omone
Upda ing Rule.
Th ee di e en o loops ha e been used in he main loop. The i s one indica es he
numbe o i e a ions o be pe o med in he algo i hm. Tha is, how many di e en
solu ions will be ob ained in o al. So, his i s loop es ablishes how many imes he an s
will do he sea ch h oughou he sea ch space. The second one indica es he numbe o
an s ha a e going o conduc he sea ch in each i e a ion. This means ha in each i e a ion
as many solu ions as an s he e a e will be ob ained, o la e choose he an which ob ains
he bes solu ion among all o hem. The las one se es o build he solu ion, so he sea ch
p ocess will be epea ed o he numbe o EVs o be cha ged in he ca pa k. In his
p ojec , a numbe o 30 i e a ions, 3 an s and 30 EVs ha e been se . I is wo h no ing ha
he mo e i e a ions he e a e, he mo e likely i is ha a be e solu ion will be ob ained.
Howe e , his g ea ly inc eases he compu a ional execu ion ime o he algo i hm, which
is why a lowe numbe o i e a ions has been used. An equilib ium has o be main ained
be ween e ec i e compu a ion ime and op imal solu ion building. This leads o he
applica ion o he Global Phe omone Upda ing ule, by which he pa h chosen by he bes
global an is chosen. The main loop is he one ha goes om i =1: MaxI and inside his
loop is he i e=1:nAn s loop. The main loop consis s on he S a e T ansi ion Rule
acco ding o which he sea ch p ocess is conduc ed. Below is a b ie explana ion o wha
each loop con ains.
• Loop i =1: MaxI
o Loop “i e=1: nAn s”
o Loop “i e a ion=1: N”
▪ The i s hing in his loop is o place each an a a di e en s a ing poin , i.e. a a
di e en ca . Tha is, each an akes a andom alue om 1 o he numbe o ca s
(in his case 30). This means ha each an s a s he EV cha ging p ocess in he
ca ha has been andomly assigned o i , so he i s alue o he solu ion o each
an will be his numbe . A e ha , each an will build up he solu ion
▪ The nex hing o be done in his loop is o apply he s a e ansi ion ule. Wi h
his ule, i is decided whe he each an will pe o m an explo a ion o an
exploi a ion. A he beginning o he p og am, he pa ame e s necessa y o he
p og am o wo k ha e been ini ialised. Among hem is he pa ame e q0. This
pa ame e se s he p obabili y ha each an will pe o m a scan o an exploi .
In his pa o he algo i hm, a andom numbe "q1" is gene a ed a each i e a ion.
Depending on he alue o "q1" he an sea ches o he nex solu ion in one way
36
o ano he . In his case i has been p og ammed as ollows; wi h p obabili y q0 he
an makes he bes decision as indica ed by he phe omone ails and he heu is ic
in o ma ion (exploi a ion) (equa ion 6), while wi h p obabili y (1−q0) he an
makes a andom decision biased by he phe omone ails and he heu is ic
in o ma ion (explo a ion) (equa ion 7). [1]
FIGURE 23. CUMULATIVE FREQUENCY OF EXPLOITATION AND EXPLORATION
o End Loop “i e a ion=1:N”
o Loop “i e=1: nAn s”
Once he 2 and 3 loops ha e been inished, i is ime o apply he Global Phe omone
Upda ing Rule. By means o his ule, he phe omone ma ix is upda ed aking in o
accoun he bes solu ion in each i e a ion. In his way, in he ollowing i e a ions, he
sequences used by he an s ha ha e ob ained he bes solu ion will ha e mo e p obabili y
o being chosen, hus minimising he objec i e unc ion.
7 Resul s
Ha ing desc ibed how he algo i hm wo ks, his sec ion will analyse he esul s ob ained,
as well as he in luence o he ini ialisa ion pa ame e s on he esul s ob ained. The bes
esul will be aken as he one ha ob ains he bes alue o he objec i e unc ion
desc ibed abo e (equa ion 15). Hence, he bes esul is he one wi h he lowes a diness
alue. This implies ha in he bes sequence ( esul ), he ime be ween a ca inishing
loading and i s due da e will be he longes , making ha ca loading sequence he mos
e icien .
In o de o ob ain esul s, a p og amme which desc ibes he p oblem scena io has been
de eloped. Tha is o say, he da a o 30 EVs a i ing a he ca pa k o cha ge hei
37
ba e ies has been ob ained. The sequence o a i al and he necessa y in o ma ion o
each EV has been abula ed in Table 4.
Table 4. In o ma ion o each ca a i ing a he cha ging s a ion
Vehicle id
A i al Time
(Minu es)
Cha gin ime le
(Minu es)
Due da e
(Minu es)
1
1197,51
377,60
1763,08
2
515,14
627,70
2164,19
3
1349,05
520,62
2098,76
4
1191,26
335,66
2295,63
5
1185,52
517,08
1825,53
6
1152,79
227,15
1852,61
7
1158,68
466,39
1891,03
8
1174,69
297,30
1995,32
9
1186,64
306,96
1666,38
10
1192,99
333,42
1934,08
11
510,49
439,53
2110,31
12
498,87
511,54
1889,77
13
523,33
173,80
1858,58
14
1167,06
538,50
2110,52
15
520,45
519,23
1780,10
16
765,00
621,08
1822,48
17
1141,00
138,48
1993,44
18
1161,83
362,99
2008,72
19
1167,09
69,62
1971,34
20
1171,86
457,41
1775,06
21
1362,38
489,91
1767,30
22
1165,83
454,13
1701,17
23
517,62
391,51
1935,30
24
1165,51
378,21
1645,72
25
495,31
251,98
1795,71
26
1349,70
354,08
2084,01
27
530,27
246,99
1818,25
28
547,89
539,07
1576,14
29
731,87
-19,79
1840,02
30
1176,78
398,27
1903,44
.
Nex , a s udy o he in luence o he ini ial pa ame e s used in he ACO has been ca ied
ou . S a ing om some s anda d alues o hese pa ame e s (Table 5), in each o he
ollowing sec ions a pa ame e has been modi ied o see i s in luence on he esul s.
44
FIGURE 27. FINAL PHEROMONE MATRIXES
As in he p e ious case, he algo i hm ge s locked in nea -op imal solu ions.
Theo e ically, i ho is oo high, he phe omones may disappea oo quickly and he an
colony agen s may lose aluable in o ma ion abou p e ious solu ions, which may lead
o p ema u e con e gence and possibly a subop imal solu ion. On he o he hand, i ho
is oo low, phe omones may pe sis oo long and an s may con inue o explo e sub-op imal
solu ions, which may lead o a longe un ime and possibly a sub-op imal solu ion.
In his case, a be e solu ion was again ob ained when highe phe omone alues, i.e.,
exploi a ion, we e a ou ed. So, we a e consis en ly seeing ha heu is ics and phe omone
accumula ion a ou be e esul s, in de imen o explo a ion and a highe deg ee o
andomness. Bu his also shows ha a ce ain s agna ion happens in hese cases, which
is why he algo i hm does no con e ge in he bes solu ion and keeps p oduc ion nea -
op imal solu ions.

45
7.3 In luence o β / α
Using he pa ame e s in he abo e able 5 as a e e ence, he ela ion o β / α has been
modi ied and he ollowing esul s ha e been ob ained. Table 8 abula es he bes a diness
o each i e a ion o each alue o q0 used. They also ha e been showed in Figu e 28.
TABLE 8. INFLUENCE OF Β / Α IN THE RESULTS
I e a ion
0,50
1,00
3,00
5,00
1,00
7330
6667
6675
6228
2,00
6487
5699
6459
5666
3,00
6801
6507
6478
7300
4,00
6529
7593
6376
6100
5,00
5726
5800
6944
8093
6,00
5518
6624
7254
6750
7,00
5719
7045
6557
6726
8,00
6630
6934
6999
7185
9,00
7284
7968
7150
6683
10,00
7053
9117
6273
7636
11,00
5474
6132
6944
7898
12,00
7908
6711
6632
6930
13,00
6652
6839
6670
6831
14,00
8381
6331
7012
5448
15,00
7316
5378
7576
6509
16,00
6995
7448
7369
6854
17,00
6273
5517
7121
6684
18,00
6605
6461
6001
7371
19,00
6447
6856
6673
6233
20,00
8179
5630
6931
6523
21,00
6136
7994
7901
6716
22,00
6465
8025
6400
6206
23,00
7041
6225
6680
7187
24,00
6040
9492
7019
6385
25,00
6081
5352
6640
7201
26,00
7118
5673
5734
7108
27,00
7368
5932
7011
6154
28,00
7279
6674
6693
6900
29,00
6775
7128
7121
7222
30,00
7304
6974
6532
5749
A e age
(Minu es)
6764
6758
6794
6749
Bes
(Minu es)
8381
9492
7901
8093
46
FIGURE 28. INFLUENCE OF Β / Α IN THE RESULTS
In his case, he alpha pa ame e con ols he deg ee o explo a ion, i.e. he p opensi y o
he an s o use new pa hs( ehicle cha ging combina ions). A high alue o alpha will
esul in a g ea e ocus on explo ing new solu ions, which can be use ul a he beginning
o he sea ch p ocess when po en ial solu ions need o be ound quickly and also o a oid
s agna ion and nea -op imal solu ions. On he o he hand, he be a pa ame e con ols he
deg ee o exploi a ion, i.e., he p opensi y o an s o isi al eady used pa hs in sea ch o
p omising solu ions. A high alue o be a will esul in a g ea e ocus on exploi ing
known solu ions, which can be use ul in la e s ages o he sea ch p ocess o imp o e
exis ing solu ions.
In his case, he pa e n o ob aining he bes solu ion nea i e a ion 22 is epea ed again,
so i will no be aken in o accoun . The e is a lo o a iabili y in he esul s, bu i is
possible o see ha a ios ha a ou a be a highe han alpha, end o deli e sligh ly
be e solu ions. Thus, when he heu is ic alue is a ou ed and guides he sea ch, once
again, be e esul s a e ob ained.
7.4 Bes Solu ion pa ame e s
In his sec ion, he alues o he ini ial ACO pa ame e s ha e been se in such a way as o
ob ain he bes possible solu ion. In his case, he bes solu ion has been ob ained using
he ollowing pa ame e s. (Table 9)
4000
5000
6000
7000
8000
9000
10000
0,00 5,00 10,00 15,00 20,00 25,00 30,00
Bes a diness (Minu es)
Numbe o i e a ion
0,50
1,00
3,00
5,00
47
TABLE 9. PARAMETERS VALUE WHICH GIVES THE BEST SOLUTION
Ini ialisa ion pa ame e s alue
MaxI (Numbe o i e a ions)
30
Nan (Numbe o an s)
3
N (Numbe o ca s)
30
q0
0,95
au0
0,5
α
1
β
2
ρ
0,1
8 Conclusions & u u e wo k
In his mas e 's hesis, exhaus i e esea ch has been ca ied ou on elec ic ca cha ging
managemen and he use o me aheu is ic algo i hms o ackle op imisa ion p oblems in
his con ex . F om he de ailed analysis and he esul s ob ained, he ollowing
conclusions ha e been eached.
On he one hand, in he coming yea s, he p ope managemen o elec ic ca cha ging
will become a c ucial ask o a oid he collapse o he elec ici y sys em in he ace o
g owing demand o EVs. The inc easing adop ion o EVs p esen s signi ican challenges
in e ms o ene gy demand and supply capaci y. I is essen ial o implemen e icien load
managemen s a egies o balance demand and a oid o e load si ua ions in he elec ici y
sys em.
On he o he hand, me aheu is ic algo i hms ha e p o en o be a powe ul ool o sol ing
op imisa ion p oblems ela ed o elec ic ca cha ging. These algo i hms, such as ACO,
BCO and gene ic algo i hm, o e a lexible and e icien app oach o ind op imal o
app oxima e solu ions o complex p oblems.
The algo i hm ha has been de eloped was able o each op imal solu ions e e y ime,
howe e , hey we e nea -op imal solu ions, con e gence o he bes global solu ions was
no achie ed, e en a e ex ensi e pa ame e iza ion es s. This aises he ques ion i his
kind o algo i hm is eally adequa e o sol ing his p oblem and how can i s beha iou
be imp o ed, wi hou aising he compu a ion ime excessi ely and s ill keeping i simply.
As has been seen in he esul s, he sea ch is d i en p ima ily by he heu is ic, hen
phe omone accumula ion and a limi ed explo a i e cha ac e is ic.
Conside ing his, he p oposals o u u e wo k ha would imp o e he esul s would
include:
• One eason why good and simila solu ions ha e always been ob ained may be ha
he sample o ca s gene a ed by he "samplesimula o " is e y simple. Tha is o say,
all ca s ha e a e y la ge due da e, so i is e y easy ha hey a e always going o be
loaded be o e hey ha e o lea e he ca pa k ( e y nega i e a diness). The e o e, by
48
c ea ing a sample wi h a igh e due da e, i could be be e app ecia ed i he algo i hm
is able o ob ain he bes solu ion and see ha he e is a much be e solu ion han he
es , since, in his case, almos all he solu ions ob ained he same alue o o al
a diness.
• Ano he way o imp o e he esul s could be o widen he sample o ca s, so ha he e
would be mo e possible esul s.
• In his p ojec , he local phe omone upda ing ule has no been aken in o accoun
when implemen ing he algo i hm, so i i had been aken in o accoun , be e esul s
could ha e been ob ained.
• Fu he mo e, a hyb id algo i hm, which combines mo e han one ype o op imisa ion
men ioned abo e, could be used and see i i wo ks be e han his one. In addi ion o
his, i could be possible o change he objec i e unc ion o see how he change o he
heu is ic alue a ec s o he sea ch, and see i be e esul s a e ob ained.
49
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