A GA(TS) Hyb id Algo i hm o Scheduling in
Compu a ional G ids
Fa os Xha a1, Juan A. Gonzalez1, Kesha P. Dahal2, and Aji h Ab aham3
1Depa men o Languages and In o ma ics Sys ems
Technical Uni e si y o Ca alonia, Ba celona, Spain
[email p o ec ed]
2School o In o ma ics, Uni e si y o B ad o d, UK
[email p o ec ed]
3Cen e o Excellence o Quan i iable Quali y o Se ice
No wegian Uni e si y o Science and Technology, No way
[email p o ec ed]
Abs ac . The hyb idiza ion o heu is ics me hods aims a explo ing
he syne gies among s and alone heu is ics in o de o achie e be e e-
sul s o he op imiza ion p oblem unde s udy. In his pape we p esen
a hyb idiza ion o Gene ic Algo i hms (GAs) and Tabu Sea ch (TS)
o scheduling in compu a ional g ids. The pu pose in hyb idizing hese
heu is ics is o bene i he explo a ion o he solu ion space by a popu-
la ion o indi iduals wi h he exploi a ion o solu ions h ough a sma
sea ch o he TS. Ou GA(TS) hyb id algo i hm uns he GA as he
main algo i hm and calls TS p ocedu e o imp o e indi iduals o he
popula ion. We e alua ed he p oposed hyb id algo i hm using di e en
G id scena ios gene a ed by a G id simula o . The compu a ional esul s
showed ha he hyb id algo i hm ou pe o ms bo h he GA and TS o
he makespan alue bu canno ou pe o m hem o he low ime o he
scheduling.
1 In oduc ion
Me a-heu is ics a e he de ac o app oach o cope in p ac ice wi h he compu a-
ionally ha d op imiza ion p oblems. Me a-heu is ics a e in ac hyb id in hei
na u e since hey consis o a high le el algo i hm ha guides he sea ch us-
ing o he pa icula me hods. Fo ins ance, in popula ion based me a-heu is ics,
such as Gene ic Algo i hms, he solu ion space is explo ed h ough a popula ion
o indi iduals and he e a e used me hods o gene a ing he ini ial popula ion,
compu ing he i ness o indi iduals as well gene ic ope a o s o ansmi he
gene ic in o ma ion om pa en s o o sp ings.
Besides using me a-heu is ics as s and alone app oaches o sol ing ha d
combina o ial op imiza ion p oblems, du ing he las yea s, he a en ion o e-
sea che s has shi ed o conside ano he ype o high le el algo i hms, namely
hyb id algo i hms. These algo i hms do no ollow any conc e e me a-heu is ic,
bu a he hey combine o he me a-heu is ics and/o o he me hods (e.g. exac
me hods) yielding hus hyb id me a-heu is ics.
Xha a, F., González, J. A., Dahal, K. P., Ab aham, A. A GA(TS) hyb id algo i hm o scheduling in compu a ional g ids. A:
In e na ional Con e ence on Hyb id A i icial In elligence Sys ems. "Hyb id A i icial In elligence Sys ems, 4 h In e na ional
Con e ence, HAIS 2009: Salamanca, Spain, June 10-12, 2009: p oceedings". Be lín: Sp inge , 2009, p. 285-292.
The inal au hen ica ed e sion is a ailable online a h ps://doi.o g/10.1007/978-3-642-02319-4_34
The a ionale behind he hyb idiza ion esides in he “no ee lunch he-
o em” [16] s a ing ha “... all algo i hms ha sea ch o an ex emum o a
cos unc ion pe o m exac ly he same, when a e aged o e all possible cos
unc ions. In pa icula , i algo i hm A ou pe o ms algo i hm B on some cos
unc ions, hen loosely speaking he e mus exis exac ly as many o he unc ions
whe e B ou pe o ms A.” Essen ially, he heo em s a es ha he e is no any
sea ch me hod o op imiza ion which ou pe o ms all o he sea ch me hods.
This sugges s ha one can use exis ing algo i hms as componen s o designing
new e icien sea ch algo i hms and expec imp o ed pe o mance o he newly
ob ained algo i hm o some cos unc ions.
The e a e a leas wo majo issues in designing hyb id me a-heu is ics: (a)
how o choose he (exis ing) heu is ic me hods o combine, and (b) how o com-
bine he chosen heu is ic me hods in o new hyb id app oaches. Un o una ely,
he e a e no heo e ical ounda ions o hese issues. Fo he o me , di e en
classes o sea ch algo i hms can be conside ed o he pu poses o hyb idiza ion,
such as exac me hods, simple heu is ic me hods (ad hoc me hods) and me a-
heu is ics. Mo eo e , me a-heu is ics hemsel es a e classi ied in o local sea ch
based me hods, popula ion based me hods and o he classes o na u e inspi ed
me a-heu is ics. The e o e, in p inciple, one could combine any me hods om he
same class o me hods om di e en classes. Rega ding he la e , he e a e some
a emp s o axonomies o hyb id me a-heu is ics [8, 5]; in ac , he common ap-
p oach is o y ou in sma ways, based on domain knowledge o p oblem a
hand and cha ac e is ics o heu is ics me hods, di e en hyb id app oaches and
shed ligh on he pe o mance o he hyb id app oach h ough empi ical s udies.
F amewo ks ha acili a e he as p o o yping ha e been also p o ided in he
me a-heu is ics li e a u e [2, 4].
In his pape , we p esen a hyb id algo i hm o he p oblem o scheduling
independen asks in compu a ional g ids. A compu a ional g id is a dis ibu ed
in as uc u e o compu a ional esou ces (ha dwa e, so wa e, da a s o ages,
e c.) highly he e ogenous, in e connec ed h ough he e ogenous ne wo ks. One
key issues in G ids is o design e icien schedule s, which will be used as pa o
middlewa e se ices o p o ide e icien planning o use s’ asks o g id nodes.
Recen ly, heu is ic app oaches ha e been p esen ed o he p oblem [1, 7, 9,
11, 10, 12], howe e , p ope hyb id app oaches a e lacking. Ou hyb id app oach
combines Gene ic Algo i hms (GAs) and Tabu Sea ch (TS) me hods. Roughly,
ou hyb id algo i hm uns he GA as he main algo i hm and calls TS p ocedu e
o imp o e indi iduals o he popula ion. Ou hyb id algo i hms deals wi h he
scheduling p oblem as a bi-objec i e op imiza ion p oblem, in which makespan is
conside ed a p ima y objec i e and low ime a seconda y one. Such op imiza ion
scheme is usually e e ed o as hie a chic op imiza ion. The p oposed algo i hm
has been expe imen ally e alua ed and he esul s a e con as ed agains bo h
GAs and TS o he p oblem.
The es o he pape is o ganized as ollows. In Sec ion 2, we b ie ly p esen
he scheduling o independen asks conside ed as a bi-objec i e op imiza ion
p oblem in his wo k. In Sec ion 3, ypes o hyb idiza ions a e p esen ed. The
GAs and TS o he p oblem as well as he hyb id app oach a e gi en in Sec ion 4.
The expe imen al s udy and some compu a ional esul s a e gi en in Sec ion 5.
We conclude in Sec ion 6 wi h some ema ks and indica ions o u u e wo k.
2 Scheduling o independen asks in compu a ional g ids
Many applica ions a e being de eloped o be un in compu a ional g ids o ben-
e i om he la ge amoun o compu a ional esou ces in such sys ems. In simple
G id sys ems such as en ep ise g ids o campus g ids, he use can use queuing
sys ems such as Condo o Sun G id Engine; e en, manual selec ion o he ap-
p op ia e machines o unning he applica ion is possible in such g ids. In la ge
scale and highly he e ogenous g ids, howe e , his edious ask is au oma ically
handled by g id schedule s, which a e expec ed o ind planning o use s’ asks
and applica ions o mos app op ia e machines.
One class o g id schedule s a e ba ch schedule s, ha is, schedule s ha
compu e a planning o a se o asks/applica ions al oge he o a se o g id
nodes. Me a-heu is ic app oaches a e use ul o he design o such schedule s,
since hey usually p o ide quali y solu ions in sho imes.
In his wo k we a e in e es ed in scheduling o independen asks o g id
esou ces. The o mal de ini ion o he p oblem is based on he de ini ion o he
Expec ed Time o Compu e (ETC) ma ix in which ET C[j][m] indica es an
es ima ion o how long will i ake o comple e ask jusing esou ce m. Unde
he ETC ma ix model, he independen scheduling can be de ined as ollows:
–A numbe o independen asks o be alloca ed o g id esou ces. Each ask
has o be p ocessed en i ely in a single esou ce and is no p eemp ed (once
s a ed, a ask uns un il comple ion).
–A numbe o machines candida es o pa icipa e in he alloca ion o asks.
–The wo kload (in millions o ins uc ions) o each ask.
–The compu ing capaci y o each machine (in Mips).
–The eady imes, deno ed eadym, indica ing when machine mwill ha e
inished he p e iously assigned asks. A he beginning, usually eady imes
a e conside ed equal o ze o (all machines in he machine se a e a ailable
o ask alloca ion).
–The ET C ma ix o size nb asks ×nb machines, whe e ET C[j][m] is he
alue o he expec ed ime o compu e o ask jin machine m.
The quali y o a schedule can be measu ed using se e al op imiza ion c i e ia,
such as minimizing he makespan ( ha is, he inishing ime o he la es ask),
he low ime (i.e., he sum o inaliza ion imes o all he asks), he comple ion
ime o asks in e e y machine (closely ela ed o makespan), o maximizing he
esou ce u iliza ion. In his wo k we conside ha he mos impo an c i e ion
is ha o minimizing he makespan. Addi ionally, we conside he minimiza ion
o he low ime o he g id sys em as a seconda y c i e ion. These wo c i e-
ia a e o mally de ined as ollows: makespan: minSi∈Sched{maxj∈T asks Fj}and,
low ime: minSi∈Sched{Pj∈T asks Fj}, whe e Fjdeno es he ime when ask j
inalizes and Sched is he se o all possible schedules. No ice ha by consid-
e ing he makespan as he main objec i e o op imize and he low ime as a
secunda y goal, we aim a designing a hie a chical algo i hm, in which he alue
o makespan can no be wo sened when op imizing he low ime.
3 Hyb idiza ion o me a-heu is ics
As men ioned ea lie , he hyb idiza ion s a ed as an app oach ha ies o
combine ully o pa ially wo o mo e algo i hms o enhance he pe o mance
o s and alone sea ch me hod o op imiza ion p oblems. To achie e such goal,
he hyb idiza ion should be able o embed he bes ea u es o he combined
algo i hms in o a new high le el algo i hm.
Cu en hyb id models ake in o accoun wo main aspec s: (1) Type o
me hods o hyb idize, and (2) Le el o hyb idiza ion. The i s e e s o he
ype o he me hods o be hyb idized. Essen ially we could conside wo cases:
(a) me a-heu is ics + me a-heu is ics and (b) me a-heu is ics + speci ic sea ch
me hod. In he i s case he componen s a e me a-heu is ics while in he la e ,
a me a-heu is ic is combined wi h ano he ype o sea ch me hod, which could
be an exac algo i hm, dynamic p og amming, cons ain p og amming o o he
AI echniques. In his wo k we a e conside ing he i s case, being he me a-
heu is ics he GAs and TS me hod.
The le el o hyb idiza ion, on he o he hand, e e s o he deg ee o coupling
be ween he me a-heu is ics, he execu ion sequence and he con ol s a egy.
Le el o hyb idiza ion. Loosely coupled: in his case he hyb idized me a-
heu is ics p ese e hei iden i y, namely, hei low is ully used in he hyb idiza-
ion. This case is also e e ed o as high le el o hyb idiza ion.S ongly coupled:
in his case, he hyb idized me a-heu is ics in e -change hei inne p ocedu es,
esul ing in a low le el o hyb idiza ion.
Execu ion sequence. Sequen ial ( he me a-heu is ics lows a e un sequen-
ially) o Pa allel ( he me a-heu is ics lows a e un in pa allel.)
Con ol s a egy. Coe ci e: he main low is ha o one o he me a-heu is ics,
he o he me a-heu is ics low is subo dina ed o he main low. Coope a i e: he
me a-heu is ics explo e he solu ion space coope a i ely (e en ually, hey can
explo e di e en pa s o he solu ion space.)
4 The p oposed GA(TS) hyb id app oach
Fo he design o ou hyb id app oach we conside wo well-known me a-heu is ics:
Gene ic Algo i hms (GAs) and Tabu Sea ch (TS). Bo h GAs and TS ha e been
de eloped o he independen ask scheduling in Xha a e al. [11] and [12] in
sequen ial se ing. We ha e conside ed he S eady-S a e GA in his wo k. The
choice o hese wo me a-heu is ics is based on he ollowing obse a ions. Fi s ,
g id schedule s should be e y as in o de o adap o dynamic na u e o compu-
a ional g ids. The e o e, a as con e gence o he main algo i hm is p e e able
in his case, which can be achie ed h ough a good adeo be ween explo a ion
and exploi a ion o he sea ch. Second, in o de o achie e high quali y planning
in a e y sho ime, i is sugges i e o combine he explo a ion o he solu ion
space by a popula ion o indi iduals wi h he exploi a ion o neighbo hoods o
solu ions h ough local sea ch. In such case, GAs and TS a e among he bes
ep esen a i es o popula ion based and local sea ch me hods, espec i ely.
We a e hus conside ing he case o hyb idiza ion o wo me a-heu is ics
unning in sequen ial en i onmen . We ha e conside ed a low le el hyb idiza ion
and he coe ci e con ol s a egy. Roughly, ou hyb id algo i hm uns he GA
as he main algo i hm and calls TS o imp o e indi iduals o he popula ion.
The hyb idiza ion scheme is shown in Figu e 1. I should be no ed ha in he
hyb idiza ion scheme in Figu e 1, ins ead o eplacing he mu a ion p ocedu e o
GAs by he TS p ocedu e, we ha e added a new unc ion o he GA Popula ion
class (namely apply TabuSea ch) o applying he TS. This new unc ion could
be applied o any indi idual o he cu en popula ion, howe e , his is compu-
a ionally cos ly. In ou case, gi en ha we wan o un he G id schedule in
sho imes, he apply TabuSea ch is applied wi h small p obabili y4. In ac ,
his pa ame e can well be used o une he con e gence o he GA since TS
usually p o ides subs an ial imp o emen s o indi iduals.
Fig. 1. The hyb id GA(TS) scheme.
We sho ly p esen nex bo h he GA and TS me a-heu is ics o independen
ask scheduling in compu a ional g ids ( e e o [11] and [12] o de ails.)
4.1 GAs o he scheduling p oblem in G ids
GAs a e a popula ion-based app oaches whe e indi iduals ep esen possible so-
lu ions, which a e successi ely e alua ed, selec ed, c ossed, mu a ed and eplaced
by simula ing he Da winian e olu ion ound in na u e. We ha e implemen ed
he S eady S a e e sion o GAs. In S eady S a e GAs, a ew good indi idu-
als o popula ion a e selec ed and c ossed. Then, he wo s indi iduals o he
popula ion a e eplaced by he newly gene a ed descendan s; he es o he in-
di iduals o he popula ion su i e and pass o he nex gene a ion. The es o
gene ic ope a o s and me hods a e as ollows: Ini ializa ion me hods a e MCT
and LJFR-SJFR implemen ed in [14, 15]; Selec ion ope a o : Linea anking;
4This is a use inpu pa ame e . Fo he pu poses o his wo k, apply TabuSea ch is
applied oughly o 30% o indi iduals

Table 1. Simula o s’ con igu a ion.
Small Medium La ge
Ini ./To al hos s 32 64 128
Mips n(1000, 175)
Ini ./To al asks 512 1024 2048
Wo kload n(250000000, 43750000)
Hos selec ion All
Task selec ion All
Local policy SPTF
Numbe o uns 30
C osso e ope a o : Cycle C osso e (CX); Mu a ion ope a o : Mu a e Rebal-
ancing. The conc e e alues o he es o pa ame e s a e gi en in Sec ion 5.
4.2 Tabu Sea ch o he scheduling p oblem in G ids
Tabu Sea ch (TS) has shown i s e ec i eness in a b oad ange o combina o-
ial op imiza ion p oblems and dis inguishes o i s lexibili y in exploi ing do-
main/p oblem knowledge. The main p ocedu es used in TS a e summa ized nex .
The ini ial solu ion is ound using Min-Min me hod [14]. Rega ding his o ical
memo y, bo h sho and long e m memo ies ha e been used in TS algo i hm.
Fo he ecency memo y, a ma ix T L (nb asks×nb machines) is used o main-
ain he abu s a us. In addi ion, a abu hash able (T H) is main ained in o de
o u he il e he abu solu ions. The neighbo hood explo a ion is done using a
s eepes descen - mildes ascen me hod using wo ypes o mo emen s, namely,
ans e (mo es a ask om a machine o ano he one, app op ia ely chosen) and
swap ( wo asks assigned o wo di e en machines a e swapped). Fu he , se -
e al aspi a ion c i e ia a e used o emo e he abu s a us o mo emen s. They
a e de ined using he i ness o solu ions as well as in o ma ion om ecency ma-
ix. In ensi ica ion is implemen ed using eli e solu ions while so di e si ica ion
uses penal ies o ETC alues, ask dis ibu ion and ask eezing. Finally, s ong
di e si ica ion is implemen ed using la ge pe u ba ions o solu ions.
The conc e e alues o he es o pa ame e s a e gi en in Sec ion 5.
5 Expe imen al s udy
We ha e used a G id simula o [13] o e alua e ou hyb id algo i hm.
Simula ion en i onmen se ing. Fo he e alua ion o he GA(TS) hyb id algo-
i hm, we ha e used h ee G id scena ios: small, medium and la ge size. They
consis , espec i ely, o 32 hos s/521 machines, 64 hos s/1024 machines, and 128
hos s / 2048 machines. Each scena io is gene a ed om he simula o bu he
numbe o asks and machines a e kep cons an , ha is, o bo h o hem, espec-
i ely, he numbe o ini ial asks equals he o al numbe o asks in he sys em
and and he ini ial numbe o machines equals he o al numbe o machines.
The con igu a ion o simula o ollows he pa ame e s gi en in Table 1. In he
able n(·,·) e e s o no mal dis ibu ion; SPTF s ands o Sho es P ocessing
Time Fi s local policy. The pa ame e alues o he GA and TS algo i hms used
in he hyb id algo i hm a e gi en in Tables 2 and 3.
Table 2. Pa ame e alues o GA.
Pa ame e Value
e olu ion s eps 20 ·nb asks
popula ion size 4 ·(log2(nb asks)−1)
in e media e pop. (pop size)/3
c oss p obab. 1.0
mu a ion p obab. 0.4
Table 3. Pa ame e alues o TS.
Pa ame e Value
#i e a ions nb asks ·nb mach
max. abu s a us 1.5·nb mach
# epe i ions
be o e ac i a ing 4 ∗ln(nb asks)·
in ensi ic./di e si ic. ln(nb mach)
#i e a ions pe
in ensi ic./di e si ic. log2(nb asks)
#i e a ions max abu/2−
o aspi a ion c i e ia −log2(max abu)
Compu a ional esul s and e alua ion. The simula o is un530 imes o each
scena io and compu a ional esul s o makespan and low ime a e a e aged.
S anda d de ia ion (a 95% con idence in e al) is also epo ed. The esul s o
makespan and low ime a e gi en in Table 4 and Table 5, esp.
Table 4. Makespan alues.
Small Medium La ge
GA (hie a chic)
2808662.116 2760024.390 2764455.222
±1,795% ±1,010% ±0,745%
TS (hie a chic)
2805531.301 2752355.018 2748878.934
±1,829% ±1,056% ±0,669%
GA(TS)
(hie a chic) 2805519.428 2751989.166 2812776.300
±1,829% ±1,058% ±1,176%
Table 5. Flow ime alues.
Small Medium La ge
GA (hie a chic)
709845463.699
1405493291.442
2811723598.025
±1,209% ±0,655% ±0,487%
TS (hie a chic)
710189541.278
1408001699.550
2812229021.221
±1,124% ±0,616% ±0,455%
GA(TS)
(hie a chic) 711183944.069
1409127007.870
2811605453.116
±1,174% ±0,604% ±0,465%
As can be seen om Table 4, o makespan alue he GA(TS) ou pe o ms
bo h GA and TS o small and medium size g id scena ios bu achie es wo se
alue o la ge size scena io. On he o he hand, om Table 5, we can see ha
GA(TS) pe o ms be e han bo h GA and TS o low ime alue only o la ge
size ins ances. So, GA(TS) pe o ms be e o makespan alue, which is consid-
e ed p ima y objec i e in hie a chic e sion, han o low ime pa ame e , which
is a seconda y objec i e. In ac , close o (sub-)op imal solu ions, makespan and
low ime beha e as con adic o y objec i es and hus unde ou hie a chic model,
he imp o emen s o low ime a e di icul o happen.
6 Conclusions
In his pape we ha e p esen ed a hyb id GA(TS) algo i hm o he p oblem o
independen scheduling in compu a ional g ids. The hyb idiza ion ollows a low
le el app oach in which GA is he main low and TS is subo dina ed o i . The
5AMD A hlon 64 3200+, 2GB RAM.
objec i e unc ion conside ed is ha o bi-objec i e in which makespan is p ima y
objec i e and low ime is seconda y. The expe imen al e alua ion showed ha
GA(TS) ou pe o ms bo h GA and TS o makespan alues o small and medium
size g id scena ios and o low ime alues o la ge size g id scena ios.
The GA(TS) hyb idiza ion scheme is e y app op ia e o pa allel implemen-
a ion, by unning TS me hod o all indi iduals o GA popula ion in pa allel.
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