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Building the Core Architecture of a NASA Multiagent System Product Line

Abstract

The field of Software Product Lines (SPL) emphasizes build- ing a family of software products from which concrete products can be derived rapidly. This helps to reduce time-to-market, costs, etc., and can result in improved software quality and safety. Current Agent-Oriented Software Engineering (AOSE) methodologies are concerned with devel- oping a single Multiagent System. The main contribution of this paper is a proposal to developing the core architecture of a Multiagent Systems Product Line (MAS-PL), exemplifying our approach with reference to a concept NASA mission based on multiagent technology.

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Building the Core Architecture of a NASA Multiagent System Product Line

Author: Peña Siles, Joaquín; Hinchey, Michael G.; Ruiz Cortés, Antonio; Trinidad Martín Arroyo, Pablo
Publisher: Springer Verlag
Year: 2007
DOI: 10.1007/978-3-540-70945-9_13
Source: https://idus.us.es/bitstreams/6bff7eb3-b02f-4922-a259-ae2b195b5e5e/download
Building he Co e A chi ec u e o a NASA
Mul iagen Sys em P oduc Line⋆
Joaquin Pe˜na1, Michael G. Hinchey2, An onio Ruiz-Co ´es1, and
Pablo T inidad1
1Uni e si y o Se ille, Spain
{joaquinp, a uiz}@us.es, [email p o ec ed]
2NASA Godda d Space Fligh Cen e , USA
Michael.G.Hinc[email p o ec ed]
Abs ac . The ield o So wa e P oduc Lines (SPL) emphasizes build-
ing a amily o so wa e p oduc s om which conc e e p oduc s can be
de i ed apidly. This helps o educe ime- o-ma ke , cos s, e c., and can
esul in imp o ed so wa e quali y and sa e y. Cu en Agen -O ien ed
So wa e Enginee ing (AOSE) me hodologies a e conce ned wi h de el-
oping a single Mul iagen Sys em. The main con ibu ion o his pape is
a p oposal o de eloping he co e a chi ec u e o a Mul iagen Sys ems
P oduc Line (MAS-PL), exempli ying ou app oach wi h e e ence o a
concep NASA mission based on mul iagen echnology.
1 In oduc ion
Many o ganiza ions, and so wa e companies in pa icula , de elop a ange o
p oduc s o e pe iods o ime ha exhibi many o he same p ope ies and
ea u es. The mul iagen sys ems communi y exhibi s simila ends. Howe e ,
he communi y has no as ye de eloped he in as uc u e o de elop a co e
mul iagen sys em (he ea e , MAS) om which conc e e (subs an ially simila )
p oduc s can be de i ed.
The so wa e p oduc line pa adigm (he ea e , SPL) augu s he po en ial o
de eloping a se o co e asse s o a amily o p oduc s om which cus omized
p oduc s can be apidly gene a ed, educing ime- o-ma ke , cos s, e c. [3], while
simul aneously imp o ing quali y, by making g ea e e o in design, implemen-
a ion and es mo e inancially iable, as his e o can be amo ized o e
se e al p oduc s. The easibili y o building MASs p oduc lines is p esen ed
in [16], bu no speci ic me hodology is p oposed. In his pape , we p opose an
app oach o pe o ming he i s s ages in he li ecycle o building a mul iagen
sys em p oduc line (MAS-PL).
⋆The wo k epo ed in his a icle was suppo ed by he Spanish Minis y o Science
and Technology unde g an s TIC2003-02737-C02-01 and TIN2006-00472 and by
he NASA So wa e Enginee ing Labo a o y, NASA Godda d Space Fligh Cen e ,
G eenbel , MD, USA.
Fo enabling a p oduc line, one o he impo an ac i i ies o be pe o med
is o iden i y a co e a chi ec u e o he amily o so wa e p oduc s. Un o u-
na ely, he e is no AOSE me hodology ha demons a es how o do his o
MAS-PLs. Ou app oach is based on he Me hodology o analysing Complex
Mul iagen Sys ems (MaCMAS) [18], an AOSE me hodology ocused on dealing
wi h complexi y, which uses UML as a modeling language and builds on ou
cu en esea ch and de elopmen expe ience in he ield o SPLs.
Roughly, ou app oach consis s o using goal-o ien ed equi emen docu-
men s, ole models, and aceabili y diag ams in o de o build a i s model o
he sys em, and la e use in o ma ion on a iabili y and commonali ies h ough-
ou he p oduc s o p opose a ans o ma ion o he o me models ha ep esen
he co e a chi ec u e o he amily.
The main con ibu ions o his pape a e: (i) we in oduce ea u e models
in he agen ield in o de o documen a iabili ies and commonali ies ac oss
p oduc s; (ii) we p o ide an au oma ic algo i hm and a p o o ype o pe o ming
commonali y analysis ( ha is o say, o au oma ically analyze he p obabili y
ha a ea u e appea s in a p oduc ); (iii) we p opose an ope a ion o compose he
models co esponding o a ea u e ha allows us o build he co e a chi ec u e
which includes hose ea u es whose p obabili y o appea ing is abo e a gi en
h eshold.
2 Mo i a ing MAS-PL wi h a NASA case s udy
The e has been signi ican NASA esea ch on he subjec o agen echnology,
wi h a iew o g ea e exploi a ion o such echnologies in u u e missions.
The ANTS (Au onomous Nano Technology Swa m) concep mission,1 o ex-
ample, will be based on a g ouping o agen s ha wo k join ly and au onomously
o achie e mission goals, analogous o a swa m in na u e.
Lande Amo phous Ro e An enna (LARA) is a sub-mission, en isaged o
he 2015-2020 ime ame, ha will use a highly econ igu able-in- o m o e
a i ac . Tens o hese o e s, beha ing as a swa m, will be used o explo e he
Luna and Ma ian su aces. Each o hese “ ehicles” o o e s will ha e he
abili y o change i s o m om a snake-like o m, o a cylinde , o o an an enna,
which will p o ide hem wi h a wide ange o unc ional possibili ies. They a e
en isaged as possible building ma e ials o u u e human luna bases.
P ospec ing As e oid Mission (PAM) is a concep sub-mission based on he
ANTS concep s ha will be dedica ed o explo ing he as e oid bel . A housand
pico-spacec a (less han 1kg each) may be launched om a poin in space
o ming sub-swa ms, and deployed o s udy as e oids o in e es in he as e oid
bel . Sa u n Au onomous Ring A ay (SARA) is also a concep sub-mission
simila o PAM bu whose goal is analysis o he Rings o Sa u n.
Al hough based on mainly he same concep s, hese sub-missions di e . Fo
example, in PAM, spacec a should be able o p o ec hemsel es om sola
1h p://an s.gs c.nasa.go /
s o ms, while in SARA his is no o conce n, bu as a highe g a i a ional o ce
exis s, he spacec a should be capable o a oiding g a i a ional “pull” and
collisions wi h pa icles o he ings, as well as wi h o he spacec a . Ano he
example is he mechanism used o mo ion in hese missions. Some o hem
equi e g ound-based mo ion, i.e. LARA, while o he missions in ol e lying
spacec a employing gas p opulsion and sola sails o powe .
Thus, ANTS ep esen s a numbe o sub-missions, each wi h common ea-
u es, bu wi h a wide ange o applicabili y, and hence se e al p oduc s.
Being able o build a MAS-PL o hese se s o sub-missions, wi h a se o
eusable asse s a all he le els (so wa e a i ac s, so wa e p ocesses, enginee ing
knowledge, bes p ac ices, e c.), can d as ically educe empo al and mone a y
cos s in he de elopmen o such missions.
In [16], a numbe o challenges a e p esen ed in he con ex o MAS-PL. In
his pape we co e some o hese challenges, which has mo i a ed his esea ch
o add ess he ollowing issues:
SPL o dis ibu ed sys ems. Dis ibu ed sys ems ha e no been a ho opic
in he SPL ield. We will explo e a case s udy based on he ANTS concep
mission p esen ed abo e, which is a highly complex dis ibu ed sys em. Thus,
his ep esen s a i s s ep owa ds add essing his challenge.
AOSE de iciencies. AOSE does no co e many o he ac i i ies o SPL. These
a e mainly concen a ed on commonali y analysis, and i s implica ions o
he en i e SPL app oach. This mo i a es us o co e his issue, alida ing
ou app oach wi h he case s udy p esen ed.
3 Backg ound in o ma ion
As a esul o combining wo di e en ields, we ha e o con ex ualize ou wo k
in bo h esea ch a eas. In his sec ion, we p o ide an o e iew o SPL and AOSE
illus a ing he poin s o syne gy be ween hem.
3.1 So wa e P oduc Lines
The ield o so wa e p oduc lines co e s he en i e so wa e li ecycle needed
o de elop a amily o p oduc s whe e he de i a ion o conc e e p oduc s is
achie ed sys ema ically o e en au oma ically when possible.
I s so wa e p ocess is usually di ided in o wo main s ages: Domain Engi-
nee ing and Applica ion Enginee ing. The o me is esponsible o p o iding
he eusable co e asse s ha a e exploi ed du ing applica ion enginee ing when
assembling o cus omizing indi idual applica ions [19]. Al hough he e a e o he
ac i i ies, such as p oduc managemen , in his sec ion we do no y o be
exhaus i e, bu only discuss hose ac i i ies di ec ly ela ed o his pape and
ele an o ou app oach. Thus, ollowing he nomencla u e used in [19], he
ac i i ies, usually pe o med i e a i ely and in pa allel, o domain enginee ing
ha co ela e wi h ou app oach a e:
The Domain Requi emen s Enginee ing ac i i y desc ibes he equi emen s
o he comple e amily o p oduc s, highligh ing bo h he common and a iable
ea u es ac oss he amily. In his ac i i y, commonali y analysis is o g ea im-
po ance o aiding in de e mining which a e he common ea u es and which
o hem a e p esen only in some p oduc s. The models used in his ac i i y o
speci ying ea u es show when a ea u e is op ional, manda o y o al e na i e
in he amily. One o he mos accep ed models he e is ea u e models [4]. A
ea u e is a cha ac e is ic o he sys em ha is obse able by he end use [7].
Fea u es ep esen a concep qui e simila o sys em goals (used in AOSE) and
he models used o ep esen hem p esen a co ela ion wi h hie a chical sys em
goal equi emen documen s [16]. Ou app oach is based on his co ela ion.
In Figu e 1, we show a subse o he ea u e model om ou case s udy.
As shown, in his kind o model he ea u es o all p oduc s a e shown along
wi h in o ma ion on whe he hey a e manda o y, op ional, o al e na i e. Fo
example, he ea u e ligh and o bi is manda o y, while he ea u e walk is
op ional. In addi ion, he ea u es snake,amoeba, e c. mus be p esen only i
hei pa en is p esen , and, as hey a e ela ed by an o - ela ion, when a p oduc
possesses he ea u e walk i mus also possess a leas one o he o me ea u es.
The Domain Design ac i i y p oduces a chi ec u e-independen models ha
de ine he ea u es o he amily and he domain o applica ion. Many app oaches
ha e been discussed in he li e a u e o pe o m his modeling. Some o hese
app oaches use ole models o ep esen he in e aces and in e ac ions needed
o co e ce ain unc ionali y independen ly (a ea u e o a se o ea u es). The
mos ep esen a i e a e [6,21], bu simila app oaches ha e appea ed in he OO
ield, o example [5,20]. We build on his co ela ion using agen -based ole
models a he acquain ance o ganiza ion o ep esen ea u es independen ly.
Then, in he Domain Realiza ion ac i i y, a de ailed a chi ec u e o he amily
is p oduced adding mechanisms such as componen s ha can be cus omized,
o amewo ks o hese componen s, in o de o enable he apid de i a ion o
p oduc s. In SPL, he e exis some app oaches whe e collabo a ion-based models
( ole models) a e composed o p oduce he co e a chi ec u e, e.g. [6,21]. In hese
app oaches, componen -based models a e used whe e each componen is assigned
a se o in e aces and a se o connec o s o speci y in e ac ions among hem.
Again, his is simila app oach o he app oach o some AOSE me hodologies in
building he a chi ec u e, called he s uc u al o ganiza ion, e.g. [22].
3.2 O e iew o MaCMAS/UML
The o ganiza ional me apho has been p o en o be one o he mos app op ia e
ools o enginee ing a MAS, and has been success ully applied, e.g., [10,12,22].
I shows ha a MAS o ganiza ion can be obse ed om wo iewpoin s [22]:
Acquain ance poin o iew: shows he o ganiza ion as he se o in e ac-
ion ela ionships be ween he oles played by agen s.
S uc u al poin o iew: shows agen s as a i ac s ha belong o sub-o ga-
niza ions, g oups, eams. In his iew agen s a e also s uc u ed in o hie a -
chical s uc u es showing he social s uc u e o he sys em.
Manda o y Op ional
A leas one
o hem
Only one
o hem
I a he p esen , he hei is:
Dependency
Fligh and
O bi
...
Mo e
Snake Amoeba Rolling
Walk
Gas
p op.
Use Sail
o O bi
and ligh
Fig. 1. Sub-se o he ea u e model o ou case s udy
Bo h iews a e in ima ely ela ed, bu hey show he o ganiza ion om ad-
ically di e en iewpoin s. Since any s uc u al o ganiza ion mus include in e -
ac ions be ween agen s in o de o unc ion, i is sa e o say ha he acquain-
ance o ganiza ion is always con ained in he s uc u al o ganiza ion. The e o e,
a na u al map is o med be ween he acquain ance o ganiza ion and he co e-
sponding s uc u al o ganiza ion. This is he p ocess o assigning oles o agen s
[22]. Then, we can conclude ha any acquain ance o ganiza ion can be modeled
o hogonally o i s s uc u al o ganiza ion [8].
MaCMAS is he AOSE me hodology ha we use o ou app oach and is
based on p e iously de eloped concep s [18]2. I is specially ailo ed o model
complex acquain ance o ganiza ions [17].
We ha e adop ed his app oach because i p esen s se e al common ea u es
wi h SPL app oaches, ha eases he in eg a ion o bo h ields. Going in o de ails,
he main easons a e: Fi s , a e applying i we ob ain a hie a chical diag am,
he aceabili y diag am, ha is qui e close o a ea u e model. Second, i ma ches
well wi h p oduc lines, since i also p oduces a se o ole models ha ep esen
he ma e ializa ion o each sys em goal a he analysis le el. Thi d, i p o ides
UML-based models which a e he de- ac o s anda d in modeling, and which
will dec ease he lea ning-cu e o enginee s. Fou h, i p o ides echniques
o composing acquain ance models, which is needed o building he s uc u al
o ganiza ion o he sys em, allowing us o g oup oge he hose ea u es ha
a e common o all o he p oduc s in he p oduc line and hus, build he co e
a chi ec u e.
Fo he pu poses o his pape we only need o know a ew ea u es o MaC-
MAS, mainly he models i uses. Al hough a p ocess o building hese models
is also needed, we do no add ess his in his pape , and e e he in e es ed
eade o he li e a u e on his me hodology. F om he models i p o ides, we
a e in e es ed in he ollowing:
2See h p://james.eii.us.es/MaCMAS/ o de ails and case s udies o his me hodol-
ogy

A) Plan Model
B) Role Model
Measu e
isk o sola
s o ms P o ec ing
[SelP o ecSC.s o mIn ensi y
> RiskFo Sys emsFac o ]
SailAsShield
[SelP o ecSC.s o mIn ensi y
> RiskFo Sys emsFac o ]
o SubSys
Measu eS o ms
Space
<<En i onmen >>
Space
s o mVec o : Vec o 3
s o mIn ensi y:Real
Sel P o ecSC
S o mVec o : Vec o 3
s o mIn ensi y : Real
as e oidRela i ePos: Pos
s o mType: S o mTypes
no malizeSTVec (Vec o 3):Vec o 3
Role Goal: Sel -p o ec ion
mRI Measu e S o ms Goal:
P o ec om sola s o m
mRI o SubSys Goal: P o ec
om sola s o m
mRI SailAsShieldGoal: P o ec
om sola s o m
Sel P o ecSC
Sel P o ecSC
Sel P o ecSC
Gua d:
SelP o ecSC.s o mIn ensi
y > RiskFo Sys emsFac o
o SubSys
Goal: Powe o subsys ems
Pa e n: sel -p ocedu e
In: Ou :
Sel P o ecSC.s o mIn ensi y
SailAsShield
Goal: Use sail as shield
Pa e n: sel -p ocedu e
In: Ou :
Sel P o ecSC.s o mVec o
Sel P o ecSC.s o mIn ensi y
Measu eS o ms
Goal: Measu e S o m Risk
Pa e n: Sense En i onmen
In:
Space.s o mVec o
Space.s o mIn ensi y
Ou :
Sel P o ecSC.s o mIn ensi y
Sel P o ecSC.s o mVec o
Gua d:
SelP o ecSC.s o mIn ensi
y > RiskFo Sys emsFac o
Fig. 2. “Sel -p o ec ion om sola s o ms” au onomic p ope y model
a) S a ic Acquain ance O ganiza ion View: This shows he s a ic in e ac-
ion ela ionships be ween oles in he sys em and he knowledge p ocessed
by hem. In his ca ego y, we can ind models o ep esen ing he on ology
managed by agen s, models o ep esen ing hei dependencies, and ole
models. Fo he pu poses o his pape we only need o de ail ole models:
Role Models: show an acquain ance sub-o ganiza ion as a se o oles col-
labo a ing by means o se e al mul i-Role In e ac ions (mRI) [14]. mRIs
a e used o abs ac he acquain ance ela ionships amongs oles in he
sys em. As mRIs allow abs ac ep esen a ion o in e ac ions, we can
use hese models a wha e e le el o abs ac ion we desi e.
In Figu e 2.B), we show he ole model co esponding o an au onomic
ea u e o ou case s udy ha models how o ma e ialize p o ec ion om
a sola s o m a he domain design le el. Roles a e ep esen ed as UML-
in e ace-like shapes, and mRIs a e shown as UML-collabo a ion-like
shapes. Bo h no a ions a e ex ended wi h some in o ma ion equi ed o
modeling agen s, such as goals, o collabo a ion pa e ns. One example
o ole a is Sel P o ec SC ; i shows i s goals, he knowledge ha should
be managed o ul ill hese goals, and he se ices i p o ides o be able
o achie e i s goals. One example o an mRI is Measu e S o ms: i is
linked o i s pa icipan oles, and i shows he goal i ul ills, he pa -
e n o collabo a ion be ween i s pa icipa ing oles, and he knowledge
i bo h needs and p oduces in o de o ul ill he goal.
b) Beha io o Acquain ance O ganiza ion View: The beha io al aspec
o an o ganiza ion shows he sequencing o mRIs in a pa icula ole model.
I is ep esen ed by wo equi alen models:
Plan o a ole: sepa a ely ep esen s he plan o each ole in a ole model
showing how he mRIs o he ole sequence. I is ep esen ed using UML
2.0 P o ocolS a eMachines [11]. I is used o ocus on a ce ain ole, while
igno ing o he s.
Plan o a ole model: ep esen s he o de o mRIs in a ole model wi h
a cen alized desc ip ion. I is ep esen ed using UML 2.0 S a eMachines
[11]. I is used o acili a e he unde s anding o he whole beha io o a
sub-o ganiza ion.
In Figu e 2.A), we show he plan o he ole model. As can be seen,
each ansi ion in he s a e machine ep esen s an mRI execu ion. In his
model, we can show ha we ha e o execu e he mRI measu e s o ms un-
il he isk o sola s o ms is highe han a cons an , shown wi h a gua d.
Thus, when he gua d holds, we ha e o execu e he mRI sailAsShield.
c) T aceabili y iew: This model shows how models in di e en abs ac ion
laye s ela e. I shows how mRIs a e abs ac ed, composed o decomposed
by means o classi ica ion,agg ega ion,gene aliza ion o ede ini ion. No ice
ha we usually show only he ela ions be ween in e ac ions because hey
a e he ocus o modeling, bu all he elemen s ha compose an mRI can also
be ela ed. Finally, since an mRI p esen s a di ec co ela ion wi h sys em
goals, aceabili y models clea ly show how a ce ain equi emen sys em
goal is e ined and ma e ialized. No ice ha we do no show his model
since, adding commonali ies and a iabili ies, i is equi alen o he ea u e
model ha we show la e .
4 O e iew o ou app oach o building he co e
a chi ec u e
F om all he ac i i ies ha ha e o be pe o med o se ing up a p oduc line,
we show he e a subse conce ning he de elopmen o he co e a chi ec u e om
he modeling poin o iew. Thus, we do no co e ac i i ies such as p oduc
managemen since i alls ou o he scope o his pape .
In Figu e 3, we show he So wa e P ocess Enginee ing Me amodel (SPEM)
de ini ion o he so wa e p ocess o ou app oach. The i s s age o be pe o med
consis o de eloping a se o models in di e en laye s o abs ac ion whe e we
ob ain a MaCMAS aceabili y model and a se o ole models showing how
each goal is ma e ialized. This is achie ed by applying he MaCMAS so wa e
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           
      

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
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       
       

    

  
!
      

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
  
!
      
Fig. 3. O e iew o ou app oach
p ocess. The second ac i i y shown is esponsible o adding commonali ies and
a iabili ies o he aceabili y model. La e , we pe o m a commonali y analysis
o ind ou which ea u es, called co e ea u es, a e mo e used ac oss p oduc s.
Finally, we compose he ole models co esponding o hese ea u es o ob ain
he co e a chi ec u e. The ollowing sec ions desc ibe hese ac i i ies.
5 Building he acquain ance o ganiza ion and he ea u e
model
A e applying MaCMAS, as we we e building a MAS ha co e s he unc-
ionali y o all p oduc s in he amily, we ob ain a model o he acquain ance
o ganiza ion o he sys em: ole models, plan models and a aceabili y model.
Once we ha e buil he acquain ance o ganiza ion, we ha e o modi y he ace-
abili y diag am o add in o ma ion on a iabili y and commonali ies, as shown
in Figu e 5, o ob ain a ea u e model o he amily. We do no de ail his p ocess
since i elies on aking each node o he aceabili y diag am and de e mining i
i is manda o y, op ional, al e na i e, o -exclusi e, o i i depends on o he (s),
as shown in he igu e.
MaCMAS guides his en i e p ocess using hie a chical goal-o ien ed equi e-
men documen s om which all o he models a e p oduced. Thus, he e is a
di ec aceabili y be ween sys em goals and ole models. This aceabili y is
easible since when a sys em goal is complex enough o equi e mo e han one
agen in o de o be ul illed, a g oup o agen s a e equi ed o wo k oge he .
Hence, a ole model shows a se o agen s, ep esen ed by he ole hey play,
ha join o achie e a ce ain sys em goal (whe he by con en ion o coope a-
ion). MaCMAS uses mRIs o ep esen all o he join p ocesses ha a e equi ed
and a e ca ied ou amongs oles in o de o ul ill he sys em goal o he ole
Space
<<En i onmen >>
Sola Disc
s o mVec o : Vec o 3
s o mIn ensi y:Real
Sel P o ecSS
S o mVec o : Vec o 3
s o mIn ensi y : Real
as e oidRela i ePos: Pos
s o mType: S o mTypes
Role Goal: Sel -p o ec ion
mRI Meassu e S o ms Goal:
P o ec om sola s o m
mRI o SubSys Goal: P o ec
om sola s o m
mRI SailAsShieldGoal: P o ec
om sola s o m
Sel P o ecSS
Sel P o ecSS
Sel P o ecSS
Gua d:
SelP o ecSC.s o mIn ensi
y > RiskFo Sys emsFac o
o SubSys
Goal: Powe o subsys ems
Pa e n: sel -p ocedu e
In: Ou :
Sel P o ecSS.s o mIn ensi y
SailAsShield
Goal: Use sail as shield
Pa e n: sel -p ocedu e
In: Ou :
Sel P o ecSS.s o mVec o
Sel P o ecSS.s o mIn ensi y
Meassu eS o ms
Goal: Meassu e S o m Risk
Pa e n: Sense En i onmen
In:
Space.s o mVec o
Space.s o mIn ensi y
Ou :
Sel P o ecSS.s o mIn ensi y
Sel P o ecSS.s o mVec o
Gua d:
SelP o ecSC.s o mIn ensi
y > RiskFo Sys emsFac o
A oid
C ashing
A oid un a
ou o
powe
P o ec
om sola
s o ms
Sel -
P o ec ion
Measu e
sola s o ms
Swi ch o
sub-sy ems
Use sail as
a shield
A oid
c ashing
A oid
Ou powe
P o .
Sola S
Sel
Sel -
-P o ec ion
P o ec ion
Role
Role
<<
<<en i onme
en i onme >>
>>
Space
Space
Abs ac ion Laye 3
Abs ac ion Laye 4
Fig. 4. Role model/ ea u es ela ionship
model. These also pu sue sys em sub-goals as shown in Figu e 4, whe e we can
see he co ela ion be ween hese elemen s and he ea u e model ob ained om
he aceabili y diag am. No e ha he ole model o his igu e can be also seen
in Figu e 2.
6 Commonali y analysis
To build he co e a chi ec u e o he sys em we mus include hose ea u es
ha appea in all he p oduc s and hose whose p obabili y o appea ing in a
p oduc is high. In [1,2] he au ho s de ine he commonali y o a ea u e as he
pe cen age o p oduc s de ined wi hin a ea u e model ha con ains he ea u e.
A calcula ion me hod o his and many o he ope a ions ela ed o ea u e
models analysis is p oposed using Cons ain Sa is ac ion P oblems (CSP). The
de ini ion o commonali y is he ollowing:
De ini ion 1 (Commonali y). Le Mbe a ea u e model and F he ea u e
wi hin Mwhose commonali y we wan o calcula e. Le Pbe he se o p oduc s
de ined by Mand PF he subse o p oduc s Pcon aining F.commonali y(F)
is de ined as ollows:
commonali y(M, F ) = |PF| · 100
|P|
a e p omising and o e ime we en isage signi ican bene i s om employing a
p oduc line app oach o such missions.
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