An e olu iona y app oach o es ima ing so wa e de elopmen p ojec s
q
Jesu
Âs S. Aguila -Ruiz*, Isabel Ramos, Jose
ÂC. Riquelme, Miguel To o
Depa amen o de Lenguajes y Sis emas In o ma
 icos, Uni e sidad de Se illa, Ad a. Reina Me cedes s/n, 41012 Se illa, Spain
1. In oduc ion
The use o dynamic models and simula ion en i onmen s
(S ella, Vensim, iThink, Powe sim, e c.) in connec ion wi h
so wa e p ojec s pa ed he way o ools ha allow us o
simula e he beha iou o such p ojec s a he s a o he
1990s. Wi h hese ools, which a e named So wa e P ojec
Simula o s (SPS), he p ojec manage could expe imen
wi h di e en managemen policies a no cos , in o de o
ake a decision ha migh be he mos sui able and accu a e.
Ques ions such as ªwha would happen i ¼?º o ªwha is
happening¼?º o ªwha would ha e happened i ¼?º a e
some imes c ucial.
The achie emen o he goals o a so wa e p ojec
depends on h ee ac o s:
²The ini ial es ima ions o he necessa y esou ces.
²The managemen policies o be applied.
²The cha ac e is ics o he o ganiza ion: ma u i y le el,
expe ience, a ailabili y o esou ces, e c.
The dynamic models o so wa e p ojec s ha e a se o
ini ial pa ame e s ha de®ne he managemen policies o be
applied. These policies a e associa ed wi h he o ganiza ion
(ma u i y le el, a e age delay, u no e o he p ojec 's
wo k o ce, e c.) and he p ojec (numbe o asks, ime,
cos , numbe o echnicians, so wa e complexi y, e c.).
The use o an SPS [10] will be complex i he numbe o
pa ame e s is e y la ge. Fo example, he dynamic model
shown in Re . [1] has abou 60 pa ame e s. The e o e, he
impac on he p ojec o 60 di e en ea u es could be
known. The mo e pa ame e s he model has, he mo e
complex he de elopmen o he p ojec and he use o he
model. I someone asked he p ojec manage ªwha will be
he a e aged dedica ion o he echnicians?º, he answe
would p obably be ª om 70 o 80%º, o some hing like
ha . G ea e p ecision is unlikely ( o example, an answe
like `76%'). The p ojec manage usually adds con ingency
ac o s. Machine lea ning echniques a oid some o hese
p oblems by using in e als ins ead o simple alues. In
gene al, hese echniques p oduce decision ules. When
decision ules a e used as managemen policies, hey a e
called managemen ules.
Managemen ules a e ob ained by ollowing he s eps
shown in Fig. 1.
Decisions made in any o ganiza ional se ing a e based on
wha in o ma ion is ac ually a ailable o he decision-
make s. The compu e simula ion ools o dynamical
sys ems p o ide us wi h he possibili y o changing one o
se e al ac o s while he emaining ones a e kep
unchanged. The implica ions o manage ial policies on he
q
The esea ch was suppo ed by he Spanish Resea ch Agency CICYT
unde g an TIC99-0351.
* Co esponding au ho .
E-mail add esses: [email p o ec ed] (J.S. Aguila -Ruiz), isabel. a-
[email p o ec ed] (I. Ramos), [email p o ec ed] (J.C. Riquelme), miguel. o -
[email p o ec ed] (M. To o).
so wa e de elopmen p ocess could be analysed o in e he
bes decision.
Howe e , a knowledge-based sys em migh help us o
de e mine a subse o decisions mo e accu a ely. The
simula ion o he p ojec p oduces his knowledge wi h
he da abase. Then, we only ha e o ex ac ha knowledge
in a comp ehensible way, o example, decision lis s o
decision ees. In hese da a s uc u es we can ®nd an
easy- o-unde s and ac ion o ma ch he ac ual p ojec esul s
wi h he p ojec es ima ions. The sea ch o good decisions
om he da abase gene a ed by simula ion is a highly
complex ask. E olu iona y algo i hms p o ide us wi h a
me hod o ®nding good solu ions (in ou case, decision
ules) in a complex sea ch space (da abase gene a ed by
an SPS) whe e pa ame e s do no ha e an ob ious ela ion-
ship.
O he modelling echniques ha e been applied o
es ima ing e o o cos o so wa e p ojec s: o dina y
leas -squa es eg ession, analogy-based es ima ion
[5,13,15], gene ic p og amming [3].
2. Decision ees: C4.5
Decision ees a e a pa icula ly use ul echnique in he
con ex o supe ised lea ning. A decision ee is a classi®e
wi h he s uc u e o a ee, whe e each node is a lea indi-
ca ing a class, o an in e nal decision node ha speci®es
some es o be ca ied ou on a single a ibu e alue, and
one b anch and sub ee o each possible ou come o he
es . The main ad an age o decision ees is hei immedia e
con e sion o ules easily meaning ul by humans. Howe e ,
classi®ca ion ees wi h uni a ia e h eshold decision
bounda ies migh no be sui able o p oblems whe e he
co ec decision bounda ies a e non-linea mul i a ia e
unc ions.
The mos commonly used ool is C4.5 [9], which basi-
cally consis s in a ecu si e algo i hm wi h di ide and
conque echnique ha op imises he ee cons uc ion on
basis o gain in o ma ion c i e ion. The p og am ou pu is a
g aphic ep esen a ion o he ound ee, a con usion ma ix
om classi®ca ion esul s and an es ima ed e o a e. C4.5
is e y easy o se up and un; i only needs a decla a ion o
he ypes and ange o a ibu es in a sepa a e ®le o da a and
i is execu ed wi h UNIX commands wi h e y ew pa a-
me e s.
3. E olu iona y algo i hm
E olu iona y algo i hms (EA) a e a amily o compu a-
ional models inspi ed by he concep o e olu ion. These
algo i hms employ a andomised sea ch me hod o ®nd solu-
ions o a pa icula p oblem [6]. This sea ch is qui e di e -
en om he o he lea ning me hods. An EA is any
popula ion-based model ha uses selec ion and ecombina-
ion ope a o s o gene a e new sample examples in a sea ch
space. The main ask in applying EAs o any p oblem
consis s in selec ing an app op ia e ep esen a ion (coding)
and an adequa e e alua ion unc ion (® ness). In classical
EA, he membe s o he popula ion ( ypically main aining a
cons an size) a e ep esen ed as ®xed-leng h s ings o
bina y digi s. The leng h o he s ings and he popula ion
size Pa e comple ely dependen on he p oblem. The popu-
la ion simula es he na u al beha iou , since he ela i ely
`good' solu ions p oduce o sp ing which eplace he ela-
i ely `wo se' ones, e aining many o he ea u es o hei
pa en s. The es ima e o he quali y o a solu ion is based on
a ® ness unc ion, which de e mines how good an indi idual
is wi hin he popula ion in each gene a ion. New indi iduals
(o sp ing) o he nex gene a ion a e o med by using
(no mally) wo gene ic ope a o s: c osso e and mu a ion.
C osso e combines he ea u es o wo indi iduals o c ea e
se e al (commonly wo) indi iduals. Mu a ion ope a es by
andomly changing se e al componen s o a selec ed indi-
idual.
Ou sys em used an EA o sea ch he bes solu ions and
p oduced a hie a chical se o ules [11]. The hie a chy
ollows ha an example will be classi®ed by he i h ule i
i does no ma ch he condi ions o he (i21) h p eceden
ules. The ules a e sequen ially ob ained un il he space is
o ally co e ed. The beha iou is simila o a decision lis
[12]. The s uc u e o he se o ules will be as shown in Fig.
2.
As men ioned in Re . [4], one o he p ima y mo i a ions
o using eal-coded EAs is he p ecision o ep esen
Fig. 1. Au oma ic gene a ion o managemen ules.
a ibu es alues and ano he is he abili y o exploi he
g adualness o unc ions o con inuous a ibu es. Fo ha
eason ou algo i hm uses eal coding.
3.1. Coding
In o de o apply EAs o a lea ning p oblem, we need o
selec an in e nal ep esen a ion o he space o be sea ched
and de®ne an ex e nal unc ion ha assigns ® ness o candi-
da e solu ions. Bo h componen s a e c i ical o he success-
ul applica ion o he EAs o he p oblem o in e es .
The ep esen a ion o an indi idual akes he o m shown
in Fig. 3, whe e l
i
and u
i
a e alues ep esen ing an in e al
o he a ibu e. The las posi ion (class) is he alue o he
class. The numbe o classes de e mines he se o alues o
which i belongs, i.e. i he e a e ® e classes, he alue will
belong o he se 0, 1, 2, 3, 4.
Each ule will be ob ained om his ep esen a ion, bu
when liminaio uimaxai;whe e a
i
is an a ibu e,
he ule will no ha e ha alue. Fo example, in he ® s
case he ule would be [±, ] and in he second case [ ,±],
being any alue wi hin he ange o he a ibu e. I bo h
alues a e equal o he bounda ies, hen he ule [±,±] a ises
o ha a ibu e, which means ha i is no ele an . Unde
hese assump ions, some a ibu es migh no appea in he
se o ules.
3.2. Algo i hm
The algo i hm is a ypical sequen ial co e ing EA [7]. I
chooses he bes indi idual o he e olu iona y p ocess,
ans o ming i in o a ule which is used o elimina e da a
om he aining ®le [14]. In his way, he aining ®le is
educed o he ollowing i e a ion. A e mina ion c i e ion
could be eached when mo e examples o co e do no exis .
The me hod o gene a ing he ini ial popula ion consis s in
andomly selec ing an example om he aining ®le o
each indi idual o he popula ion. A e wa ds, an in e al
o which he example belongs is ob ained by adding and
sub ac ing a small andom quan i y om he alues o he
example.
3.3. Fi ness unc ion
The ® ness unc ion mus be able o disc imina e be ween
co ec and inco ec classi®ca ions o examples. Finding an
app op ia e unc ion is no a i ial ask, due o he noisy
na u e o mos da abases. The e olu iona y algo i hm maxi-
mizes he ® ness unc ion o each indi idual. I is gi en by
Eq. (1)
i2N2CEi 1Gi1co e agei1
whe e Nis he numbe o examples being p ocessed; CE(i)
is he class e o , which is p oduced when he example i
belongs o he egion de®ned by he ule bu does no ha e
he same class; G(i) is he numbe o examples co ec ly
classi®ed by he ule; and he co e age o he i h ule is
he p opo ion o he sea ch space co e ed by such ule.
Each ule can be quickly expanded o ®nd mo e examples,
hanks o he co e age in he ® ness unc ion.
4. Pos -mo em analysis o a so wa e p ojec
The p ojec selec ed o s udy in his pape is a pe sonnel
managemen sys em p ojec which was ca ied ou join ly
by wo local so wa e companies. The da a pe ains o he
design, coding and es phases. The e o e, he analysis phase
and o he ®nal ac i i ies a e no conside ed. The da a o
ini ialising he pa ame e s o he SPS we e collec ed om
he acking documen s o he o iginal p ojec and he
expe ience o he p ojec manage .
Ini ially, he e o expended on he p ojec was es ima ed
o equi e 208 man-days and he p ojec was es ima ed o be
Fig. 2. Hie a chical se o ules.
Fig. 3. Rep esen a ion o an indi idual o he gene ic popula ion.
Table 1
Pa ame e s and a iables o he en i onmen o he p ojec and o ganiza ion
Name In e al Desc ip ion Es ima ed alue
ADMPPS (0.3±1) A e age daily manpowe pe
s a (day/day)
0.4
AQADLY (5±15) A e age delay o quali y
assu ance (days)
5
HIASDY (5±100) A e age hi ing and
assimila ion delay (days)
20
INUDST (0.3±1) Ini ial unde s a ®ng ac o
(dimensionless)
1
MNHPXS (1±4) Mos new hi es pe
expe ienced s a ( ech./ ech.)
1.5
MXSCDX (1±1E6) Maximum schedule
comple ion da e ex ension
(dim.)
5
TRNSDY (1±15) Time delay o ans e people
ou (days)
1
DLINCT (5±15) A e age delay in inco po a ing
disco e ed asks (days)
5
AVEMPT (500±1000) A e age employmen ime
(days)
1000
TRPNHR (0.1±0.4) Numbe o aine s pe new
employee (dimensionless)
0.15
UNDESM (0±50) Man-days unde es ima ion
ac ion (dimensionless)
48
UNDEST (0±50) Tasks unde es ima ion ac ion
(dimensionless)
15
comple ed in 101 days. The ac ual ®gu es we e 404 man-days
and 141 days, espec i ely. The e o e, he unde es ima ions o
e o and ime o his p ojec we e 48 and 28%, espec i ely.
Thea e age numbe o echnicians in ol edin he p ojec was
six and he numbe o lines o code (LOC) was 67,800. The
p ojec manage de®ned a ask as 270 LOC.
The eal e o spen on he ac i i ies o de elopmen
(design and coding) was 85% (404 £0.85 343), he es
being spen on es s. Assuming ha he 10% o he e o
expended on de elopmen (343 £0.1 34) was used o
e ision ac i i ies, he o al e o o de elopmen was
309 man-days (343 234 309).
Thus, he de elopmen p oduc i i y o his p ojec was
as ollows:
so wa e de elopmen p oduc i i y size in LOC
de elopmen e o
67;800
309 219:4 LOC=man-days
Some in e es ing da a om he p ojec a e shown in Table
1. Each ow con ains he name o he pa ame e in he
model, he ange o alues i can assume, a b ie desc ip ion
o i s meaning and he es ima ed alue a he beginning o
he p ojec . (This no a ion is he one used in he wo ks o
Abdel-Hamid [1].)
Se e al quali a i e labels, which a e illus a ed in Table
2, we e assigned o each pa ame e , depending on i s ange
o nume ic alues. This in o ma ion was p o ided by he
p ojec manage .
4.1. P ojec simula ion
The e olu ion o he necessa y e o , deli e y ime and
pending asks equi ed in o de o comple e he pe sonnel
managemen sys em ob ained by he SPS is illus a ed in
Fig. 4. I he esul s a e compa ed wi h he eal alues, we
can obse e ha , in he simula ion he es ima ed deli e y
ime is 151 days (ins ead o 141) and he es ima ed e o is
410 man-days (ins ead o 404). This means ha he absolu e
pe cen age e o was abou 6.62 and 1.46%, espec i ely. I
an SPS had been used a ® s , we would ha e known he
beha iou o he p ojec , and he absolu e pe cen age e o
migh ha e been smalle . In addi ion, in Fig. 4 i is possible
o no e ha he ® s adjus men s we e made nea he middle
o he p ojec (a ound 70 days) when i was de ec ed ha he
numbe o pending asks was g ea e han ha expec ed. The
decision coincided wi h he eal e olu ion o he pe sonnel
managemen sys em, since mo e han hal o he es ima ed
ime had been spen when mo e han hal o he pending
asks emained un®nished. Time and ®nal e o migh
inc ease i he g adien o he pending asks does no change.
Two addi ional conside a ions can be obse ed in Fig. 4:
® s , he es ima ed ini ial e o is modi®ed be o e he
ime, as is usual in he majo i y o he p ojec s being de el-
oped by he wo local so wa e-de elopmen companies;
and second, he changes applied o e o and ime a e
made simul aneously.
Da a om he eal e olu ion o he p ojec we e no
collec ed by he companies. We only know he ini ial and
®nal da a p o ided by he p ojec manage . The e o e, i
bo h simula ed and eal beha iou s a e compa ed ( his
was possible, hanks o he help o he p ojec manage ),
we could only see ha he ®nal es ima ed ime and e o
ob ained by means o simula ion a e in ag eemen wi h he
eali y. This is especially ue in wo espec s:
²The ea ly e isions we e done when hal o he ime had
been spen .
Table 2
Quali a i e desc ip ion o he pa ame e s
Name Nume ic in e al Quali a i e desc ip ion
ADMPPS (0.3±0.5) Low
(0.5±0.75) A e age
(0.75±1.0) High
UNDESM (0±15) Low
UNDEST (15±35) A e age
(35±50) High
TRPNHR (0.1±0.15) Low
(0.15±0.25) A e age
(0.25±0.40) High
Fig. 4. E olu ion o he necessa y e o , deli e y ime and pending asks o he pe sonal managemen so wa e (nominal simula ion), ob ained by he SPS.
²The e isions ha we e ca ied ou o adjus he de ec ed
de ia ions a ec ed bo h he ime and he e o simul a-
neously.
The u ili y o an SPS in analysing he e olu ion o
p ojec s ca ied ou by ou local so wa e-de elopmen
companies has been demons a ed, and gene ally any
p ojec could be analysed in he same way [1].
5. Managemen ules
5.1. The goals o he p ojec
Two goals o he managemen ules ha we a e going o
ob ain a e he ollowing:
²We would wish ha he alues o e o we e less han o
equal o he alue ob ained by he simula ion (410 man-
days). These possible alues a e labelled as GOOD. The
alues g ea e han 410 man-days a e labelled as BAD.
²We would wish ha he de elopmen ime we e less han
o equal o he alue ob ained by he nominal simula ion
(151 days). These alues a e labelled as GOOD. The
alues g ea e han 151 a e labelled as BAD.
5.2. Managemen ules om he e olu iona y algo i hm
Managemen ules a e ob ained by he ollowing s eps
(Fig. 1):
²De®ne he in e als o alues o he pa ame e s o he
dynamic model (Table 1).
²De®ne he goals o he p ojec ( alues o ime and cos ).
²Gene a e he da abase au oma ically. Each simula ion
p oduces a eco d wi h he alues o he pa ame e s and
he alues o he a iables (cos and ime) and his eco d
is sa ed in a ®le.
²F om he ®le gene a ed in he p eceding s ep, a se o
managemen ules is p o ided au oma ically o he deci-
sion-making ask.
I is impo an o no e ha he ® s wo s eps a o emen-
ioned a e pe o med by he p ojec manage and he nex
wo i ems a e execu ed au oma ically. The managemen
ules ob ained by e olu iona y algo i hms o es ima ing
simul aneously GOOD esul s o bo h ime and e o a e
shown in Fig. 5. The numbe o he ule and he numbe o
eco ds om he da abase co e ed by he ule a e shown
espec i ely, in b acke s.
The ules chosen o analyse he p ojec a e ules 1 and
2, since ule 1 co e s mo e han hal he cases o ecas
as GOOD and ule 2 has he smalle numbe o pa a-
me e s. Ano he good c i e ion o selec ing he mos
adequa e decision ule is choosing he ule ha ing
pa ame e s which a e easie o modi y and con ol and,
i possible, he ule in ol ing he smalles numbe o
pa ame e s. Once he ule se is ob ained, we ha e o
selec which pa ame e s do no ma ch he ini ial alues.
Obse ing Table 1, we could ew i e he managemen -
ule se by elimina ing he condi ions ha a e ma ched
wi h he ini ial alues. The new managemen - ule se is
illus a ed in Fig. 6.
Fo example, in he ule 1 om Fig. 5 he alues o he
pa ame e s TRP-NHR, UNDESM, UNDEST and HIASDY
we e ini ially es ima ed as belonging o he in e al de®ned
by he ule (Table 1), so ha he pa ame e s ADMPPS and
INUDST mus be he only ones o be modi®ed in o de o
ob ain good esul s (Fig. 6), since he p ojec is al eady
®nished.
Analysing he ules, we could s a e he ollowing:
²Rule 1: i he a e age daily manpowe pe s a
(ADMPPS) was g ea e han 52% and he ini ial unde -
s a ®ng ac o (INUDST) was less han 96%, hen he
p ojec ended o be owa ds GOOD.
²Rule 2: i he man-days unde es ima ion ac ion
(UNDESM) was less han 37%, hen he p ojec ended
o be owa ds GOOD (i he e o in he ini ial necessa y
e o had been less han ha es ima ed; in his p ojec he
alue o UNDESM was 48%).
Fig. 5. Managemen ules ob ained by he e olu iona y algo i hm o es ima ing good esul s o he necessa y e o and deli e y ime simul aneously.
Fig. 6. Final hie a chical se o managemen ules.

Al hough each ule pe mi s good es ima es, he SPS
allows us o compa e he esul s o he simula ion wi h
hose which would be ob ained by applying each manage-
men ule.
Fo example, he esul s ob ained by he applica ion o
ule 2 a e shown in Fig. 7. Bo h e o and ime a e ema k-
ably lowe han hose ob ained om he simula ion. In
conc e e e ms, he necessa y e o and ime would be
educed o 26 man-days and 13 days, espec i ely, i ule
2 had been applied. Wi h his in o ma ion, he p ojec
manage decides which ule is mo e app op ia e o achie -
ing he aims.
The SPS plays an impo an ole in he decision-making
ask: ® s , pos -mo em p ojec s can be analysed in o de o
in e which ac ions could imp o e he esul s; second, an a
p io i analysis would indica e he in e als wi hin which he
alues o he pa ame e s ha e a endency o achie e he
aims o he p ojec .
Taking an e ec i e decision is a e y complex ask. Some
c i e ia a e con adic o y. Fo example, in gene al, keeping
o he p ojec deadline has highes p io i y, i.e. i he p ojec
schedule is a isk, mo e manpowe will be added o he
p ojec [8]. Howe e , he B ooks' law s a es ha adding
mo e people o a la e so wa e p ojec makes i u he
delayed [2].
5.3. Managemen ules om C4.5
The managemen ules ob ained by he C4.5 ool o es i-
ma e simul aneously GOOD esul s o bo h e o and ime
a e shown in Fig. 8.
Those ules in ol ing less numbe o pa ame e a e easie
o s udy. Analysing ule 1, GOOD esul s could be ob ained
i he numbe o aine s pe new employee is less han 11%,
he man-days unde es ima ion ac ion is less han 31 and
he a e age hi ing and assimila ion delay is less han
69 days. Now we selec he pa ame e s ha do no ma ch
he ini ial alues. As we did wi h he ules gene a ed by he
e olu iona y algo i hm, we could ew i e he managemen -
ule se by elimina ing he condi ions ha a e ma ched wi h
he ini ial alues om Table 1. The new managemen - ule
se is shown in Fig. 9.
5.4. Compa ing he esul s ob ained by he e olu iona y
algo i hm and C4.5
In gene al, he e olu iona y algo i hm is mo e accu a e in
®nding solu ions in he sea ch space. This can be obse ed
examining he numbe o examples om he da abase ha
ha e been co e ed and he pe cen age o e he o al numbe
o GOOD examples (Table 3).
Fig. 7. Resul s ob ained by applying ule 2.
Fig. 8. Managemen ules ob ained by he C4.5 ool o es ima ing good esul s o he necessa y e o and deli e y ime simul aneously.
The bes ule ob ained by C4.5 con ains 6 (GOOD) exam-
ples. Howe e , he bes o he e olu iona y algo i hm
con ains 21 (GOOD) examples. Fo ou analysis, he mo e
accu a e ule is ha which is capable o co e ing g ea e
numbe o GOOD examples. The e o e, ule 1 om he
e olu iona y algo i hm is much be e han any ule
ob ained by C4.5. In addi ion, he o al numbe o GOOD
examples co e ed by he e olu iona y algo i hm is abou
90% wi h ou ules, in compa ison o he ® e ules equi ed
by C4.5 o co e abou 63%.
6. Ano he app oach
In Sec ion 5, we saw how an e olu iona y algo i hm au o-
ma ically p o ides managemen ules om a da abase
gene a ed by an SPS. Ano he in e es ing app oach consis s
in p esen ing g aphically he ela ionship be ween wo pa a-
me e s in he cases in which good esul s we e ob ained.
These g aphics in o m he p ojec manage abou he
ange o alues o he pa ame e s being analysed. An exam-
ple o his kind o analysis is shown in Fig. 10, whe e he
pa ame e s TRPNHR and ADMPPS a e compa ed, indica -
ing when he e o and he ime a e simul aneously good. In
Fig. 10, each axis is a pa ame e o he model and each case
labelled as GOOD (in he da abase) is ep esen ed by a poin
(in he ®gu e). In mos o he cases in which he necessa y
e o and he deli e y ime a e simul aneously GOOD, he
numbe o aine s pe new employee (TRPNHR) is less
han 25% and he a e age daily manpowe pe s a
(ADMPPS) is g ea e han 75%.
Logically, his in o ma ion is no ob ained au oma ically,
and we could no know whe he he pa ame e s ha a e
ep esen ed ha e an in¯uence on he esul s.
7. Conclusions
The use o simula o s and sys ems ha lea n decision
ules helps o es ima e so wa e p ojec s and o p oduce
managemen ules au oma ically o he decision-making
ask. These managemen ules could be applied:
²Be o e he p ojec has begun: de®ning mo e adequa e
manage ial policies.
²A e he p ojec has ®nished: doing a pos -mo em
analysis.
²When he p ojec is unning: aking immedia e decisions
(moni o ing).
Managemen ules make i possible o:
²ob ain alues conside ed as good ( e y good, no mal,
bad, e c.) o any a iable o in e es ( ime, e o , quali y,
numbe o echnicians, e c.), independen ly o oge he
wi h o he a iables;
²analyse manage ial policies capable o achie ing he
aims o he p ojec ;
²know o which ange o alues he pa ame e s mus
belong in o de o ob ain good esul s.
In sho , i is possible o gene a e managemen ules au o-
ma ically o any so wa e p ojec and o know he manage-
ial policies ha ensu e he achie emen o he ini ial aims.
The de ia ions om he ini ial o ecas could be de ec ed
(moni o ing) and he beha iou o he p ocess is well unde -
s ood h ough he managemen - ule se .
E olu iona y compu a ion p o ides an in e es ing app oach
o dealing wi h he p oblem o ex ac ing knowledge om
Fig. 9. Final se o managemen ules ob ained by C4.5.
Table 3
Compa ing he numbe o examples co e ed by he ules
Rule 1 2345To al
C4.5 5(12%) 6(14%) 5(12%) 5(12%) 5(12%) 26(63%)
EA 21(51%) 7(17%) 6(14%) 3(7%) ± 37(90%)
Fig. 10. Rela ionship be ween he a e age daily manpowe pe s a and he numbe o aine s pe new employee.
da abases gene a ed by SPS. The quali y o he se o ules
p oduced by he e olu iona y algo i hm has been compa ed
o hose gene a ed by C4.5. The esul s demons a e ha ou
app oach ®nd be e solu ions in he sea ch space, co e ing
mo e GOOD examples wi h less numbe o ules. And, wha
is mo e impo an , is ha he esul s (managemen ules) a e
applicable and bene®cial.
The au ho s conside ha his echnique con ibu es o
coping wi h he complex p oblem o decision-making
wi hin he so wa e p ojec de elopmen amewo k, and
i acili a es he use o dynamic models, since he p ojec
manage only has o p o ide he aims o he p ojec and he
ange o he pa ame e s, especially o hose ha ing a high
deg ee o unce ain y. We a e cu en ly wo king on he
applica ion o o he machine lea ning echniques ( uzzy
logic, associa ion ules, e c.) o he da abases gene a ed by
he SPS.
Acknowledgemen s
The au ho s a e g a e ul o J.J. Dolado o help ul
commen s and o he e iewe s o hei sugges ions.
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