Generating Fuzzy Term Sets for Software Project Attributes using and Real Coded Genetic Algorithms

Transcription

1 Generatng Fuzzy Ter Sets for Software Proect Attrbutes usng Fuzzy C-Means C and Real Coded Genetc Algorths Al Idr, Ph.D., ENSIAS, Rabat Alan Abran, Ph.D., ETS, Montreal Azeddne Zah, FST, Fes Internatonal Conference on ICT for Musl World Noveber,, 2-23, 23, 26, Kuala Lapur,, Malaysa Al Idr/ENSIAS

2 2 Outlne Motvatons and Obectves Fuzzy C-Means for Clusterng Software Proect Attrbutes Buldng Mebershp Functons of Fuzzy sets usng Real Coded Genetc Algorths Overvew of Eprcal Results Conclusons and Future Work Al Idr/ENSIAS

3 3 Motvatons and Obectves Software proect attrbutes are used by estaton odels n software engneerng to predct soe portant attrbutes of future enttes such as software developent effort, software relablty and prograers productvty Software cost estaton odels use as nputs software sze, software relablty, and experence of the personnel to estate the requred software developent effort Proble : Many software proect attrbutes are easured ether on Nonal or Ordnal scale type coposed of lngustc values such as, low, very low, coplex, etc. In the COCOMO II software cost estaton odel 7 aong 23 cost drvers are easured on an Ordnal scale coposed of sx lngustc values, very low, low, nonal, hgh, very hgh, and extra-hgh Al Idr/ENSIAS

4 4 when dealng wth lngustc values handlng precson, uncertanty and partal truth s unavodable However, the software engneerng county often uses nubers or classcal ntervals to represent these lngustc values Such transforaton and representaton does not c the way n whch huans nterpret lngustc values and consequently cannot deal wth precson and uncertanty To overcoe ths ltaton, we have suggested the use of fuzzy sets rather than classcal nterval (or nubers) to represent lngustc values taton (Idr, 2-26) Al Idr/ENSIAS

5 The fuzzy sets and ther ebershp functons are defned by usng: 5 Eprcal technques whch construct ebershp functons fro expert knowledge; or Autoatc technques, whch construct ebershp functons fro hstorcal data usng clusterng technques Because, n any cases, the descrptons gven of the software attrbutes are nsuffcent to eprcally buld ther fuzzy representatons -> Autoatc technques Obectve we suggest the use of the Fuzzy C-Means clusterng technque (FCM) and a Real Coded Genetc Algorth (RCGA) to buld the fuzzy representatons of the software attrbutes Al Idr/ENSIAS

6 Attrbute Nuercal data Clusterng by FCM 6 Fuzzy clusters Centers, Mebershp degrees Approxatng by RCGA Fuzzy sets Mebershp functons The valdaton s done on a dataset that contans 263 hstorcal software proects Each proect s descrbed by 3 attrbutes Software sze easured n ters of KDSI 2 attrbutes related to the software developent envronent such as software coplexty, the ethod used n the developent and the te and storage constrants posed on the software Al Idr/ENSIAS

7 7 Attrbues Desgnaton SIZE Software Sze DATA Database Sze TIME Executon Te Constrant STOR Man Storage Constrant VIRTMIN, Vrtual Machne Volatlty VIRT MAJ TURN Coputer Turnaround ACAP Analyst Capablty AEXP Applcatons Experence PCAP Prograer Capablty VEXP Vrtual Machne Experence LEXP Prograng Language Experence SCED Requred Developent Al Idr/ENSIAS

8 8 Fuzzy C-Means for Clusterng Software Proect Attrbutes The FCM algorth s a fuzzy clusterng ethod used to generate a known nuber of clusters (c) fro a set of nuercal data The deternaton of ths nuber s stll an open proble n clusterng. Often, eprcal knowledge or a set of evaluaton crtera s used. In ths work, we use the Xe-Ben fuzzy cluster valdty crteron proposed FCM s an teratve algorth that as to fnd cluster centers ( C ), c and the atrx U = ( u ), n, c that nze the followng obectve functon: Mn J = c 2 c = x c = = = n ( U,C ) = ( u ) =, =,..., n where s the control paraeter of fuzzness; U = u s the partton atrx, contanng the ebershp values of all data n all clusters; u ( ) Al Idr/ENSIAS

9 9 The outlne of the FCM algorth can be stated as follows (Bezdek, 98): Step : Randoly ntalze the ebershp atrx (U) that has the followng constrants: c = Step 2: Calculate centrods(c ) by usng the equaton: c u =, =,...,n; u n = = n u = Step 3: Copute dsslarty between centrods and data ponts. Stop f ts proveent over prevous teraton s below a threshold. u x Step 4: Copute a new U usng the followng equaton. Go to Step 2. u = 2 /( ) c x c k = x c k Al Idr/ENSIAS

10 For each COCOMO 8 software attrbute, several experents were conducted wth the FCM algorth, each te usng a dfferent ntal atrx U. The desred nuber of clusters (c) s vared wthn the nterval [3,6] The paraeter s fxed to 2 n all experents. We use the Xe-Ben crteron to decde on the nuber of clusters. For each attrbute, we choose the nuber of clusters that nzes the value of the Xe-Ben crteron.,8,6,4,2 5 5 Cluster Cluster 2 Cluster 3,8,6,4,2 5 Cluster Cluster 2 Cluster 3 Cluster 4 Data attrbute Te attrbute Al Idr/ENSIAS

11 Buldng Mebershp Functons of fuzzy sets for the COCOMO 8 attrbutes After generatng fuzzy sets (clusters ) wth ther partton by eans of FCM, we use an RCGA to buld ebershp functons for these clusters; Mebershp functons can be trapezodal, trangular or Gaussan. Our RCGA conssts n buldng a set of ebershp functons that nterpolates and nzes the ean square error, whch s defned as follows: subect to = n MSE( µ,.., µ c ) = ( µ ( x ),.., µ c( x ))-( u n 2,..,uc, ) = c = µ µ x ) = u, n; c ( x ) = ( Al Idr/ENSIAS

12 2 The use of an RCGA to fnd ebershp functons requres the deternaton of certan paraeters, such as: the codng schee, the ftness functon, and the varous genetc operators (selecton, crossover and utaton). Concernng the codng schee, a chroosoe represents the set of the unknown ebershp functons, ( µ ), c, assocated wth the c fuzzy sets generated by the FCM The shape of the ebershp functons can be trapezodal, trangular or Gaussan Thus, each chroosoe encodes a set of ebershp functons n a K real vector (,..., ). The genes are obtaned fro the shape of the ebershp functons. Al Idr/ENSIAS

13 For trapezodal ebershp functons For trangular ebershp functons Al Idr/ENSIAS

14 For Gaussan ebershp functons 4 c,σ c 2, σ 2,.. c k-, σ k-, c k, σ k k 3, k 2, k, k Al Idr/ENSIAS

15 The ftness functon F s obtaned usng the followng forula 5 MSE( = n ) = µ ( x ) - n = y 2 F ( ) = = M = MSE ( MSE ) ( ) For the three genetc operators (selecton, crossover and utaton), we use those that are specfc to RCGAs Al Idr/ENSIAS

16 Data attrbute Te attrbute Al Idr/ENSIAS

17 7 Concluson and Future Work We have used the Fuzzy C-Means clusterng technque (FCM) and a Real Coded Genetc Algorth (RCGA) (the FCM-RCGA process) to buld the fuzzy representatons for the COCOMO 8 attrbutes The ebershp functons generated ay be trapezodal, trangular or Gaussan. We are currently lookng at the accuracy of cost estaton odels based on CBR when usng the FCM-RCGA process rather than eprcal knowledge for buldng fuzzy sets (SETIT, March, 27). Al Idr/ENSIAS

18 8 Thank you Al Idr/ENSIAS