VOL. 2, NO. 7, August 2012 ISSN ARPN Journal of Science and Technology All rights reserved.

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1 A Novel Imputaton Technque for Software Effort Estmaton Suresh Joseph. K, 2 Dr. Ravchandran.T Assstant Professor, Department of Computer Scence, School of Engneerng & Technology, Pondcherry Unversty, Puducherry, Inda. 2 Prncpal, Hndusthan Insttute of Technology, Combatore, Inda. ksjoseph.csc@gmal.com, 2 dr.travchandran@gmal.com ABSTRACT Statstcal analyss s greatly hndered wth mssng nformaton. It represents a loss of key data, but worse, t can ntroduce based results n the analyss. A way to rectfy the problem of mssng data s to employ a sound method of mputaton, a way to replace mssng values wth reasonable estmates. Ther exsts varety of estmaton models lke SLIM, COCOMO and other models lke machne learnng models whch requre accurate nputs for estmaton of effort. It s very dffcult to obtan such accurate nformaton at the early development stage of a software project. These ssues led to the ntroducton of varety of technques to solve the relevant ssues. The proposed approach s a hybrd approach whch works based on Genetc algorthm and emprcal estmaton model COCOMO - II. Keywords: Imputaton, Effort Estmaton, COCOMO II, Software Engneerng, Genetc Approach. INTRODUCTION Imputaton s the replacement of mssng values n data wth estmaton technques and assumptons. The major problem that hampers useful applcaton of mputaton methods s bas, when an estmator s long-run average (expectaton) dffers from the quantty beng estmated. The devaton becomes a danger. When ths dfference s systematcal, the results of analyses may be based and false conclusons are easly drawn. (Husman 2000) Defntely, an mputaton method wll be plausble and consstent, reduce bas whle preservng the relatonshp between tems wthn the data, and can be evaluated for bas and precson (Sande 982). Mssng data are exasperaton to a certan extent. Imputaton s one of the key strateges that researchers employ to fll n mssng data n a gven dataset. Solvng such ssues s very ntrcate to put nto operaton and t s problem specfc. Imputed data s used n order to fnd a sutable replacement for better accurate analyses. Imputaton s a method of modfyng for lost nformaton. Mssng reactons to nformaton artcles s a normal stuaton n any survey. Ths mssngness regularly happens snce the respondent denes or s unable to furnsh nformaton for a partcular feld or many and also because of typographcal mstakes. Mssng nformaton may lkewse effect from ms-keyng or by edtng process. a. Whether mputaton s a better model? Defntely mputaton model s a compatble one and s affluent enough whch confrms based on the assocatons and relatonshps among the other varables n the data set. Imputaton mposes models lke probablty model, Decson tree models, neural models on the complete data set and also other models. Ths paper provdes a performance comparson of COCOMO and proposed hybrd method for handlng mssng values n effort estmaton. The paper s organzed as the follows. Secton II, descrbes the related work on effort estmaton; Secton III. Approach to software estmaton; Secton IV. Explores the Evaluaton and performance analyss used n ths work and Result dscussons there on; Secton V concludes the outcome of the proposed research. 2. RELATED WORK a. Effort Estmaton The success n Engneerng and evaluaton of Software depends only when the stages of the SDLC are completed on tme. One of the crucal tasks assocated wth Software Project Management s estmatng cost estmaton. Now-a-days software development has become compettve and software developers struggle because of many reasons lke delverng product on tme at the specfed cost ensurng desrable qualty. Ths helps us to understand the mportance of estmatng effort, schedule n early stages of development of the software. It cannot be concluded that exact value of effort cannot provde accurate schedules though both are closely related wth each other. Schedules may slp when vague Requrements / Specfcatons are to be executed;.e. when clents make unantcpated change, mproper 69

2 tranng and personnel avalablty, sometmes mstakes can happen n ntal stages f not corrected n the begnnng. b. Classfcaton Analogue estmaton models Formal Estmaton model Expert estmaton Emprcal parametrc estmaton models Emprcal non-parametrc estmaton models Combnaton based estmaton c. Effort Estmaton By Analogy Ths method uses nformaton from smlar projects and derve estmate based on the past features of data, because t s a smlar form of reckonng as human problem solvng capablty (Angels and Stamelos, 2000; Leung, 2002). Ths method fnds the smlartes between projects t can be used n the early phase of the project. It s an easy way of fndng effort of the project. The major problem wth exstng analogy-based technque s lmted because of ther nablty to handle wth non-quanttatve data and mssng values. Analogy based method shows best results n 60% of the cases and 30% of the cases fal because of worst predcted accuracy, hence suggestng some nstablty (Ruhe et al., 2003). It can be a promsng n majorty cases but fals n certan cases. The smlartes between functons are dentfed by Eucldean smlarty (ES) and Manhattan smlarty (MS) (Sheppard and Schofeld, 997). The smlarty computaton s done as follows Where p and p' are the projects, WI s the weght assgned to each feature and t can vary between 0 and. F and f' dsplays the th feature of a project and n demonstrates the number of features. δ s used to obtan non zero results. The MS formula s smlar to the ES but t does computaton by fndng the absolute dfference between the features. The smlarty functon s as follows. After selectng the K most smlar projects, t s made possble to estmate the effort and cost of the new project as per the feature selected. The most common soluton functons are: the closest analogy as most smlar project (Walkerden and Jeffery, 999), the average of most smlar projects (Sheppard and Schofeld, 997), the medan of most smlar projects (Angels and Stmulus, 2000) and the nverse dstance weghted mean (Kadoda et al., 2000). The mean descrbes the average of the effort of K most smlar projects, where K >. The medan descrbes the medan of the effort of K most smlar projects, where K > 2. The nverse dstance weghted mean adjusts the porton of each project n estmaton by usng the Equaton. Where p shows the new project, pk llustrates the k th most smlar project, Cpk s the effort value of the k th most smlar project pk, Sm (p, pk) s the smlarty between projects pk and p and K s the total number of most smlar projects. d. Expert Estmaton Technques Ths estmaton schema was developed by Barry Boehm n 70s (Software Engneerng Economcs, Boehm), each group member n the estmaton team provdes an anonymous estmate, the coordnator assesses the estmates gven by the team and combnes the estmate, If the estmates are crazy reassessment s done fnally effort s computed. e. SEER SEER (System Evaluaton and Estmaton of Resources) s a propretary model owned by Galorath Assocates, Inc. In 988, Galorath Incorporated ths work on the orgnal verson of SEER-SEM whch resulted n an ntal soluton of 22,000 LOC. SEER s an algorthmc software project management applcaton planned specfcally for effort estmaton. Ths model s reled on the ntal effort of Dr. Randall Jensen. The mathematcal equatons that are used n SEER were not avalable to the publc, but Dr. Jensen n hs wrtngs made the basc equatons avalable for revew. The basc equaton of Dr. Jensen s also referred as "software equaton". 620

3 S e = C te (Kt d ) 0.5 Where, S s the effectve LOC, ct s the effectve developer technology constant, k s the total lfe cycle cost n man-years, and td s the development tme n years. f. COCOMO COCOMO (Constructve Cost Model) s an emprcal estmaton scheme proposed n 98. It s a model for estmatng effort, cost, and schedule for development of software projects. Ths parametrc model certanly provdes better results. Barry Boehm defnton towards hs model "Basc COCOMO s good for rough order of magntude estmates of software costs, but ts accuracy s necessarly lmted because of ts lack of factors to account for dfferences n hardware constrants, personnel qualty and experence, use of modern tools and technques, and other project attrbutes known to have a sgnfcant nfluence on costs." 3. APPROACH TO ESTIMATION To derve effort estmates and tme schedule requred to develop a software system; f the sze of the system s S and E s effort then F(S) = E and E= (a+bs c ) m(x) m(x) s the multplers ( The factors whch nfluences the effort ), a, b and c are constants. Based on ths relatonshp COCOMO model has been bult. a. COCOMO II Ths unque COCOMO Model has now been super-ceded by COCOMO II. In COCOMO II effort s expressed as Person-Month or the amount of tme a person spends workng on the software project for one month. b PM = a* Sze * Where a and b are the doman constants n the COCOMO model. It has 5 effort multplers. Ths estmaton scheme accounts the experence and data of the past projects, whch s extremely complex to understand and apply the same. 5 = E = B + 0.0* SF 5 j= j EM Hence, n prncple, the effort s calculated by multplyng the estmaton varable wth the constant a n the frst stage, and some effort can be added wth or deducted from the calculated effort at the second stage. In addton to that, each user should calbrate the model and the attrbute values n accordance to ther own hstorcal projects data, whch wll reflect local crcumstances that greatly nfluences accuracy of the model. From these vewpont, whenever usng the algorthmc effort estmaton models, t s preferred that the mpacts of cost drves have to be quantfed and assessed n a proper way. Snce the sgnfcance of the vagueness and uncertanty features that are nhabted n the effort drves due to the cogntve judgments are less, ths Imputaton approach can be preferred and appled to change the estmaton scheme of the COCOMO II, whch can substtute values n the place of vague nformaton. Recently many machne learnng algorthms were proposed and used as the mputaton technques for estmatng the effort. In majorty of the cases we fnd that the mputaton models posses sgnfcance compared to other models n terms of performance. In ths seres, ths research proposes a hybrd model of mputaton technque, whch holds better sgnfcance than other recent models. Ths s a comprehensve model whch uses Graphcal and Genetc Approaches. Genetc Algorthms (GA) are stochastc especally n domans where a drect search method cannot reveal better outputs and of course n the large search spaces. They have an advantage to operate wth ncomplete data to extract sgnfcant rules. Ths proposed hybrd effort estmaton model produces accurate outputs. It s observed that the accuracy of the COCOMO II s reled on three attrbutes; the value of estmaton varable, the overall value of the effort multplers and ther mpact n the estmaton scheme. Here the estmaton varable s the prmary attrbute and standard methods avalable for estmatng the estmaton varables (e.g. LOC, FP count, etc )[7]. It s smple to estmate the overall value of the effort multplers after assgnng the approprate values as per the requrements. But the complcated ssue s to estmate mpact of the effort multplers, whch plays a major role n the estmaton scheme and causes for overestmaton or underestmaton of the software development effort. In ths vew, ths work s amed at refnng the cost drvers and scale factors handlng mechansms n COCOMO II estmaton scheme. There are 7 effort multplers as cost drvers and they are devsed nto two groups; Optmstc Group and Pessmstc Group. 62

4 Defnton-: Pessmstc Group: Ths group can be defned as a set of effort multplers of whose range of values are drectly proportonal to the overall effort to be predcted and t can be descrbed as follows: RELY DATA CPLX RUSE DOCU TIME Pessmstc Group PG= {EM 0, EM 7 } EM,.. Where, α and β are number of non Nomnal effort multplers n the PG and OG. Further, the above equaton s gven as nput to the Genetc Part. Ths Genetc approach s used for optmzaton problems and t curtals the resdual values wth the Hybrd Imputatonal approach. Genetc algorthm s used n ths research to enhance the performance of effort estmaton. Ths approach s useful to select the most relevant features of effort estmates and cost drvers whch have certanly sgnfcant nfluence on the COCOMO effort estmaton model even f the nput level s ncomplete. If uncertanty exsts n the nput parameters, errors n the estmates are more or accuracy may not be good. STOR PVOL Defnton-2: Optmstc Group (OG): Ths group can be defned as a set of effort multplers of whose range of values are nversely proportonal to the overall effort to be predcted and t can be descrbed as follows: ACAP PCAP PCON AEXP PEXP LTEX TOOL SITE SCED Optmstc Group OG= {EM, EM 9 } Ths classfcaton makes a sense n the estmaton scheme and plays a sgnfcant role n mprovng the accuracy of the COCOMO II estmaton model. The three attrbutes model can be vsualzed as a three edged object n a graphcal form. The effort s E α 2 PG β 2 0.5* LOC * EM 0.5* LOC / E = * 0.88 = LOC = LOC OG 0.88 EM 2,.. EM The general procedure of a genetc algorthm s as follows [Goldberg, 989; Mchalewcz, 996]. Randomly generate a populaton of solutons. 2. Calculate the ftness value for each of the populaton. 3. Creaton of offsprng a. Reproducton b. Cross over c. Mutaton 4. Computaton of new soluton and ftness of each soluton. 5. Repeat step 3 to 4 untl optmum soluton s attaned. The Genetc Approach follows a cyclc process of Reproducton, Crossover and Mutaton for N populatons. Estmaton process starts wth an ntal populaton of N project (chromosomes) wth 7 EM s (genes) as nput whch follows genetc operatons of Reproducton, Crossover and Mutaton. In reproducton ntal populaton chromosomes are grouped based on project mode and each chromosomes n each group s ranked based on ftness functon. For the opted par of parental chromosomes crossover non-nomnal effort multplers weght age through adjustment. Weght age of operaton s performed for reparng OG each non-nomnal multpler are adjusted by addng or deductng weght age based on, trackng made on all the chromosomes for specfc effort multpler. b. Wlcox on Sgned-Rank Test The performance measure of a model predctng numerc values s the correlaton between predcted and 622

5 actual values. Correlaton ranges from + to - and a correlaton of + means that there s a perfect postve lnear relatonshp between varables. And can be calculates as follows The correlaton coeffcent for COCOMO II s and the correlaton coeffcent for proposed model s EVALUATION AND PERFORMANCE ANALYSIS The performance of ths model s valdated by means of Magntude of Relatve Error (MRE), Mean Magntude of Relatve Error (MMRE), Root Mean Square (RMS) and Relatve Root Mean Square (RMS & RRMS). A. PERFORMANCE EVALUATION CRITERIA Crtera Formula Descrpton MAE MMRE RMS RRMS 00 MMRE = N RMS RRMS N predcted actual actual 2 ( predcted actual ) = N N actual RMS * N = N actual 0.5 MAE measures of how far the estmates are from actual values. It could be appled between any two pars lke actual and predcted or estmate MMRE s the average percentage of the absolute values of the relatve errors over an entre data set. RMS s the square root of the arthmetc mean of the squares of the orgnal values Relatve Root Mean square s the rato between RMS and the average of the actual effort 623

6 SF range COCOMO SF Range 3 SF value Proposed model SF Range 0.5 COCOMO Scale Factor for Project Number Proposed model Scale Factor for MRE rate MRE value Project Number COCOMO II MRE Rate MRE rate of Proposed Model A. MRE ANALYSIS COCOMO II Proposed model Sl. No. MRE range No. of No. of Acceptance Status Project Project Acceptance Status >50 Under estmaton to 50 Under estmaton to 29.9 Under estmaton 5 Under estmaton 4 5 to Under estmaton 5 Under estmaton to accepted 69 accepted 6-5. to -0 5 Over estmated 4 Over estmated 7-0. to Over estmated 3 Over estmated to Over estmated 0-9 <-00 6 Over estmated 0-624

7 B. PERFORMANCE COMPARISON CHART Parameters COCOMO Effort Estmaton Proposed Effort Estmaton No. of Cost drves 7 7 No. of Scale Factors 5 5 Scale Factors range.0 to to No. of Project le wthn the SF range No. of project does not le wthn the SF range 5 Maxmum MRE (%), MMRE (%) RMS RRMS Correlaton Coeffcent No. of Project over estmated No. of project under estmated Standard devaton for over estmated projects Standard devaton for under estmated projects Varance for over estmated projects Varance for under estmated projects 5. CONCLUSION 28, The purpose of ths research was to provde nsght nto how sophstcated mputaton technques are and ths facltates the understandng. It also ntegrates between statstcans and software engneers to make successon effort estmaton. All decson makng process requres qualty data whch s of greater mportance for any valdaton process. In ths paper the valdaton of COCOMO effort estmaton model along wth the proposed hybrd model was nvestgated. It has been found that the hybrd estmaton model enhances the performance of effort estmaton n early stages of software development lfe cycle. REFERENCES [] Satyananda, An mproved fuzzy approach for COCOMO s effort estmaton usng Gaussan Membershp Functon Journal of Software, vol 4, 2009 [2] Lttle RJA, Rubn DB (987) Statstcal analyss wth mssng data, Wley seres n probablty and statstcs, st edn. Wley, New York. [3] B.W. Boehm, Software Engneerng Economcs, Prentce-Hall, 98. [4] Al Idr, Abdelal Zakran and Azeddne Zah Desgn of Radal Bass Functon Neural Network for software effort estmaton, IJCSI, July 200. [5] Musflek p, Pedrycz W, Succ G, Reformat M, Software Cost Estmaton wth Fuzzy Models Appled Computng Revew, Vol. 8, pp 24-29, 2000 [6] Kpaus Dohmen, An Improvement of the Incluson Excluson Prncple, Journal of Archv Der Mathematk, Sprnger, Vol. 72, pp , 999 [7] Jovan Žvadnovć, Ph.D*, Zorca Medć, Dragan Maksmovć, Aleksandar Damnjanovć, M.Sc, Slañana Vujčć, Methods of effort estmaton n software engneerng", Internatonal Symposum Engneerng Management And Compettveness 20 (EMC20)June 24-25, 20, Zrenjann, Serba 625