A Novel Hybrid Algorithm for Software Cost Estimation Based on Cuckoo Optimization and K-Nearest Neighbors Algorithms

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1 Egieerig, Techology & Applied Sciece Research Vol. 6, No. 3, 26, A Novel Hybrid Algorithm for Software Cost Estimatio Based o Optimizatio ad K-Nearest Neighbors Algorithms Elaz Eskadaria Miadoab Departmet of Computer Egieerig, Urmia Brach, Islamic Azad Uiversity, Urmia, Ira Elaz_es_m@yahoo.com Farhad Soleimaia Gharehchopogh Departmet of Computer Egieerig, Urmia Brach, Islamic Azad Uiversity, Urmia, Ira boab.farhad@gmail.com Abstract The iheret ucertaity to factors such as techology ad creativity i evolvig software developmet is a major challege for the maagemet of software projects. To address these challeges the project maager, i additio to examiig the project progress, may cope with problems such as icreased operatig costs, lack of resources, ad lack of implemetatio of key activities to better pla the project. Software Cost Estimatio (SCE) models do ot fully cover ew approaches. Ad this lack of coverage is causig problems i the cosumer ad producer eds. I order to avoid these problems, may methods have already bee proposed. Model-based methods are the most familiar solvig techique. But it should be oted that model-based methods use a sigle formula ad costat values, ad these methods are ot resposive to the icreasig developmets i the field of software egieerig. Accordigly, researchers have tried to solve the problem of SCE usig machie learig algorithms, data miig algorithms, ad artificial eural etworks. I this paper, a hybrid algorithm that combies COA- optimizatio ad K-Nearest Neighbors () algorithms is used. The so-called compositio algorithm rus o six differet data sets ad is evaluated based o eight evaluatio criteria. The results show a improved accuracy of estimated cost. Keywords- Software Cost Estimatio; COCOMO model; COA- optimizatio algorithm; algorithm I. INTRODUCTION Nowadays, software maufacturer orgaizatios are expected to geerate computer tools to maipulate ad maage usually large amouts of data. The mai problem usually observed is the mismatch betwee the project cost estimatio ad the Sactual cost. I order to reduce this differece, software developers eed to collect certai iitial iformatio. These socalled iformatio ca be classified as follows []: Iformatio relatig to the capabilities ad major ad mior objectives of the software. Iformatio relatig to the orgaizatio that will operate the software. Iformatio relatig to the orgaizatio that will produce the software. Prevalet use of software packages ready i certai parts of software projects reduces the cost of software developmet. At the same time, ew software developmet processes are preseted ad maufacturers are tryig to adapt to these processes. Some of these processes iclude risk-based ad dyamic software processes, ew programmig laguages, software applicatios for software developmet as well as commercial software, which improve the quality of software products, reduces productio costs, reduces the risk ad the produced software life cycle [2]. However, curret models of estimatig software developmet cost do ot fully cover ew approaches. Ad this lack of coverage causes problems i the cosumer ad producer eds. II. PREVIOUS WORKS With the itroductio of machie learig algorithms i the field of software egieerig, may researchers have used such algorithms for SCE. Some of these models ca be briefly described as follows: I [3] fuzzy logic was implemeted for SCE. They itroduced cost estimatio projects as oe of the most importat challeges ad activities i software developmet. The researchers used 4 projects icluded i KEMERER projects collectios. Accordig to their results, the mea absolute error percetage of relative error ad productivity rate improved compared to algorithmic methods. Oe of the software process criteria havig a direct impact o estimated cost is the umber of applicatio lies ad applicatio thousad-lie. I [4], the compositio of at coloy optimizatio algorithm ad chaos optimizatio algorithm was used for SCE. The researchers used Lorez mappig to geerate radom data for the chaos optimizatio algorithm ad for traiig they used the at coloy algorithm. This compositio algorithm was evaluated o NASA 63 data set, ad the results showed that the compositio of at coloy optimizatio algorithm ad chaos optimizatio algorithm has a better performace compared to the COCOMO model ad also has a relative lower error tha the COCOMO model [4]. The compositio of multilayer perceptro etworks ad is used i [5]. To evaluate the proposed method, 63 software projects have bee used. The mai objective of this compositio is better traiig of the multilayer Miadoab ad Gharehchopogh: A Novel Hybrid Algorithm for Software Cost Estimatio Based o

2 Egieerig, Techology & Applied Sciece Research Vol. 6, No. 3, 26, perceptro. I the compositio model, effort factors ad scale factors are taught by the itermediate layer ad evaluated by the model. The Sigmoid Fuctio was used as the activatio fuctio for the itermediate layer. Backpropagatio is used for teachig. The data traiig ad testig phases are 8% ad 2%, respectively. The experimet results show that the stadard error of relative error i the compositio model is less tha the model. A ew methodology for SCE based o particle swarm optimizatio algorithm ad fuzzy logic was proposed i [6]. Estimatio of the software cost depeds o the estimatio of the size of the project ad its parameters. For measuremets ucertaity, fuzzy logic is applied ad particle swarm optimizatio is used for parameters. I the proposed method, the triagular membership fuctio is used. Evaluatio is implemeted o NASA63 dataset. The results show that the proposed method has lower error compared to other models. A compositio of firefly ad geetic algorithms was bee proposed i [7]. Evaluatio is implemeted o NASA93 dataset. I the proposed method, the geetic algorithm, via elitism operatio, tries to obtai the best aswer for effort factors ad evaluate the fitess fuctio, ad provide the lowest error solutio as the fial aswer. The results show that the average value of the relative error i COCOMO model is 58.8, ad i geetic ad firefly algorithms is 38.3 ad 3.34, respectively ad i the compositio model is Note that (25) PRED o geetic ad firefly algorithm models is 77.4 ad 8.64 respectively ad i the compositio model is Comparisos show that the compositio model compared with COCOMO model icreased the efficiecy of the estimated precisio about 2.88%. III. BASIC CONCEPTS A. SCE ad Amog the algorithmic models preseted for SCE, is the most popular. This model provides a basis method to predict the umber of people eeded per moth for software developmet i the idustry. This model ca also estimate the developmet time, the amout of effort required i each software developmet phase ad the required cost [8]. The formulas used are listed i Table I. TABLE I. COCOMO MODEL FORMULAS Formula PM=2.4 (size) Project Type.5 EMi Orgaic.2 PM=3 (size) PM=3.6 (size) EM i Semi Orgaic.2 EMi Embedded The size parameter is the project s size i thousads of lies of KSLOC code, ad the EM parameter is the effort coefficiet B. Algorithm The algorithm was described for the first time i [9]. The selectio of K i this method is very crucial. If the value of K is selected too small, the algorithm becomes sesitive to oise. If the value of K is selected too large, the records of other classes may also be icluded amog the earest eighbors. Whe K is selected as a large umber, it leads to a classificatio error []. The algorithm searches the test space for k samples close to the ukow sample. This closeess is defied by the Euclidea distace. The, the label havig the majority amog k eighbors is give to the ukow sample. C. COA- optimizatio algorithm COA- optimizatio meta-heuristic algorithm was first developed i 29 []. I the first step of the algorithm, the first primary settlemet sites are produced. I a N-dimesioal optimizatio problem, settlemet areas will be a N* array, showig the curret positio of cuckoo livig areas. The appropriateess of the curret livig locatio is obtaied by assessig the utility fuctio at the locatio. Each cuckoo has a specified rage for the umber of layig eggs. After cuckoo chicks growth, theses chicks migrate to other areas for layig eggs ad the assumed migratio locatio is also calculated [2]. D. Evaluatio Criteria i SCE Fially, ay research work to determie the accuracy of the work doe should be evaluated by a series of criteria. A umber of the criteria used to assess SCE techiques is show i Table II [2, 3]. TABLE II. EVALUATION CRITERIA Criteria Formula = å N esti å = N act i =Media( å ) N acti ì,if MRE m PRED()= ï å í N ïî, otherwise 2 = å (acti-est i) N 2 = å (acti-est i) N = å acti-esti N = å acti Criteria Name Mea Magitude Error Relative () Mea Magitude of Relative Error () Media Magitude of Relative Error () PRED(m) Mea Squared Error () Root Mea Squared Error () Mea of Absolute Errors () Mea Absolute Percetage Error () Miadoab ad Gharehchopogh: A Novel Hybrid Algorithm for Software Cost Estimatio Based o

3 Egieerig, Techology & Applied Sciece Research Vol. 6, No. 3, 26, I these criteria the N variable deotes the total umber of data i the data set; the act variable represets the real cost; the est variable represets the estimated cost; the i variable idicates ay data idex, which rages from to N. IV. PROPOSED METHOD I the first step of the algorithm, the data is ormalized ad vague ad empty data are deleted. After this stage, a compositio algorithm is implemeted, ad i the first stage of the implemetatio, the data are classified radomly ito two subsets of traiig ad test (2% ad 8% respectively). After this iitial classificatio, data i traiig ad testig data set are classified ito three differet categories usig based o the features available i the data set, ad the traiig data set is set to COA- algorithm for traiig. I the first stage of traiig, the primary parameters of COA- optimizatio algorithm such as the umber of iitial cuckoo populatio, the umber of algorithm iteratios, the miimum ad maximum eggs to be laid for each cuckoo, ad radom variables are iitialized. After determiig the umber of cuckoos, the cuckoos are radomly iitialized. Upo completio of this stage, cuckoos lay eggs i differet ests. At this stage, if alie eggs are idetified by a adult cuckoo, these eggs will be destroyed; otherwise, the eggs grow ad the are coverted to mature cuckoo chicks. After the growth of cuckoos, if the umber of cuckoos is greater tha the the iitial populatio predetermied, cuckoos that live i the worst place will be lost. After that, the optimal amout of each livig locatio is assessed ad the best place is selected. The, the adult cuckoos migrate to places close to this locatio. It should be oted that the coditio of completio of the algorithm is the umber of iteratios or a miimum value that reachig this miimum value idicates obtaiig the goal. I Table III ad Figure, the proposed scheme is show. As show i Figure, after fiishig each traiig phase, the results of this phase are stored, ad the are applied as peer to peer test o test data set that is divided ito three categories, ad fially, the results obtaied are displayed i the form of charts ad text data. TABLE III. THE OUTLINE OF THE PROPOSED APPROACH Iputs: User selected data sets iclude: factors affectig the estimate ad the actual cost of ay software project Outputs: Costat amouts of COMOCO model ad classified data Step : Read the existed data i the dataset Step 2: Breakdow to traiig ad testig data Step 3: Classificatio of traiig ad testig data based o Step 4: Ivokig optimizatio algorithm for each class of software Step 5: Givig the iitial value to optimizatio algorithm parameters ad costat parameters of COMOCO model Step 6: Ovipositig of s i differet ests Step 7: Killig the alie kow eggs Step 8: Checkig the size of s populatio ad i the case of large populatio, elimiatig the worst places of residece Step 9: Checkig Fitess Fuctio Step : Fidig the best places to grow s (Maximum Fitess) Step : Determiig cuckoo populatio ad migratio to ew residetial areas Step 2: Determiig the layig radius for each Step 3: I the case of o-completio algorithm go to the sixth stage Step 4: Fializig optimizatio algorithm Step : Save the geerated values for fixed parameters of Cocomo model (by optimizatio algorithm) ad store classified samples Fig.. The way of performace of the proposed approach V. DISCUSSING AND EVALUATING THE RESULTS The NASA6, NASA63, NASA93, MAXWELL, KEMERER, ad MIYAZAKI data sets are used. The results are displayed i Tables IV to IX i terms of error rate. For the NASA6 dataset (Table IV) the proposed method has acted i all criteria better tha comparative approaches. For the NASA63 dataset (Table V) the proposed method performs equally to for the criterio, ad better tha the COCOMO model ad for the criterio ad worse tha the COA- optimizatio algorithm. For the NASA93 dataset (Table VI) the proposed method performs equally to for the evaluatio criterio, ad better tha all comparative algorithms for rest of the criteria. For the MAXWELL dataset (Table VII) the proposed method performs better for all criteria, except for,,. For these criteria, it has performed better tha COA- ad worse tha COCOMO model ad. For the KEMERER dataset (Table VIII) the proposed method has performed better i all criteria, ad oly i criterio has performed equally to COA-. For the MIYAZAKI dataset (Table IX) the proposed method has performed better i all criteria ad oly i criterio it has performed equally to the. Miadoab ad Gharehchopogh: A Novel Hybrid Algorithm for Software Cost Estimatio Based o

4 Egieerig, Techology & Applied Sciece Research Vol. 6, No. 3, 26, TABLE IV. EVALUATION OF THE PROPOSED METHOD ON THE NASA6 DATASET TABLE V. EVALUATION OF THE PROPOSED METHOD ON THE NASA63 DATASET TABLE VI. EVALUATION OF THE PROPOSED METHOD ON THE NASA93 DATASET TABLE VII. EVALUATION OF THE PROPOSED METHOD ON THE MAXWELL DATASET TABLE VIII. EVALUATION OF THE PROPOSED METHOD ON THE KEMERER DATASET TABLE IX. EVALUATION OF THE PROPOSED METHOD ON THE KEMERER DATASET TABLE X. EVALUATION OF THE PROPOSED METHOD ON THE MIYAZAKI DATASET VI. CONCLUSION Before presetig the ew estimatio methods, software projects cost estimatio process of software projects was doe with some simple algorithms. But with the passage of time ad presetig ew methods i the field of artificial itelligece, may methods have bee proposed to solve this problem but oe of the proposed methods are able to resolve this issue with oe hudred percet accuracy. I this paper, a hybrid of two algorithms of optimizatio ad was used to solve this problem. This hybrid algorithm was evaluated the 6 differet data set ad based o eight evaluatio criteria that the data set icludes: KEMERER, MAXWELL, MIYAZAKI, NASA 6, NASA 63, NASA93 ad evaluatio criteria iclude:,,,,,, PRED (N),. Based o the obtaied results, it ca be cocluded that the proposed method i KEMERER, MIYAZAKI, NASA6, NASA93 datasets outperformed i all criteria better tha Miadoab ad Gharehchopogh: A Novel Hybrid Algorithm for Software Cost Estimatio Based o

5 Egieerig, Techology & Applied Sciece Research Vol. 6, No. 3, 26, COCOMO, ad optimizatio algorithm but i NASA63 dataset i criterio ad i the Maxwell dataset i the evaluatio criteria of,, has ot a good performace compared to the comparative algorithms, ad its reaso ca be the lack of cosistet data.. REFERENCES [] F. S. Gharehchopogh, Neural etworks applicatio i software cost estimatio: a case study, 2 IEEE Iteratioal Symposium o Iovatios i Itelliget Systems ad Applicatios, pp , Istabul, Turkey, Jue -8, 2 [2] B. Boehm, B. Clark, E. Horowitz, R. Shelby, C. Westlad, A overview of the COCOMO 2. software cost model, Software Techology Coferece, 995 [3] K. Parkash, H. Mittal, Software cost estimatio usig fuzzy logic, ACM SIGSOFT Software Egieerig, Vol. 35, No., pp. -7, 2 [4] Z. A. Dizaji, F. S. Gharehchopogh, A hybrid of at coloy optimizatio ad chaos optimizatio algorithms approach for software cost estimatio, Idia Joural of Sciece ad Techology, Vol 8, No. 2, pp , 2 [5] C. S. Reddy, P. S. Rao, K. Raju, V. V. Kumari, A ew approach for estimatig software effort usig RBFN etwork, Iteratioal Joural of Computer Sciece ad Network Security, Vol. 8, No. 7, pp , 28 [6] A. B. Krisha, T. K. R. Krisha, Fuzzy ad swarm itelligece for software effort estimatio, Advaces i Iformatio Techology ad Maagemet, Vol. 2, No., pp , 22 [7] I. Maleki, L. Ebrahimi, F. S. Gharehchopogh, A hybrid approach of firefly ad geetic algorithms i software cost estimatio, MAGNT Research Report, Vol. 2, No. 6, pp , 24 [8] S. Sarwar, Proposig effort estimatio of cocomo ii through perceptro learig rule, It. J. Comput. Appl., Vol. 7, No., pp , 23 [9] T. M. Cover, P. E. Hart, Nearest eighbor patter classificatio, IEEE Tras. Iform. Theory, Vol. IT-3, pp 2-27, 967 [] T. Bailey, A. K. Jai, A ote o distace weighted k-earest eighbor rules, IEEE Tras. Systems, Ma Cyberatics, Vol. 8, pp. 3-33, 978 [] X. S. Yag, S. Deb, " search via levy flights", World Cogress o Nature &Biologically Ispired Computig (NaBIC29). IEEE Publicatios, pp. 2 24, 29 [2] R Rajabiou, optimizatio algorithm, Applied Soft Computig, Vol., pp , 2 [3] L. F. Capretz, V. Marza, Improvig effort estimatio by votig software estimatio models, Advaces i Software Egieerig, Article ID , pp. -8, 29 [4] S. Kumari, S. Pushkar, Performace aalysis of the software cost estimatio methods: a review, Iteratioal Joural of Advaced Research i Computer Sciece ad Software Egieerig, Vol. 3, No. 7, pp , 23 Miadoab ad Gharehchopogh: A Novel Hybrid Algorithm for Software Cost Estimatio Based o