NEW APPROACH FOR SOLVING SOFTWARE PROJECT SCHEDULING PROBLEM USING DIFFERENTIAL EVOLUTION ALGORITHM

Transcription

1 Inrnaonal Journal n Foundaons of Compur Scnc & Tchnology (IJFCST), Vol.5, No.1, January 2015 NEW APPROACH FOR SOLVING SOFTWARE PROJECT SCHEDULING PROBLEM USING DIFFERENTIAL EVOLUTION ALGORITHM Maghsoud Amr 1 and Javad Pasha Barbn 2 1 Asssan Profssor, Dparmn of Indusral Managmn, Faculy of Managmn and Accounng, Allamh Tabaaba Unvrsy, Thran, Iran 2 Dparmn of Compur Engnrng, Naghadh Branch, Islamc Azad Unvrsy, Naghadh, Iran ABSTRACT Sofwar Proc Schdulng Problm (SPSP) s on of h mos crcal ssus n dvlopng sofwar. Th maor facor n complng h sofwar proc conssn wh plannd cos and schdul s mplmnng accura and ru schdulng. Th subc of SPSP s an mporan opc whch n sofwar procs dvlopmn and managmn should b consdrd ovr ohr opcs and sofwar proc dvlopmn mus b don on. SPSP usually ncluds rsourcs plannng, cos smas, saffng and cos conrol. Thrfor, s ncssary for SPSP us an algorhmc ha wh consdrng of coss and lmd rsourcs can sma opmal m for complon of h proc. Smulanously rduc of m and cos n sofwar procs dvlopmn s vry val and ncssary. Th ma-hursc algorhms has good prformanc n SPSP n rcn yars. Whn sofwar procs facors ar vagu and ncompl, cos basd schdulng modls basd on ma-hursc algorhms can look br a schdulng. Ths algorhm works basd on h Collcv Inllgnc and usng h fnss funcon, has mor accura ably for SPSP. In hs papr, Dffrnal Evoluon (DE) algorhm s usd o opmz SPSP. Exprmnal rsuls show ha h proposd modl has br prformanc han Gnc Algorhm (GA). KEYWORDS Sofwar Proc Schdulng Problm, Dffrnal Evoluon, Gnc Algorhm. 1. INTRODUCTION Managmn and conrol of sofwar procs basd on sofwar ngnrng sandards nsurs ha h procss of mplmnaon of asks n ams and allocang rsourcs o hm prform basd on h proc applcaon plan and Proc Managr n cas of obsrvng non-complanc n h mplmnaon procss aks corrcv acons. Usng SPSP caus Proc Managr o hav srong suppor for makng varous dcsons hroughou h sofwar dvlopmn cycl. Also h proc managr, analyss, dsgnr, and ohr sofwar dvlopmn popl know how much mony and m hy nd for dvlopng a sofwar proc. Whou havng a suabl schdulng program of m and f for sofwar procs, h proc managr canno dnfy how much m and f nd for mplmnng proc and n h cas of faul, h proc ncounrs rsk or dfn fal [1]. SPSP s an mporan sp n h sofwar dvlopmn procss and s usd for h analyss of rsourcs, m and ovrall proc navgaon [2]. Sng m dpndnc for dong a srs of rlad asks ha ar formng proc n rms of cos s vry mporan. In SPSP, h man am s DOI: /fcs

2 Inrnaonal Journal n Foundaons of Compur Scnc & Tchnology (IJFCST), Vol.5, No.1, January 2015 h allocaon of rsourcs o asks and sub-acvs of h proc whch hs rsourc can b hardwar, sofwar, and human rsourc. Many classc modls, lk PERT [3], CPM [4], and GERT [5] hav prsnd for SPSP by rsarchrs. Proc managr usng h classcal modl canno hav accura and rlabl schdulng from fnal saus of sofwar procs n rms of m and cos rqurd o compl procs. In h classcal modls, schdulng facors ar usually oband from xprmnal daa of varous procs and prvous procs. Th prformanc of hs modls s carrd basd on rlaonshps bwn procs and changs n rlaonshps of asks lads o svral changs n h amoun of m. An ncorrc valu of cos facors may caus maor changs n h fnal rsuls of SPSP. Thrfor, n hs papr w wll valua h facors affcng h mng and schdulng of h proc usng h algorhm DE [6] and wll gan mor accura m for SPSP and wll compar h rsuls wh GA [7]. In sofwar ngnrng, h ssu of SPSP s vry mporan bcaus h human rsourcs and fundng mus b opmally managd so ha h proc s rmnad succssfully. In rcn yars, much rsarch has bn don n h fld of SPSP usng ma-hursc algorhms. Today, usng h ma-hursc algorhm has bn mor common n h opmzaon of h mhod of solvng h complx problms [8, 9 and 10]. Th GA s usd o solv SPSP [7]. Assssmn s don from varous aspcs such as sar and nd ms of ach proc, h proc's ovrall m and oal cos of h proc. Th xprmnal rsuls show ha h GA algorhm has good prformancs n smang h cos and m. An Colony Opmzaon (ACO) algorhm s usd for SPSP [11]. On of h mos mporan ssus n sofwar proc managmn s choosng h bs soluon for ach proc consun asks, n h cas ha h nd m and cos of h proc hav h possbl las amoun of hm. Du o h larg numbr of asks and h soluon of choc for any acvy, usually hs choc has no a unqu answr, bu wll b formd a s of answrs. Non of h soluons ar prfrrd ovr ohrs. On h ohr hand, n acual procs, usually prdcd coss o prform asks normally assocad wh uncrany whch lad o consdrabl changs n h cos of h fnshd proc. In classcal mhods for proc schdulng, proc's m rducon s n a hghr prory han cos. Bu, n many cass, rducng h m of proc causs h ncras of cos. Thy mad vas h schdulng sarch spac wh prsnng h ACO algorhm of h procss of schdulng, and also bcaus h prformanc of ACO algorhm s wll shown, s rsuls hav bn compard wh GA algorhms and n many cass ACO algorhms fnd opmal or nar opmal mood. Our ovrall srucur of hs papr s organzd as follows: n Scon 2, w wll sudy SPSP; n Scon 3, w wll dscrb h DE algorhm; n Scon 4, w wll prsn h proposd modl; n Scon 5, w wll dscuss h valuaon and rsuls and fnally n Scon 6, w wll sudy h conclusons and fuur works. 2. SOFTWARE PROJECT SCHEDULING PROBLEM Schdulng s sng a squnc of m-dpndn funcons o prform a s of dpndn asks ha mak up a proc [12]. Dpndnc of asks s vry mporan n rms of prory and prcdnc. So s possbl ha dong a ask rlad o dong som asks whch n hs cas, s sad ha proc conans prory lmaons. Drmnng a schdulng program has bn don wh consdrng h purpos or spcfd purposs. Almos, hr ar prors lmaons bwn asks n all of h procs, bu n addon o hs lmaons may b hr s anohr knd of lmaons bwn asks basd on rsourc lmaons. So n proc schdulng n addon o consdrng prory lmaons, schdulng should b don n such a way as o b conssn wh rsourc consrans. In SPSP, consdrng a s of applcaons such as rsourcs and so on ar rqurd for asks. Th man facors affcng h SPSP has bn shown n Tabl (1) [7]. 2

3 Inrnaonal Journal n Foundaons of Compur Scnc & Tchnology (IJFCST), Vol.5, No.1, January 2015 Tabl 1. Paramrs Affcng h SPSP SK s, s,..., s } S of sklls rqurd n h proc managmn { 1 2 SK TK,,..., } S of ask { 1 2 TK EM,,..., } S of mploy { 1 2 EM V= TK S of Vrx (ask) for TPG n proc Schdulng A {( 1, 2),( 3, 4),...( m, n)} S of arc(prcdnc rlaon bwn ask) G(V,A) TPG (Task Prcdnc Graph) n Proc Schdulng Workload of ask whch s n PM (Prson-Monh) ffor sklls SK S of Rqurd sklls of ask sklls SK S of Sklls Of mploy salary Th monhly salary of mploy Maxd Th Maxmum Ddcaon Of mploy o ask sar Sar m of ask nd End m of ask Cos of ask cos duraon Duraon of ask duraon p Toal Duraon of Sofwar Proc Cos p Toal Cos of Sofwar Proc Ovr p Toal ovrwork of Whol Sofwar Proc Ovr Ovrwork of Employ M ( ) Soluon Marx of SPSP m ET SPSP s an mporan sp n h sofwar dvlopmn procss and s usd for h analyss of m and rsourcs and h ovrall gud of h proc. In h proc schdulng problm, h man am s h allocaon of rsourcs o acvs and asks of h procs on whch hs rsourc can b hardwar, sofwar and human rsourc. Th goal s opmally allocang rsourcs so ha wh rgardng prcdnc rlaonshps among asks, complon m and coss ar rducd. Sar and nd m of ach ask s don usng quaons (1) and (2). sar 0 fk,( k, ) A nd max{ k ( k, ) A} ls nd sar duraon Th valuaon of xcuon m of ach ask s calculad usng quaon (3). duraon ffor E m 1 (1) (2) (3) 3

4 Inrnaonal Journal n Foundaons of Compur Scnc & Tchnology (IJFCST), Vol.5, No.1, January 2015 Th valuaon of xcuon m of h proc s carrd ou usng quaon (4). p duraon nd max{ k (, ) A Esmang coss for ach ask s carrd ou usng quaon (5). k (4) cos E salary. m. 1 duraon Esmang h coss of all h proc asks s carrd ou usng quaon (6). p cos T cos 1 Employ prformanc s don usng quaons (7, 8 and 9). duraon p ovr 0 whr, work ramp( work ( ) x ramp( x) 0 ( ) m sar nd { max dd ) d fx 0 fx 0 Esmang ovrall ask for sofwar procs s don usng quaon (10). (5) (6) (7) (8) (9) p ovr E ovr 1 (10) In Fgur (1) h numbr of mploys and h cos of ach of hm for dong sofwar procs ar shown n [7]. Fgur 1. Facors Affcng h Proc In Fgur (2), h asks, rlaonshps bwn asks and hr prformng mng and amoun of ndd rsourcs o prform ach of hm n dffrn moods has bn shown [7]. 4

5 Inrnaonal Journal n Foundaons of Compur Scnc & Tchnology (IJFCST), Vol.5, No.1, January 2015 Fgur 2. Dsplay of h Tasks and hr Rlaonshps 3. DIFFERENTIAL EVOLUTION ALGORITHM Th algorhm DE s of ma-hursc algorhm whch was nvnd n 1995 [6]. DE algorhm s a populaon-basd probablsc sarch algorhm whch solvs opmzaon problms. Ths algorhm usng h dsanc and drcon nformaon from h currn populaon carrs ou h sarch opraons. Th advanags of hs algorhm ar spd, sng h paramrs, s ffcvnss n fndng opmal soluons, bng paralll, hgh accuracy and lack of nd o sorng or marx mulplcaon. DE Algorhm n ordr o fnd h opmal soluons, has h ably o ffcnly sarch h procss n h drcon of coordna axs of opmsc varabls and also changs n h drcon of h coordna axs n h rgh drcon. DE Algorhm sars h voluonary sarch procss from a random nal populaon. Thr opraors of muaon and slcon, and h ngraon and hr conrol paramrs, ncludng h numbr of populaon, scal facor and h possbly of ngraon ar vry mporan n h DE algorhm. DE algorhm procsss ar as follows: Inal Populaon Gnraon: n DE algorhm, h nal populaon wh soluon vcors s randomly chosn from h problm rang. Th vcor of soluons poson s dfnd accordng o quaon (11). X x, x,..., x ) x k wh x mn k (, 1,2, D rand(0,1).( x max k [1, Np], k [1, D] Slcon of random numbrs x k from h doman s carrd ou usng quaon (12). In quaon (12) D s qual o h dmnson of h soluons. Np s h nal populaon. Th funcon of rand(0,1) Random gnrad random numbrs (wh unform dsrbuon) n h nrval of (0, 1). Obvously, n h cas of usng quaon (12), oband valus wll b for x k n h rang of max mn [ x, x ] and h vcor poson of ach ponal soluon s a ponal answr o h opmal problm. Muaon Opraor: n h muaon phas, hr vcors ar chosn randomly and muually. For any vcor X n h populaon, a nw soluon s gnrad n ach rpon accordng o quaon (13). v, G 1 xr1, G F.( xr2, G xr3, G) (13) x mn k ) (11) (12) 5

6 Inrnaonal Journal n Foundaons of Compur Scnc & Tchnology (IJFCST), Vol.5, No.1, January 2015 In quaon (13), r 1, r2, r3 whch ar hr unqual random numbrs ar n h nrval [ 1, Np ]. G s h numbr of gnrad gnraon. And F facor s a ral, posv and consan numbr whch s ofn consdrd o b 0.5. Crossovr Opraor: crossovr opraor wll ncras dvrsy n h populaon. Ths opraor s h sam as crossovr opraor n GA [13]. In crossovr opraor, nw vcors ar gnrad wh x and v composon accordng o quaon (14). u, G1 v x, G1, G1 f ( r CR) ohrws or In quaon (14), CR paramr s n h rang [0, 1). Paramr of randomly gnrad. Also h valu of s 1,2,..., D;. rand (14) r n h rang [0, 1] s Slcon Opraor: n ordr o slc h vcors wh h hghs fnss, h vcors gnrad by h muaon and ngraon opraors can b compard and ach of hm whch hav mor fnss s ransfrrd o h nx gnraon. Th slcon opraor s carrd ou by quaon (15). x 1 Fnss Valu ( u, G 1, x, ) (15), G G Soppng Crra: h sarch procss connus unl a soppng crron s m. Usually, h algorhm's soppng crron can b h bs soluon or h algorhm's raon basd on conssncy of fnss changs. 4. PROPOSED MODEL Thr s h probably of rror n sofwar proc schdulng n classcal modls and as a rsul, smang proc cos and m n sofwar procs s dffcul. In classcal modls schdulng affcng valus, ar no known valus, bu ar consdrd accordng o h avrag and prvous procs and hrfor canno asly nsur o h smad valus. Rlaonshps bwn facors n SPSP hav an mporan mpac on proc succss. For sofwar procs can b cra balancs among h facors of m and cos and can prdc h accura cos for h sofwar procs. I s dal for proc managrs ha h proc's acual complon m s no sgnfcanly ncrasd han h dlvry m. On h ohr hand, s possbl ha h condon of som procs may b n h cas ha undr h xsnc of any varaon n h ons m of som acvs, h consdrabl cos b forcd on h proc's sysm. In hs conx, applyng an ffcn algorhm for fndng h opmal soluon would b hghly dsrabl. For SPSP can b ulzd svral algorhms. In hs papr w hav usd h DE for SPSP. SPSP s ha a h bgnnng of sofwar dvlopmn, dald nformaon of h opraon of sysm, h proc scop and asks s no avalabl. Thrfor, n hs papr, w ry o mnmz dffrn sourcs for sofwar dvlopmn such as hardwar, sofwar and saffng sofwar usng DE. In Fgur (3) h Flowchar of h proposd modl usng DE algorhm s shown. 6

7 Inrnaonal Journal n Foundaons of Compur Scnc & Tchnology (IJFCST), Vol.5, No.1, January 2015 Fgur 3. Flowchar of h Proposd Modl In Fgur (4), quas cod of h proposd modl s shown. 1. Bgn 2. Inalz Paramrs 3. Evaluaon 4. Rpa Slcon Crossovr Slcon 5. Tran Daa 6. Compu opraonal coss 7. Evalua Fnss 8. Unl (no rmna condon) 9. Evaluaon Crra 10. Dsplay Rsuls Fgur 4. Quas Cod of h Proposd Modl. In h proposd modl, calculad h fnss of ach vcor basd on h cos. Thn w ordrd hm basd on h oband valu for ach vcor, and w chos h bs vcors whch hav h las cos and do h muaon and ngraon opraon n ordr o opmz h vcors. Thus, f h mos opmal schdul s no opmal, h muaon and crossovr opraon ovr h asks causs changng asks opraon and h mos appropra soluon can b provdd for schdulng of acvs. In fac, wh changng h way of dong varous acvs and sarchng among schdulng applcaon forms n any mod of acvy, h mos opmal schdul program n h oupu s dsplayd. In h proposd modl, o prform h asks a any m, an appropra combnaon for h rsourc s slcd. 5. EVALUATION AND RESULTS In hs scon h rsuls oband from h proposd modl has bn valuad wh GA [7]. In ma-hursc algorhms, drmnng nal paramrs s vry mporan o valua h rsuls. 7

8 Inrnaonal Journal n Foundaons of Compur Scnc & Tchnology (IJFCST), Vol.5, No.1, January 2015 Thrfor, h ma-hursc algorhms wr vry snsv o s paramrs and paramr sngs can hav a sgnfcan mpac on hr prformanc. Thrfor, paramr sng can rsul n grar flxbly and ffcncy of h proposd modl. In ma-hursc algorhm, slcon of populaons s vry mporan. If h numbr of populaon s low, h problm s suffrng from prmaur convrgnc and w won' b rach o h dsrd rspons and clos o h global opmum and f h populaon s larg, much m s ndd o rach h convrgnc of h algorhm. Thrfor, h numbr of ssus should b n appropra lm and n proporon wh dsrd problms n ordr o achv h opmal soluon. In Tabl (2) h paramrs ha mos affc h prformanc of h proposd modl ar dmonsrad. Tabl 2. Paramr Valus Paramrs No. Populaon Muaon Crossovr F Slcon Gnraon Valus Randomz 50 In Tabl (3) w hav valuad and compard Employs crron of h proc. Th rsuls n Tabl (3) show ha h proposd modl whn compard wh h GA crra has rducd avrag m crra and h numbr of mploys n prformng h asks. Tabl 3. Th Evaluaon of Employs Crra Employs Iraon GA [7] Avg. duraon Avg. E P dur Proposd Modl Avg. duraon Avg. E P dur In Tabl (4) w hav valuad and compard proc Sklls crra. Rsuls n Tabl (4) show ha h proposd modl n comparson wh h GA crra has rducd avrag m crra and cos. Thrfor h proposd modl s usful for mng and has lss rror han h GA. Tabl 4. Th Evaluaon of Sklls Crra Sklls Iraon GA [7] Avg. duraon Avg. Pcos / , , , , , P dur Proposd Modl Avg. duraon Avg. Pcos / , , , , , P dur In SPSP h ffcv ndx n cos and m should hav opmal sa n ordr o apply h xac mng of h proc. Thrfor h algorhms mus b usd ha do h asks n lss m and wh grar accuracy, and n fndng h las rsourcs hav good prformanc. 8

9 Inrnaonal Journal n Foundaons of Compur Scnc & Tchnology (IJFCST), Vol.5, No.1, January CONCLUSIONS AND FUTURE WORKS In hs papr w hav valuad SPSP usng DE. In SPSP, h am s drmnng h appropra mng for allocang rsourcs o asks n such a way ha h ovrall cos of h proc and complon m s opmal. In SPSP, h cos facor for h sak of mplmnng h proc asks maks h suaon of ask mor complcad du o nrdpndnc of asks and smang h m of hr mplmnaon. To dmonsra h ffcvnss of h proposd modl w usd a sampl of proc ha was prvously smad usng GA. Th man obcv of hs work s o dmonsra h ably of h proposd modl n accura convrgnc o opmal soluons. Th rsuls oband from mplmnaon showd ha h proposd modl compard wh GA has br prformanc and has lss rror. W hop ha n h fuur wh prsnng hs rsarch mak opmal h avrag of m crron of dong asks and h cos of asks usng ohr ma-hursc algorhms. REFERENCES [1] M.Lu,H.L, Rsourc Acvy Crcal Pah Mhod for Consrucon Plannng,Journal of Consrucon Engnrng and Managmn,Vol.129,No.4, pp ,2003. [2] F.Lunaa,D.L.Gonzalz-Alvarzb,F.Chcanoc,M.A.Vga-Rodríguz, Th Sofwar Proc Schdulng Problm: A Scalably Analyss of Mul-Obcv Mahurscs,Appld Sof Compung,2013. [3] R.J.Frman,A gnralzd PERT,Opraons Rsarch,Vol.8,No.2,1960. [4] J.E.Klly Jr., Crcal pah plannng and schdulng,mahmacal bass,opraons Rsarch,Vol.9,No.3,pp ,1961. [5] W.Fx,K.Numann,Karlsruh, Proc Schdulng by Spcal GERT Nworks Compung,Vol.23,pp ,Sprngr-Vrlag,1979. [6] R.Sorn,K.Prc, Mnmzng h Ral Funcons of h ICEC 96 Cons by Dffrnal Evoluon,Inrnaonal Confrnc on Evoluonary Compuaon,Nagoya,Japan,1995. [7] E.Alba,J.F.Chcano, Sofwar proc managmn wh GAs,Informaon Scncs,Vol.177,No.11,pp ,2007. [8] I.Malk,S.R.Khaz,M.M.Tabrz,A.Baghrna, A Nw Approach for Ara Covrag Problm n Wrlss Snsor Nwork wh Hybrd Parcl Swarm Opmzaon and Dffrnal Evoluon Algorhms,Inrnaonal Journal of Mobl Nwork Communcaons & Tlmacs(IJMNCT),Vol.3,No.6,pp.61-75,Dcmbr2013. [9] F.S.Gharhhopogh,I.Malk,M.Farahmandan, Nw Approach for Solvng Dynamc Travlng Salsman Problm wh Hybrd Gnc Algorhms and An Colony Opmzaon, Inrnaonal Journal of Compur Applcaons (IJCA),Vol. 53,No.1,pp.39-44,2012. [10] I.Malk,A.Ghaffar,M.Masdar, A Nw Approach for Sofwar Cos Esmaon wh Hybrd Gnc Algorhm and An Colony Opmzaon,Inrnaonal Journal of Innovaon and Appld Suds,Vol.5,No.1,pp.72-81,2014. [11] J.Xao,Xan-TngAo,Y.Tang, Solvng Sofwar Proc Schdulng Problms wh An Colony Opmzaon,Compurs & Opraons Rsarch,Vol.40,pp.33-46,2013. [12] A.Mngozz,V.Manzzo,S. Rccardll,L.Banco, An Exac Algorhm for Proc Schdulng wh Rsourc Consrans Basd on a Nw Mahmacal Formulaon,Managmn Scnc,Vol.44,No.5,pp ,1998. [13] J.Holland, Adapaon n Naural and Arfcal Sysms,Unvrsy of Mchgan,Mchgan,USA,