Journal of Chemical and Pharmaceutical Research, 2014, 6(5): Research Article

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1 Avalable onlne.jopr.om Journal o Chemal Pharmaeual Researh, 014, 6(5:44-48 Researh Arle ISS : CODE(USA : JCPRC5 Perormane evaluaon or engneerng proje managemen o parle sarm opmzaon based on leas squares suppor veor mahnes Dong Qao-Tng 1, Geng L-Yan 1 Shen Yng-Mng 1 Shool o Eonoms Managemen, Shjazhuang Tedao Unversy, Chna Deparmen o Sene Tehnology, Shjazhuang Tedao Unversy, Chna ABSTRACT As or he lmaon o usng ross valdaon mehod o hoose he parameers o leas squares suppor veor mahnes (LSSVM, hs paper proposes a ne lassed model hh ombnes adapve parle sarm opmzaon (APSO algorhm h LSSVM. The ne model uses APSO algorhm o sele opmal parameers or LSSVM. Aordng o he analyss o he managemen perormane evaluaon or engneerng proje, e onlude ha LSSVM-APSO has beer evaluaon perormane han LSSVM hh bases on ross valdaon mehod. On searhng or he opmal parameers o LSSVM, APSO algorhm s obvously aser han ha by ross valdaon mehod. Keyords: leas squares suppor veor mahne; parle parm opmzaon; engneerng proje; perormane evaluaon ITRODUCTIO Engneerng proje managemen s a mehod hh apples sysem sene o managng he engneerng onsruon proje, haraerzed as sysemazaon, omplexy dynamsm[1]. Engneerng proje managemen perormane s aeed by he nernal aors, suh as qualy, os, shedule saey. The neraon among hese aors maes more dul o evaluae he perormane. The ommon quanave evaluaon mehods manly nlude Key Perormane Index (KPI, Analy Herarhy Proess (AHP, Exenson Theory, Fuzzy Comprehensve Evaluaon so on. Amng a he omplex nonlnear relaonshp beeen proje managemen perormane s evaluaon ndex, evaluaon o he neural neor s nrodued no he engneerng proje managemen perormane, has aheved good resuls[-3]. Bu he neural neor bases on experenal rs mnmzaon prnple o esablsh model. o only does oen enouner loal mnmum pon he over-ng problems n prae, bu also needs a large number o daa samples or ranng. Suppor veor mahne (SVM s a ne mahne learnng algorhm [4-5], hh s heoreally based on sruural rs mnmzaon prnple model. And an solve he problems o nonlneary, hgh dmenson, small sample loal mnmum pon. LSSVM s a nd o learnng algorhm based on SVM[6]. I regards he leas square lnear sysem as he loss unon, hh smples he proess o alulaon nreases he speed o solve. The LSSVM perormane depends on s parameers, he radonal mehod o deermnng parameers ross valdaon mehod s a ral error mehod, shor o eran heoreal gudane. Ths paper uses LSSVM o evaluae he proje managemen perormane, uses adapve parle sarm opmzaon algorhm o hoose he bes parameer or LSSVM. By analyzng ases o es he resuls o he perormane evaluaon mehod, provdes a ne ay or hoe n he sen evaluaon or engneerng proje managemen perormane. 44

2 Dong Qao-Tng e al J. Chem. Pharm. Res., 014, 6(5: LEAST SQUARES SUPPORT VECTOR MACHIES d L = Le {( x, y = 1,, L, } be he se o ranng samples, x R as he d dmenson npu veor, y R s one-dmensonal oupu. LSSVM uses he leas square lnear sysem as he loss unon. I ransorms he o programmng problem o he sard suppor veor mahne no a lnear problem. Opmzaon problems are as ollos: 1 T 1 mn J ( ω, ζ = ω ω + γ ζ = 1 T y[ ω φ( x + b] = 1 ζ (1 Among hem, φ( s a nonlnear mappng unon. The orgnal npu daa are mapped o a hgh dmensonal eaure spae, ω b are respevely he egh veor he error onsans, γ as he regularzaon parameer, ζ R as error. To solve he above opmzaon problem, e nrodue Lagrange mulpler onsru he orrespondng Lagrange unon. α, = 1 ( T L( α, ω, b, ζ = J ( ω, ζ α { y [ ω φ x + b] 1 + ζ } ( Lagrange unon respevely srves or he paral dervaves o ransormed no solvng a se o lnear equaons as ollos: α, ω, b, ζ, so he opmzaon problem s T 0 1 b 0 = 1 + I / γ α Y Ω (3 Among hem, 1 s order olumn veor, he elemens are 1, I s deny marx, [,, T Y = y1 L y ], [,, T α = α1 L α ],Ω s marx, he elemens o Ω = K ( x, x = φ ( x T φ ( x K j j j, ( x, x j are ernel unons sasyng he Merer ondons. By (3 o oban α b, he lassaon unon an be LSSVM: j = 1 ( y ( x = sg n[ α y K x, x + b ] Sep unon j j j (4 1 x 0 sg n ( x = 0 x < 0 (5. ADAPTIVE PARTICLE SWARM ALGORITHM Parle sarm opmzaon (PSO algorhm s a global evoluonary algorhm proposed by Kenney Eberhar[7,8], he algorhm s smple adops real odng. And s dely used o solve omplex opmzaon problems. Adapve parle sarm opmzaon (APSO s a nd o mproved PSO algorhm[9,10]. By updang he nera egh, APSO eevely balanes he global loal searh ably, mproves he onvergene o he algorhm. Assumng ha n dmensonal searh spae, here are a group o parles, m s he oal number. Poson veor o he parles s = ( x 1,..., x. Veloy veor s V = ( v1,..., v. Eah parle searhes he opmal poson aordng o he ness value o he opmal poson o ndvdual Pb e s = ( x 1 b e s,..., x b e s he parle sarm opmzaon, namely he global opmal poson G b e s = ( x 1 b e s,..., x b e s. The speed poson o eah parle s updaed aordng o he ollong ormula: + 1 V = V + 1r1 ( Pbes + r ( G bes = + V (6 Among hem, V respevely are he parle K eraon o veloy poson, V V max ; 45

3 Dong Qao-Tng e al J. Chem. Pharm. Res., 014, 6(5:44-48 s parles n he K eraon poson; Pbes G b e s are he opmal poson o ndvdual global n he K eraon o parle; 1 are he sudy aors; r1 r are rom numbers beeen [0,1]. W s nera egh, hh s used o oordnae he ably o loal searh global searh o parle sarm. The updae ormula s dened as ollos: ( max mn ( mn mn, avg = ( avg mn max, > avg (7 m ax Among hem, ness value o parle. mn a v g respevely are he maxmum egh mnmum egh, s he urren m n are average ness parle degree value he mnmum ness value. 3. APSO OPTIMIZES THE PARAMETERS OF LSSVM The ey o apply he LSSVM s o reasonably hoose ernel unon s parameers. The ommon Kernel unons are lnear unon, polynomal unon, RBF unon, Sgmod unon so on. Beause he RBF unon s he mos dely used ernel unon, hs paper seles RBF unon. Form s as ollos: (, j = exp( j / K x x x x σ (8 Among hem, σ s nulear parameer. As a resul, LSSVM needs o deermne he parameers o γ σ. In order o ge he bes lassaon perormane, e need o searh or he bes parameer values. We oen use ross valdaon mehod o deermne values o γ σ.bu he ross valdaon mehod has eran blndness romness. The parameers are no alays he opmal soluon, hus aes he lassaon auray o LSSVM. And he large alulaon orload ll slo don he onvergene speed o LSSVM. In hs paper, e use he APSO algorhm o adjus he parameers o LSSVM, sele he value o γ σ opmally (remember LSSVM - APSO. The essene o APSO algorhm seleng he LSSVM parameers s a proess n hh sruure o LSSVM algorhm ombnes h APSO algorhm, he enre proess s as ollos: Sep 1 Inalze he parle sarm. Se he parle populaon sze m, learnng aor 1,, maxmum number o max eraons max, maxmum speed V as ell as he maxmum mnmum value o he nera egh max mn, nalzaon LSSVM parameers γ σ. Sep Dene he ness unon. Le he reproal o LSSVM orre lassaon rae as ness unon: 1 F = 1 / y ( ˆ x y ( x = 1 (9 Among hem, y ( x ˆ y ( x are respevely he arge value he oupu value, s ranng sample. Sep 3 Searh or he opmal parle loaon. Calulae he ness value o eah parle. Aordng o he ness value o parles, he ndvdual opmal poson o parles updaes or mn( F (, F ( Gbes, he global opmal poson o parles updaes or mn( F (, F ( Gbes. Use (6 o adjus he speed loaon o he parles. Sep 4 Deermne ermnaon ondons. I he number o eraons or all parles mees he requremens, hen oupu he opmal parameer values o γ * σ *.Oherse, go o sep. 46

4 Dong Qao-Tng e al J. Chem. Pharm. Res., 014, 6(5:44-48 Sep 5 Esablsh lassaon model. Calulae α b hrough opmal parameer values o γ * σ *, hen subsue he resuls no (4 o esablsh APSO - LSSVM model. Meanhle, use he es sample o he s lassaon perormane. 4. CASE AALYSIS Esablsh perormane evaluaon model o onsruon engneerng proje managemen hh s based on LSSVM-APSO. The model uses he daa o Leraure [] o analyze ases. Corre lassaon, he oupu o LSSVM s 1. Error lassaon, he oupu o LSSVM s 0. Ten samples o daa an be dvded no o groups. Use he prevous seven daa sample o ran LSSVM - APSO very s lassaon auray, hen reuse raned LSSVM - APSO o evaluae he perormane o he remanng hree. Among hem, regard shedule, os, qualy saey o our ndaors as npu o he model, he arge value as he oupu o he model. To alae he omparson o he eeveness o he APSO algorhm, a he same me, use ross valdaon mehod o sele LSSVM parameers or he perormane evaluaon (remember LSSVM - CV, ompare he o evaluaon resuls o he model. In he LSSVM - APSO model, he parameers o he APSO algorhm sel respevely se o: populaon sze m = 10, he maxmum number o eraons = 30, learnng aor 1 = =, maxmum mnmum nera egh max=0.9,mn=0.4. The LSSVM opmal parameer values hosen by APSO algorhm ross valdaon mehod are shon n able 1. Table 1 The opmal parameers hosen by APSO ross valdaon mehod Parameers APSO algorhm ross valdaon mehod γ σ The opmal parameers ge by APSO ross valdaon mehod are used o reran LSSVM model respevely. Use LSSVM - APSO LSSVM - CV o evaluae he ranng samples, he resuls are shon n able. Table shos ha LSSVM - APSO perormane evaluaon resuls are good, LSSVM - APSO oupu values are n omplee aord h he arge, he ranng samples o he orre lassaon rae s 100%. Bu LSSVM - CV or sample 3, 5, 6, 7, he oupu value s onssen h he arge value, he orre lassaon rae s 57.14%. Ths s manly due o he he a ha global searhng ably o APSO algorhm has mproved he auray o hoosng parameers, hus mproved he orre lassaon rae o LSSVM. Cross valdaon mehod deermnes parameers hrough many expermens, hose blndness resrs he LSSVM rae o orre lassaon. The me o APSO algorhm searhng or he opmal parameers o LSSVM s relavely shor, jus 7.47 seonds. Bu, beause o he large amoun o alulaon, he me o ross valdaon mehod o searh he opmal parameers has nreased o 8.34 seonds. Ths shos ha opmzng parameers o LSSVM by APSO algorhm no only mproves he orre lassaon rae, bu also speeds up he model. LSSVM - APSO, hereore, an be used n he perormane evaluaon o onsruon proje managemen. Table The evaluaon resul o he ranng samples Samples The arge LSSVM - APSO oupu values LSSVM - CV oupu values Use LSSVM - APSO o evaluae he perormane o hree samples (proje managemen. The oupu values are shon n Table 3. I he oupu value s 0, he proje managemen perormane s normal; I he oupu value s less han 0, sad ha he poor proje managemen perormane; I he oupu value greaer han 0, sad he proje managemen perormane s good. The Table 3 shos ha he managemen perormanes o projes 1 are bad, hey need approprae mprovemens. The managemen perormane o he proje 3 s good. Table 3 The evaluaon resuls o managemen perormane Samples 1 3 LSSVM - APSO oupu values LSSVM - CV oupu values

5 Dong Qao-Tng e al J. Chem. Pharm. Res., 014, 6(5:44-48 COCLUSIO Ths paper nrodues APSO algorhm o LSSVM model, esablshes he LSSVM - APSO lassaon model. And se he perormane evaluaon o onsruon proje managemen o he ompany as an example o analyze. Resuls sho ha usng APSO algorhm o sele LSSVM opmal parameers, no only mproves perormane evaluaon, bu also redues he modelng me. I has eran value o popularzaon applaon. Anoledgemens Ths or as nanally sponsored by So Sene Researh Base o Hebe Provne: Researh Base on Proje Consruon Managemen he So Sene Program o Hebe Provne (o.: D-37. REFERECES [1] Wang Hongzh; Yong Je,Journal o Shanx Buldng, 010,36 (0: [] Yan Wenzhou; u Jng; u Yuanmng, Journal o an Buldng Unversy o Sene Tehnology (naural sene edon,005, 37 (4 : [3] Han Zhguo;Wang Jmng;Chen Zhgao, Journal o Ol (Ol Proessng 010,6 (3 : [4] VAPIK V.., IEEE Transaons on eural eors,1999,10(5 : [5] Dlan Jayaarna; Alan W Pearson,Inernaonal Journal o Tehnology Managemen, 003,6(8: [6] Suyens J A K;Vevalle J, eural Proessng Leers, 1999,9(3: [7] Wu Zhou; Tan Peng; Pan Feng. Auomaon Tehnology Applaons,009,8 (1:6-9 [8] Sh Y; Eberhar R, Proeedngs o IEEE Inernaonal Conerene on Evoluonary Compuaon. Anhorage, Alasa,1999: [9]P.C.Foure;A.A.Groenold,Sruural Muldsplnary Opmzaon,00, 3 (4: [10] Abar;Reza;Zara;Koorush, Journal o Compuaonal Appled Mahemas,011,35(8: