Convergence and Calculation Speed of Genetic Algorithm in Structural Engineering Optimization

Transcription

1 Carographca Snca 22(2) p.p Kmes D S Sellers P J. (985) Inferrng hemsphercal reflecance of he earh s surface for global energy budges from remoely sensed nadr or dreconal radance values. Remoe Sensng of Envronmen 8(3) p.p Shua Y Masek J G Gao F C.C. (20) An algorhm for he rereval of 30-m snow-free albedo from Landsa surface reflecance and MODIS BRDF. Remoe Sensng of Envronmen 5(9) p.p Chulam Abduwas Qn Q M. (2007) Calculaon of ETM+ Broadband Albedos by Radave Smulaons. Aca Scenarum Nauralum Unversas Peknenss p.p Neo H Sandhol I Aguado I C.C. (20) Ar emperaure esmaon wh MSG-SEVI- RI daa: Calbraon and valdaon of he TVX algorhm for he Iberan Pennsula. Remoe Sensng of Envronmen 5() p.p Wloczyk C Borg E Rcher R C.C. (20) Esmaon of nsananeous ar emperaure above vegeaon and sol surfaces from Landsa 7 ETM+ daa n norhern Germany. Inernaonal Journal of Remoe Sensng. 32(24) p.p Ryu Y Kang S Moon S C.C. (2008) Evaluaon of land surface radaon balance derved from moderae resoluon magng specroradomeer (MODIS) over complex erran and heerogeneous landscape on clear sky days. Agrculural and Fores Meeorology 48(0) p.p Snno R W. (994) Sunrse and sunse: A challenge. Sky & Telescope 88(2) p.p Lang S. (200) Narrowband o broadband conversons of land surface albedo I: Algorhms. Remoe Sensng of Envronmen 76(2) p.p Convergence and Calculaon Speed of Genec Algorhm n Srucural Engneerng Opmzaon Yunhua Zhu Xao Ca College of Busness Admnsraon Huaqao Unversy Quanzhou Fujan Chna Absrac In vew of he exsng genec algorhm n srucural engneerng opmzaon has poor convergence compuaonal speed s slow a opmzaon scheme of genec algorhm s proposed n hs paper based on he crossover operaor and fness funcon. The frs use of he hybrd mechansm of he sngle pon crossover operaor of genec algorhm s mproved n order o mprove he searchng space and hen he small o adap o he opmzaon of he haba mechansm of sharng funcon convergence. The smulaon resuls show ha he crossover operaor and fness funcon based genec algorhm opmzaon n srucural engneerng opmzaon has beer faser and beer sably. Meallurgcal and Mnng Indusry 259

2 Key words: Srucural Engneerng Opmzaon Improved Genec Algorhm Convergence Opmzaon Fness Funcon Opmzaon.. Inroducon A any mes we need o desgn and consruc he engneerng srucures. Era progress he requremen for srucure s hgher facors o consder n he desgn s more complex and wh he radonal desgn mehod s ofen dffcul o deal wh[. If you wan o desgn he srucure o conform o he deal as far as possble would be more n need of new modern srucural opmzaon heory and mehod. Srucure desgn opmzaon can make he srucure o acheve he requremen of he economc and secury[2. So he opmzaon desgn s he new developmen and achevemens of srucure desgn has mporan engneerng sgnfcance and wde applcaon prospecs [3. Srucure opmzaon desgn has a hsory of hundred years snce Maxwell's heory and Mchelle s papers on he ssue of mnmum volume frame srucure desgn appear snce Schm used mahemacal programmng o solve he srucure opmzaon desgn also had a hsory of 45 years especally n he pas 35 years srucure opmzaon desgn n he aspecs of heory algorhms and applcaons have made grea developmen[4. Amercan Scens Danzg proposed smplex mehod hs mehod s suable for solvng lnear programmng problem[5.then Kamaka proposed neror-pon mehod and ellpsod algorhm(namely polynomal algorhm) [6. For he nonlnear problem people use lnear heory o solve he nonlnear problem a he begnnng hen based on he quadrac funcon approxmae o oher nonlnear funcon on he such bass here are many classcal opmzaon mehods such as unconsraned mehod ncludes: he conjugae graden mehod he seepes descen mehod (seepes) Newon's mehod (Newon algorhm) quas-newon mehod (pseudo Newon algorhm) rus regon mehod ec. [7.The scence and echnology are n a muldscplnary cross each oher and complemen each oher and he rapd developmen of compuer echnology he reques for effcen opmzaon echnques and nellgen compung s hgher based on he mahemacal opmzaon echnology by opmum denfcaon defnon and modelng solvng varous knds of opmzaon problems s wdely used n many felds[8. Mc- Culloch and Ps esablshed arfcal neural nework model and was exended "percepron" opmzaon models laer and hen Hopfeld appled neural nework o he combnaoral opmzaon problems successfully because of he arfcal neural nework has srong adapably learnng ably and massve parallel compung ably has been wdely appled o varous knds of praccal engneerng such as conrol and opmzaon predcve modelng sgnal processng communcaons ec. [9. In hs paper he genec algorhm of srucural engneerng opmzaon s mproved opmze he crossover operaor and fness funcon n order o mprove s convergence and compuaon speed n he opmzaon of srucural engneerng. 2. Genec Algorhm GA algorhm s an erave process based on fness funcon and hrough applyng genec operaons o speces ndvduals o realze he ndvdual srucure reorganzaon of he spece. In hs process he spece ndvdual s opmzed by generaons and gradually approxmae he opmal soluon [0. Genec algorhm uses n fness funcon o evaluae he ndvdual srenghs and weaknesses n operaon he desgn of fness funcon has an mporan nfluence on he performance of genec algorhm. ()The maxmum opmzaon problem: Fness( f ( x)) = f ( x) () The mnmum opmzaon problem: Fness( f ( x)) = f ( x) (2) The fness funcon wh a smple expresson form n he real lfe applcaon exsed he followng problems: mos of he me does no sasfy he nonnegave requremen of he roulee wheel selecon; If some funcon value has large dfference wll lead o he populaon average fness value canno reflec he average performance of populaon wll ulmaely affec he effec of he algorhm. (2) The bgges opmzaon problem: f( x) + Cmn f( x) + Cmn > 0 Fness( f ( x)) = (3) 0 f( x) + Cmn 0 Cmn s a preesablsh suable small number s he smalles funcon value of he objecve funcon snce we have esmaed. The mnmum opmzaon problem: Cmax f( x) Cmax f( x) > 0 Fness( f ( x)) = 0 Cmax f( x) 0 (4) Cmax s a preesablsh suable bg number s he bgges funcon value of he objecve funcon snce we have esmaed. Because C max Cmax s pror esmaed s no precse enough and ofen makes he fness funcon 260 Meallurgcal and Mnng Indusry

3 no sensve enough o cause algorhm performance degradaon. (3) The bgges opmzaon problem: Fness ( f ( x )) = 0 ( ) 0 + c f( x) c c f x The mnmum opmzaon problem: (5) Fness ( f ( x )) = 0 ( ) 0 + c+ f( x) c c + f x (6) Among hem c s he pror esmaed value so has he smlar problem n (2). The basc process and srucure of he sandard genec algorhm s shown n fgure. Fgure. The basc process of genec algorhm b b 3. The Operaor Opmzaon of Genec Algorhm 3.. Crossover Operaor Opmzaon Crossover operaon s he man operaon of genec algorhm only by consanly crossover operaon o produce he new ndvdual so ha we can ge he excellen ndvduals. In order o ncrease he searchng space of populaon hs paper proposed a crossover operaor based on mxed sngle pon. Suppose when evolues o he h generaon wo male paren respecvely are: Xa = [ xa... xak... xan and Xb = [ xb... xbk... xbn afer crossover we can ge Xb = [ xb... xbk... xbn he + h generaon ndvduals are + and + + [ + X b = xb... xbk... xbn Inersecon are respecvely x ak and k. The cross way here s o calculae he k h genes of ndvdual X a and x + as hrough ype (7) wo new genes x + as and k + are produced and pu back n place and hen exchange he k + h o X bh genes of X and X evenually produces wo new ndvduals he calculaon of he k h gene s as follows: + xas = αxak + ( α) xbk (7) + xbs = ( α) xak + αxbk rank( X a ) α = Among hem rank( X a) + rank( X b) rank( X ) s he column rank of ndvdual α. Along wh he growng of evoluon algebra α s more and more end o be 0.5. In he h generaon he man seps of mxed sngle pon are as shown below. () Choose wo male paren from he populaon p = [ xa... xak... xan p2 = [ xb... xbk... xbn randomly and and choose he kh of he varables n he wo male paren among hem k = round( rand ( n ) + ) n s he number of decson varables; (2) If rand < pc pc s crossover probably rank( p) α = ge no (3) or rand > pc rank( p) + rank( p2) ge no (5); Meallurgcal and Mnng Indusry 26

4 ch ( k) = αxak + ( α) xbk (3) ch2 ( k) = ( α) xak + αxbk s he ransformaon form of ype (7); (4) The new generaon of wo ndvduals are: ch + = [ p (: k ) ch ( k) p2 ( k + : n) (8) ch2 + = [ p2 (: k ) ch2 ( k) p ( k + : n) (9) (5) Make he faher ndvdual whch s chosen be- fore as chld ndvdual ch + = p ch2 + = p2. Repea he process unl he number of new ndvdual s equal o he number of populaons ha sop crossover operaon The Fness Funcon Sharng Opmzaon Based on Nche Drec purpose of fness sharng funcon s o separae he dfferen peak of search space on geography each peak acceps a ceran percenage number of he ndvduals he sze of he rao has relaon wh peak hegh. In order o realze he dsrbuon use sharng mehod o reduce he goal of ndvdual fness namely he fness value ms dvded by a nche coun m for sharng funcon make nche coun m as an ndvdual adjacen se nensy esmaes. m = sh[ d[ j (0) j Pop Among he ype above d [ j s he dsance of j and j sh [0 = s a sharng funcon s a decreasng funcon sh [0 = and sh[ d σ = 0. The followng s a ypcal rangle d funcon: d d σ sh( d ) = σ () 0 d > σ Hereσ s he nche radus r s gven by users hemselves s he mnmum dsance beween good peak ndvduals. The ndvdual whn he scope of dsance σ o cu each oher fness. Because hese ndvdual nche sze s he same so hey convergence n a nche avod he convergence of he enre populaon.when a nche s full he nche coun ncreases wll make sharng funcon lower han oher nche. In order o defne a nche hs paper adops a mehod whch combned hammng dsance measure and fness dsance.if d ( ) x xj s he hammng dsance of any wo ndvduals x and x j d ( ) 2 x xj s he fness dsance hen sharng funcon can be defned as: d( x xj) d( x xj) < σ d2( x xj) σ2 σ d2( x xj) d( x xj) σ d2( x xj) < σ2 Sh( x x j) = σ 2 d ( x x ) d ( x x ) < < 0 else j 2 j d( x xj) σ d2( x xj) σ2 σσ 2 (2) Here σ andσ 2 are he nche radus namely s he maxmum ndvdual dsance of he genoype and phenoype respecvely whn a a nche. Fnally he fness funcon of he ndvdual afer sharng change no he form of he followng: f ( x ) = M j= f( x ) sh( x x ) j (3) Here f( x ) andσ + = 20are he expressons of ndvdual fness funcon when s before d and afer d. 4. The Algorhm Smulaon In order o verfy he effecveness of he mproved genec algorhm proposed n hs paper he smulaon expermen was done. In hs paper make 3 pole plane russ as example modulus of elascy s E =.0E+ 6 he allowable sress of each bar are σ + = 20 σ = 5. he lower lm of cross-seconal area s up o 2.9 s srucure s shown n Fg 2: Fgure 4. Overall opmzaon russ rod Usng he mproved genec algorhm (IGA) proposed n hs paper he srucural opmzaon s carred ou and compared wh he sandard genec algorhm he resuls are shown below. Two algorhms are used o opmze he srucure of each bar and he srucure wegh of he srucure s reduced. The resuls are shown n he followng dagram. As shown he mproved genec algorhm n opmzaon of srucural engneerng has beer convergence han he radonal genec algorhm and n he qualy opmzaon of he 3 pole plane russ has beer effec and has good sably. 262 Meallurgcal and Mnng Indusry

5 Fgure 3. Opmzaon of russ srucure Fgure 4. Overall opmzaon russ rod 5. Concluson The exsng genec algorhm n he applcaons of he srucural engneerng opmzaon here are problems of premaure convergence genec drf and he conradcory problem beween compung effcency and dversy preservaon. In vew of he defecs of radonal genec algorhm hs paper pus forward he genec algorhm of crossover operaor and fness funcon opmzaon can be seen from he expermen smulaon resuls ha he mproved sraegy pued forward hs paper s effecve grealy mprove he convergence performance of he orgnal algorhm n he opmzaon of srucural engneerng. References. Ge S W (203) Mul-objecve opmzaon of hull srucure based on BP-GA algorhm. Marne Scence and Technology 9 p.p Xue C G (203) Objec knowledge nework srucure opmzaon research based on he me performance. Compuer Applcaon Research 8 p.p Yuan Y (203) Opmzaon of shp srucure based on suppor vecor machne. Shp Scence and Technology 7 p.p Peng D L (203) Srucure opmzaon of me-grang wh varable couplng coeffcen based on BP-neural neworks and genec algorhms. Insrumen Technque and Sensor 4 p.p Tong C H (203) Model of waer-savng agrculure ndusry srucure opmzaon and adjusmen based on mul-objecve genec algorhm. The Agrculural Research of Dry Areas p.p Dng M (203) Dynamc adapve genec algorhm n he applcaon of he ple anchor supporng srucure opmzaon desgn. Buldng Srucure 2 p.p Zheng C Y (202) Applcaon of mproved genec algorhm n srucural opmzaon desgn of aqueduc. Journal of Yangze Rver Scenfc Research Insue 7 p.p Zhang G Q (20) Srucure opmzaon of mechancal pars based on he mproved mmune genec algorhm. Journal of Cenral Souh Unversy: Naural Scence p.p Zhao Y M (20) Seel russ srucural opmzaon desgn based on he genec smulaed annealng algorhm. Journal of Zhengzhou Unversy: Engneerng Scence 6 p.p Hu X L (20) Grder opmum desgn of brdge erecon machne based on neural neworks and genec algorhms. Manufacurng Auomaon 7 p.p Meallurgcal and Mnng Indusry 263