Parameter Calibration of VISSIM Simulation Model Based on Genetic Algorithm

Transcription

1 Internatnal Cnference n Advanced Cmputer Scence and Electrncs Infrmatn (ICACSEI 2013) Parameter Calbratn f VISSIM Smulatn Mdel Based n Genetc Algrthm Nuerlan Muhan1, Yng Qn2, Qnghua Zhang3, Yanfang Yang1 and Zundng Zhang1 1 2 Schl f Traffc and Transprtatn, Beng Jatng Unversty, Beng , Chna State Key Labratry f Ral Traffc Cntrl and Safety, Beng Jatng Unversty, Beng , Chna 3 Jnhua Insttute f Cty Plannng and Desgn, Jnhua , Chna Abstract - Genetc algrthm s used t calbrate fur drvng behavr parameters and a set f calbratn prcedure s put frward based n VISSIM. Usng the apprach maxmum queue length and travel tme as the evaluatn ndexes and applyng the calbratn methd t a sngle sgnalzed ntersectn f Yzhuang Zne n Beng, whch valdates the effectveness and practcablty f the genetc algrthm n VISSIM parameter calbratn. Index Terms - Parameter calbratn,genetc algrthm, mcrscpc traffc smulatn, sngle sgnalzed ntersectn. rthgnal experment t calbrate sx parameters f a mdel buldng at a sngle ntersectn f Beng Suth-Mddle Crrdr based n VISSIM. In ths artcle, we put frward a calbratn prcess based n the genetc algrthm and select fur senstve parameters t acheve the autmatc crrectn. We select VISSIM as the smulatn platfrm and apply the calbratn methd t a sngle ntersectn f Yzhuang Zne n Beng, and verfy the valdty f ths mdel by analyzng the errrs f tw evaluatn ndexes. We chse the maxmum queue length and travel tme as the evaluatn ndexes, and lay the fundatn fr analyzng the ntersectn quantfcatnally and cmprehensvely. We als ntrduce the weght ceffcent t determne the relatnshp between maxmum queue length ndex and travel tme ndex, whch has a certan practcal sgnfcance. Let s begn wth the genetc algrthm. I. Intrductn Wth the develpment f Intellgent Transprtatn System n ur cuntry, the traffc smulatn technlgy has been wdely used n traffc management, traffc cntrl and ther felds. In traffc smulatn mdel, a large number f parameters are used t descrbe the traffc envrnment, vehcle perfrmance and drvng behavr characterstcs, and the values f thse parameters have great nfluences n the result f the smulatn. Hwever, the default values f thse parameters are ften cnfrmed accrdng t the traffc stuatn f the sftware develpment cuntres, and are nt sutable fr the traffc flw characterstcs f ur cuntry. Fr a specfc smulatn sftware, we must calbrate the mdel parameters t ensure the accuracy f the smulatn result. Dmestc and fregn schlars have studed the calbratn f mcrscpc smulatn mdels ne after anther. Benekhal[ 1 ] was the frst ne t establsh the framewrk f the calbratn and verfcatn f mcrscpc smulatn mdel; Hellnga[2] put frward the gudng prncple f parameter calbratn fr VISSIM, but he ddn t ndcate the specfc calbratn methd; Cheu[3] was the frst ne t apply the genetc algrthm t the parameter calbratn f mcrscpc smulatn mdel and bult the FRESIM mdel f an expressway, and then calbrated 12 parameters f traffc flw mdel; Park and Schneeberge[ 4 ] came up wth a parameter calbratn prcess ncludng 9 steps and calbrated a mdel buldng at a sngle ntersectn based n VISSIM; Park and Q[5] appled the genetc algrthm t the parameter calbratn f VISSIM and chse average travel tme as the evaluatn ndex t calbrate eght parameters; Zhmng L[6] chse vehcle average delay as the evaluatn ndex and used the genetc algrthm t calbrate seven parameters f ne ntersectn mdel fr Shazhuang cty; Yang Wang[7] chse speed and flw as the evaluatn ndexes, and used the rthgnal experment t calbrate the mdel buldng at the access f urban expressway; Quan Yu[8] and thers used the The authrs - Publshed by Atlants Press II. Genetc Algrthm The genetc algrthm s a knd f heurstc ptmzatn algrthm, whch cmbne natural genetcs wth cmputer scence rgancally wth strng prblem-slvng ablty and wde adaptablty, and acqure a gd effect n the feld f traffc engneerng. The basc dea f the genetc algrthm s that cmparng the ndvdual ftness n every generatn f genetc algrthm t fnd ut the fne ndvdual and prduct a new-generatn wth ndvduals by usng genetc manpulatn such as genetc crssver and genetc varatn. After many teratns we get the ptmal ndvdual[9]. Basc steps fr algrthm n GA are as fllws [10]: 1) Intalze a ppulatn f chrmsmes. 2) Evaluate chrmsmes n the ppulatn 3) Create ffsprng r new chrmsmes by mutatn and crssver frm the pl. 4) Evaluate the new chrmsmes by a ftness test and nsert them n the ppulatn. 5) Check fr stppng crtera, f satsfes return the best chrmsme else cntnue frm step 3. 6) End After we chse the algrthm, we shuld cnfrm the calbrated parameters whch have sgnfcant nfluences. III. Cnfrm the Calbrated Parameters Befre calbratng the traffc mdel, we need t cnfrm the mdel parameters whch have sgnfcant effects n the ndexes f the mdel perfrmance measurement, whch s called parameter senstvty analyss. The cre prncple f 591

2 senstvty analyss s that changng the value f ne undetermned parameter n the case f ther parameters reman unchanged. Thrugh multple smulatn tests, we get multple smulatn utput values under dfferent levels f ths undetermned parameter. Then usng the sngle-factr analyss f varance t cnfrm whether the undetermned parameter has a sgnfcant nfluence n the evaluatn ndexes, and whch has a sgnfcant mpact wuld be lsted as the calbrated parameter [7]. Establsh a typcal urban rad ntersectn t fnsh the senstvty analyss, and the gemetrc cndtn f ths ntersectn s as fllws: the east apprach has a exclusve rght-turn lane, a exclusve straght lane, a lane shared by left turnng and straght ahead traffc and a nnmtr vehcle lane. The gemetrc characterstcs f the west apprach, the nrth apprach and the suth apprach s cnsstent wth the east apprach. In ths artcle, eght mdel parameters f VISSIM ncludng maxmum lk-ahead dstance, average standstll dstance, addtve part f safety dstance, multple part f safety dstance, watng tme befre dffusn, mnmum headway, maxmum deceleratn, accepted deceleratn are selected fr the senstvty analyss. Takng maxmum lkahead dstance as an example t descrbe. The unt f maxmum lk-ahead dstance s meter, and the values f ths parameter are: 175, 200, 225, 250, 275, 300. The smulatn utput values f maxmum queue length and travel tme under maxmum lk-ahead dstance s dfferent levels n dfferent perds (10 mnutes) are as TABLE I: TABLE I Maxmum Queue Length and Travel Tme under Maxmum Lk-Ahead Dstance s Dfferent Levels Levels Perds maxmum queue travel length tme maxmum queue travel length tme maxmum queue travel length tme maxmum queue travel length tme maxmum queue travel length tme maxmum queue travel length tme TABLE II Varatn Analyss f Maxmum Queue Length by Maxmum Lk-Ahead Dstance TABLE III Varatn Analyss f Travel Tme by Maxmum Lk-Ahead Dstance Varatn Surces SS df MS F P-value F-crt Intergrup Wthngrup Ttal Usng the maxmum queue length and travel tme n TABLE I t perfrm a varance analyss, see TABLE II and TABLE III. In the tw tables, SS s the sum f squares, df s the degree f freedm, MS s the mean square devatn, F s the test statstcs, P-value s the prbablty value under the apprprate F, F-crt s the crtcal value f F(5,30) dstrbutn under 5% sgnfcance level. Thrugh the varance analyss, the test statstcs value fr maxmum queue length s less than F-crt, and the test statstcs value fr travel tme s als less than F-crt, whch means maxmum lk-ahead dstance have n sgnfcant mpact n these tw evaluatn ndexes. Fr the fur mdel parameters ncludng maxmum lkahead dstance, watng tme befre dffusn, mnmum headway, accepted deceleratn, the test statstc values fr maxmum queue length and travel tme are less than F-crt, whch means the fur mdel parameters have nt sgnfcant mpacts n maxmum queue length ndex and travel tme ndex. We select average standstll dstance, addtve part f safety dstance, multple part f safety dstance and maxmum deceleratn as the calbrated parameters. Then we thnk abut the calbratn prcess based n the genetc algrthm. IV. The calbratn prcess fr mdel parameters f VISSIM based n genetc algrthm Accrdng t the prncple f genetc algrthm, we buld a calbratn prcess fr calbrated parameters as Fg. 1 belw: Start Bnary cdng Bnary decdng Read Smulatn fles And data Cnfrm ftness functn and weght Wrte the drvng behavr parameters Run VISSIM autmatcally VISSIM np fles Queue length data Travel tme data Mutatn peratn Varatn Surces SS df MS F P-value F-crt Intergrup Wthngrup Ttal Evaluate the ndvdual ftness Output f the drver parameters and ftness values Whether reach the maxmum teratns? stp Y Crssver peratn Selectng peratn N Fg. 1 Calbratn prcess fr calbrated parameters f VISSIM 592

3 V. The desgn f calbratn methd fr VISSIM calbrated parameters based n genetc algrthm Cmbnng the prncple f genetc algrthm wth the characterstcs f VISSIM, we gan the calbratn methd fr VISSIM calbrated parameters based n genetc algrthm, ncludng the selectn f the evaluatn ndexes, the encdng and decdng methd f chrmsmes, the determnatn f ftness functn, the selectn f peratrs and s n. A. Select the Evaluatn Indexes The purpse f parameter calbratn n VISSIM s t make the smulatn utput as clse as pssble t the measured value. We select maxmum queue length and travel tme f each apprach as the evaluatn ndexes t prve the valdty f ths mdel. Maxmum queue length and travel tme can mre fully reflect the characterstcs f the ntersectn. B. The Encdng and Decdng Methd f Chrmsme Ths artcle use bnary strngs whch cnsst f the dgts 0 and 1 t encde the calbrated parameters, and the length f bnary strng s related t the requred accuracy. The accuracy f cdng can be btaned usng (1) [11]. In ths equatn, U represents the maxmum value f the calbrated max parameter, U represents the mnmum value f the calbrated mn parameter and l represents the length f the strng. U max l U 2 1 mn, (1) The crrespndng decdng equatn s shwn n (2) [11]. In ths equatn, x represents the th calbrated parameter (=1,2,3,4); represents the mnmum value f the th calbrated parameter; represents the cdng accuracy f the th calbrated parameter; a1 a2 a3 a l, s gene expressn wth the vectr methd, and equals 0 r 1 1. (2 l T,...,4,2,1). x, (2) The length f the bnary strng and the accuracy f cdng nvlved n ths artcle can be receved by TABLE IV, and the length f the parameter set s 15. In ths artcle, the number f ntal ppulatns s 10 and ntal ppulatns are generated by randm numbers. In ths table, represents the average standstll dstance; represents the addtve part f safety dstance; represents the multple part f safety dstance; represents the maxmum deceleratn. TABLE IV The Length f Bnary Strng and the Cdng Accuracy fr Calbrated Parameters Parameters Defult Maxmum Mnmum Length Accuracy (m) (m/s 2 ) C. The Determnatn f Ftness Functn Ths artcle use the mnmum tatal ftness as the slvng cndtn. Set F as the ttal ftness, and x 1, x 2, x 3, x 4 respectvely represent the fllwng parameters: average standstll dstance, addtve part f safety dstance, multple part f safety dstance and maxmum deceleratn. The ttal ftness functn s expressed by (3): F f ( x, x, x, x ), (3) ttal Usng the sum f squared errr t buld the ftness functn, and the sum f squared errr s expressed by (4). In ths equatn, whle equals 1, t represents the calbratn accuracy ndex fr queue length, whle equals 2, t represents the calbratn accuracy ndex fr travel tme; j represents the number f tme bucket n data cllectn; represents the mdel detectr data f queue length r travel tme n jth tme bucket; a represents the cllected feld nvestgatn data f queue length r travel tme n jth tme bucket. F j s ( a a ) a 2 s a, (4) Usng weght ceffcent transfrmatn methd t determne the ttal ftness functn n the cndtn f calbratng the queue length and travel tme at the same tme. represents weght ceffcent n (5). Whle equals 0.5, t means the calbratn accuracy ndex f queue length and the calbratn accuracy ndex f travel tme are equally mprtant; whle s greater than 0.5, t means the calbratn accuracy ndex f queue length s mre mprtant. F af (1 a) F, (5) ttal D. Genetc Operatrs 1 2 1) Selectn peratr: Accrdng t the ftness f each ndvdual, and the prbablty that each ndvdual s selected s prprtnal t the ndvdual ftness value. Assume that the ppulatn sze s I, the ndvdual ftness value fr s F, the prbablty that the ndvdual s selected nt the next generatn s P, and P can be expressed by (6) [11]. P F I F 1, (6) 2) Crssver peratr: Select the sngle-pnt crssver methd t cnfrm the crssver peratn, and the ndvduals are made pars. Set a crssng randmly t the tw pared ndvduals, then exchange the part chrmsme f the tw pared ndvduals n that crssng. After that, we gan tw new ndvduals. In ths artcle, the number f ndvdual genes s 15, s we have 14 pssble crssngs. The crssver prbablty [12] n ths artcle s defned as

4 3) Mutatn peratr: Select the basc bt mutatn peratr t cnfrm the mutatn peratn. Use the mutatn prbablty t determne the change-pnt fr each ndvdual. Invert the gene s value f the change pnt, then we gan a new generatn. The mutatn prbablty [12] n ths artcle s defned as The number f ths ppulatn genes s 150, s we have abut 8 genes t fnsh the mutatn peratn. VI. Example Analyss Select the ntersectn f Rnghua Suth Rad and Rngjng East Street n Yzhuang Ecnmc and Technlgcal Develpment Zne f Beng as the expermental regn. The gemetrc cndtn f ths ntersectn s as fllws: the nrtheast apprach has a exclusve rght-turn lane, a exclusve straght lane, a lane shared by left turnng and straght ahead traffc and a nnmtr vehcle lane; the gemetrc cndtn f the suthwest apprach s cnsstent wth the nrtheast apprach; the sutheast apprach has a exclusve left-turn lane, three exclusve straght lane, a lane shared by rght turnng and straght ahead traffc and a nn-mtr vehcle lane; the gemetrc cndtn f the nrthwest apprach s cnsstent wth the sutheast apprach. The traffc flw data came frm the vde cllectn frm 5:00 pm t 6:00 pm n July 13th, The smulatn mdel f the expermental regn s shwn belw n Fg. 2: Fg. 3 Cnvergence perfrmance f the ftness average and ptmal values n generatns by equal weght ceffcent Makng a cmparsn amng the average value f the real measured maxmum queue length (travel tme), the average value f the maxmum queue length (travel tme) when the calbrated parameters get the default values and the average value f the maxmum queue length (travel tme) after the parameters are calbrated n a smulatn hur. The results are shwn n Fg. 4: Fg. 2 The ntersectn f Rnghua Suth Rad and Rngjng East Street A. Equal Weght Ceffcent When the weght ceffcent equals 0.5, whch means the queue length and travel tme are equally weghted. The values f drvng behavr parameters after calbratn are shwn n TABLE V, and the letters n ths table has been defned abve: TABLE V The Values f Default and Optmal Values by Equal Weght Ceffcent Parameters Defult Values Values after Calbratn (m) (m/s 2 ) Usng the ftness functn defned n Chapter 5 t analyze the cnvergence perfrmance f the ftness average and ptmal values n generatns under equal weght ceffcent as Fg. 3: Fg. 4 Cmparsn f the maxmum queue length and travel tme by equal weght ceffcent 594

5 Usng the mean abslute relatve errr as the ttal errr, and the mean abslute relatve errr f maxmum queue length and travel tme can be expressed by (7): MARE 4 s 1, (7) 4 j 1 s In ths equatn, whle equals 1, and crrespnd t the smulatn utput maxmum queue length and the real measured maxmum queue length fr each apprach, and the unt s meter; Whle equals 2, and crrespnd t the smulatn utput travel tme and the real measured travel tme fr each apprach, and the unt s secnd. Fr the maxmum queue length ndex, MARE s befre calbratn, and MARE s after calbratn. The mean abslute relatve errr f maxmum queue length fr each apprach decreases by and the mprvement rate s 68.7%, whch means the mprvement f maxmum queue length s bvus. Fr the travel tme ndex, calbratn, and MARE s MARE s befre s after calbratn. The mean abslute relatve errr f travel tme fr each apprach decreases by The mean abslute relatve errr f travel tme has been less than 0.15 befre calbratn, and the mprvement f travel tme s nt bvus. B. Unequal Weght Ceffcents It can be btaned frm the abve artcle that the mean abslute relatve errr f travel tme has been less than 0.15 befre calbratn and the mean abslute relatve errr f the maxmum queue length has been mre than 0.30 befre calbratn. We need t fcus n the calbratn f maxmum queue length when we calbrate the maxmum queue length and the travel tme at the same tme. Change the weght ceffcent f maxmum queue length frm 0.5 t 0.8 t cntnue the calbratn f ths case and get the results f drvng behavr parameters after calbratn. Shwn as TABLE VI, and the letters n ths table has been defned abve: Fg. 5 Cnvergence perfrmance f the ftness average and ptmal values n generatns by equal and unequal weght ceffcents Makng a cmparsn amng the average value f the real measured maxmum queue length (travel tme), the average value f the maxmum queue length (travel tme) when the calbrated parameters get the default values and the average value f the maxmum queue length (travel tme) after the parameters are calbrated n a smulatn hur. The results are shwn n Fg. 6: TABLE VI The Values f Default and Optmal Values by Equal and Unequal Weght Ceffcents Parameters Defult Values Values after Calbratn (weght s 0.5) Values after Calbratn (weght s 0.8) (m) (m/s 2 ) Usng the ftness functn defned n Chapter 5 t analyze the cnvergence perfrmance f the ftness average and ptmal values n generatns under equal and unequal weght ceffcents as Fg. 5: Fg. 6 Cmparsn f the maxmum queue length and travel tme by equal and unequal weght ceffcents 595

6 Usng the mean abslute relatve errr as the ttal errr t analyze the mpact f weght ceffcent n the maxmum queue length and travel tme: when the weght ceffcent equals 0.5, the mean abslute relatve errr value f maxmum queue length( MARE ) s 0.098, and the mean abslute relatve errr value f travel tme ( MARE ) s When the weght ceffcent s adjusted t 0.8, the mean abslute relatve errr value f maxmum queue length( MARE ) s 0.093, and the mean abslute relatve errr value f travel tme MARE ) s In ths case, after ncreasng the weght ( ceffcent f maxmum queue length, the errr f maxmum queue length under the ptmal parameters shws sme mprvement. Fr gettng a mre cmprehensve analyss n the mpact f weght ceffcent, we analyze the utput results when the weght s changed t a mnmum value f 0 and a maxmum value f 1. Usng the abve methd t calbrate ths case and usng the mean abslute relatve errr t analyze the mpact f weght ceffcent n the maxmum queue length and travel tme respectvely. The results are shwn n Fg. 7: Fg.7 Cmparsn f evaluatn ndexes by fur dfferent weght ceffcents Frm the abve fgure, whle the weght ceffcent equals 0, the mean abslute relatve errr f maxmum queue length s greater than the errrs f maxmum queue lengths under ther weght ceffcents, and the mean abslute relatve errr f travel tme s relatvely lw. Whle the weght ceffcent equals 1, the mean abslute relatve errr f maxmum queue length s the lwest ne and the mean abslute relatve errr f maxmum queue length s the hghest ne. When the weght ceffcents are 0.5 and 0.8, the varatn trends f these tw curves bascally cnfrm t the defntn f ftness functn, see (5). Accrdng t the descrbed calbratn methd n ths artcle, the weght ceffcent shuld be cnfrmed by the practcal stuatn f the researched ntersectn. After we balance the mpact f maxmum queue length ndex aganst the mpact f travel tme ndex, we can cnfrm a fne weght ceffcent t cmplete the parameter calbratn f ths mdel. VII. Cnclusn Ths artcle studed the parameter calbratn methd f VISSIM smulatn mdel, and put frward a calbratn prcess fr VISSIM based n genetc algrthm, and prved the practcalty and effectveness f ths calbratn methd wth an example. The errrs f smulatn results were wthn the acceptable lmts, and ths methd truly reprduced the runnng cndtn and prvded a apprprate platfrm fr the frmulatn f later ptmzatn scheme. Acknwledgment Prf. Yng Qn put frward a lt f valuable pnns n my study, Ph. D. Yanfang Yang and Qnghua Zhang helped me a lt n the prcess f ths artcle, I express my sncere thanks t them. References [1] R. F. Benekhal, Prcedure fr valdatn f mcrscpc traffc flw smulatn mdels, 70 th Transprtatn Research Bard Annual Meetng, Washngtn D.C, USA, [2] B. R. Hellnga, Requrements fr the calbratn f traffc smulatn mdels, Canadan Scety f Cvl Engneerng, Ontar, CA, [3] R. L. Cheu, et al, Calbratn f Fresm fr a Sngapre s expressway usng genetc algrthm, Jurnal f Transprtatn Engneerng, vl. 124, pp , [ 4 ] B. Park and J. D. Schneeberger, Mcrscpc smulatn mdel calbrat-n and valdatn: case study f VISSIM smulatn mdel fr a crdnated actuated sgnal system, Transprtatn Research Recrd, n. 1856, pp , [5] B. Park and H. Q, Develpment and evaluatn f smulatn mdel calbratn prcedure, 84 st Transprtatn Research Bard Annual Meetng, Washngtn D.C, USA, [ 6 ] Z. M. L and X.Y.Yan, Study n crrectn methd f traffc smulatn mdel based n genetc algrthm, Cmmuncatns Standardzatn, ss. 4, pp , [7] Y.Wang, Study n the relatnshp between the access f urban express-way and bus statn based n mcr-smulatn, Beng, Chna: Beng Unversty f Technlgy, [8] Q. Yu, M. Wang and X. H. Deng, Smulatn parameter calbratn f sngle sgnalzed ntersectn based n rthgnal experment methd, Jurnal f Hghway and Transprtatn Research and Develpment, vl. 29, pp , [9] Y. X. Lu, The analyss and mdelng f the capacty f the expressway resurce allcatn wth the bus lane based n mcrscpc smulatn, Beng, Chna: Beng Jatng Unversty, [10] N. Kshrjt and B. Svaj, Genetc algrthm n feature selectn fr CRF based manpur multwrd expressn dentfcatn, Internatnal Jurnal f Cmputer Scence & Infrmatn Technlgy, vl. 3, [11] X. P. Wang and L. M. Ca, Genetc algrthms thery, applcatn and sftware mplementatn, Xan: Jada Press, 2002: [12] A. Q. Wang and W. Zeng, Tw traffc vlume frecast methds based n genetc algrthms, Cmmuncatns Standardzatn, ss. 5, pp ,