MODELLING OF STOCHASTIC PARAMETERS FOR CONTROL OF CITY ELECTRIC TRANSPORT SYSTEMS USING EVOLUTIONARY ALGORITHM

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1 MODELLING OF STOCHASTIC PARAMETERS FOR CONTROL OF CITY ELECTRIC TRANSPORT SYSTEMS USING EVOLUTIONARY ALGORITHM Mkhal Gorobetz, Anatoly Levchenkov Inttute of Indutral Electronc and Electrotechnc, Rga Techncal Unverty 1 Kronvalda blvd., Rga, LV-1010, Latva E-mal: mgorobetz@latnet.lv, leva@latnet.lv KEYWORDS Modellng, evolutonary algorthm, electrc tranport ABSTRACT Th work baed on reearch n a feld of ntellgent ytem, negotaton algorthm olvng tak of energy avng, optmal electrc vehcle control and tranport flow control n traffc jam. Man goal of reearch energy avng for publc electrc tranport. Mathematcal model and evolutonary algorthm propoed n the paper to olve mult-crtera optmzaton tak mnmzng dle tme and electrc energy ued by publc electrc tranport and maxmze average peed of the flow n traffc jam. Paper preent a computer experment to tet propoed mathematcal model and workablty of evolutonary algorthm. The pecfc dynamc model wth tochatc parameter of cty tranport ytem created and reult of evolutonary optmzaton are mulated. INTRODUCTION Author propoe to ue electronc ntellgent ytem to control traffc lght correpondng to the tranport flow. The target to mnmze of total electrc energy uage by electrc tranport and total dle tme for all tranport flow partcpant ung evolutonary algorthm for ntellgent of traffc lght [1]. Paper decrbe the problem of decon-makng for cty tranport control. The decon makng modelng for tranport problem decrbed, ung method of decon makng theory [2] and proce optmzaton n ntellgent tranport ytem. A the tranport ytem a cooperatve ytem, where behavor of one partcpant depend on other. That why the negotaton proce for ntellgent neceary. Each control h own object endng data to the uper, whch reponble for optmzaton and coordnaton of negotaton proce. PROBLEM FORMULATION Tranport flow n the cty growng and traffc jam become the common problem for mot of bg cte. Publc electrc tranport hould have hgher prorty than prvate car, by crteron of tranported paenger number, electrc energy conumpton and ervce level evaluated by chedule fulfllment. Publc electrc tranport, uch a tram and epecally trolleybue, whch are more enble to traffc jam, ue more electrc energy durng frequent acceleraton and brakng n traffc jam and nfrnge cheduled tme. Alo traffc lght are not ynchronzed and workng ndependently from tranport flow. Publc electrc tranport, uch a tram and epecally trolleybue, ue more electrc energy durng frequent acceleraton and brakng n traffc jam. That why, traffc lght green lght hould be ynchronzed wth the chedule of publc electrc tranport. For all other partcpant of the tranport flow the mnmzaton of dle tme n traffc jam needed. It mult-crtera optmzaton tak wth followng crteron: mnmzaton of electrc energy and dle tme and maxmzaton of average flow peed. The purpoe of th paper to defne ftne functon for evolutonary algorthm. Evolutonary algorthm realzed for ntellgent uper to optmze green and red lght tme. Ftne functon hould nclude normalzed value of dle tme and average peed for all tranport partcpant n traffc jam and electrc energy conumpton. METHOD OF SOLUTION Author propoe to ue ntellgent ytem 3 for tak oluton. Each ntellgent reponble only for h own object. The ntellgent ha all neceary nformaton about the object and ha poblty to make decon for the object. Intellgent the element of artfcal ntellgence 4 - are ncorporated n the electrc tranport control ytem. Th ytem managed and controlled by the uper. The uper reponble for ntellgent negotaton and to cooperate the work of autonomou to acheve common goal of the ytem. A uper an ntellgent, whch not reponble for any object, but for procee where more then one object' ntellgent partcpate. Proceedng 22nd European Conference on Modellng and Smulaton ECMS Louca S. Louca, Yorgo Chryanthou, Zuzana Oplatková, Khald Al-Began (Edtor) ISBN: / ISBN: (CD)

2 Intellgent nput and proce of the nformaton on the phycal tranport unt a well a end t to ntellgent uper for the analy of the tuaton of the tranport ytem n general to realze the deconmakng procedure. Ala the uper realze negotaton of the ntellgent, defnng a negotaton et. It play a role of the arbtraton judge, whch nomnate what player have to do proceedng from reult of negotaton. Vehcle Vehcle1 Vehcle1 engne Vehcle M Vehcle M engne SUPERAGENT Croroad1 Croroad1 traffc lght Fgure 1: Intellgent ytem Croroad Each electrcal tranport unt ha own ntellgent. An ntellgent a oftware package that reponble for an object (fg. 1.) or a proce. Controller e 0 f 0 Mcrocomputer e 2 f 2 e f 4 f 3 e 3 Software Actuator Intellgent Engne Fgure 2: Intellgent for mechantronc ytem control A ntellgent cont of three neceary component: databae, oftware, whch baed on artfcal ntellgence tructure and algorthm, and electronc devce-controller. All nformaton about an object uch a techncal charactertc and parameter, tratege, chedule, calculated data and o on ncorporated n ntellgent ' databae. The oftware ued to proce th data wth evolutonary algorthm. Electronc devce are ued to realze ntellgent control on machne level. Each publc electrc tranport unt ha own ntellgent, whch reponble only for the current unt. Phycally each tranport unt equpped wth the U m I e e 1 f 1 Databae T U I Croroad N Croroad N traffc lght Electrcal contact network Senor \ Mechatronc ytem telemetrc ytem (enor) that collect data for databae 5. MATHEMATICAL MODEL FOR INTELLIGENT AGENT Th part preent mathematcal model for tak oluton. Mathematcal model of publc electrc tranport ytem ha a et of dynamc parameter. Such parameter can be number of car watng on the croroad, number of paenger watng on paenger top. Alo number of lane, whch very gnfcant parameter for traffc jam problem oluton, may be changed n cae of breakdown and crah of car. All thee varable are changng contnuouly. That why evolutonary algorthm neceary to adopt optmal oluton to current nput dynamc parameter. Dynamc parameter ha tochatc behavour. For ntance, drver reacton tme, dtance between car, acceleraton tme and movng peed dpend on human factor, that why t hould be modeled a tochatc parameter. Statc Input Data et of croroad K length of a car - c ; Stochatc Dynamc Input Data number of tranport unt n jk, where j drecton, k - croroad; average peed of movng car (wthout top) v; flow rate of croroad (number of lane) l; Parameter for th tranport unt drver average reacton tme r ; acceleraton tme for one tranport unt a ; dtance between car n traffc jam - d ; poton n traffc jam - p. Varable green lght tme x k ; red lght tme y k ; where k croroad. Target functon Average watng tme T = t / n mn Average flow peed - V = v max Electrc energy - E = e mn Auxlary functon tme of movng from poton to the croroad - ( p 1) ( c d ) t ( r a ) p v flow rate of traffc lght: v x c d f l; f c d ( r a ) v

3 red lght tme (green lght mng): rt p / f ; f red lght watng tme: rt y; t r poton before pang croroad: p' p tr ( r a ); f Ftne functon for optmzaton T n 1 n 0 t ( x, y) ' ( p 1) ( c d ) ' ( r a ) p t v r rt x mn (1) Normalzaton functon Let u aume, that maxmal value of target functon are: T max = 3600 ; V max = 50 kmh; E max = 1000 kwh. Accordng to th value normalzaton : Tmax T 3600 T T ' ; T 3600 max V V V ' ; V 50 max Emax E 1000 E E'. Emax 1000 Let u aume the prorte for optmzaton parameter are T = 0.3; V = 0.3; E = 0.4. Ftne functon for optmzaton: F = T T + V V + E E max (2) EVOLUTIONARY ALGORITHM FOR INTELLIGENT AGENT From evolutonary pont of vew the parameter of the problem are preented a gene of chromoome. Each chromoome preent problem oluton. Each oluton hould be evaluated by ftne functon. The goal of genetc algorthm to fnd the chromoome wth optmal value of ftne functon. In our cae the chromoome contan green lght tme and red lght tme of each traffc lght: = (x 1, y 1, x 2, y 2,, x k, y k ) Populaton n the tak preented a a et of traffc lght workng mode for all analyzed croroad: S { 1, 2,..., p} Each tate evaluated by ftne functon (2): V F ) General evolutonary algorthm for tak oluton followng: Step 1: Intalze populaton: ( S { 1, 2,..., p} ; Step 2: Evaluate populaton: S V { F( 1), F( 2),..., F( p )}; Step 3: Arrange populaton by evaluaton: S S { 1, 2,..., p}, F( 1) max( V ) ; Step 4: Select bet parent to elte S E S ; Step 5: Select other parent for croover S C S ; Step 6: Apply croover, where ' j j; j j,, j 1, p ; Step 7: Apply mutaton, where x j x j 1, S', ; j rand(1, k), rand(1, p) Step 8: Evaluate populaton: S ' V { F( 1 ), F( 2 ),..., F( p )} ; Step 9: Arrange new populaton by evaluaton: S ' S' { 1, 2,..., p }, F( 1 ) max( V ) ; Step 10: Combnng wth elte: S ( SE S '); Step 11: Delete lat: S S /{ p 1, p2,...}; Step 12: IF F ) F( ) ( 1 p THEN Goto Step 2 ELSE End of Evolutonary Algorthm wth oluton 1. PRACTICAL EXAMPLE An abtract croroad elected for a computer experment (Fg.3). Functon (1) optmzed n th experment wth followng parameter: n 3 n 1 n 2 Fgure 3: Schema of croroad for computer experment. Let u aume, number of vehcle on the frt treet: n 1 + n 2 = 100 n 4

4 number of vehcle on the econd treet: n 3 + n 4 = 200 number of lane: l = 2 average peed of movng vehcle: v = 25; drver average reacton tme: r = 1; acceleraton tme a = 3; length of a car: c = 4; dtance between car n traffc jam: d = 0,5; Target to mnmze average watng tme for all vehcle by optmal traffc lght regulaton (1). T ( x, y) mn Input data for evolutonary algorthm are preented on Fgure 4-6. Fgure 6: Input parameter for evolutonary algorthm Reult of evolutonary algorthm are preented on fgure 7. Fgure 4: Settng lmt for traffc lght optmzaton algorthm Fgure 7: Reult of evolutonary algorthm Fgure 5: Input parameter for croroad SIMULATION OF CITY TRANSPORTATION SYSTEM The pecfc modellng envronment developed by author for computer experment 6. For the practcal example object the tram ytem n Rga centre taken hown on the fgure 8. The part of the route elected for tet the way from the paenger top "Centraltrgu" to the top "Grecneku ela" for one tram.

5 All mulaton dynamc parameter of a tram are taken from the real tram T3-A. Author reult prove, that the applcaton of propoed algorthm for green wave organzaton can be very ueful for olvng energetc and electrotechnology problem n publc electrc tranport ytem. Fgure 10: Reult of mulaton wthout optmzaton Fgure 11 provde total watng tme wth evolutonary algorthm reult. Fgure 11: Reult of mulaton ung evolutonary algorthm On current tage of reearch 8% of tme aved by ung of evolutonary algorthm reult. Fgure 8: Smulaton of ntellgent traffc lght control The man advantage of propoed algorthm energy avng by more than 20% at leat and tme avng by more than 40%. That mean, the reult of ung ntellgent n publc electrc tranport moton control allow to reduce runnng cot and to cut down load on traffc network by decreang tme pent n the cty centre a well a offer of much fater ervce. Th reearch preent reult of traffc control ung evolutonary optmzaton of traffc lght workng tme. Fgure 9: Computer model for traffc control Fgure 9 preent the model of traffc jam wthout evolutonary algorthm. Model how current tuaton n Rga, where traffc jam very actual problem. Reult of evolutonary algorthm how the necety to et up maxmal allowed tme for green lght. Fgure 10 how total watng tme for uual traffc lght workng mode. ACKNOWLEDGMENT Th work ha been partly upported by European Socal Fund wthn the Natonal Programme "Support for carryng out doctoral tudy program' and potdoctoral reearche" project "Support for the development of doctoral tude at Rga Techncal Unverty" (grant Nr..2004/0002/VPD1/ESF/ PIAA/04/NP/ /0002/0007) CONCLUSION Reult of practcal example on th tage of reearch prove that evolutonary algorthm ueful for traffc control tak oluton. Advantage of ung evolutonary algorthm the poblty of contnuou optmzaton of traffc control. Evolutonary algorthm very entve to t parameter. That why neceary to fnd out the mot utable algorthm of electon, croover a well a number of bt, populaton ze, number of loop and mutaton. Alo mnmal and maxmal lmt of varable x and y very mportant. Experment how that n cae of hgh maxmal lmt of green lght, algorthm tre to wtch on green lght a long a poble to allow all vehcle to pa the croroad. Otherwe, the mnmal lmt of green lght optmal. REFERENCES 1. J. Branke. Evolutonary Optmzaton n Dynamc Envronment, Kluwer Academc Publher, 2002, 224 p. 2. M. Gorobetz, A. Levchenkov, N. Kuncna, L. Rbck. Modellng of Decon Support Sytem for Intellgent Publc Electrc Tranport. //In Proceedng of Internatonal Conference on

6 Indutral Engneerng and Sytem Management, Bejng, Chna, 2007, 334 p. 3. S. J. Ruel, P. Norvg. Artfcal Intellgence. A Modern Approach, 2nd edton. Prentce Hall, 2006, 1408 p. 4. G. F. Luger. Artfcal Intellgence. Structure and Stratege for Complex Problem Solvng, Wllam, J. Grevul, I. Ra. Iekrtu vadba elektronke element un mezgl. - Rga: Avot, lpp. 6. M.Gorobetz, A.Levchenkov, L.Rbck. Intellgent Electrc Vehcle Moton And Croroad Control. //In Proceedng of 12th Internatonal Power Electronc and Moton Control Conference. Portoroz, Slovena, p AUTHOR BIOGRAPHIES ANATOLY LEVCHENKOV Profeor at Rga Techncal Unverty, Faculty of Power And Electrcal Engneerng, Inttute of Indutral Electronc and Electrotechnc from Snce 1997 he ha been Aocate Profeor at the Tranport Ralway Inttute and from 1992 to 1997 wa Head of the Rga Techncal Unverty Department of Decon Support ytem. He tuded Electrcal Engneerng n Automaton and Telemechanc from 1964 to MIKHAIL GOROBETZ graduated Mater of Informaton Technology at Rga Techncal Unverty Computer Scence and Informaton Technology Faculty Informaton Technology Inttute n At preent he a reearcher and lat year PhD tudent at Rga Techncal Unverty Inttute of Indutral Electronc and Electrotechnc..