Optimizing Traffic Signal Settings in Smart Cities

Transcription

1 1 Zhiyi Li Studet Mebe IEEE Mohaad Shahidehpou Fellow IEEE Shay Bahaiad Seio Mebe ad Ai Khodaei Seio Mebe IEEE Abstact affic sigals play a citical ole i sat cities fo itigatig taffic cogestios ad educig the eissio i etopolita aeas. his pape poposes a bi-level optiizatio faewok to settle the optial taffic sigal settig poble. he uppe-level poble deteies the taffic sigal settigs to iiize the dives aveage tavel tie while the lowe-level poble ais fo achievig the etwok equilibiu usig the settigs calculated at the uppe level. Geetic algoith is eployed with the itegatio of icoscopic-taffic-siulatio based dyaic taffic assiget (DA) to decouple the coplex bi-level poble ito tactable sigle-level pobles which ae solved sequetially. Case studies o a sythetic taffic etwok ad a eal-wold taffic subetwok ae coducted to exaie the effectiveess of the poposed odel ad elevat solutio ethods. Additioal stategies ae povided fo the extesio of the poposed odel ad the acceleatio solutio pocess i lage-aea taffic etwok applicatios. Idex es Sat cities taffic sigal settig bi-level optiizatio dyaic taffic assiget. I Optiizig affic Sigal Settigs i Sat Cities I. INODUCION NELLIGEN taspotatio systes (IS) ae becoig iceasigly ipotat i sat cities [1]. athe tha coutig solely o developig ew oads o iceasig oad capacities IS utilizes advaced ifoatio ad couicatio techologies such as eal-tie vehicle-tovehicle (V2V) [2] ad vehicle to ifastuctue (V2I) [3] couicatios to sooth out taffic flows ad educe oad cogestio. IS povides dives with the citical taffic ifoatio that would help ipove oad safety ad taffic efficiecy [4]. As a vital copoet of IS taffic sigals ca play a vey ipotat ole i stategic taffic aageet that would lead to a pefeed distibutio of taffic flows [5]. he taffic aageet authoity would eed to coside offset tie split tie (i.e. gee tie) cycle tie ad phase sequeces of taffic sigals i ode to appopiately cotol taffic sigals ad educe the tavel tie i cogested oads. he lack of coodiatio aog taffic sigals ca affect dives total tavel tie ad icu cogestios i soe aeas which would futhe polog the total tavel tie. O the othe had a pope coodiatio aog taffic sigals ca also espod positively to eissio cotol ad evioetal coces. IS allows dives ad the taffic aageet authoity exchage ifoatio i eal tie. Dives epot thei tip his poject was fuded by a gat fo the Coowealth Ediso Copay (CoEd). Zhiyi Li ad Mohaad Shahidehpou ae with the obet W. Galvi Cete fo Electicity Iovatio at Illiois Istitute of echology (zhiyi.li@hawk.iit.edu; s@iit.edu); Mohaad Shahidehpou is also a eseach pofesso i the ECE Depatet at Kig Abdulaziz Uivesity i Saudi Aabia. Shay Bahaiad is with CoEd (Shay.Bahaiad@CoEd.co); Ai Khodaei is with the ECE Depatet Uivesity of Deve ( Ai.Khodaei@du.edu). ifoatio (i.e. oigi destiatio ad depatue tie) befoe depatue. he taffic aageet authoity uses the dives ifoatio to update the taffic sigal ad tip dead database peiodically. Give the IS tip data dives ae eabled to have oe accuate peceptios of futue etwok coditios ad taffic aageet authoity aages to iiize potetial taffic cogestio ad be esposive to dives tip deads by appopiately settig taffic sigals. Diffeet fo othe studies [6][7] which optiized taffic sigal settigs coditioed o pe-defied dives outes we coside itedepedecies of dives choices ad taffic sigal settigs i this pape. he taffic-sigal-settig poble i atue is a leade-followe Stackelbeg gae which ca be foulated as a bi-level optiizatio poble whee the uppe ad the lowe level pobles belog to the leade (taffic aageet authoity) ad the followe (dives) espectively. affic aageet authoity wats to iiize dives aveage tavel tie by choosig the optial taffic sigal settigs. Note that taffic aageet authoity will be able to evaluate the effects of a paticula set of taffic sigal settigs oly by takig dives outes ito accout. I tu dives solve thei ow optiizatio poble to fid the fastest oute based o the deteied taffic sigal settigs. As a esult the taffic-sigal-settig poble is foulated as a bi-level optiizatio poble i ou pape. he bi-level poble ca be expessed as a atheatical poga with equilibiu costaits (MPEC) by covetig the lowe-level poble as a set of additioal costaits of the uppe-level poble. Fo istace if the lowe-level poble is covex the this lowe-level poble ca be ecast usig its Kaush Kuh ucke coditios ad itegated ito the uppe-level poble as a set of additioal copleetaity costaits. I this way the bi-level optiizatio poble is coveted ito a MPEC. he bi-level optiizatio poble is difficult to solve aily due to the tight coupligs betwee the two levels. hus we use the Geetic Algoith (GA) to decouple the oigial bi-level poble ito two sigle-level pobles ad solve the sequetially. he ai cotibutios of this pape ae suaized as follows: (1) he pape poposes a optiizatio-based faewok fo deteiig adaptive taffic sigal tie settigs i sat cities. (2) he pape foulates a copehesive bi-level optiizatio odel which optiizes ad coodiates split tie cycle tie phase sequeces ad offsets siultaeously fo taffic sigals at all itesectios. (3) he pape decouples the bi-level poble ito tactable sigle-level pobles ad eploys GA to fid ea-optial solutios with easoable coputatio effots. (4) he pape develops a icoscopic siulatio-based dyaic taffic assiget odel fo captuig the etwok equilibiu i taffic flows. he eaide of this pape is ogaized as follows: Sectio

2 2 II foulates the bi-level optiizatio odel to deteie the optial settig of taffic sigals. Sectio III explais the solutio ethods fo the poposed optiizatio poble. Sectio IV pesets ad aalyzes the ueical esults fo case studies. Sectio V gives soe ideas o odel extesio as well as solutio pocess acceleatio stategies fo eal-wold lage-aea etwok applicatios. elevat coclusios ae suaized i Sectio VI. A. affic Sigal Itegatio II. MODEL FOMULAION I pactice taffic lights located at ay itesectios ae sychoized that would follow specific pattes fo aagig the taffic flow ad safety. Accodigly egioal taffic sigals at a give taffic diectio ca be itegated ito a sigle taffic sigal which would siultaeously egulate the flow of all vehicles appoachig coespodig itesectios fo diffeet diectios. Such itegatio could educe the ube of cotol vaiables ad acceleate the solutio pocess i the taffic flow optiizatio poble. his pape assues each itegated taffic sigal efeed to as a taffic sigal hecefoth pefos taffic flow egulatios i two pepedicula N-S ad E-W diectios. Fig. 1 shows the two distict sigal phases egulatig the taffic at a itesectio (aows efe to allowable taffic diectios). he taffic light colo states i these two diectios ae utually exclusive i each phase. Fo siplicity we oly discuss the colo states i the E-W diectio heeiafte. L W (a) Gee i the N-S diectio (b) Gee i the E-W diectio Fig. 1 affic flow egulatio affic Sigal at Itesectio i Offset Cyclic Gee Cyclic ed Cyclic Gee Cyclic ed N S E L t=1 affic Sigal at Itesectio j t=n Offset Cyclic ed Cyclic Gee Cyclic ed Cyclic Gee Fig. 2 Sigal phases of taffic light Each taffic sigal copises a sequece of phases (show i Fig. 2) ad each phase idicates the coespodig colo state fo taffic cotol. I this pape each taffic sigal is assued to have thee phases (i.e. offset gee ad ed). Followig the iitial offset phase gee ad ed phase ae epeated peiodically. he two phase sequece is depedet o the iitial offset phase. Although the yellow phase exists i pactice its duatio i the optiizatio pocess is subtacted fo that of gee state ad oly teated sepaately i the ipleetatio pocess. B. Foulatio of Bi-level Optiizatio his subsectio descibes the foulatio fo the optial taffic sigal settig poble. A list of otatios ad the coespodig defiitios ae give as follows. N M Notatios Defiitio Idices Idex fo itesectios Idex fo dives Idex fo tie itevals Vaiables I Biay vaiable epesetig taffic sigal at t itesectio i tie iteval t if equal to 1 diectio E-W is gee othewise diectio N-S is gee Offset of taffic sigal at itesectio Cyclic gee tie of taffic sigal at itesectio Cyclic ed tie of taffic sigal at itesectio O G oute choice fo dive Optial (fastest) oute fo dive otal tavel tie fo dive to fiish the tip by choosig oute Paaetes N Nube of itesectios M Nube of dives N Nube of tie itevals I Iitial status of taffic sigal at itesectio 0 G Iitial gee tie of taffic sigal at itesectio 0 Iitial ed tie of taffic sigal at itesectio 0 G G i Miiu ad axiu gee tie of taffic sigal at ax itesectio i Miiu ad axiu ed tie of taffic sigal at ax itesectio Cadidate outes fo dive Depat Depatue tie fo dive fo its oigi Fuctios avel () otal tavel tie fo dive o its tip duig the tie peiods ude study () otal tie fo dive to fiish its tip ip he objective fuctio ad costaits i the optiizatio poble ae listed as follows. Objective Fuctio he objective is to iiize the aveage tavel tie fo all dives duig the studied tie itevals which could also be viewed as the suogate easue fo the eductio of pollutio ad fuel cosuptio. he objective fuctio is epeseted as 1 i avel ( ) (1) M whee Depat if avel + N ( ) = (2) Depat Depat N if + > N Costaits o Gee/ed Phases A vey log gee phase ight esult i pologed waitig ties fo othe dives i a itesectio wheeas a vey shot gee phase ight hape the taffic safety. hus the gee phase duatio ust be withi a easoable age as G G G i ax (3) Siilaly ed phase duatio ust be withi a easoable age as

3 3 (4) i ax Costaits fo Offset Phase Duatio affic sigals should be switched soothly which could othewise icu uexpected iplicatios of taffic safety. his would iclude the offset phase (i.e. iitial colo state i the ew settigs). So O O O (5) whee i ax { 0 ( ) ( 1 ) ( )} ( ) ( 1 ) ( ) = ax I + I (6) O G G i 0 i 0 0 i 0 = I + I (7) O G G ax 0 ax 0 0 ax 0 Costaits fo affic Sigal States he duatios of taffic sigal states ae solely depedet o G sigal settig decisios (i.e. ad fo each itesectio ). he elatioships aog states ae epeseted as follows. he colo ad phase duatio i the iitial (offset) states is deteied by O epeseted as whe 1 O I t = I0 t (8) Afte offset phase the duatio of taffic sigal cycles is the G su of plus. Note that the cycle sequeces ae affected by the iitial state. Accodigly the fist cycle is epeseted as whee I O X 0 t = X O G I0 whe + 1 t + + O 1 I whe + 1 t ( 1 ) X O G = (9) I I (10) he colo cycles will be epeated as I = I O G t G whe t N (11) t oute Costaits Each dive will use the taffic sigal ifoatio ad othe dives oute decisios to look fo a oute with the iiu tavel tie which is odeled as Depat ( ) = ag i I... I (12) ip N N M III. SOLUION MEHODOLOGY A. he Faewok of the Poposed Solutio he faewok of the poposed bi-level optiizatio poble is depicted i Fig. 3. he uppe ad the lowe level pobles ae aaged by the taffic aageet authoity ad dives espectively. he taffic aageet authoity would iiize dives aveage tavel tie by optiizig taffic sigal settigs as it takes dives oute choices ito accout. I tu dives look fo the fastest oute based o the ifoatio o the taffic sigal settigs. he objective fuctio (1) with costaits (2)-(11) fos the O G uppe-level poble whee ad ( ) ae decisio vaiables fo adjustig taffic sigal settigs ad I t ( t) ae state vaiables epesetig taffic sigal state. I essece give the taffic sigal states I ( t) t costait (12) itself is a optiizatio poble fo the fastest oute petaiig to a paticula dive ( ). Cosideig the behavio of dives o cogested oads the fastest-oute poble at the lowe-level ais at achievig the etwok equilibiu based o the taffic sigal ifoatio deteied i the uppe-level poble. I tu the lowe-level poble passes the dives oute ifoatio to the uppe-level poble. he pocedue fo appoxiatig a etwok equilibiu is efeed to as the dyaic taffic assiget (DA) [10] which is detailed i Sectio III.D. At such equilibiu o dive ca educe its tavel tie by uilateally chagig its oute withi ay tie iteval. Diffeet fo deteiistic use equilibiu assiget which assues dives ae idetical ad have coplete kowledge of the etwok coditios the stochastic use equilibiu assiget is capable of odelig the vaiatios i dives peceptios of etwok coditios ad i dives decisios o oute choices. I othe wods eve with the help of advaced itelliget taspotatio systes techologies dives peceptios of etwok coditios ad thei pefeeces of oute choices ae hadly idetical. Accodigly we odel the lowe level poble as a stochastic use equilibiu DA poble which is oe appopiate i the evioet of sat cities. Uppe Level Objective: Miiize the Aveage avel ie Decisio: affic Sigal Settigs Sigal 1 Sigal 2... Sigal N Sigal States & Duatios Dive 1 Dive 2... Dive M Lowe Level Objective: Achieve the Netwok Equilibiu Decisio: Dives Ow Fastest outes Dives outes & ip ie Fig. 3 Bi-level optiizatio faewok B. Hybid Geetic Algoith he bi-level optiizatio poble is itisically difficult to solve aily due to the tight coupligs betwee the two levels. So we eploy GA to solve the poposed bi-level optiizatio odel by selectig the optiu cycle splits ad offsets siultaeously. GA could offe a high-quality ea-optial solutio with a affodable coputatioal cost as copaed with covetioal optiizatio ethods [8]. I paticula the icoscopic taffic siulatio is successfully itegated with the global seach capability povided by GA. o diffeetiate it fo the taditioal GA we use a Hybid Geetic Algoith (HGA) fo covetig the bi-level optiizatio ito a itegated poble with coputatioally feasible solutios. he itegated poble is coposed of two sigle-level pobles which ae solved sequetially. he ai pocess fo applyig HGA is illustated i Fig. 4 ad descibed as follows. Step 1: Iitializatio. Fo the ado iitial populatio whee the choosoe of each idividual epesets a cadidate solutio ecoded as eal-itege-valued stig of legth 3 N. Hee subscipt s efes to idividual s. Each gee i

4 4 O G the choosoe is a decisio vaiable ( s s o s ) epesetig the phase duatio of a taffic sigal. So s s s O O O i s ax G G G i s ax i s ax (13) I tu each taffic sigal s settig is joitly deteied by a subgoup copised of thee successive gees. I Fig. 5 the peutatio of gees coespods to the sequeces of cyclic phases. Populatio Iitializatio Fitess Evaluatio Solve Lowe-Level Pobles: Dyaic affic Assiget Get the Aveage avel ie eiated? Ed Yes No Evolutio Selectio Matig ad Cossove Mutatio Fig. 4 Hybid Geetic Algoith Fig. 5 Choosoe epesetatio Elitis he subgoups ae cosecutively placed i the choosoe fo appig the coplete taffic sigal settigs. Such choosoe epesetatio takes ito accout the itedepedecy of decisio vaiables aog adjacet taffic sigals ad phase duatios of idividual taffic sigals [9]. Step 2: Fitess evaluatio. his is the ost distictive step i the poposed algoith whee a idividual s fitess value i the cuet populatio is evaluated. he idividual s fitess is the objective value of the uppe-level poble which is coputed afte solvig the lowe-level poble oce the taffic sigal settigs (epeseted as idividual choosoes) ae give. I othe wods idividuals coespod to a feasible solutio of the oigial bi-level poble which is calculated sequetially by pefoig a global seach fo best idividual(s) at the uppe-level poble ad fidig the coespodig solutio i the lowe-level poble. Specifically taffic sigals ae set accodig to (8)-(11) fo O G idividual s defiig s s ad s ( ) ad the coespodig fitess value is calculated by solvig the followig poble M avel fs= ( s ) s (14) whee Depat ( + ) = ag i I... I s ip s s s s11 snn s1 s 1 s 1 sm (15) Ituitively the fitess value is obtaied by siultaeously locatig the optial oute fo each dive (i.e. etwok equilibiu) which is decoupled fo the uppe-level poble. Step 3: Evolutio. he populatio is updated by eplacig all idividuals at the cuet geeatio with ew potetial solutios based o fitess values. his step is ipleeted usig the followig fou geetic opeatos: Elitis: A subset of idividuals with the best fitess value(s) is selected ad passed o to the ext geeatio which guaatees that the solutio quality at the ext geeatio will ot be ay wose tha that of the cuet geeatio theeby avoidig ay solutio oscillatios. Note that these elitist idividuals will ot go though the followig thee opeatos. Selectio: he eaiig idividuals of the cuet geeatio ae adoly chose as the paets of the ext geeatio usig the touaet selectio echais (epesetig the best fitess value of each touaet) util the ube of paets is equal to the size of the populatio excludig the elitist idividuals. Matig ad Cossove: he selected paets ae adoly aaged i pais to poduce two solutios fo the ext geeatio. Fo siplicity a sigle-poit cossove is ipleeted by adoly selectig a poit i each pai ad swappig the ight-side substigs of the paet stigs i the pai. Mutatio: Idividuals ae adoly self-utated to achieve a local seach aoud the cuet solutios theeby avoidig the peatue covegece ad aitaiig the populatio divesity. We utilize a idividually adaptive echais which adapts the idividual s utatio pobability accodig to its fitess value so as to pobably aitai the idividuals with above-aveage fitess values ad disupt those with below-aveage fitess values. Paticulaly a idividual s u utatio pobability ps ( s) is deteied by the followig equatio [11] [12]: ax u u f fs u avg ( ax i ) ax i if u p p + p f avg s f ps = f f s (16) u avg pax if fs < f u u whee p ax ad p i deote the pe-specified axiu ad ax avg iiu utatio pobability espectively; f s f ad f epeset the fitess value of idividual s the global best fitess value (which is equal to the best fitess value of the cuet geeatio) ad the aveage fitess value of the cuet geeatio espectively. he a ado ube is geeated fo each gee of idividual s ad copaed with the deteied u utatio pobability p s ; if the ado ube is lage tha u p s this gee is eplaced by a ew ado value withi its age. Step 4: eiatio citeio. If eithe the geeatio ube is at the theshold o the fitess level is viewed satisfactoy (e.g. the global best fitess value has ot chaged fo 50 cosecutive geeatios) the algoith will be teiated with

5 5 the global best value as the fial solutio; othewise the ext geeatio stats with the ew populatio ad go though the pocess statig fo Step 2. C. evised Dijksta s Algoith Hee we deteie the expected fastest oute fo each dive at its depatue poit. Fist taffic etwok is abstacted to ode-edge gaph by epesetig itesectios as odes ad laes as diected edges. If the cuise tie fo all edges does ot vay though the tip this fastest-oute poble ca the be solved by evisig the Dijksta s algoith [13]. Algoith 1 ( ) calculates the fastest oute as show below. Algoith 1: evised Dijksta s Algoith Iput: Dive s oigi ad destiatio odes s ad d ad its depatue tie Depat Output: Dive s fastest oute 1: { all the odes} U V Aive Depat 2: o 3: fo each i U \ {o } do 4: Aive i 5: Pev[ i] 6: while d U do Aive 7: i ag i{ i } i U ad tavel tie 8: U U \{ i } V VU { i } 9: fo each adjacet ode j of i i U do Aive Aive Cuise Wait 10: if j > + + the i i j i j + + Aive Aive Cuise Wait 11: j i i j i j 12: [ ] Pev j i 13: i d 14: while Pev[ i] do 15: U { i} 16: i Pev[ i] Aive 17: = d Aive o he tavel tie cosists of the cuise tie alog tavesed edges ad the waitig tie at tavesed odes. Neglectig the Cuise acceleatig ad deceleatig pocesses the cuise tie i j of dive alog the diected edge i-j is deteied by Cuise = L / V (17) i j i j i j whee Li jis the legth of edge i-j; Vi j is the expected speed o edge i-j fo dive. I additio whe dives aive at the ed ode of the tavesed edge they will ete the dowstea edge iediately if thee is o taffic sigal at this ode o the taffic sigal is gee; othewise they will joi the queue at the ed of the edge ad wait util the taffic sigal tus gee at a late tie. o be oe ealistic the effect of yellow sigals is also cosideed hee which deped o the divig behavio (aggessive o ild). I othe wods whe the sigal is yellow a aggessive dive teds to pass the itesectio quickly but a ild dive teds to stop. Accodigly the waitig tie fo dive at ode i who is tavelig to ode j is calculated by 0 if gee Wait NextG Aive = if ed i j i i Next Aive d ( + ) if yellow i i i (18) whee Next ad NextG ae the tie istats whe the taffic i i sigal at ode i tus gee ad ed espectively; δ is a biay idicto epesetig divig behavio of dive (if dive is aggessive δ equals 1 othewise 0). Fo siplicity the aggessiveess of dive is sapled by 0if ad ( 01) < 0.5 d = (19) 1if ad ( 01) 0.5 i which ad ( 01) is a uifo distibuted sigle ado ube which is betwee 0 ad 1. D. Dyaic affic Assiget Each dive s choice fo the fastest oute depeds o ot oly taffic sigal sequeces but also the level of taffic cogestio. he cogestio level i tu depeds o the outes selected by othe dives. Cosideig that such itedepedecies ake it difficult to pedict the actual edge-cuise tie the fastest oute caot be coputed solely by the evised Dijksta s algoith. Futheoe the optial solutio of the lowe-level poble coespods to the etwok equilibiu fo all dives. It is also difficult to solve the lowe-level poble aalytically aily due to the utual iteactios aog dives. Istead we esot to the icoscopic siulatio-based DA which is executed by ivokig the evised Dijksta s algoith ad icoscopic taffic siulatio iteatively. At each iteatio DA fids the expected fastest oute fo each dive usig the evised Dijksta s algoith. As this iteative pocess cotiues the fastest outes ad the esultig taffic assiget ted to be bought close to the etwok equilibiu. Note that if all dives choose the expected fastest outes at each step these outes ight becoe cogested ad would o loge be the fastest. hus alteative outes should be also cosideed by taveles at each iteatio. Oce all the dives have chose thei outes at depatue the oad taffic dyaics ae obtaied by icoscopic taffic siulatio whee dives follow thei outes without futhe updates alog thei tips. I this pape icoscopic taffic siulatio is coducted usig the Siulatio of Uba Mobility (SUMO) [14] which is a ope-souce aget-based icoscopic oad taffic siulato. I SUMO the oveet of idividual vehicles is siulated based upo ca-followig [15] ad lae-chagig [16] theoies which ede the siulatio to be oe cosistet with the eal-wold sceaios. hus the tavel ties calculated by the icoscopic taffic siulatio ae eliable. Futheoe SUMO povides tajectoies fo each vehicle which ae vitally helpful i extactig tepoal ad spatial dyaics of dives behavios. Fo istace it is coveiet to obtai the aveage cuise tie speed o desity o idividual edges duig ay specified tie itevals. he pocedue fo pefoig the icoscopic-siulatio based DA is show i Fig. 6 ad illustated as follows. Step 1: Iitializatio. Iitialize the taffic etwok ad deteie each edge s iitial expected cuise tie fo dives depatig at diffeet tie.

6 6 Step 2: Fidig expected fastest outes. Deteie the expected fastest oute fo each dive i the taffic coditio with tie-depedet expected edge-cuise tie. I such coditio edge-cuise tie is appoxiated by the aveage Depat speed o this edge fo dive s depatue tie to the ed of siulatio. he speed is obtaied based o the esults of icoscopic taffic siulatio discussed i the ext subsectio. Note that if thee is o dive o this edge duig the elevat siulatio peiods the edge s speed liit is used as its expected speed. Step 3: Foig o updatig oute choice set. Dives ae assued to opt fo othe feasible outes besides the expected fastest outes at each iteatio. hat is to say each dive adoly chooses his outes fo the cadidate oute set ad the pobabilities of these cadidate outes ae deteied by the evised ethod of successive aveages [17][18] as show below. Pepae Data Set oad etwok ifoatio affic sigal cotol logics Dives tip ifoatio ad depatue tie Deteie Iitial Expected Cuise ie of Each Edge Based o the iitial etwok coditio Obtai the Expected Fastest oute fo Each Dive Usig evised Dijksta s Algoith Fo/Update Cadidate oute Set fo Each Dive Usig the evised Method of Successive Aveages Coduct Micoscopic Siulatio fo oad affic I the evioet of SUMO eiated? No Yes Ed Adjust Each Edge's Expected Cuise ie fo Each Dive Based o each edge s aveage cuise speed fo the siulatio Fig. 6 Dyaic affic Assiget Fist iteatio (whe k=1) Hee supescipt k efes to the k-th iteatio. he iitial cadidate oute set is foed fo each dive which icludes its iitial expected fastest oute ad soe othe feasible outes. Note that thee is o eed to exhaustively seach all feasible outes. Istead at ost five epesetative outes fo each dive ae icluded i the iitial set i ode to acceleate the covegece speed. Accodigly the cadidate oute set is defied as ( k) ( k) { } U { iitial assiged outes} (20) ad the pobability fo each oute is deteied by η if = k + 1 p = (21) η 1 α if k + 1 whee α e = e (22) I the above equatio η is a use-defied costat withi the age [0 2]; p is the pobability to choose the oute at the k-th iteatio fo dive ; is the expected tavel tie o oute as a esult of the expected taffic coditio at the k-th iteatio. Note that ( k ) ca be ultiplied by a use defied paaete fo epesetig dive s avesio to the loge tavel tie. Subsequet iteatios (whe k>1) If the expected fastest oute is icluded i the pevious ( k 1) cadidate oute set ( k) ( k 1) (i.e. ) the pobabilities ae deteied by η ( k 1) η ( k) ( k) 1 p + a if = k + 1 k + 1 η ( k 1) ( k) ( k 1) p = 1 p if ad (23) k + 1 η ( k) ( k 1) a if k + 1 whee α ( k) e ( k 1) = o = e + ( k 1) e (24) he the cadidate oute set eais uchaged (i.e. ( k) ( k 1) ). If the expected fastest oute is ewly ( k) ( k 1) geeated (i.e. excluded i the pevious cadidate ( 1) oute set k ) the pobabilities ae deteied by whee p α η ( k) ( k 1) α if k + 1 = η ( k 1) ( k 1) 1 p if k + 1 ( k) e ( k 1) = ( k 1) e (25) (26) ( he the cadidate oute set is updated as k ) ( k 1) ( ) { k } U. Clealy the outes with loge tavel ties ae assiged lowe pobabilities. Besides the cadidate oute set cotais the expected fastest oute fo all pevious iteatios. I fact those etaied fo vey ealy iteatios ae pobably vey eote fo the oe ecetly idetified fastest outes. Meawhile the ewly-geeated expected fastest outes idetified at late iteatios ae pesuably close to the actual fastest outes but eceive lowe pobabilities. hus a estatig echais is applied to eset the iteatio coute to 1 at desigated iteatios (e.g. evey 10 iteatios i this pape) i ode to iiize the diect iflueces of ealie iteatios ad adjust the pobabilities fo outes idetified at late iteatios. Accodigly this algoith teds to offe a bette covegece pefoace. Step 4: Micoscopic taffic siulatio. Pefo the icoscopic taffic siulatio i SUMO usig the chose

7 7 outes so as to obtai the actual tavel tie alog dive s chose oute ( ). Step 5: eiatio Check. Appoxiated eo fo the etwok equilibiu solutio is easued by the followig elative gap at each iteatio Gap = 100% k (27) If eithe a pe-specified toleace level fo the appoxiated eo (e.g. 5% [19]) o axiu ube of iteatios is eached this algoith will be teiated ad the chose outes at the last iteatio will be assued to epeset the etwok equilibiu; othewise the ext iteatio will stat by adjustig each edge s expected cuise tie accodig to the icoscopic siulatio esults ad eiitiatig the pocess fo Step 2. ip =800 s ip =860 s Fig. 9 avel tie copaisos ip =880 s he the selectio of outes will lead to distict total tavel tie which caot be distiguished by the oigial Dijksta s algoith. Obviously the oute with a total tavel tie of 800 s is the fastest oute which is also the optial solutio accodig to the evised Dijksta s algoith. he poposed algoith offes a oe suitable solutio fo the optial taffic sigal settig poble. IV. CASE SUDIES A. Sythetic affic Netwok o copae the pefoace of the evised Dijksta s algoith with the oigial oe we ceate a sythetic taffic etwok (see Fig. 7) with the paaetes i able 1. Without the loss of geeality we assue each itesectio is cotolled by taffic sigals with the sae settigs fo taffic flow egulatios i two pepedicula diectios (see Fig. 8). Assue that a aggessive dive etes at the botto-left itesectio ad fiishes its tip at the top-ight itesectio i the fee-flow coditio. Without cosideig the waitig tie i calculatig the total tavel tie thee will be ultiple ad equally desigated fastest outes that ae coputed by the oigial Dijksta s algoith. Fig. 9 lists thee of such outes as a exaple. Howeve it is clea that these outes all have the sae total cuise tie of 800 s with a totally diffeet waitig tie (0 s 60 s 80 s espectively). t=1 able 1 Paaetes fo case studies Netwok Size 8 k 8 k Equally-divided Block Legth 2 k Vehicle Speed Liit 20 /s affic sigals Locatio At each itesectio Fig. 7 A sythetic sigal etwok Peiodically epeated affic Sigals 54 s 6 s 60 s 54 s 6 s 60 s Fig. 8 affic sigal settigs W N S L E B. Uba affic Subetwok o futhe exaie the effectiveess of the poposed odel ad the coespodig solutio ethod a uba taffic subetwok (i.e. viciity of Illiois Istitute of echology ad the Bozeville couity i Chicago) show i Fig. 10 ad obtaied fo OpeSteetMap [20] is used i ou expeiets Fig. 10 Uba taffic subetwok i Chicago he itesectios i ou study ae all labeled i which the taffic sigals ae cotolled by logics. he dives tip ifoatio is estiated by the aveage daily taffic couts [21]. he estiated ifoatio is close to the actual ube of vehicles cossig the poits with istalled sesos i cetai steets o a aveage weekday which is deoted as the base case. he studied tie is 1000 s ad all the dives ae assued to uifoly iset ito the subetwok i the fist 500 s. he taffic sigal equieets ae listed i able 2 ad the HGA paaetes ae listed i able 3. he taffic subetwok is built i SUMO as show i Fig. 11 with the elevat vehicle settigs give i able 4. able 2 affic sigal equieets # Iitial State Gee ie ed ie State Duatio/s Mi/s Max/s Mi/s Max/s 1 ed ed Gee Gee

8 8 5 ed Gee Gee ed Gee Gee Gee Gee ed ed able 3 Paaetes of HGA Populatio Size 20 Max. Geeatio 50 Elite Nube 1 ouaet Pool Size 4 Mi. ad Max. Mutatio Pobability Fo istace able 5 shows the coodiated settigs i the base case fo lik-based sigals i Fig. 12. Hee default settigs ae geeated by SUMO to adhee to taffic ules. o coside the suitability of the poposed odel ad the coespodig solutio ethods we double the ube of dives i the ew case to fo a heavy-loaded case. he covegece pocess of HGA i the base ad heavy-loaded cases is show i Figs. 13 ad 14 espectively. Obviously the fial settigs optiized by HGA afte 50 geeatios ae bette tha the default settigs i both cases. Specifically i the base case the aveage tavel tie is educed fo s with default settigs to s with optial settigs afte 50 geeatios; i the heavy-loaded case the aveage tavel tie is educed fo s with default settigs to s with optial settigs afte 50 geeatios. It is clea that HGA pefos bette i hadlig heavy-loaded cases whe thee ight be oe potetial cases of cogestio. able 5 Lik-based sigal coodiatio at itesectio 8 Itesectio Sigal Duatio Itesectio # Phase Default Optial A ed Gee B ed Yellow C Gee ed D Yellow ed 6 6 Fig. 11 est taffic subetwok i SUMO able 4 Vehicle settigs i SUMO Acceleatio Ability 2.6 /s 2 Deceleatio Ability 4.5 /s 2 Dive s Ipefectio 0.5 Dive s eactio ie 1.0 s Vehicle Legth 4 Miiu Gap betwee Vehicles 2 I additio vehicles oveets alog evey lae-to-lae lik (lae-to-lae lik eas tuig left o ight o goig staight) at ay itesectio ae cotolled by the elevat taffic sigals (see Fig. 12). he calculated optial phases of itegated taffic sigals ae thus divided ito a set of coodiated lik-based sigals at each itesectio i SUMO. Aveage avel ie (s) Aveage avel ie (s) Geeatio Coute Fig. 13 HGA covegece pocess i the base case Optial Settigs Default Settigs Optial Settigs Default Settigs Geeatio Coute Fig. 14 HGA covegece pocess i the heavy-loaded case he epesetative esults fo the DA covegece i both cases ae show i Fig. 15. Hee DA coveges to the etwok equilibiu i both cases. Especially fo the base case DA would oly equie thee iteatios to covege aily because thee ae vey few cases of cogestio duig the siulatio pocess ad the expected fastest outes ae vey close to the actual fastest oes. Fig. 12 affic sigals at itesectio 8

9 9 he epesetative covegece pocess of DA fo idetifyig the expected fastest outes with ad without waitig tie ae show i Figs. 16 ad 17 espectively. Ituitively the calculatio of the expected fastest outes with waitig tie edes the gap to covege oe apidly i both cases. Hece DA with the cosideatio of waitig tie is a oe efficiet appoach to achievig the etwok equilibiu Base Case Heavy-loaded Case Appoxiatio Eo flow i eal tie ad efficietly espodig to ay chages i the taffic situatio. he poposed bi-level optiizatio odel ca be easily exteded to coside the taffic-adaptive sigals. Iitially the ope-souce iteface aci4matlab [22] is eployed to eable Matlab to iteact with SUMO fo the ipleetatio of aget-based algoiths i a seve-cliet echais as show i Fig. 18. SUMO (Seve) Micoscopic affic Siulato 50 Gap (%) aci4matlab (Iteface) CP-based Achitectue Gap (%) Gap (%) Iteatio Coute Fig. 15 DA s covegece pocess With Waitig ie Without Waitig ie Acceptable Eo Iteatio Coute Fig. 16 DA covegece pocess i the base case With Waitig ie Without Waitig ie Acceptable Eo Iteatio Coute Fig. 17 DA covegece pocess i the heavy-loaded case V. MODEL EXENSION AND SOLUION ACCELEAION FO EAL-WOLD LAGE-AEA APPLICAIONS A. Model Extesio fo affic-adaptive Cotol Logics Although the taditioal fixed-tie taffic sigal cotol echais is used ost widely i pactical cases the fixed-tie teds to cause taffic cogestio especially whe the taffic desity is high i uba aeas. I this cotext adaptive taffic cotol echaiss becoe iceasigly popula. he adaptive appoach ca ovecoe the disadvatages of the fixed-tie cotol by detectig the taffic Matlab (Cliet) Ipleetatio of Cotol Algoith Fig. 18 Iteactive siulatio faewok I additio gee (ed) phase duatios of taffic sigals cotolled by the taffic adaptive echais ca be adjusted i eal tie withi allowable ages G G G i ax (28) i ax G G whee i ( i ) ad ax ( ax ) athe tha G ( ) ae G to be optiized ( ) ad ( ) is cofigued i eal tie based o the aget-based algoiths. hus (3) ad (4) fo taffic-adaptive sigals ae eplaced by the followig set i the bi-level optiizatio odel Gi G Gax i i i Gi G Gax ax ax ax (29) i ax i i i i ax ax ax ax B. Acceleatio of Solutio Pocess at Uppe-level Poble 1) Paallel Pocessig fo HGA he poposed HGA ca be paallelized i tes of the aste-slave ipleetatio. Accodigly a aste is the ai pocesso which geeates ad evolves the full populatio of choosoes ad assigs a cetai factio of the idividuals to slave pocessos. he slaves evaluate fitess values by coductig siulatio sepaately fo the assiged factio ad etu thei values (see Fig. 19). Accodigly paallel pocessig boosts the speed of global seach ad offes a full advatage fo seachig the etie feasible egio. Slave Pocesso 1 Fitess Evaluatio Maste Pocesso Iitializatio Evolutio Slave Pocesso 2 Fitess Evaluatio... Slave Pocesso S Fitess Evaluatio Fig. 19 Ipleetatio of paallel fitess evaluatio 2) Multi-laye Patitio ad elaxatio fo affic Sigals I a lage taffic etwok the ube of taffic sigals is

10 10 cooly vey lage ad the siultaeous optiizatio of all taffic sigal settigs would be uealistic due to its pohibitive coputatioal cost. Geeally taffic sigals oly affect local taffic flows i a geogaphical aea. hat is taffic sigal settigs i a cetai aea would have egligible effects o dives tavellig i othe aeas. Accodigly it is easoable to optiize taffic sigal settigs locally. Accodigly we patitio the etie etwok ito seveal subaeas ad allocate layes to these subaeas. Each laye is coposed of seveal subaeas with ucoelated taffic sigal settigs aog the subaeas. Figue 20 shows a thee-laye patitio. Hee the oute ad the ie layes ae ubeed the lowest ad the highest espectively. he optiizatio stats fo the lowest-ubeed laye ad poceeds upwad though the layes util all taffic sigal settigs i the etie etwok ae optiized. Duig the pocess of fidig optial taffic sigal settigs i a cetai laye the optiizatio algoith is executed i paallel fo all subaeas while taffic sigals i the highe-ubeed (lowe-ubeed) layes ae cotolled by thei default (optial) settigs. betwee its oigi ad destiatio) as well as the edges coectig these odes. I case thee exists o feasible oute fo soe tip withi its educed etwok that etwok is the expaded by icludig all the eighboig odes ad i-betwee edges of the pevious etwok. his expasio pocess cotiues util thee is at least oe feasible oute i the ewly-foed etwok. Fig. 21 povides a siple exaple i the gid etwok fo foig two types of pued etwoks fo two dives with diffeet tip distaces. I accodace with dives ituitio fo choosig outes i eal life this heuistics appoach educes the etie etwok to dive-depedet local aeas which ae aoud the diagoals egadig the staight-lie distaces of thei tips theeby leadig to cosideable icease i the subsequet fastest-oute algoith with easoable esults. educed Netwok ie 1 ie 2 Laye 1 Laye 2 Laye 1 ie 1 Laye 2 Laye 1 Fig. 20 Multi-laye patitio Laye 3 Laye 2 Laye 2 Laye 1 3) Pe-defied Settigs fo Cetai affic Sigals Accodig to vehicle couts the settigs of cetai taffic sigals ca be pe-defied to educe cogestio. Fo istace whe the taffic flow i oe diectio is uch lighte tha that i the pepedicula diectio we ay fix the gee (ed) tie i this diectio to be set at its iiu (axiu) value. his appoach could help educe the seach space ad theeby acceleate the solutio pocess. C. Acceleatio of Solutio Pocess at Lowe-level Poble 1) Netwok Puig fo Fidig the Expected Fastest outes Siila to the oigial Dijksta s algoith the evised Dijksta s algoith ight becoe quite costly fo fidig the fastest outes i lage-aea taffic etwoks [23]. Ituitively this algoith will be expedited if the etwok size is educed. Hee we popose a heuistic appoach to speed up the outefidig pocess by puig the etwok fo each dive. he heuistic appoach woks as follows: Fist we classify all the tips ito two categoies of shot ad log distace by copaig the Euclidea distaces betwee oigis ad destiatios with a pe-specified value. Secod we fo the educed etwok fo each dive with efeece to its tip. Specifically fo a shot distace tip ectagle boudaies ae foed by the fou coected stictly hoizotal ad vetical paths betwee its oigi ad destiatio. Oly the odes ad edges iside o o the boudaies ae etaied to fo the equied educed etwok. Meawhile fo a log distace tip we keep the closest odes o both sides alog the diectio of the staight lie (coespodig to the Euclidea distace Fist Expasio Fig. 21 Netwok puig heuistic ethod 2) Paallel Multi-subaea Micoscopic affic Siulatio Whe the siulated taffic etwok is lage we ca pefo a spatial decopositio by dividig the etie etwok ito seveal cotiguous subaeas ad the u icoscopic taffic siulatio fo each subaea i paallel. Such ulti-subaea siulatio ca also be ipleeted usig the aste-slave echais (see Fig. 22). Accodigly vehicle oveets withi each subaea ae siulated locally by icoscopic siulatio. A aste cotolle is esposible fo sychoizig ad coodiatig the siulatio pocess of each subaea whe vehicles ae cossig the bodes betwee ay two adjacet subaeas. Sice the siulatio speed depeds lagely o the poble size paallelized icoscopic taffic siulatio fo each subaea us faste tha that fo the etie aea which leads to a icease i the etie siulatio pocess. Subaea 1 Micoscopic Siulatio Maste Cotolle Sychoizatio Coodiatio Subaea 2 Micoscopic Siulatio Subaea NS Micoscopic Siulatio Fig. 22 Ipleetatio of paallel icoscopic taffic siulatio 3) Sequetial Multi-subiteval Dyaic affic Assiget Whe the siulatio iteval is log we ca pefo tepoal decopositio by cuttig the whole iteval ito seveal successive subitevals ad the assigig ubes i sequece to dives depatig each subiteval. I each subiteval a coplete DA pocess is ipleeted ad etwok coditios i the subsequet subitevals ae updated by covetig the DA esults ito a tie-depedet...

11 11 backgoud taffic. his pocess is show i Fig. 23. With the ipleetatio of this heuistic ethod the etwok equilibiu is appoxiated i each subiteval istead of the etie iteval theeby esultig i ea-optial solutios with fewe coputatioal effots. Pepae Data Sets i this Subiteval oad etwok coditios affic sigal cotol logics Dives tip ifoatio ad depatue tie Pefo Dyaic affic Assiget i this Subiteval Based o icoscopic siulatio i the evioet SUMO Update Netwok Coditios fo Subsequet Subitevals By covetig taffic assiget decisios i this subiteval ito tie-depedet backgoud taffic Fiished? Ed Yes No Next Subiteval Fig. 23 Sequetial ulti-subiteval dyaic taffic assiget VI. CONCLUSIONS AND FUUE WOK his pape poposes a bi-level optiizatio faewok fo optially settig the egioal taffic sigals. he fequecy fo optiizig taffic sigals aily depeds o taffic pattes. Specifically whe the taffic patte is dyaically chagig (e.g. peak hous) taffic sigal settigs should be optiized oe fequetly to accoodate the coplex taffic deads; whe the taffic patte eais steady (e.g. late ight hous) taffic sigal settigs should be optiized less fequetly. Note that this optiizatio faewok ca be easily exteded to coside acyclic sigal pattes which ae oe suitable fo cases whe taffic coditios ae dyaically chagig withi a shot tie peiod. I additio the poposed optiizatio faewok allows sooth tasitios betwee successive taffic sigal settigs by takig offsets ito accout. o solve the poposed optiizatio poble i a satisfactoy ae the pape applies HGA to the coespodig solutio faewok. Sice HGA decouples the uppe ad the lowe level pobles oe sophisticated odels ca be plugged ito uppe-level ad lowe-level faewoks fo achievig oe easoable esults. Note that othe efficiet atificial itelliget ethods (e.g. Paticle Swa Optiizatio [24] Haoy Seach Algoith [25]) ca be used i place of GA to pefo the global seach fo the optial settig. I additio we ae validatig the poposed acceleatio stategies fo uch lage-aea taffic etwok applicatios. [4] H. Y. Cheg V. Gau C. W. Huag ad J. N. Hwag Advaced foatio ad delivey of taffic ifoatio i itelliget taspotatio systes Expet Syst. Appl. vol. 39 o. 9 pp [5] J. Ki H. S. Mahassai. Hou ad. M. Alfelo Developet of eal-tie siulatio-based decisio suppot syste fo weathe esposive taffic sigal opeatios Itelliget aspotatio Systes (ISC) 2014 IEEE 17th Iteatioal Cofeece o pp [6] J. Gacia-Nieto A. C. Olivea ad E. Alba Optial cycle poga of taffic lights with paticle swa optiizatio IEEE as. Evol. Coput. vol. 17 o. 6 pp Dec [7] W. H. Li ad C. Wag A ehaced 0-1 ixed-itege LP foulatio fo taffic sigal cotol IEEE as. Itell. asp. Syst. vol. 5 o. 4 pp Dec [8] L. Davis Hadbook of Geetic Algoiths New Yok: Va Nostad eihold [9] J. Gacía-Nieto E. Alba ad A. C. Olivea Swa itelligece fo taffic light schedulig: Applicatio to eal uba aeas Eg. Appl. Atif. Itell. vol. 25 o. 2 pp [10] Y.-C. Chiu J. Botto M. Mahut A. Paz. Balakisha. Walle ad J. Hicks "Dyaic taffic assiget: A pie" aspotatio eseach E-Cicula E-C [11] M. Siivas ad L. M. Pataik Adaptive pobabilities of cossove ad utatio i Geetic Algoiths IEEE as. Syst. Ma Cybe. vol. 24 o. 4 pp Ap [12] X. Ma J. Ji ad W. Lei Multi-citeia aalysis of optial sigal plas usig icoscopic taffic odels asp. es. Pat D asp. Evio. vol. 32 pp Oct [13] E. W. Dijksta A ote o two pobles i coexio with gaphs Nue. Math. vol. 1 o. 1 pp [14] D. Kajzewicz affic siulatio with SUMO Siulatio of uba obility i Fudaetals of affic Siulatio Spige New Yok 2010 pp [15] S. Kauß Micoscopic odelig of taffic flow: Ivestigatio of collisio fee vehicle dyaics Uivesitat zu Kol [16] J. Eda SUMO s Lae-Chagig Model i Modelig Mobility with Ope Data Spige Iteatioal Publishig 2015 pp [17] H.. Vaia ad S. L. Dhiga Dyaic use equilibiu taffic assiget o cogested ultidestiatio etwok J. asp. Eg. vol. 130 o. 2 pp [18] H.. Vaia P. J. Gudaliya ad S. L. Dhiga Applicatio of Geetic Algoiths fo joit optiizatio of sigal settig paaetes ad dyaic taffic assiget fo the eal etwok data es. asp. Eco. vol. 38 o. 1 pp [19] C. O. og ad S. C. Wog A pedictive dyaic taffic assiget odel i cogested capacity-costaied oad etwoks asp. es. Pat B Methodol. vol. 34 o. 8 pp [20] M. Haklay ad P. Webe Opesteetap: Use-geeated steet aps Pevasive Coput. IEEE vol. 7 o. 4 pp Oct.-Dec [21] City of Chicago. "Aveage daily taffic couts" [Olie Available]: ts/pfsx-44. Ma [22] A. F. Acosta J. J. Espiosa ad J. Espiosa aci4matlab: e-egieeig the Pytho ipleetatio of the aci iteface i SUMO2014-Modelig Mobility With Ope Data [23] P. Sades ad D. Schultes Egieeig fast oute plaig algoiths Poc. 6th It. Cof. Exp. Algoiths pp [24] J. Keedy "Paticle swa optiizatio" Ecyclopedia of Machie Leaig Spige US pp [25] Z. W. Gee J. H. Ki ad G. V. Logaatha "A ew heuistic optiizatio algoith: Haoy seach" Siulatio vol.76 o.2 pp EFEENCES [1] H. Chouabi. Na S. Walke J.. Gil-Gacia S. Mellouli K. Naho. a. Pado ad H. J. Scholl Udestadig sat cities: A itegative faewok Poc. Au. Hawaii It. Cof. Syst. Sci. pp [2] S. A B.-H. Lee ad D.-. Shi A suvey of itelliget taspotatio systes 2011 hid It. Cof. Coput. Itell. Cou. Syst. Netwoks pp [3] V. Milaés J. Villagá J. Godoy J. Sió J. Péez ad E. Oieva A itelliget V2I-based taffic aageet syste IEEE as. Itell. asp. Syst. vol. 13 o. 1 pp Ma BIOGAPHIES Zhiyi Li (GSM 14) eceived the B.S. degee i electical egieeig fo Xi a Jiaotog Uivesity Xi a Chia i 2011 ad the M.S. degee i electical egieeig fo Zhejiag Uivesity Chia i He is cuetly pusuig the Ph.D. degee i the Electical ad Copute Egieeig Depatet Illiois Istitute of echology. His eseach iteests iclude cybe-physical systes ad powe syste optiizatio. Mohaad Shahidehpou (F 01) eceived the Hooay Doctoate degee fo the Polytechic Uivesity of Buchaest Buchaest

12 12 oaia. He is the Bodie Chai Pofesso ad a Diecto of the obet W. Galvi Cete fo Electicity Iovatio Illiois Istitute of echology Chicago IL USA ad also a eseach Pofesso at the Kig Abdulaziz Uivesity i Saudi Aabia. Shay Bahaiad (SM 14) is Diecto of Sat Gid ad echology ad Iovatio Abassado at CoEd. He esposibilities iclude leadig developig ad ipleetig Micogid ad Sat City iitiatives i CoEd s sevice teitoy. D. Bahaiad is also a Adjuct Pofesso at the Illiois Istitute of echology. She is the Chai of the IEEE Powe & Eegy Society (PES) Woe i Powe echical Chai of the 2016 IEEE PES &D Cofeece ad Vice Chai of the IEEE PES Distibutio Subcoittee. She holds a Ph.D. degee i Electical Egieeig fo the Illiois Istitute of echology. Ai Khodaei (SM 14) eceived his Ph.D. degee i electical egieeig fo the Illiois Istitute of echology i He was a visitig faculty ( ) i the obet W. Galvi Cete fo Electicity Iovatio at II. He joied the Uivesity of Deve Deve CO USA i 2013 as a Assistat Pofesso. His eseach iteests iclude powe syste opeatio plaig coputatioal ecooics ad sat electicity gids.