A Method of EV Detour-to-Recharge Behavior Modeling and Charging Station Deployment

A Method of EV Detour-t o- Recharg e Behav ior Modeling a nd C harging Stat ion Deployment Tianshu O uyang †, 1 , Jia hong Cai †, 2 , Yuxuan Gao † , 3 , Xi n yan He † , 4 , Huimiao Chen † , 1 , * , Kexi n H ang 1 † These aut hors co ntribute d equa lly to t his work . 1 S parkzone I n stitut e ; 2 U nivers ity of C hicago; 3 The Wharto n School of th e Universi ty of Pennsyl vania ; 4 P rinceton U niversity * hche n@ sparkz one . org Abstract — El ectric v ehicles (EVs) are i ncreasin gly used in tran sp ortation. Worldwid e use of EVs, for their limited battery c apacit y, cal ls f or ef fect ive p lanni ng of EVs charg ing s tati ons to enhance the effici ency of usi ng EVs. This pa per provide s a metho d ology of d e scribing EV detouri ng behavio r for recha rging , and ba sed o n t h is, we adopt the extra driving l ength caused by deto uring and the le ngth of uncom pleted ro ute as t he in dicator s of eval uatin g a n EV charging stat ion deploymen t plan . In this way, we ca n simulate EV beh avior bas ed on tr avel d ata ( d emand ). Then, a g enetic algori thm (GA ) ba sed EV ch arging stati on sitting optim ization metho d i s developed to obtain a n e ffective p lan . A detai led case st udy based on a 1 00 - nod e 203 - bra nch tra nsportat ion net w ork within a 3 0 km × 30 km reg ion is included to test the effectivene ss of our meth od. I nsights from our method ma y be appl icab le for char ging s tat ion pl an ni ng in vario us trans por tati on netw ork s . Keyword s — electric veh icle s; detouring behavi or ; cha rging st ations; t ransportatio n networ k ; g enetic algo rithm . I. I N TR ODUCTION T h e continued g rowth in use of convent ional vehicles in tr an spo rtati on w ill u nav oida bl y caus e nat ura l gas oli ne re sour ce dw ind ling . As an unrene wable fuel source, gasol ine will be in sho rtage i n t he ne ar future due to human’ s immoderat e exp lo ita tion, which wi ll also r esu lt in sev ere environ ment al degrad ation, e.g. , exc essiv e emission o f greenhou se gases. With the awareness of the limited fossi l fuels, governments hav e imp leme nted nume r ous po lic i es to pr omo te pu rcha se an d use of elect ric v ehicl es ( EVs), w hich r ely on elect rici ty t hat ca n be genera ted from wind p ower, hyd r auli c pow er, et c. Howe ver, th e pec uli ari tie s of E Vs, in clu din g in suf fic ient ba tter y capacit y to r each a remo te d e stin at ion , co m monl y r ef er red a s “rang e a nxiety”, and fre quent d emand to charge, h ave been th e dom inant hind eran ces to m arke t ac cept ance of E V s . The refore, EV us ers are res tri cte d t o dr iv e onl y s hort tri ps a nd l es s an nual miles due to inconven ience to char ge, which no t o n ly dis co ur age s custom er ad option of EV s but also impedes the tran s ition f rom gasol ine - pow ered vehi cl es t o the mor e envi ron ment a lly fr iend ly E Vs. Therefore, effect ive EV charging station s planning is urg entl y ne eded to cou nt er the iss ues o f inaccess ibil i ty to c ha rgin g sta tio ns and ex cess ive inc reme nt of dr ivin g du e to r echar ging, or el se EVs w ill fail to r eceiv e pu blic market ac ceptan ce. I ncor por a ting EV charging station netwo rks into current transportat ion netwo rks require s thoroug h consi d er atio ns an d s i mulatio ns beca use of t he co mpli ca cies of urba n are as. Howev er, wi th th e rapidly grow ing populatio n densi ty and increa sing deman d for veh icles, eff e ctive planning of c har gin g s tati ons i n cit y a reas c an bri ng s iza ble so cial ben efits . In exis t i ng lite ra tur e, there a re stu di e s fo cus in g o n plann ing of dif fer en t type s of energy supply infr as tru ctur e in transpo rtation, e. g. , gas stat io n s a nd c har gi ng st ati ons. Refe ren ce [ 1] e xpl ores the choos in g of gas stat io ns and the fac tor s th at in flu enc e th e de c ision. In [2], the a ut ho rs introduce a model for po sitioning the opt imum location o f a sma ll s ize fuel statio n with the hel p of Geospati al Inf or mati on S ys tem , and meth ods such as Boolean logic, index overl ay, and fuzzy opera tors are d emon strat ed . Sweda et al . em ploy an a gent - ba se d decision suppor t syst em pr esented f or ide ntifying pa tter n s in residential EV owne rs hip an d dri vin g act ivi tie s to ena ble stra tegic deploym ent of new charging infrastruc ture [3]. The aut hors of [ 4 ] pre sen t a mu lti - obj ect ive co llabo r a ti v e planning s trat eg y to deal with th e optimal p lanning is sue in int egr ate d powe r di stribution a nd EV ch arg ing syst ems. The us er e qu ilib riu m - ba sed tr affi c assig nm ent mod el is integ rated to addre ss the m aximal tra ffic flow capturing pro blem, and deco mpos i ti on bas ed mul ti - objec ti ve e vo luti ona ry algo r ithm is empl oye d t o s eek the n on - domi nat ed sol ut ions . Ref erence [ 5 ] propose s a two - ste p mod el fo r al loca tin g E V recha rging stations tha t fir st qu an tif ies t he r oad inf orm ati on into dat a poi nts a nd s ubs equ ent ly c onverges into ‘ dem and cl uste r s ’ over an ur banize d area by hi erar chical cl usteri ng anal ysi s ; o ptimizat ion techn iques are then app li ed on t he de mand cluster s with the a im of mee ting the suppl ies and demand s, and cer tain con st raint s and co st fact ors are con s i dered . Dong et al . inv es tigate the influenc e of publi c charging s tations depl oym en t on increa sing EV ma rket p enetra tion ; a n act ivi ty - based as s essm en t meth od se rv es to te st th e fe asib il ity fo r the heterog eneous trave ling population, and gen etic algorith m (GA) is us ed t o f ind the o pt imal loca tio ns f or cha rgi ng st ati ons ; Don g et al . ba se o n GP S - ba sed trav el survey data to co ndu ct case studies [6]. Pay am et al . propos e a dy nami c ap proa c h to the opti miz ati on of c harg ing s tat ion loc ati ons an d siz in g th at b est su f fic e the ch arg i ng de ma nd s a nd mi nimi ze p ower loss in t he transportatio n of electri cit y fr om cent ra l pow er gr ids [7]. The research o f Xiong e t al . focus es on the charging b ehaviors an d mutual impact on var ied traff ic condi tions of EV dr ivers [8]. L i et al. [9] establish mathe matic al m odel ba sed on bi - lev el program ming to formu late governme nt's infrastru cture location strategy , the c ompany's f leet comp osition and routing plan in orde r to promo te EV ad opti on i n com pani es. A hy brid heur ist ic met hod is th en emp l oyed to solve the formu lated problems. Bou guerr a et al . [10] stu dy t he r eal ca se of the cent er o f Tuni s City, Tunisia wit h existing data to fi nd opt imized loca tion and size o f cha rging stati ons of this speci fic area . R efer ence [ 10 ] uses the c as e in the ce n tral urb an are a , a 30 km b y 30 k m area, in Beijing to stu dy th e d a ta -d riv en p lanni ng of ele ctr ic tax i s cons ide rin g the op tim iza tio n of bot h inve stm en t and oper ation costs . Despite th e already d one w ork , d es crib ing E V d rivi ng beh avior an d eval uating a n EV c harging sta tion si ttin g p lan ar e still challeng eable due to fact ors inc lu din g li mit ed data of E Vs. How t o m odel t he EV b eha vi or from co nventi o na l veh icl e r ou te da ta and u se i t in sta tio n p lanning is a m ea ning ful pro blem whi ch has not be en investigat ed ade q ua tely. Henc e, in this w ork, w e pr ovide a n EV be havi or mod el and a station planning method d er ived from it . T he main pro cedures and co n trib ut i ons of t he pape r are su mmar ized below . • P res ent a me th od ol ogy o f de scribing the EV de touring beha vio r for rec har gi n g. • A dopt the ext ra drivin g length caused b y detouring and the l engt h of uncompleted rout e as the indicator to evaluat e of station planning . • De velop a GA b ased method to p lan EV charg ing st at ion i n a tr ans po rt ati on ne twork with tr av el d a ta no t from EVs . • St udy a det ail ed case wi th a 1 00 - nod e 203 - bran ch transpo rtation ne twork within a 30 km × 30 k m region to test th e effect iven ess of the planning . The rem aind er of the p aper i s organiz ed a s fo l low s. S ec ti on II i llus trates t he methodology of descr ibing E V deto u r in g beha vior for r echarging . Sectio n III intro du ce s the G A for EV charg ing sta tion pla nni ng and Sec tion I V sho w s the cas e . Section V co n c lud e s. II. M ETHODOLOGY OF D ESCRI BING EV D ETOURING B EHAV IOR FOR R EC HARGING In thi s sec tio n, we i ntr oduc e our m etho dol ogy o f desc ribi ng the EV de touring behavio r for rech arg ing. We co nsid er a transpo rtation network con sisting of a series of nodes (in ters ecti on s) and br anches ( roads) wi th vehicle travel da t a given. The ne twork h er e is lim ited to a conn ected grap h beca use a n unco n nected g r aph ca n be tr eat ed as mu ltip le conne cted graphs. Vehicl e travel data i s in form of a set of routes , each of which includes a series o f nod es th at th e veh icl e needs t o p ass i n order. Bes ide s, for ea ch route re cord , ther e is a corresp onding ini tial stat e of charge ( SOC). Detouring t o rechar ge their batt eries is the key dif feren ce between EV and conventiona l vehicle travel beha vior. He re in, we firs t intr odu ce som e assu mpt io ns for the desc r ip tion of E V deto uri ng. 1) A n EV onl y c harg es once in a det o u r, bu t i t ca n detour mul tiple times in a rou te deviating f rom differ ent bra nches . Thi s co nsi dera tio n i s for th e pur pose of ma kin g th e detour r u le simp le, cl ear, reason ab le and pra cti ca l. 2) Th e len gth of ea ch br anch is t he shor test length between the two c onn ected n odes. This assumption ensures tha t t aking detour will absol ut el y make the le ngt h of dri vi ng lo nge r tha n not taking de tour, so th e t i mes of taking detour is intended to be m inimized. 3) Ev er y nod e in a rou te mu st be p assed to com pl ete th e rou te . I f an EV de tours from a node to charge, it mu st return to the o riginal rout e by p assing the next node afte r char gin g. In ot her wo rds , all nodes in a ro ute mu st be pass ed. Befo re elab o rating on th e d etou r r ul es, we def ine som e notation s. We u se ij L − ( i jk L −− ) to denote the length of the shorte st path from no d e i to n ode j (f rom node i to no de j to node k ) an d n detour L to d en o te th e d iffere n ce o f th e lengt hs o f the detou r path and the bran ch, i.e. , = n detour i c j i j LL L −− − − ( c is a no de wi th ch arg ing sta tion , n repres ents that node i i s the n th no de in the r out e ) , and use rest L to den ote t he len gth of t he unco mpl eted par t of t he ro ute. The deto ur rules i nclude mult iple st eps of ju dgi ng , computa tions, and record ing. Wh en an EV arrive s at a n ode of a rout e, it nee ds to co nd uct the fol low in g ste ps to d e ter min e wh ether and how to detour. Fo r a r oute r whose no des a re 123 ={ , , , , } rN xx x x N  , if th e rem aine d SOC of t he EV at n x ca n ful fil l th e dr iv ing f ro m n x to +1 n x , we le t =0 n detour L . I f the remain ed EV SO C cannot f ulfill the dr iv ing fro m n x to +1 n x , we s elect all char gin g stat ions tha t can be reac hed w ith th e remain ed SOC as a set , 12 3 ={ , , , } n rx cc c  C . I f , n rx C i s an empty set , i.e., n o cha rging stati on i s ac ces si ble, th e E V wil l no t be able to detour to c harge. We ca lcu lat e rest L and r ecord a ne w 1 1 i n rest detour i LL L − = = + ∑ . If , n rx C is no t empt y, th ere ar e cha rgi ng stations access ible for th e EV. If t he EV do es no t ch oo se to de tour t o char ge, w e ca lcul ate rest L and rec ord a n ew 1 1 i n rest detour i LL L − = = + ∑ . If EV detou rs to char ge, we cal culat e n1 n x cx L + −− for all , n rx c ∈ C and sel ect the s ta tion with the m ini mum va lue f or t his ch argi ng , and calculat e n detour L . If ther e ex ist mult ip le sta tio ns with the s ame min imu m n1 n x cx L + −− , wh ic h prod uce s a se t min C , we sele ct th e st ation with the m inimum n1 cx L + − for this charging and calculat e n detour L becau se in this way t he EV wi ll ha ve a hi ghe r SOC w hen arri vi ng a t th e n ext node. If there exist mor e than one sta ti on s w it h b oth the same min im um n1 n x cx L + −− a nd n1 cx L + − , we select one sta tion ran d omly fro m thes e cha rgi n g sta ti ons a nd ca lc ula te n detour L . Fig . 1 gives an example of how to select the station for c har gin g when the SOC is insu ff icie nt, whe re the green nodes wi thin th e yellow da sh circle, i .e., 1 c , 2 c , 3 c , 4 c and 5 c , are with access i ble cha rg ing stat ion s, w hil e th e sta tio n at 1 d is ina ccessi ble . The gree n no des o n the b l ue dashe d ellipse, i.e., 1 c , 2 c and 3 c , have the smallest n1 n x cx L + −− , and among them 2 c a nd 3 c have the smallest n1 cx L + − . T hus, 2 c and 3 c are bo th the op tim al loc atio n s for th e ch ar gin g, and the E V will ran domly d etour to cha r ge at 2 c or 3 c .                  C i r cl e w i t h center on   and r a di us = m i n(      ) Ellip s e w it h f o c i o n   and   and m a j or ax i s = m i n(         ) C i r cl e w i t h center on   and r adi us = E V r em ai ni ng dr i vi ng r ange S hor test path l engt h betw een tw o node s N ode w i thout c har gi ng stati on N ode w i th cha r gi ng s tati on B r anch w i th di r ect i on betw een tw o node s Fig. 1 . Diagram o f describing jud ging and computations in EV detouring be ha vio r. C alculate   Calcu lating th e     for all access ib le charg i ng s tation s Cha rgi ng s tation is acces sible Obtain initial SO C an d route n odes of an EV EV arrives at   Ch oos e one detou r random ly Choos e the only available detour Ye s No Calculate   Ye s No Ye s No Ye s R ecord    +         Start sim u lation R ecord a new  =    +         Calculat e      Ye s No Let n= 1 Let n= n+ 1 Rou te is com pleted No Rem ai ned SOC can fu lfill the drivin g fr o m   to   Mu ltiple ch arg ing station s hav e the sam e sm allest     Mu ltiple ch arg ing station s hav e the sam e sm allest     R ecord    +         Let      = 0 Ye s Let n= n+1 L et   =0 R ecord    +         Rou te is com pleted L et   =0 EV does not detou r to char ge E V de t our s t o cha rge No End s im ula tion Select t he m i nim um value   from all L as t he o ut p ut Fig. 2 . F low chart of describing EV detouring beha vior for recharging. Af ter d riv ing fr om n x to +1 n x , if the rout e is comp leted , i. e., the c urr ent no de i s N x , we let 0 rest L = , c alcu late 1 i n detour i L = ∑ , the t otal incre ment in drivi ng leng th due to detouring, an d rec ord a n ew 1 i n rest detour i LL L = = + ∑ . If the r oute is no t co mple ted , we le t 1 nn = + and continu e the simulation by repeating t he above d etour ste ps . A t la st, we sel ect th e min imu m va lue min L fro m a ll L as the output an d end si mulation. The abov e des cription of EV d etouring b ehavior is illu st ra ted b y Fig. 2. III. G ENETIC A LGORITHM FOR C HARGING S TAT ION S ITING O PTIMIZATION IN T RANSPORT ATION N ETWO RKS GA is adopted and utili zed to obtai n an op timal cha rg i n g statio n deployment plan in given t ranspo rtati on networ ks wit h EV travel data. In t his s ection, we des cribe our de signs of key steps, i.e., i ni tial ization, s electi on, cross over and mutatio n, of th e GA. A. I ni tializa tion The initial popu lation i s r andoml y g e nerated , wher e a chr omos ome of an i ndi vid ual cons ists of a give n numbe r of the nodes tha t are selec ted from all can didate n odes as char ging st at ion loca tio ns. A ll ind iv idu al s form a se t of c hargin g statio n depl oyment pl ans , aka pop ulat ion in th e GA. Ea c h p lan is u nique in the set, a nd the ser ial number s of node s are sorted i n ascend ing order in an individual’ s chr omosome, ma them atica lly expr ess e d by a vect or. No ne of the c hos en nodes h ave a d uplicat e in th e chromosome. The size of each chr omos ome e quals th e pred ete rmine d number of new st ati ons. B. S election S electi on is the part wher e the new ge nerati o n is sel ected from the old. In this proce ss, the roulette choo sing method is use d. T he proba bil ity of b eing c ho sen for each chromosom e is determ ined by the ir fi t v alu e s. I n our process , a smalle r ( be tter ) fi t va lue br ing s a hi gher pr obabil it y f or the ind ividual to be sel ected as a m embe r of a ne w gen er a tio n , which m ay have mul tip le same ind i vid uals . C. Cross o ver D ur i ng the p rocess of th e GA cr ossove rs, a predet e rm i ned cros sov er pr obabil it y rest ricts the occ urr ence of a cr oss ove r. If a cro ssover hap pens, two individu als’ ch romos omes are random ly selected to perform the opera tion. The mut ual and exclusi v e par t of tw o c hromo some s are collected i nto two separat e pa rt s. The elem ents in the ex clu sive part ar e ran domi zed a nd spli t in to tw o equ all y lon g parts , whi ch l ater ea ch com bin e wi th t he one s et of mutua l e l eme nts to for m two new chromo somes. Th e se n ew c hro moso m es r ew ri t e th e pare nt chr omos o mes in the po pulation fo r t h e purpo s e of m aint ain in g populat ion size. Fig . 3 giv es an exam ple. D. Muta tion Th e mutat ion proc ess c hanges a n ind ivi dual’s chr omos ome, in which sim ila r to th e cros sove r the oc curre nce i s con trol led by a li mi ting probab ility. If an i ndividua l is r e que ste d to mutate, a random node in its chromosome wi ll be replac ed by a new one r andomly selected from the r emaining node cand idates. The po pulation si ze is m ainta ined here . Fig . 4 gi ves a n e xample . IV. C ASE S T UD IE S A. T ra nsport ation Net work Settings and T ravel D emand Ge n eration In this sub section, an assumed transpor tation network with 100 node s and 203 branche s is const ructed to simulate a real - worl d trans po r ta tion n etw ork and v erif y the me thod olo gy proposed in the pr e vi o us text . The genera tio n of grap h obeys the f o l lo w ing cond iti ons : 1) any two bra nches do no t intersect except at nodes, which avo ids addition al nodes; 2 ) the node s and bra nches form a c onnecte d graph, whi ch ensures the connect ivity of th e tr ans po r ta tio n gr id. The network pr ojects to a r egion s izing 30 k m × 3 0 k m. Ea ch o f the n odes is as si gne d an id entit y fr om fou r types of fun ct ion alit ies , i.e ., co mmer c ial are as, in du str ial a reas , resid ential ar eas, and oth er pla ces. As show n in F i g. 6 , 10 0 node s are e v en ly distrib uted into the four categories with n ode s of each type c los ely ga th er in c lus ter. A ll th e 10 0 node s are reg arded as potentia l charging s tation po sitions . Th e leng th s of all the branch es are des igned t o be s mall er tha n 7 km, wh ic h be tter r esembl e s t he roads in urban ar eas. Around 10000 travel r ou t es (ve hi cle t rave l deman d n ot of EVs ) are gene rated with t heir origi ns distr ibuting i n residential, commerci al and i ndustr ial a reas and ot her places with a pro babi lit y of 45%, 30%, 15% , and 1 0%, re s pective ly . A route gener ally include s 2 to 24 n odes. On e n od e only e xists once i n a route, e nsurin g the resem blance of real - world trave l d eman d . The rou te distributio n in general refe rs to the analy si s o f traveling data in May 2016 Beijing. S ee Append ix for r ou te gene rat ion met hod. According to typ ica l E V s on t h e ma rket , the c apaci ty of EV batt er y i s set a s 50 k Wh and a con suming spe ed of 0.25 kWh/km . A corresponding initia l State of C harge ( SOC) o f a n EV is assigned to each r oute. The value i s random between t he SOC r equ ired to compl ete th e rou t e (EV w it h no ch a rging dema nd is usel ess to t he s imu lat ion since a deto ur is not necessa ry) a nd the minimu m SOC th at ens ures t he E V could rea ch th e near es t cha r gin g s tatio n. 4 12 15 16 32 33 40 1 4 12 15 16 32 33 40 17 19 20 22 27 30 39 6 21 26 36 37 46 48 49 6 21 26 36 37 46 48 49 4 12 15 16 32 33 40 1 17 19 20 22 27 30 39 4 12 15 16 32 33 40 6 21 26 36 37 46 48 49 1 17 19 20 22 27 30 39 46 48 49 1 17 22 27 39 6 21 26 36 37 19 20 30 4 12 15 16 32 33 40 4 12 15 16 32 33 40 4 12 15 16 32 33 46 48 49 1 17 22 27 39 6 21 26 36 37 19 20 30 4 12 15 16 32 33 40 40 Or i gi nal C hr o mo so me s Find M u tua l & E xcl usive P ar t s Ran dom ly Split the E xcl usive int o Two E qua l Lo ng P ar t s New Ch romos o mes Reorder Fig. 3. Pro ce ss d iag ram o f c rossove r . 4 12 15 16 32 33 40 6 21 26 36 37 46 48 49 4 12 15 16 32 33 40 6 21 26 36 37 46 48 49 4 12 15 16 32 33 40 6 26 36 37 46 48 49 39 4 12 15 16 32 33 40 6 26 36 37 46 48 49 39 Or i gi nal Chrom osome Random ly Select an Elemen t Random ly Select a New E lemen t Reorder F ig. 4 . Proce ss d iag ram o f mu tation . The number of times that a branch is included by a route is rec orded an d proj ect ed to a c orrespond ing col o r in th e “jet ” colo rbar. W i th red re pre senti ng the highest int ensi ty o f tra ff ic flow whic h is ab out 90 0 pa ssings a nd blue th e low est approx imately 250, Fig. 7 de monst r ate s th e d is tribu tio n o f traveling demand intensity for each branch. B. Results and Anal ysi s We s elect a popu lation of s ize 1500 and s et th e c ro ssover and mutation prob abilit ies as 0. 3 an d 0 .2 respect ive l y. The large pr obabili t y values are d ue to the extr em ely sm all r at io of the popu lation si ze to th e total solu tio n sp ac e, whi ch in clu des about 2.5 ×10 17 solutions . Th e m aximum iteratio n is set as 300 . Calc ula te Fit V alu e Ou tpu t Final Plan Popu lation I n itialization Selecti on C r o sso v e r Mu tation Find the Bes t Indiv idua l and Calcu late BFV If It is the Max im um Iteration ? Ye s No Cho o se t he F i na l I nd i vi d ual from th e Bes t Ind ivid ua ls of A ll Iteration s Fig. 5 . Flow chart of GA . 0 5 10 15 20 25 30 km 0 5 10 15 20 25 30 km Commerce Industry Residence Other Place F ig. 6 . 100 - n ode 203 -b ranch t ransportation ne twork . Chargi ng Stati on Fig. 7 . Branch t raf fic f lo w d ensity b ased on the g enerated r outes. 0 50 100 150 200 250 300 Iteration 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 Fit value 10 4 Fig. 8 . Best f it value s in all iter ations . Fig. 8 show s th e b est f it va lue in e ach it era tion , f rom w h i ch we can s ee that t he va lue decline s fas t before the 100 th iteration and tend s to con verge a fter t hat . T he b est f it valu e gen erat es af ter the 250 th iter ati on and the cor respondin g s t at io n depl oyment pla n i s sign if i ed by red circl e s in Fig . 7. The b ig sol u tio n space is the ma in facto r of t he slow converge nce ra te . From th e fi nal s ta ti on s itting plan, it can be obse rved th at most stations a r e l ocat ed a t the nodes with h igh t raf fic flo w or s ervin g as a hub of a sm al l reg ion . For e xam ple , t w o st ati ons are set in t he bottom rig ht cor ner of the networ k be ca us e th i s area is far from the ma in part . The code of our me tho d i s ed ited and run in M ATLAB 20 18 enviro n ment on a n i Mac w ith an Inte l C ore i5 p roces s or and 8 GB rand om - access memory . For o ur settings, each iteration costs less th an 1 m inu te an d the e nt ir e pr ocess tak es 4 to 5 h ours. V. C ONSLUSIONS In th is wo rk, we fi rst propo se a me thodology of de sc r ib ing the EV detour - to - rec harge behavi or w here a ne w ind ica tor is created to e valuat e EV c hargi n g station pl anning . Secon d, w e come u p with an EV cha rging statio n plann ing met hod usi ng this indicat or base d on GA . Fin all y, an assum ed t ranspo rtat ion ne two rk is formulated sim ilar to that of a full f unctional city, so th at th e re sul t can be c los e to th at of a real case as possi ble. T he fin al p lan sh ow s that sta tion s a re pr eferr ed to be l oc ated in areas with h igh tr af fic flo w and at distant places. In fu tur e wo rk , the computation eff iciency an d larg er net work optimization will be put on th e agen da. A P PE ND IX : R OUTE G ENERAT ION In this subsection, the generation of rou tes in a transpo rtation network is introd uced. Before generat ing a route, an or igin are a, wh ere the ori gin node lo cates in, and a de stina tion ar ea, wh ere the d estina tion node locates in, shou ld be p rede term ined . We g ener ate the no des o f a rout e fro m th e orig in t o the des tinat ion th rough adding next su ita ble nod e to a route. Fir st, a node is r andom ly sele cted from the or ig in are a a s the fir st node of a rout e. The last node i n a rou te is regard ed as t he cu rre nt no de (a t fir st, th e ran do mly sele cted nod e is s et as the current n ode) to generate the ne xt nod e. Before generat ing the next node of a rout e, an exam ination is conduc ted and sho w wh ether thi s rou te ha s met req uire ments . Thr ee re quir ement s are s e t: 1) if t he last node has been in the destination area; 2) if the length of the route is between the maximum and minimu m boundar ies; 3) if the route is different from any already gen erat ed rout e. Only when an sw ers of th e above th ree requ irem ent s are all “ Yes”, the rou te is l abeled a va lid one. For a va lid rou te , it w ill b e pu t in to the r ou te po ol and ther e is a given proba bility for it to con tinue genera tio n of ne w node s (note that if a ne w node i s added to a valid r ou te, the r oute may become invalid agai n ); otherwise, if t h e route’s l ength is la rger than the maximum boun dary, the ge nerated wil l be terminate d, and e lse , it is m andat ory t o ge nera te new n odes. While gener ating the next no de for a rou te, based on t he current nod e and othe r gener ated node s, we extract the eligible nodes set, in which any node can be the nex t node, from the whole nodes in the n etwor k acc ording t o the foll owing t hree c rit eri a: 1) t h e node is con nect ed to the c urrent n ode b y a branc h; 2) the no d e lies wi thin the a s pecial area (ex p lained in t he next pa ragraph) defined by the current node a nd the d estinat ion area; 3) the node has not bee n visite d before, i.e. , the n ode is dif fer ent fr om any n ode whi ch has be en in t he ro ute, that is, a rout e incl u ding a ri ng is n ot c onside red. Al l nod es satis f y these three crite ria will be put into the eli gibl e n odes set . T he fi nal next node wi ll be sel ected r ando mly fr om this s et. If the s et is empt y, th is gen erat ion w ill be stop ped. The Flow ch ar t of the g ener ati o n i s shown in Fig. A 1. Start Route Generation. Let i =1. Randomly Select A Node from Origin Area as First Node of Route i . Put Route i into Route Pool. Set Last Node of Route i as Current Node. Check If Route i has met Requirements. Check If Length of Route i Exceeds Maximum Boundary . No No Ye s Judge If to Continue Generation of New Nodes Appended to Route i (Based on A Predetermined Probability). No Let Route i +1 Be Same as Rou te i . Let i = i +1. Ye s Generate Special Area According to Current Node and Destination Area. Extract Eligible Node Set For Next Node. Check If Eligible Node Set Is E m p t y. No Select Next Node Randomly From Eligible Node Set And Add It T o Route i . Let i = i +1. Ye s Ye s F ig . A1 . Flo w c hart o f r oute g eneration . Th e speci al are a is deter mine d by the locati ons of the cur ren t nod e and the d es tina tion are a. Fir st, we id en tify the c ir cum sc ribed rectang le o f the de stin ation ar ea. Th en we d ivid e the s ur rounding area of the d estination a rea int o 8 par ts, as Fig. A2 shows. Whe n the curr ent node l ies in one of the 4 c orner surround ing area s , i.e., are as I, III , V, and VII, con nec t the current no de and three ver texes o f th e circ ums cribed re ctang le wh ich ar e the farthe st from th e current node to form a quad ril atera l as the spec ial ar ea. As Fig. A2 shows, w e connect the r ed cur rent node , D1 , D3 an d D4 (the re d quadr ilat eral s i n Fig. A2 ) . When th e cu rre nt node li es in othe r fo ur surroundin g areas , i.e., areas I I , IV, VI, and VIII, connect the current node and four vertexe s of the circ umscr ibed rectan gle t o form a pentagon as t he sp ecial area ( the blue pentago n in Fig. A2 ). I II III IV V VI VII VIII Nodes of Destination Areas Two Examples of Current Nodes Two Examples of Special Areas Vertexes of Circumscribed Rectangle of Destination Area D 1 D 2 D 3 D 4 Fig. A2 . Diagr am of speci al a rea s (c urrent node s outside the circumsc ribed rectangl e ). I II III IV V VI VII VIII D 1 D 2 D 3 D 4 Nodes of Destination Areas Example of Current Nodes Four Potential Special Areas Vertexes of Circumscribed Rectangle of Destination Area Fig. A3 . Diag ram of special area candidates (current node inside the circumscribed re ctangle). When the current node lies in the circ umscrib ed rect angle , we connec t the current node wit h th re e of f our v ertex es of destina tion node, and to tally fo rm four q uadri later als. Fig. A3 shows the four quad rila teral s : conn ecting the current no de , D1, D2 and D3 ( the gr een quad rilat eral s i n Fi g. A3 ); conn ect ing the current nod e, D1, D2 and D4 (the blue qua dr il ate ral s in Fig . A3 ) ; connect ing the current n ode, D 1, D3 an d D4 (the red quadrilate rals in Fi g. A3 ) ; conn ecting the current nod e, D2, D3 and D4 (the o range q uadr il ater al s in F ig. A3 ) . 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