Major Maintenance Schedule Optimization for Electric Multiple. Unit Considering Passenger Transport Demand

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1 Mjor Minennce Schedule Opimizion for Elecric Muliple Uni Considering Pssenger Trnspor Demnd Jinping Wu 1, Boling Lin 1*, 1 School of Trffic nd Trnsporion, Beijing Jioong Universiy, Beijing 144, Chin @bju.edu.cn, bllin@bju.edu.cn Absrc I is n imporn objecive pursued in rilwy gency or compny o reduce he mjor minennce coss of elecric muliple uni (EMU). The EMU mjor minennce schedule decides when o undergo mjor minennce or undere rnsporion s foin-se, bsed on prcicl requiremens, such s pssengenspor demnd, worshop inspecion cpciy, nd minennce requiremens. Experienced rilwy prciioners cn generlly produce fesible mjor minennce schedule; however, his mnul process is ime-consuming, nd n opiml soluion is no gurneed. This reserch consrucs ime-spce newor h cn disply he rin-se sus rnsformion process beween vilble nd mjor minennce sus. On his bsis, -1 ineger progrmming model is developed o reduce he mjor minennce coss wih considerion of ll necessry regulions nd prcicl consrins. Compred wih he mnul process, he geneic lgorihm wih simuled nneling survivl mechnism is lso developed o improve soluion quliy nd efficiency. I cn reduce he complexiy of he lgorihm subsnilly by excluding infesible soluions when consrucing he model. Keywords Elecric muliple uni, mjor minennce schedule, ime-spce newor, geneic lgorihm Inroducion According o he sisicl bullein of Nionl Rilwy Adminisrion of he People s Republic of Chin, he rilwy pssengeffic volume reched 295 million during he Spring Fesivl Trvel Rush in 215 (from Feb.4 o Mr.15, 4 dys in ol), mong which people rvelling by high-speed ril ccouns for 41.4%. Chin Rilwy High-speed (CRH) opered by Chin Rilwy Corporion (CR) is more nd more populr for is convenience nd comforbleness. How o ensure enough rolling soc o fulfill hevy rnsporion ss rush hours (Spring Fesivl Trvel Rush in priculr) hs long been he difficul problem for CR. The high purchse cos nd compliced minennce sysem of elecric muliple uni (EMU), which is he unique vehicle running on CRH, mes he problem even worse. CRH runs differen EMU rin-ses, he designs for which re impored from oher nions nd designed CRH1 hrough CRH5 nd CRH38A(L), CRH38B(L), CRH38C(L), CRH38D(L) nd so on. 1 In CR sysem, regulr prevenive minennce mechnism is implemened for CRH series rin-ses. There re five levels of minennce, e.g., firs-level (dily inspecion), second-level (specil inspecion), hird-level (bogie inspecion), fourh-level (sysem decomposiion inspecion) nd fifh-level (generl inspecion). Minennces he firs nd second level re boh operionl inspecion wih shor inspecion cycle nd inspecion ime. Typiclly, he minennce plns of hese wo levels re co-opimizion wih he rolling soc operionl pln respecively. The res belong o mjor minennce. Mjor minennce re scheduled in dvnce for ech rin-se during cicl minennce plnning, which re drwn up once yer. Th is becuse i requires comprively

2 longer inspecion cycle, longer inspecion ime nd he limied inspecion cpciy. In generl, he mjor minennce schedule srs from Sepember or Ocober, nd ends before he second Spring Fesivl Trvel Rush coming. The whole plnning horizon lss for bou 18 monhs or so. Therefore, he plnning horizon is longer hn he inervl of plnning, nd some rin-ses belong o his plnning horizon will go o worshop for inspecing during he nex schedule. For exmple, mjor minennce schedule srs from Oc. 18 h every yer (e.g. 215), nd some rin-ses will go o worshop on Nov. 2 h, 216. So, he minennce de of hese rin-ses will be djused ccording o cul siuion or no, nd hen, s he nown condiions inpu he nex schedule. Becuse of he mjor minennce is ime-consuming, i will led o he lc of rin-ses for undering rnsporion ss when he process of mjor minennce be undergone rush hours. However, mjor minennce hs long cycle, is rrngemen is flexible. Therefore, his pper focuses on he opimizion of elecric muliple uni mjor minennce schedule (EMUMMS), rying o void rush hours (especilly he Spring Fesivl Trvel Rush), nd es he cos of mjor minennce ino ccoun o preven frequen minennce, which is of gre significnce in supply enough rin-se for pssengenspor pe demnd. In he menime, i lso provides decision suppor for cpciy configurion of worshop. Lierure review For he minennce sysem, Suchly e l. 2 nlyzed he minennce mngemen sysems, nd developed minennce mngemen sysem bsed on relibiliy-cenered minennce which could help engineers o schedule he minennce scheme resonbly ccording o he echnicl condiions refleced by he EMU rel-ime monioring d. Shimd 3 inroduced new minennce sysem of cciden prevenion bsed on he minennce echnology siuion of Jpnese Shinnsen, hereby reducing he minennce coss nd improving he uilizion efficiency of EMU. Cheng nd Tso 4 proposed selecion sregy of EMU minennce bsed on he chrcerisics of he prevenive nd correcive minennces. The esimion mehod for he spre prs quniies nd replcemen inervls of specific componens of EMU were lso provided. For he opimizion of EMUs minennce schedule, he exising lierure is more concerned bou he firs- nd he second-level minennces. Srisndrjh e l. 5 opimized he EMU overhul pln using he geneic lgorihm. The geneic lgorihm improves he quliy of pln nd reduces he coss of operion. Mrói nd Kroon 6,7 developed mulicommodiy flow model for prevenive minennce rouing. Given he EMU require minennce in he forhcoming one o hree dys, he operion schedule mus be djused so h hese urgen unis rech he minennce fciliy in ime. Alfieri e l. 8 proposed mulicommodiy flow model for efficien rolling soc circulion on single line of he Duch rilwy newor. Their objecive is o minimize he disnce run by rin unis of vrious ypes. Shor-erm minennce requiremens re no considered in heir formulions. Rezvniznini e l. 9 discussed he implemenion of Relibiliy Cenered Minennce o me rolling soc minennce of he Rj Pssenger Trin Corporion more cos effecive by reducing erroneous minennce nd unnecessry minennce. Tsuji e l. 1 nlyzed he influence fcors of EMU operion nd minennce problems combined wih he Jpnese Shinnsen. And hey developed novel pproch bsed on n colony opimizion o solve he problems. Wng e l. 11 proposed -1 ineger progrmming model o sudy EMU minennce, bu

3 he model cnno be pplied in mjor minennce prcice. Gicco e l. 12 provided mixed-ineger liner-progrmming formulion for inegring shor-erm minennce plnning in newor-wide rilwy rolling soc circulion problem, nd he opimizion objecive is o minimize he cos wih service pirings, empy runs, nd shor-erm minennce ss. Li e l. 13 sudied n exc opimizion model o improve he efficiency in rolling soc usge wih considerion of prcicl operion consrins nd muli-level minennce. Compred o he mnul process, hybrid heurisic process is developed o improve soluion quliy nd efficiency. For he locomoive, Ziri e l. 14 sudied he locomoive operion by consrucing lrge ineger progrmming model, hey focused on he influence of minennce for operion. Lingy e l. 15 described model for operionl mngemen of locomoive huled rilwy crs. They sough for mximum expeced profi schedule h sisfied vrious consrins, mong hem minennce requiremens were lso included. Wng e l. 16 developed -1 ineger progrmming model o sudy locomoive operion nd minennce, nd pplied geneic lgorihm o solve he model. Bu he model ignored he minennce cpciy. In he opimizion of plnes minennce schedule reserch, Moudni nd Félix 17 sudied he problems of ssigning plnes o flighs nd of flee minennce operions scheduling. And hey lso proposed dynmic pproch o cope wih he flee ssignmen problem nd heurisic echnique o solve he embedded minennce scheduling problem. Budi e l. 18 presened mhemicl formulion for he long-erm plnning of rilwy minennce wors. The objecive is o minimize he ime required for minennce, expressed s cos funcion. Heurisic lgorihms compued nerly opiml soluions by combining minennce civiies on ech rc. Mehme nd Bilge 19 developed ineger liner progrmming model by modifying he connecion newor represenion which provided fesible minennce roues for ech ircrf in he flee over weely plnning horizon wih he objecive of mximizing uilizion of he ol remining flying ime of flee. The proposed model is solved by using brnch-nd-bound under differen prioriy seings for vribles o brnch on. In ddiion, Grigoriev e l. 2 sudied he problem of scheduling minennce services, nd he objecive ws o find cyclic minennce schedule of given lengh h minimized ol operion coss. A brnch nd price lgorihm ws pplied o solve he model. Compred o he exising reserches, his sudy mes he some new conribuions. The gol of his pper is o explore he opimizion of EMUMMS o mee pssenger flow pe demnd. Opimize elecric muliple uni mjor minennce schedule by consrucing ime-spce newor. And -1 ineger progrmming model is proposed o reduce he coss of mjor minennce wih considerion of ll necessry regulions nd prcicl consrins, especilly he pssenger rnspor pe demnd. An effecive nd inelligen geneic lgorihm wih simuled nneling survivl mechnism is lso developed for generl lrge-scle empiricl cse. EMU mjor minennce problem CR The EMUMMS is pln h decides he rin-se when o undergo mjor minennce nd when o undere rnsporion s. The plnner should no only ensure supply enough vilble

4 rin-se for pssengenspor pe demnd, bu lso reduce he minennce cos s much s possible. In prcice, seps of ming n EMUMMS re s follows. Firs, collec he rel-ime d of ll rin-ses, such s he ol operion milege nd dys since ls mjor minennce, he ol operion milege nd dys, he level of ls minennce, sr de of scheduled, verge dily operion milege of differen ype s rin-ses nd so on. Second, esime he sr de of mjor minennce for ll rin-ses bsed on he sisics d, nd minennce requiremens. A ls, wih he ll necessry regulions nd prcicl consrins, deermine he exc sr de of mjor minennce for ll rin-ses. These re he oucome we needed. In CR sysem, n EMU usully consiss of eigh or sixeen unis of power nd non-power rolling soc permnenly conneced ogeher, we mr i 8-EMU or 16-EMU. Therefore, ech uni wihin rin-se operes dily ss nd undergoes inspecions ogeher. Depending on he demnd of rin rips, rin cn be formed by one o wo 8-EMU or one 16-EMU. Demnd Wih he developmen of Chin s economy, he improvemen of people s living sndrd s well s huge chnge of consumpion concep, pssenger rip hs formed rend of long rvel rush e.g. Spring Fesivl, Summer Holidy nd Nionl Dy, coupled wih shovel rush, such s New Yer s Dy, Tomb-sweeping Dy, Lbor Dy, Drgon Bo Fesivl nd Mid-uumn Dy. Aimed hese rvel rushes, Chin Rilwy Corporion hs mde pssengein grph bsed on relevn documens nd files, nd every rilwy bureus hve drwn up corresponding rin-se operionl plns. The EMUMMS is o ensure supply enough well-condiioned rin-ses o implemen he operionl pln (priculrly in rvel rush). Minennce/Inspecion Tble 1 shows he mjor minennce requiremen for he CRH2 nd CRH38A(L) in erms of cumulive opering milege nd cumulive opering dys. Tble 1. Minennce regulions for CRH2 nd CRH38A in CR Type Third-level Fourh-level Fifh-level CRH2A CRH2B CRH2C-1 CRH2C-2 CRH38A 2,.6 million 5, or 1.5 yers m 5, 1.2 million 1, or 3 yers m 2.4 million ±1, m or 6 yers CRH38AL The minennce requiremen ses he limi on how much disnce nd ime rin-se cn opere before he nex mndory minennce. For exmple, he rin-se, CRH2A, mus go hrough he hird-level minennce fer opering for.6 million m or for 18 monhs before i cn be ssigned o he nex operion uilizion ph wih cul rin rips. Furhermore, he mjor minennce requiremen foin-se hs floing rnge. For exmple, cumulive opering milege floing rnge of he hird-level minennce for CRH2A is [-5,m, +2,m], i.e., CRH2A will be undergone he procedures of hird-level minennce when is ccumuled

5 operion milege is greer hn 55. m nd less hn 62, m from he ls mjor minennce. And, he inervl beween wo djcen mjor minennces should be less hn he hird-level requiremens. According o Tble 1, he fourh-, fifh-level cycle is wice nd four imes, respecively, hn he hird-level cycle. Moreover, he minennce procedures of higher-level minennce include ll minennce procedures in lower-level minennce. Thus, fer one clss of minennce process, ll cumulive opering milege nd dys ssocied wih h clss nd he corresponding lowerlevel clsses of minennce re se o zero. For exmple, ll ssocied cumulive opering milege nd dys for fourh-level nd hird-level should be se o zero fer fourh-level. Therefore, he mjor minennce requiremens equls o he hird-level requiremens, nd he rin-se undergoes wo djcen mjor minennces differen levels ccordingly. On he bsis of his rule, he mjor minennce cyclic grph could be drwn, s shown in Fig. 1. Bsed on he sequence of mjor minennce cyclic grph nd he mjor minennce requiremen, he rin-se cceps he differen levels of mjor minennces in urn unil hey re scrpped. The fifih-level minennce New EMU The hird-level minennce The hird-level minennce The fourh-level minennce Fig. 1. The mjor minennce cyclic grph According o User Mnul 21, he mjor minennce requiremens depends on he cumulive opering milege minly nd he cumulive opering dys s supplemen, nd whichever comes firs. According o he simple mhemicl clculion bsed on he d in Tble 1 nd Tble 2, we cn conclude h he cumulive opering milege for ny rin-se will finish firsly, such s CRH2A, (.6 million m)/ (15 m) =4 dys < 1.5 yers. Therefore, we could only e ino ccoun he cumulive opering milege requiremen only nd ignore he cumulive opering dys in his pper. Tble 2. Averge dily operion milege of differen ype s rin-ses Type CRH2A CRH2B CRH2C-1 CRH2C-2 CRH38A CRH38AL Averge dily milege 1,5 m 1,5 m 1,6 m 1,8 m 1,9 m 1,9 m When he rin-se needed mjor minennce, i would be deined nd sen o worshop. Since he mjor minennce is ime-consuming, i will resul in shorge of well-condiioned rin-

6 se when he mjor minennce be undergone during he pe period of pssenger flow (such s Chinese "Spring Fesivl rvel rush") wih he flee-size consrins. Bu he floing rnge ensures he sr ime of minennce is flexible. In order o void he pe period of pssenger flow, some rin-ses my choose o undergo he mjor minennce he rer of floing rnge, nd ohers my conduc minennce he hed of floing rnge. However, oo much dely will influence operion sfey, nd oo much minennce in dvnce will increse he frequency. In ddiion, s he mjor minennce is cosly, frequen minennce will led o gre wse of resources. Therefore, under he premise of sfey operion, he sr ime of mjor minennce should be posponed. Aside from hese requiremens on rolling soc, every depo hs only cerin cpciy for he number of inspecions h cn be performed per dy. An opiml mjor minennce pln is one h cn supply deque rin-se for operion during periods of pe demnd nd limiions wih minimum minennce cos hroughou he decision horizon. In CR sysem, experienced prciioners cn genere effecive nd fesible pln. However, his process is ime consuming, nd n opiml soluion is no gurneed. Mehodology In his secion, proposed pproch nd corresponding opimizion model re presened. As he opimizion objecive of EMUMMS is o ensure supply enough rin-se o fulfill rnsporion ss, no involved wih he rin-se operionl pln, we divide he sus of rin-se ino vilble sus nd mjor minennce sus (including he hird-, fourh- nd fifh-level minennce sus). The vilble sus includes operion sus, firs- nd second-level minennce sus. The reson no o se wiing sus is h floing rnge exised which is helpful o flexibly djus he sr ime of mjor minennce. The Proposed Approch A spce-ime newor is consruced bsed on grph heory, o nlyze EMUMMS. In CR sysem, he running ime of rin-se is from 5: o 24: every dy, nd from : o 5: is for minennce nd recess ccordingly. Furhermore, he woring ime of minennce worshop is lso in he durion of 5: o 24:. Therefore, we consruc spce-ime newor by seing he period from : o 5: s one node, nd regrding he durion from 5: o 24: s rc h connecs djcen nodes (see Fig.1). The horizonl direcion represens he elpse of ime, nd he vericl direcion shows differen sus of rin-se.

7 Avilble The hird-level minennce The fourh-level minennce The fifh-level minennce Avilble sus ime rc The hird-level minennce sus ime rc The fourh-level minennce sus ime rc The fifh-level minennce sus ime rc Heding for or leving from minennce sus An EMU coninued in he vilble sus An EMU coninued in he hird-level minennce sus An EMU coninued in he fourh-level minennce sus An EMU coninued in he fifh-level minennce sus Node Fig. 2. Schemic digrm of connecion relionship beween vilble nd mjor minennce sus for EMU Le V denoe he se of ll node nd le A denoe he se of ll rc. Direced grph G consiss of poin se V nd rc se A, G ( V, A). The ls column denoes virul super-node in plnning horizon. The noions, including he indices, prmeers, nd ses, used bove re lised in Tble 3. Tble 3. Noion of indices, ses, nd prmeers. Noion Indices i, j, s Descripion The sus of rin-se; i, j 1,2,3,4, denoe vilble sus, he hird-, fourh- nd fifh-level minennce sus, respecively The ordinl number of column e The rin-se; e E Prmeers v i The node loces in he i row nd he column; vi V The rc; A i The ime rc following v i ; ij i h w i The connecing rc from i o i A i c j ; ij A The smple rc presens he scope of rin-se in he sme sus h from i h A s The weigh of ime rc n The minimum vlue of w 1 b i The minimum vlue of i 1, Ses E Se of rin-se w, i 1,2,3 ih o i ;

8 A V A i c A r A s A Se of ll rc Se of ll node Se of ime rc; r Ai A Se of rc h connecs differen inds of ime rc; Se of ime rc nd is connecing rc; r A A c r A A s Se of smple rc; A A We define he rc showed by dshed line s ime rc in his pper. There re four inds of ime rcs exis in his newor (disinguished by color), which represen vilble sus, hird-level, fourh-level nd fifh-level minennce sus, respecively. Give hese ime rcs weighs ccording o he prcicl mening. Assign w i o i h presens he number of rin-ses on he nd he i-h sus. To successfully ccomplish he rnsporion ss of on he w 1 mus greer hn n, i.e. w1 n during differen periods. he -h dy -h dy, he. Noe h he vlue of n is differen wih rin-se demnds w 2 denoes he number of rin-ses in hird-level minennce sus on -h dy. Due o he resriced service cpciy of worshop, w 2 hs is mximum vlue b 1. Liewise, w3 b2 nd w4 b3. In his spce-ime newor, o show specil sus of rin-ses inuiively, we connec he ime rcs represening he sme sus o form n rc chin, depiced by solid line pined wih sme color. A he end of plnning period, direc ll he solid line rcs o he super node he end of ech row nd le ih denoe he solid rcs. In Fig.1, rin-se hs been in vilble sus from v 1,1 o v 1,5, which cn be depiced by red solid line from v 1,1 o v 1,5. The lengh of his red line denoes he durion of vilble sus. Similrly, his rin-se hs been in hird-level minennce sus from v 2,5 o v 2,9, which cn be denoed by n ornge solid line from v 2,5 o v 2,9. The lengh of his line represens he ime consumed of conducing hird-level minennce. I should be poined ou h Fig.1 is only sech mp, whose ime spn is no rue in prcice. In ddiion, he process of rin-se heding for nd leving from worshop re relively sochsic in prcicl, so we do no e ime consumpion in heding nd leving process ino considerion. For simplificion, i is ssumed h rin-se cn swich o mjor minennce sus on he sme dy fer operion ending, nd vice vers, which is depiced by deep-blue dsh-doed rc in Fig.1. The direcion of rc signifies he sus rnsiion direcion of rin-se, denoed by fensiion. is he dy of his process nd le ij, where i nd j respecively presen he sus before nd c A denoe he se of hese deep-blue dsh doed rcs. In his wy, ime rcs describing differen sus of cerin rin-se re conneced by deep-blue dsh doed rcs, forming ph hroughou he plnning cycle. On he newor, 1 nd 2, 1 nd 3, 1 nd 4 cn be lined ogeher, respecively, by ij ( i, j 1,2,3,4 ). Bu i cnno be conneced beween he 2, 3 nd 4 oher words, he sus of rin-se could rnsform from vilble o minennce, or from minennce o vilble, bu cnno rnsform from cerin level of minennce o noher level. EMUMMS deermines which dy he rin-se should go o worshop nd which level of. In

9 minennce he rin-se should undere. In word, i is problem of he sus rnsformion beween vilble nd minennce. On he newor, his process cn be shown s ph by r connecing differen ( A ) from he beginning o he ending of plnning horizon. Such s he ph r : 1,1 v2,8 2,8 1,2 v 1,1 v 9 2,9 2,1 1,9 1,15 v 1,16 v 1,16 1,17 v 1,3 1,3 1,4 v 1,2 v 1,9 1,1 v 1,1 v 5 1,5 1,2 v 2,5 v 2,5 2,6 2,6 2,7 v 1,4 1,11 1,12 v 1,12 1,13 1,14 v 1,14 v 2,7 v 1,15, s shown in Fig. 1, describes h cerin rin-se is in vilble sus from he firs dy o he fourh dy, hen underes he hird-level minennce bsed minennce requiremens from he fifh dy o he eighh dy. Afer h, his rin-se go bc o undere rnspor ss from he ninh dy o he end of plnning horizon. In his wy, ll he sus nd sus rnsiion process of cerin rin-se in plnning cycle re depiced by one ph, nd differen sus rnsiion ime poin leds o differen ph. Therefore, conver EMUMMS problem ino phwy chosen problem on he ime-spce newor. A ls, we opimize phwy chosen problem o relize he opimizion of EMUMMS. Opimizion model According o he proposed pproch,n opimizion model is consruced bsed on clssic rc-ph model. Le r denoe he fesible ph for cerin rin-se: e ( e E), nd le R e denoe he ph se including ll fesible phs on he ime-spce newor. Bsed on he chrcerisics of rc-ph model, we define he decision vribles s follows: 1 chooses he ph, r e r, r Re xe oherwise And define he ssocied vribles s follows: r 1 -rc on he r-ph of e, e E, r Re, A e oherwise The ssocied vribles describe inclusion relion beween rc nd ph. ss The objecive funcion of he opimizion model is o minimize he coss of mjor minennce. We don consider he opimizion of cerin mjor minennce processes nd regrd i s fixed vlue in his pper. So, he objecive funcion of he opimizion model cn be solved by decresing mjor minennce frequency. And he prcicl mehod of decresing mjor minennce frequency is o increse he inervl of wo djcen mjor minennces, h is o sy, o increse he cul opering milege (nd opering dys) beween wo djcen mjor minennces. Moreover, ccording o minennce requiremens of ech level, he cul opering milege (nd cul opering dys) since he ls mjor minennce cnno exceed he upper limi of floing rnge. Therefore, he objecive funcion of he opimizion model could be described by minimizing he D-vlue beween he cumulive opering milege (nd cumulive opering dys) of minennce requiremens nd he cul opering milege (nd opering dys) since he ls mjor minennce. According o he menioned bove, Le of mjor minennce requiremen for e ( e E Le denoe he vlue of cumulive opering milege ). Le l e denoe he verge dily milege for he

10 ype of e. The verge dily milege of EMU rin-se is sisic, nd i is relively precise o predic he e of mjor minennce becuse of he sisicl ime is long. The iniil vlue l e nd e denoe he ccumulive opering milege nd opering dys since ls mjor minennce. If rin-se is undergoing inspecion he beginning of plnning horizon, l e nd e will e negive vlue for simplifying he model in his pper, nd e presens h e dys re remined o finish he inspecion his momen. And he l e equls o l e e ccordingly. Le l e denoe he sus vrible h indices he expeced opering milege since ls mjor minennce when e ( e E) be sen o worshop. So, we hve he following equion. l l ( 1) x l, e E, (1) e e e e e r Re where c, i.e., 1 j A ( j 2,3,4 ). And is derived from 1 j ( j 2,3,4 ). Such s r : 5. In conclusion, he objecive of he opimizion model cn be described s follows: min Z c mx{, Le l e} (2) e where c denoes he uni coss of milege loss resuling from he inspecion hed of schedule. Consrins of he model re minly derived from he following severl specs. (1) According o he proposed pproch, ny e ( e E) cn discreionrily choose one nd only one ph from he spce-ime newor, which is he uniqueness consrin of ph in clssicl rcph model. Is formulion is lised s follows: r xe 1, e E (3) r R e (2) The minimum number of rin-ses in vilble sus is differen bsed he demnd of pssengers, nd he minimum number of rin-ses in vilble sus should be gurneed. According o he vlue of n during differen periods, 1 cn be divided ino four sges including he usul, Spring Fesivl rvel rush, summer holidy nd Nionl Dy in his pper. Le A 1,1, A 1,2, A 1,3 nd A1,4 denoe he subse of A 1 ( A1 A1,1 A1,2 A1,3 A1,4 ) on differen sges nd he minimum weighs re n 1, n 2, n 3 nd n 4, respecively. To describe his mer, se of consrins esblished s follows: e n1, A1,1 r R e e n2, A1,2 r Re e n3, A1,3 r Re e n4, A1,4 r Re (4) (5) (6) (7) (3) The number of rin-ses in ny level of minennce sus should no exceed he service cpciy. To describe his mer, se of consrins esblished s follows: e b2, A 2 r Re (8)

11 e b3, A3 r Re e b4, A 4 r Re (9) (1) (4) Due o he floing rnge of cumulive opering milege, presened in descripion of he problem, he rin-se could be sen o worshop flexime. Bu, i is obviously unresonble o be oo erly or oo le. Le l e denoe he lower bound of floing rnge nd bound for e ( e E). This mer cn be described by inequliy: l e u e u e denoe he upper le, e E (11) From he bove nlysis, he model for opimizing EMUMMS is summrized s model I. min Z c mx{, Le l e} e s.. Consrins (3) (11) r xd {,1} Moreover, le l 'e denoe he ol opering milege for e ( e E ). And he level of ls minennce is denoed by M. Algorihm design The generion of fesible ph se To solve his model, we hve o genere R e for every e ( e E ) on he newor firsly. According o he newor design, he ph is n rc chin h formed by vriey end-o-end rcs hroughou he whole plnning horizon. To find ou hese rc chins, we should recognize he subsequen rc se of ech ype of rc. A he beginning of plnning horizon, he rin-se my be in vilble or mjor minennce sus. The subsequen rc se of 1 is described s follows: As for he rin-se is vilble, he subsequen sus of i my be sill vilble or urn o mjor minennce. So he subsequen rc se of 1 is { 1, 1, j )}. 1 1 j ( 2,3,4 To undersnd he definiion of he subsequen rc se of 1 j ( j 2,3,4 ), we cn consider his cse: long wih he rin-se go o worshop, he minennce procedures of cerin level will be conduced on i. Thus, he subsequen rc se of 1 j ( j 2,3,4 The subsequen rc se of j ( j 2,3,4 ) is { j ( j 2,3,4 )}. ) is illusred s follows: when cerin level of mjor minennce foin-se is compleed, he sus of rin-se will chnge o vilble; bu, if furher 1 minennce is needed, he subsequen rc should be j, 1( j 2,3,4 ). Therefore, { j1 ( j 2,3,4 ), j, 1( j 2,3,4 )} is he subsequen rc se of j ( j 2,3,4 ). The subsequen rc se of j1 ( j 2,3,4 ) is defined s follows: once he mjor minennce of rin-se is compleed, he sus of rin-se will chnge o vilble. So he subsequen rc se of j1 ( j 2,3,4 ) is he { 1 }. Afer clering he subsequen rc ses of ll rcs on he newor, R e cn be genered.

12 Moreover, by ype. R e cn be downsized ccording o he consrin (11). So, fesible ph se denoed R e cn be genere by deph-firs serch lgorihm, he specific seps re s follows: Sep1:According o he iniil sus of rin-se, we ssign he iniil rc nd cler he rc s Sep2:Te consrin (11), l 'e, M nd minennce requiremens s crierion. Bsed on he connecion sequence of rcs menioned bove, he deph-firs serch lgorihm is pplied o find he subsequen rc nd cler he ype of subsequen rc. If none subsequen rc is found, hen urn o Sep 5. Oherwise, judge wheher or no he subsequen rc poins he virul super-node. If yes, urn o Sep 3; oherwise, urn o Sep 2. Sep 3: Connec ll rcs in he order nd oupu he ph: r. If r lredy exiss, urn o Sep5; oherwise, urn o Sep 4. Sep 4: Add r o R R ), nd delee he 1 j ( j 2,3,4 ) nd j1 ( j 2,3,4 ) exis in ph R e ( e e r from he newor. Then reconsruc he newor G nd go bc o Sep1. Sep5: End he fesible ph generion process nd oupu R e. Repply he lgorihm bove nd genere R e on he newor for every e ( e E). And, le R denoe he se of ll fesible ph, so, R R e. As consrin (11) hs lredy been used in he process of genering R, he opimizion model of mjor minennce schedule cn be simplified s model II: min Z c mx{, Le l e} e s.. r xe 1, e E (13) r R e e n1, A1,1 r R e (14) e n2, A1,2 r R e (15) e n3, A1,3 r R e (16) e n4, A1,4 r R e (17) e b2, A 2 r R e (18) e b3, A3 r R e (19) e b4, A 4 r R e (2) r xd {,1} (21) Soluion sregy of he model Geneic lgorihm is good conrolling he serch process bu my esily resul in premure

13 convergence for he problem. While he simuled nneling lgorihm performs well in locl serch bu performs bd in globl serch. Therefore, inegre hese wo lgorihms nd hen design new soluion pproch ccording o he chrcerisics of our model. (1) Consrin removing As for consrin (3) in model II, we cn relize i by seing coding principle for chromosomes, which will be described in deil. Becuse he decision vribles re -1 vribles, he binry coding pproch is proposed. Ech chromosome represens soluion of he model, i.e., he mjor minennce schedule of ll rin-ses. The lengh of chromosome is R R e ( R e denoes he number of fesible phs of e ). And he bloc coding pproch is pplied o chromosomes. Use o divide he chromosome ino blocs h presens fesible ph se for cerin rin-se. The number of blocs equl o he number of rin-ses. (see Fig. 3). x x 1 2 x R1 x x 1 2 x R2 x x 1 2 R e e e x e Fig. 3. Digrm of chromosome encoding The gene sequence in ech bloc corresponding o he order of phs in he fesible ph se. If rin-se chooses ph, he corresponding gene will be se o 1. Moreover, ccording o consrin (3), he ol vlue of genes in ech bloc equls 1. Th is o sy, only one gene in bloc cn equl1, nd he res cn only be. Through he penly funcion nd coding pproch menioned bove, he model II cn be convered o n opimizion problem wih no consrins. 4 4 Le e 1 i e e 2 e e i e i 1 A1, 2 A i r R e i i r R e (22) min Z c mx{, l }+ mx{, n x } mx{, x b } where c is.1, 1 1 nd 2 8. Since he consrin of insufficien rin-se is more inense hn h of minennce service cpciy, he vlue of 1 is greer hn 2. (2) Relevn sregies for geneic lgorihm wih simuled nneling survivl mechnism. Sregy for chromosome coding nd iniil soluion generion The chromosome coding pproch hs been previously described in deil, so his secion will focus on he sregy for iniil soluion generion. Penly funcion nd pproprie coding pproch re pplied o model II nd conver he problem ino unconsrined problem. Therefore, he generion of iniil soluion only needs o mee he requiremens of he unconsrined problem. According o he coding pproch, se cerin gene o 1 nd se ohers o in ech coding bloc. In his wy, n iniil soluion cn be obined. Then, repe his procedure nd genere he iniil populion wih required size, such s sizepop 3. I is inevible h some soluions in iniil populion do no mee he consrins of model I. Despie his, due o he srong convergence nd robus of geneic lgorihm, he generion of he opimizion soluions hrough coninuous evoluion will no be ffeced. b. Clculion sregy for individul finess Finess clculion funcion is developed o evlue he individul finess in ierion.

14 Fi j 1/ Z j (23) In equion (23), Fi j denoes he finess of chromosome j fer imes of ierion; is he objecive funcion vlue of chromosome j fer imes of ierion. In his wy, he beer quliy of chromosome, he greer finess, i.e., he smller vlue of objecive funcion, which ccords wih he lws of evluion. c. Selecion sregy The finess funcion is en s he evluion crieri in he selecion of chromosomes. Therefore, he chromosome hs high probbiliy be seleced wih he gre vlue of finess. The roulee wheel selecion sregy in sndrd geneic lgorihm is doped o selec chromosomes. The probbiliy of n individul o be seleced is s follows: p j Fi j/ Fi j (24) j The roulee wheel is divided ino differen regions ccording o he probbiliy we go. Then, rndom number ( 1 ) is genered in [, 1] nd chromosomes re seleced bsed on he region where 1 ppers. Selec repeedly unil he number of chromosomes reches sizepop, he size of populion, bsed on he roulee wheel selecion sregy. d. Crossover sregy Le p c denoe he crossover probbiliy nd se i s.88 in his pper. Pir he chromosomes rndomly, nd dop he geneic crossover pproch in unis of blocs. The deiled sregy is s follows. A rndom number ( 2 ) is genered firsly. Then, if 2 pc, rndomly produce wo inegers in [1, R ] ( 1 nd 2, 1 2) nd swp he gene blocs from 1 o 2 beween wo pren chromosomes in pir. In his wy, wo child chromosomes be obined. e. Muion sregy Le p m denoe he muion probbiliy nd se i s.8 in his pper. Jus lie crossover operion, he muion operion for chromosome is conduced in unis of blocs, oo. Firsly, genere rndom number ( 3 ) for cerin chromosome. If 3 pm, genere rndom ineger ( 3 ) in inervl [1, R ]. Secondly, genere nohendom ineger ( 4 ) in inervl [1, R ]. And 3 if he vlue of gene 4 in gene bloc 3 equls o 1, regenere 4 unil he vlue of gene 4 equls o. Finlly, se he vlue of gene 4 o 1 nd se he res genes in bloc 3 o. f. Survivl sregy of simuled nneling In geneic lgorihm, he pren chromosomes will be replced by he offspring fer selecion, crossover nd muion. However, regulr upding mehods re liely o produce locl opimum soluion. To overcome his disdvnge, simuled nneling survivl sregy should be doped for upding. The deiled procedures re s follows. If he finess of n offspring individul is beer hn is prens, ccep his offspring individul undoubedly. Oherwise, ccep he offspring 1 individul wih probbiliy: exp j j l l Fi Fi T. Where T denoes he emperure fer l Z j

15 l 1 l imes of cooling in simuled nneling process. T T nd is he cooling re is seleced s.8 in his pper. Algorihm procedure The flowchr of he lgorihm is shown in Fig. 4. Sr Iniilize prmeers Iniilize he populion, nd clcule he individul finess Selecion, crossover nd muion operion bsed on he geneic sregy Clcule he finess of he new populion vlue, nd Upde he populion Bse on simuled nneling survivl mechnism l 1 T T q l q MAXQ N Y N T l T end Y Over The specific seps re s follows: Fig. 4. The flowchr of he lgorihm Sep1: Iniilize he mximum evoluion imes MAXT 3, originl emperure T 1, end ending emperure T 1. nd se he ierion ime s. Sep 2: Genere originl populion rndomly bsed on coding sregy nd compue he finess of individuls Fi j j 1,2,, sizepop. Sep3: Genere new populion hrough selecion, crossover nd muion ccording o relevn geneic sregies. Fi Sep 4: Compue he finess of individuls in he new populion 1 Fi j, j 1,2,, sizepop. If 1 j Fi j, replce he prens wih offspring individuls; oherwise, ccep offspring individuls 1 wih probbiliy exp j j l Fi Fi T, 1. Sep5: If MAXT, go bc o Sep3; oherwise, urn o Sep 6. l end Sep6: If T T, end he lgorihm nd oupu he opimum soluion; oherwise, se

16 l 1 l, T T nd opere he simuled nneling procedures, hen go bc o Sep 3. Conclusion This reserch opimizes he elecric muliple uni mjor minennce schedule from he perspecive of newor design by rnsforming i ino he phwy chosen problem on he imespce newor. A -1 ineger progrmming model is developed considering he differen rnsporion demnd for pssengers nd he cpciy limied of worshop, ec. Compred wih he mnul process, he geneic lgorihm wih simuled nneling survivl mechnism is lso developed o improve soluion quliy nd efficiency. Using his decision suppor ool cn help rilwys wih similr chrcerisics o improve he efficiency in elecric muliple uni mjor minennce schedule. Wh hve been done in his reserch is o opimize elecric muliple uni mjor minennce sregiclly. Fuure reserch my invesige he possibiliy o opimize he minennce pln for he firs-, second-level inspecion considering he differen rnsporion demnd for pssengers nd he minennce cpciy limied of sub-depo under he finie flee-size of rin-se. References 1. hps://en.wiipedi.org/wii/chin_rilwy_high-speed. 2. Suchly, V., Grenci, J., Poprocy, R.,. Rilwy vehicle minennce nd informion sysems. Compuers in rilwys VII: Inernionl conference on compuers in rilwys, 2, pp Bologne, he Frnce. 3. Shimd N. Rolling soc minennce for sfe nd sble rnspor. Jpnese Rilwy Eng, 26; 46(2): Cheng, Y. H., Tso, H. L. Rolling soc minennce sregy selecion, spres prs esimion, nd replcemens inervl clculion. In J Prod Econ, 21; 128(1): Srisndrjh, C., Jrdine, A. K. S., Chn, C. K. Minennce scheduling of rolling soc using geneic lgorihm. J Oper Res Soc 1998; 49(11): Mrói, G., Kroon, L. Minennce rouing foin unis: he rnsiion model. Trnsp Sci 25; 39(4): Mrói, G., Kroon, L. Minennce rouing foin unis: he inerchnge model. Compu Oper Res 27; 34(4): Alfieri, A., Groo, R., Kroon, L. G., e l. Efficien circulion of rilwy rolling soc. Trnsp Sci 26; 4(3): Rezvniznini1, S. M., Vlibeigloo1, M., Asghri1 M, e l. Relibiliy cenered minennce for rolling soc: cse sudy in coches wheel ses of pssengeins of Irnin rilwy. 28 IEEE Inernionl Conference on Indusril Engineering nd Engineering Mngemen, 28, pp Wshingon. 1. Tsuji, Y., Kurod, M., Imoo., Y. Rolling soc plnning for pssengeins bsed on n colony opimizion. Trnscions of he Jpn Sociey of Mechnicl Engineers C 21; 76: WANG, Y., LIU, J., MIAO, J. R. Column generion lgorihms bsed opimizion mehod for

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