The Optimization Model and Algorithm for Train Connection at Transfer Stations in Urban Rail Transit Network

Transcription

1 Send Orders for Rerints to 690 The Oen Cybernetics & Systemics Journal, 05, 9, Oen Access The Otimization Model and Algorithm for Train Connection at Transfer Stations in Urban Rail Transit Networ Li Xuan,,* and Shi Yang 3 School of Maritime and Transortation, Ningbo University, Ningbo, Zheiang, 35, PR China; National Traffic Management Engineering & Technology Research Centre Ningbo University Sub-centre, Ningbo, Zheiang, 35, PR China; 3 Ningbo Urban Planning & Design Institute, Ningbo, Zheiang, 3504, PR China Abstract: In urban rail transit networ, the assenger transfer time deends on the train connection states in transfer stations, therefore, the otimization of the connection relations of arrival and dearture time among trains is significant to imrove the level of transfer service Here, with the sychology of waiting assengers taen into consideration, the cost function of transfer waiting times has been established On this basis, an otimization model for train connections at transfer stations was constructed, and a genetic algorithm was designed to solve this model A comuter rogram imlementing this genetic algorithm was written in Microsoft VBNET This rogram was used to otimize the train oeration lans of a simle networ which consists of four urban rail lines in Beiing The results show that the roosed method can effectively reduce the total waiting time cost of all transfer assengers in the networ Keywords: Genetic algorithm, Train connection otimization, Transfer, Urban rail transit networ INTRODUCTION With the exansion of the urban rail transit networ, the number of transfer nodes on the travelling routes of assenger has increased substantially, and transfer has become a necessary ste in most rail travels To rovide safe and efficient transfer service is ey to imroving the overall service level of the rail transit networ The time required for transfer is a direct manifestation of transfer efficiency, and it also directly reflects the level of the rail networ management Previous studies on rail transfers have focused largely on transfer station design and on transfer stream design in order to minimize the assengers waling time during transfer However, restricted by a variety of obective conditions, the room for reducing the transfer waling time is rather limited In addition, comared to reducing the waling time, reducing the transfer waiting time is more valuable to assengers The transfer waiting time is directly associated with the arrival and dearture time of trains recorded before and after transfer at the transfer station Thus, coordinating and otimizing the schedules of trains in different lines connected by transfer stations can mae otimal connection between the arrival and dearture time of trains, thereby successfully reducing the transfer waiting time of assengers at the rogram level At resent, in most maor cities, the train schedules are comiled using the method of maing schedules by line and adusting schedules at the networ level More accurately, the schedules are first made at the level of individual lines in accordance with the assengers demand and transort caacity resources; train schedules of different lines are comiled *Address corresondence to this author at the School of Maritime and Transortation, Zheiang, Ningbo 35, PR China; Tel: ; lixuan_43@6com searately Then, at the networ level, adustments are made from the ersective of coordination and overall benefits However, with this method, once the train schedules are comleted, it is difficult to change factors, such as the number of running trains, intervals and dwelling times, and adustments can only be made within a very narrow range Furthermore, because of the comlex couling relationshis between the lines, the comlexity increases as the networ scale exands, and the adustment in a single oint exerts time roagation effects on the entire networ, which further limits the imact of the adustment Therefore, it is believed that the current method of comiling train schedules does not tae into account the collaborative relationshi between the lines, directly leading to an increase in assenger waiting time in the transfer stations within the networ This has created a bottlenec at the service level of the rail transit networ Based on the existing results and issues, this aer treated the train system as a blac box and used global coordination as the guideline to develo an otimization model for train connections at transfer stations The goal is to achieve mutual coordination between the train schedules of different lines The effectiveness of the otimization method has been verified using a secific examle LITERATURE REVIEW With the exansion of the urban ublic transort networ, there has been continued growth in the roortion of time sent by assengers at the transfer nodes during their overall travel time Therefore, the coordination and otimization of transit timetables (schedules) targeting the otimization of transfer waiting times have received wide attention from researchers For a systematic review of the existing 874-0X/5 05 Bentham Oen

2 The Otimization Model and Algorithm for Train Connection The Oen Cybernetics & Systemics Journal, 05, Volume 9 69 literature, the revious research was divided into three series according to the obect of study, and then summarized In the first series, transfer nodes in the regular bus system were the obect of the study In the second series, the obect of study was the transfer hubs in the urban ublic transit system, consisting of regular bus and rail transit system In the third series, the obect of study was the transfer nodes in the urban rail transit system The first and second series investigated how to achieve efficient connections between buses in different lines or between the buses and trains at the transfer station via otimization of the bus timetables The rearation of train timetables was different from that of bus timetables rimarily due to the following reasons First, rail transit was made limited by the train running intervals; also, the running time in this section, the dwelling time in the station and the dearture interval were all relatively fixed, tolerating only small fluctuations Methods for otimizing the bus timetables cannot be directly alied to rail transit In addition, to imrove the success rate of connections via real-time scheduling (holding at station, dearture ahead of time, etc) is well suited for regular bus transortation, yet it can hardly be alied to rail transit The third series exlored connection otimization at the transfer stations between different lines within the urban rail transit system, using basis intrinsic characteristics of the urban rail transit system This study belongs to the third series, and a brief literature review here will focus on research related to the third series The number of ublished studies in the third series is relatively small, and these studies can be divided into three categories Studies in the first category otimized the schedules of multile lines intersected in a single transfer station, but merely realized train connection otimization at one transfer station, without considering the overall otimization of multile transfer stations within the networ For examle, Partha (995) [] used a single transfer node as the obect of study and set the obective to be a minimum of the sum of transfer assengers' waiting times and the initial waiting time of the arriving assengers at this node With this method, a linear rogramming model was established, and a genetic algorithm was designed to solve the model Ma (00) [] constructed models for the otimization of train timetables at the transfer stations in urban rail transit systems under the condition of transfers at the same latform and under the condition of transfers through tunnels, and designed a heuristic algorithm to design the model Studies in the second category established mathematical models using minimization of the total transfer time (cost) of all assengers in the rail transit system as the obective On the basis of existing train schedules searately comiled by line, the running times, the dwelling times or turnaround times are adusted to otimize the existing train schedules To achieve this goal, Wong et al (008) [3] designed a heuristic search algorithm, Vansteenwegen (006, 007) [4, 5] designed a discrete event simulation method and Kwan et al (008) [6] designed a non-dominated sorting genetic algorithm For studies in the third category, a second-order coordination structure, namely "connection at transfer oints coordination at the networ," was used First, inside each transfer node, the connection between the arrival and dearture times of the trains was otimized, using methods similar to those in the second category of studies, ie, on the basis of existing train schedules for searate lines, the train aths translation or allocation of buffer time was carried out for otimization Next, at the networ level, train connections between different transfer nodes were subected to global otimization To this end, Zhang et al (009) [7] designed a reference-oriented hierarchical loo coordination algorithm based on coordination levels Fang (00) [8] and Zhou et al (0, 0) [9, 0] roosed a station-by-station adustment method related to the imortance of the transfer stations In summary, studies in the first category of the third series only otimized connections between the arrival and dearture times of the trains at single transfer stations With this method, the conflicts between the otimal train connection schedules for multile transfer stations within the networ would be inevitable, yet the first-category studies did not exlore how to resolve these conflicts In the studies of the second and third categories, the general method adoted was to mae coordinative adustment on the existing train schedules of individual lines reared searately As mentioned earlier, once the train schedule is comleted, the number of running trains er line, running intervals, dwelling times and other factors are difficult to change; thus these adustments can only be made within a very small range, and are not able to fully benefit the coordinated oeration of the entire networ Moreover, to solve coordination between the transfer nodes in the networ, studies in the third category artificially considered transfer stations or lines, thereby determining the riority in coordinative otimization between different transfer stations and lines This rovides a method for resolving the conflict between the train connection schedules for different transfer stations; however, it is too subective and may generate closed-loo connections that have contradictions More imortantly, based on this method, the obtained networ train schedules do not rovide the otimal solution From the existing research results in this field, the following conclusions can be drawn First, the current coordination of networ transit timetables (oeration charts) targeting the otimization of transfer connections mostly focused on the otimization of regular bus timetables Yet vehicle management of regular buses is greatly different from that of rail transortation, and hence the method used for otimizing regular bus schedules cannot be directly alied to rail transit Secondly, the number of ublished studies on train connection otimization targeting urban rail transit networs is relatively small To achieve the otimization of train connections at all transfer stations within the networ, all train schedules must be reared with the global networ taen into consideration from the start, rather than merely maing coordinative adustments on the existing train timetables reared searately by lines This is the fundamental difference between the resent study and all the revious studies

3 69 The Oen Cybernetics & Systemics Journal, 05, Volume 9 Xuan and Yang Meanwhile, the revious studies tyically used minimization of the transfer wait times as the otimization obective, yet the transfer wait time was not entirely inversely roortional to assengers satisfaction In fact, it has been shown that when the waiting time is less than 30s, the degree of assenger dissatisfaction is highest [6] Therefore, the resent aer considered the sychology of waiting assengers and converted the transfer waiting time into the transfer cost Minimization of the transfer cost was set as the obective to construct the otimization model for train connections at transfer stations in urban rail transit systems 3 ASSUMPTIONS This study is based on the following assumtions: The transort configuration of all lines in the networ can meet the assenger s demand, and the facilities and caacities of all transfer stations can also meet the assengers demand The running times in the section, the dwelling times in the station, train running intervals and transfer waling times at all transfer stations are all nown inut arameters 3 The assenger transfer demand is relatively stable over a eriod of time 4 After arriving at the latform for the connecting direction, all transfer assengers tae the first available connecting train 5 Transfer between the u-bound and down-bound directions in the same line is not taen into consideration 6 There is no oint oeration between the lines, and for lines with multile routes, only one route is considered 7 The isolated lines in the networ are not considered in the otimization model 4 THE ESTABLISHMENT OF THE OPTIMIZATION MODEL 4 Problem Analysis The basic train oeration data, such as running time in the section, dwelling time in the station, and train running intervals are determined and the train schedule of one certain line in the coordination time eriod is determined by the dearture time of the first train in this time eriod Let the coordination time eriod be t 0, the dearture time of the first train is at time oint 0, h) (h is the train running interval) after the starting time oint of the coordination eriod t 0 In other words, the time interval between the dearture time of the first train and t 0 is variable in 0, h) Under the assumtion that there is no oint oeration between the lines, the train schedules of different lines are indeendent of each other Because loo routing is usually used in urban rail transit systems, the train schedules of ubound train and down-bound train of the same line are closely associated with each other For each line, after the train schedule in one direction within the coordination time eriod is set, the schedule of the trains in the other direction is also determined Hence, in this aer the obects of train connection otimization were restricted to one direction of each line in the networ; this direction is called the coordination direction In this way, the decision variables of the otimization model become the time intervals between t 0 and the dearture time of the first train of various lines coordination direction within the networ in t 0 The goal of train connection otimization is to achieve rational connections of trains from different lines at the transfer stations, thereby, reducing the cost of assengers transfer waiting times Therefore, the obective function of otimization model is the minimization of the total cost of assengers transfer waiting times at all transfer stations in the networ 4 The Cost Function Corresonding to the Transfer Waiting Time The transfer waiting time is the time interval between the oint when the assenger arrives at the latform of the connecting line and the oint when the assenger boards the connecting train If the connecting train arrives ust when the assenger arrives at the latform of the connecting line, the assenger s transfer waiting time is 0; if the connecting train has ust dearted, the assenger s transfer waiting time is close to the difference between the running interval of the connecting train and time when the connecting train stos at this articular transfer station These are the two extremes of the transfer status The latter is the worst scenario for the assenger, because the transfer waiting time is the longest; however, the former scenario is not ideal either A survey has shown that when the transfer waiting time is less than 30s, the dissatisfaction degree of transfer assenger is rather high [6] The main reason for this is that a fixed connection time creates sychological ressure of a otentially missed connection on transfer assengers This crisis is articularly evident when the train running frequency is low Thus, this aer introduced the concet of a comfortable assenger waiting time, which is the waiting time that satisfies the assenger's sychological comfort The otimal transfer status refers to a situation in which the transfer waiting time exactly equals the waiting time comfortable for the assenger Next, the cost function C( t) corresonding to the transfer waiting time will be established The cost corresonding to the waiting time comfortable for assengers is minimum; the cost is increased when the transfer waiting time is greater or smaller than the comfortable assenger waiting time Thus the following function is used (function lot shown in Fig (): C C RT t, t < RT; C(t) = C ( t RT ), t RT h DT a RT con con where, ()

4 The Otimization Model and Algorithm for Train Connection The Oen Cybernetics & Systemics Journal, 05, Volume t --- transfer waiting time, min; RT --- comfortable assenger waiting time, min; h --- running interval of the connecting train, min; con a DT ---the time when the connecting train stos at the con transfer station a, min; C, C ---coefficients Fig () The cost function hase of transfer waiting time The ideal transfer status can be observed when the assenger arrives at the latform of the connecting line, and the connecting train is about to arrive at the same station The oeration time from the train arriving at a station to a full sto is about 40s Hence, here the comfortable assenger waiting time RT is recommended to be 067 min The values of coefficients C and C can be determined by the assenger travel time value The waiting time of 0 brings the assenger a certain sychological stress, which is equivalent to the generation of a certain time cost, ie C Here the value of the time the assenger sends on waiting after having boarded the train is used to determine the value of coefficient C Parameter C describes the cost of waiting time when the assenger misses the exected connecting train In ublic transortation, the value of the waiting time is often determined relative to the value of the riding time [5] The er unit riding time value is set to, denoting the value of unit time that the assenger sends on the running train Then, the er unit value of time that the assenger sends on the latform waiting for the train is set to 5, meaning that the time cost of riding for 5min is equivalent to that of waiting on the latform for min If the worst transfer status is observed, the assenger will wait for a eriod of about h con DT a con In this case, the sychological anxiety of waiting is enhanced, leading to increased time value; the er unit waiting time value in this case is set to 7 [5] Comared to waiting on the latform, a assenger waiting inside the train is more comfortable, and the value of unit time sent on a waiting in the train is set to Thus, C =DT con ( ) a C = 7 h con DT con 43 Mathematical Model were set in the study and According to the above analyses, targeting the coordination time eriod t 0, the following otimization model for train connections at transfer stations in urban rail transit networs was constructed: r i g i, i= = s= m min F ( X )= C ( t i,, s ( X )) V i,, s () ( ) x 0 h st X = x, x,l, x n C(t i,, s Where, ( ) andx N n (3) i, DT con t X i,, s RT, t i,, s ( X )< RT; ( X )) = RT 7 + i, h i, con DT con RT ( t X i,, s ( ) RT ), t i,, s ( X ) RT X is the decision variable It is an n -dimensional vector and n is the number of lines in the networ (isolated lines not included); x ( n ) is the time interval between t0 and the dearture time of the first train of line s coordination direction in the time eriod t 0, and x is a natural number in the interval 0 h, min; h is the running interval of line, min; t i,, s ( ) (4) X is the transfer waiting time of the s th batch of transfer assengers in the th transfer connection at the i th transfer station in the time eriod t 0 Under the networ train schedules corresonding to X (min), a transfer connection describes a transfer from u-bound/down-bound of a feeder line to the u-bound/down-bound of a connecting line C ( t i,, s ( X )---the cost function corresonding to the transfer waiting time t i,, s ( X ); i, DT ---the time when the connecting train stos in the con th transfer connection at the i th transfer station; i, h ---the running interval of the connecting train in the con th transfer connection at the i th transfer station; V i,, s ---the total number of the s th batch of transfer assengers in the th transfer connection at the i th transfer

5 694 The Oen Cybernetics & Systemics Journal, 05, Volume 9 Xuan and Yang station in the time eriod t 0 It is estimated according to the statistics of assenger volume in this time eriod at the transfer station, and based on the assumtion that within the time window of statistics, the number of assengers in different batches wasthe same; m ---the number of transfer stations in the networ; ri ---the number of transfer connections at the i th transfer station; r i = n t e ( i + n i ) 4n t e t e ( i + n i ), where n i and n i reresent the number of lines assing through and ending at the i th transfer station g i, ---the number of batches of assengers in the th fee transfer connection at the i th transfer station in the time eriod t 0 ; t t0 i, gi, =, where h reresents the run- i, fee h ning interval of the feeder train in the th transfer connection at the i th transfer station 5 DESIGN OF THE OPTIMIZATION ALGORITHM 5 Methods for Solving the Otimization Model In the otimization model, it is difficult to exress maing from the decision variable X to the transfer wait time t i,, s ( X ): X t i,, s ( X ) using mathematical formulas Therefore, the model cannot be solved with traditional analytical methods Meanwhile, different element combinations of x ( n ) form the feasible region of X, and the number of feasible solutions is exressed as n = h This aer considered the currently oerating Shanghai rail transit networ as an examle It contains 4 lines In the simlest scenario, it was assumed that the running intervals of all lines in the coordination time eriod were 5min, then the number of feasible solutions reached 5 = Thus, it is difficult 4 to simly aly an exhaustive search method to find the otimal solution A heuristic algorithm is most commonly used to solve this tye of roblem Here a genetic algorithm has been used to solve the otimization model 5 The Stes of the Genetic Algorithm The overall stes of the genetic algorithm are as follows: The initial oulation is randomly generated to obtain the first generation of individuals Each individual is reresented as gene encoding of the chromosome The fitness of each individual is calculated 3 The fitness, gene encoding and function value of the individual with the maximum fitness in the current generation are all recorded 4 It is determined whether the condition for stoing evolution is satisfied; if yes, then the calculation is stoed here, otherwise the evolution continues 5 Regenerating individuals are selected according to fitness Individuals with high fitness have a high robability of being selected, whereas those with low fitness are liely to be eliminated 6 According to certain crossover robabilities and crossover methods, new individuals are generated 7 According to certain mutation robabilities and mutation methods, new individuals are generated The new generation of oulation is thus obtained, and the loo returns to ste 53 The Key to the Design of the Genetic Algorithm 53 Encoding and Decoding The decision variable X in the otimization model is an integer vector, and can be viewed as the henotye of the genetic algorithm The maing rocess from the henotye to the genotye involves encoding This aer used binary encoding to reresent the individual's genotye The secific encoding and decoding methods are as follows One chromosome reresents one combination of the intervals between t 0 and the dearture time of the first train of n lines in t 0 Each chromosome can be divided into n segments; the bit string in the th ( n ) segment reresents the time interval between t 0 and the dearture time of the first train of line s coordination direction in t 0 To encode the bit string in the th segment, a binary string encoding method for integer is used Let integer x 0, h ( n ) h is dissociated using the following algorithm: n = 0 ; x = h ; = 0 0 do = + n ( x ) = int log + n x = x + while x > 0 The integers n (,,, ) = L generated from the ( ) above algorithm satisfies h = n Namely, h is the sum of binary numbers with digit number (,,, ) n = L Thus, x can be reresented by ( n + n +L + n ) binary strings b n b ( n L b 0 ) = = B, ie, x = B =, where, b is the binary bit of 0 or =

6 The Otimization Model and Algorithm for Train Connection The Oen Cybernetics & Systemics Journal, 05, Volume For examle, if x 0, 5, after decomosing h = 5, three integers { n, n, n } = = 3 = are obtained, which satisfy 5 = ( )+ ( )+ ( ) Thus, x can be reresented by four-digit binary strings B = b b 0 3 namely x = B = b n b n L b 0 = 3 = ( ) 3 ( ) b ( 0 ) b ( 0 ), From the above encoding method, the chromosome decoding method can be obtained First, the chromosome is divided into n segments For =,,L, n ( ) segment, ( ) are determined, and the the binary digits n + n +L + n binary numbers with the number of digits (,,, ) n = L are then converted into decimal numbers Finally, the decimal numbers are added u to obtain x For examle, this aer considered an urban rail transit networ that contains four lines; the coordination time eriod was:00-:00, and the running intervals of the four lines in the time eriod were 6min, 7min, 5min and 7min Chromosome rovided a feasible solution It was divided into 4 segments, and the number of digits in the different segments was 4, 4, 3 and 4 Then the binary number in each segment was dissociated to obtain Then all the binary numbers were converted into decimal numbers and added together, obtaining x = 4, x = 5, x 3 = 3, x 4 = 3 Thus the dearture timings of the first train in the coordination direction entering the coordination time eriod were :04, :05, :03 and :03 53 Constructing the Fitness Function The fitness function is normally derived from the obective function, and needs to meet the basic condition of being single-valued, continuous, non-negative and maximized [] Considering that the otimization model finds the minimum value, and the value range of the obective function is ( 0, + ), the fitness function can be set as the inverse of the obective function, namely: ( )= F ( X ) Fit F ( X ) The smaller the value of the obective function, the larger is the corresonding fitness value, and the greater the robability of the individual gene to be assed on to the next generation In addition, because the value of the obective function is generally not close to 0, the fitness value determined by formula (5) does not show ositive sillover In the rocess of calculating the obective function value according to the henotye of an individual with a certain chromosome, two stes are needed The first ste is to determine the networ of train schedules based on the decision variable X and the nown basic oeration data of the trains Two rules that need to be followed during the calculation rocess are clarified as follows (5) First, if the locomotive use cycle is not an integer multile of train running intervals, the locomotive oeration cycle is enlarged by increasing the reentry time, so that the oeration cycle becomes an integer multile of the running intervals In this way, the train running intervals within the coordination time eriod remain consistent Secondly, given one solution of X = ( x, x,l, x n ), from x it can be observed that the dearture time of the first train of line s coordination direction in t 0 is t = t0 + x It can then be deduced that the dearture time of the first train of line s non-coordination direction in t 0 is: t = t 0 + x + t travel Where, + t reentry r h (6) t ---the travel time of the train of line travel s coordination direction; treentry --- the reentry time of trains of line s coordination direction; h denotes the train running intervals of line ; r = t + x + t + t 0 travel reentry, reresenting the greatest osi- h tive integer smaller than t + x + t + t 0 travel reentry h The second ste is to match the train airs for each transfer relation at all the transfer stations based on the networ train schedules, and to calculate the transfer waiting time of the assengers for each train air Next, the corresonding time cost is calculated, and finally all time costs are added to obtain the obective function value F X ( ) 533 Conditions for Stoing the Loo In this aer, the following three conditions were used to determine if the loo should be stoed The otimal solution remained unchanged in the generation GN min In one generation, the difference between the best fitness and the worst fitness was smaller than F! (%) 3 The greatest number of evolving generations was GN max 534 The Selection, Crossover and Mutation Oerators 534 The Selection Oerator In this study, fitness roortionate selection was used, combined with tournament selection Fitness roortionate selection is the most basic selection method The exected number of selections for each individual is associated with the ratio of its fitness value to the mean fitness value of the oulation This method is similar to the roulette wheel in a casino In tournament selection, before executing the selection oeration, the individual with the highest fitness value in the arent oulation is selected as the global best individu-

7 696 The Oen Cybernetics & Systemics Journal, 05, Volume 9 Xuan and Yang Fig () Partial ma of the beiing rail transit networ al After comleting the selection and crossover oerations, the best individual of the current oulation is selected as the local best individual who is then comared to the global best individual The individual with the higher fitness value is then selected as the current global best individual After one genetic oeration is comleted, the current global best individual is used to relace the individual with the lowest fitness value in the offsring generation 534 The Crossover Oerator In this aer, uniform crossover was used in which each location on the chromosome bit string was subected to random uniform crossovers with the same robability The secific stes are as follows For one air of arent individuals, whether the crossover oeration needs to be executed is determined according to the crossover robability c If yes, a 0- mas of the same length as the individual is randomly generated, and various segments of the mas determine which arent rovides value for the offsring individual in the corresonding segments, and a new individual is thus generated 5343 The Mutation Oerator The mutation oerator is imlemented by randomly reversing the binary string of a certain allele according to the mutation robability m Secifically, for a given chromosome bit string, s = aa L al, the oeration is: a i = a, if x i i m a i, otherwise i {,,L, L} (7) In this way, the new individual s = a a L a L is generated x i is the uniform random variable corresonding to each gene locus, x i 0, 6 EXAMPLE To verify the effectiveness of the model and the algorithm, in the Win7 oerating system, a rogram imlementing the genetic algorithm was written in Microsoft VBNET Using this rogram, a simle networ comosed of Line, Line, Line 5 and Line 3 in Beiing rail transit system (as shown in Fig ) was subected to the otimization of networ train oeration charts for a certain time eriod (:00- :00) The basic networ data involved in the algorithm (including running times in the section, dwelling times in the station, train running intervals, reentry times, transfer waling times, the volume of transfer assengers, etc) were set according to the actual oerational data of the Beiing rail transit networ The running intervals for each line are shown in Table The values of other relevant arameters are shown in Table Table Train running intervals of each line (:00-:00) Rail Transit Line No No No 5 No 3 Train Running Interval 4min 5min 6min 7min For all lines, the coordination direction is set to be downbound The results obtained after running the rogram are shown in Table 3 After otimization, the total cost of transfer wait times for all the assengers in this rail networ from :00-:00 was However, according to the current daily train

8 The Otimization Model and Algorithm for Train Connection The Oen Cybernetics & Systemics Journal, 05, Volume Table Parameter assignment for the genetic algorithm RT N c m GN min GN max F % 067min % Table 3 No of Line No No No5 No3 Otimization results Direction of Line The Dearture Time of the First Train U-bound :04:00 Down-bound :03:00 U-bound :04:00 Down-bound :00:00 U-bound :05:0 Down-bound :05:00 U-bound :00:30 Down-bound :05:00 The Value of the Obective Function schedules, the value of the obective function is Therefore, using the model and the algorithm roosed in the resent aer for the otimization of the networ train schedules, the value of the obective function was reduced by 359% Thus, it is roven that the method roosed in this study is effective Because this examle only includes 4 lines, the number of feasible solutions is 360; it would be ractical to aly the exhaustive search method to obtain the otimal solution A rogram imlementing the exhaustive search method was then written in Microsoft VBNET It was found that the otimal result obtained using the exhaustive search algorithm was the same as that obtained using the genetic algorithm Hence it is roven that the genetic algorithm roosed in this aer is feasible and effective in solving the otimization model CONCLUSION In order to imrove the assenger service level of urban rail transit systems under the condition of networ oeration, the oeration management deartment should coordinate and otimize the networ train schedules according to the characteristics of assenger demands in the rail networ, romoting rational connection between different lines at the transfer stations This aer considered the sychology of assenger waiting into consideration and constructed the cost function of transfer wait times On the basis of meeting the actual transfer assenger demand, this study roosed an otimization model for train connections at transfer stations in urban rail transit networs, so that benign interactions between the train flow and assenger flow can be established In addition, a genetic algorithm was designed to solve the model Finally, an actual rail networ was used as an examle to verify the effectiveness of the model and the algorithm The roosed method can rovide theoretical suort and ractical guidance for the otimized rearation of train schedules (timetables) in urban rail transit networs This heled in solving the existing roblem of the lac of coordination in the current rearation of train schedules, and romoted the formation of a good cooerative relationshi between different lines in terms of assenger transfers within the rail networ In the future studies, we will consider train delays in order to imrove the reliability of otimization results of train connection CONFLICT OF INTEREST The authors confirm that this article content has no conflict of interest ACKNOWLEDGEMENTS This wor was financially suorted by the National Natural Science Foundation of China (540833) and Zheiang Provincial Natural Science Foundation (LQ3G0000) REFERENCES [] P Charoborty, K Deb, P S Subrahmanyam, Otimal scheduling of urban transit systems using genetic algorithms, Journal of Transortation Engineering, vol, , 995 [] CY Ma, Timetable coordination and otimization for transfer stations in urban rail transit, Beiing Transortation University, 00 [3] RCW Wong, T WY Yuen, and K W Fung, Otimal timetable synchronization for rail mass transit, Transortation Science, vol 4, no, 57-69, 008 [4] P Vansteenwegen and D Van Oudheusden Develoing railway timetables which guarantee a better service Euroean Journal of Oerational Research, vol 73, , 006 [5] P Vansteenwegen and D Van Oudheusden Decreasing the assenger waiting time for an intercity rail networ, Transortation Research Part B, vol 4, , 007 [6] C M Kwan, and C S Chang, Timetable synchronization of mass raid transit system using multiobective evolutionary aroach, IEEE Transactions on Systems, Man, and Cybernetcs Part C: Alications and Reviews, vol 38, no 5, , 008 [7] M Zhang, and SM Du, Transfer coordination otimization for networ oeration of urban rail transit based on hierarchical reference, Journal of the China Railway Society, vol 3, 9-4, 009 [8] XH Fang, Study on coordination theory and method of train oeration on urban mass transit networ, Beiing Transortation University, 00 [9] YF Zhou, LS Zhou, and YX Yue, Synchronized and coordinated train connection otimization for transfer stations of urban rail networs, Journal of the China Railway Society, vol 33, 9-6, 0

9 698 The Oen Cybernetics & Systemics Journal, 05, Volume 9 Xuan and Yang [0] YF Zhou, Study on integration train timetabling theories and method for urban mass transit networ, Beiing Transortation University, 0 [] MQ Li, and JS Qou, Basic theories and alication of the Genetic Algorithm, Science Press, Beiing, 004 Received: Aril 0, 05 Revised: May 3, 05 Acceted: June 06, 05 Xuan and Yang; Licensee Bentham Oen This is an oen access article licensed under the terms of the Creative Commons Attribution Non-Commercial License (htt://creativecommonsorg/- licenses/by-nc/40/) which ermits unrestricted, non-commercial use, distribution and reroduction in any medium, rovided the wor is roerly cited