a simulation-based optimization approach to...

Scientia Iranica A (2018) 25(2), 646{662

Sharif University of TechnologyScientia Iranica

Transactions A: Civil Engineeringhttp://scientiairanica.sharif.edu

A simulation-based optimization approach torescheduling train tra�c in uncertain conditions duringdisruptions

M. Shakibayifara;�, A. Sheikholeslamia, and F. Cormanb

a. Department of Transportation Engineering and Planning, School of Civil Engineering, Iran University of Science & Technology,Narmak, Tehran, P.O. Box 1684613114, Iran.

b. Department of Maritime and Transport Technology, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands.

Received 5 May 2016; received in revised form 10 August 2016; accepted 12 November 2016

KEYWORDSTrain rescheduling;Simulation-basedoptimization;Train delays;Dynamic priority;Blockage.

Abstract. Delays and disruptions reduce the reliability and stability of the rail operations.Railway tra�c rescheduling includes ways to manage the operations during and after theoccurrence of such disturbances. In this study, we consider the simultaneous presence oflarge disruptions (temporary full or partial blockage of tracks) as well as stochastic variationof operations as a source of disturbance. The occurrence time of blockage and its recoverytime are given. We designed a simulation-based optimization model that incorporatesdynamic dispatch priority rules with the objective of minimizing the total delay time oftrains. We, moreover, designed a variable neighborhood search meta-heuristic scheme forhandling tra�c under the limited capacity close to the blockage. The new plan includesa set of new departure times, dwell times, and train running times. We evaluated theproposed model on a set of disruption scenarios covering a large part of the Iranian railnetwork. The result indicates that the developed simulation-based optimization approachhas substantial advantages in producing practical solution quickly, when compared tocommercial optimization software. In addition, the solutions have a lower average andsmaller standard deviation than the currently accepted solutions, determined by humandispatcher or by standard software packages.

© 2018 Sharif University of Technology. All rights reserved.

1. Introduction

Railway systems are frequently characterized by high ow density and mixed tra�c, which makes themsensitive to various types of disturbances [1]. Railwayrescheduling deals with disturbances that create delays

*. Corresponding author.E-mail addresses: m [email protected] (M.Shakibayifar); [email protected] (A. Sheikholeslami);[email protected] (F. Corman)

doi: 10.24200/sci.2017.4186

of some trains in the rail network. Rail transit systemsseek to schedule trains in order to avoid passengerdissatisfaction and improve service reliability [2]. Theimpact of larger disturbances (termed disruptions) ismore pervasive and can propagate easily in time andspace. In this situation, there is a need to updateand re-schedule train services in a short period. Trainrescheduling problem is a dynamic decision-makingprocess that involves dispatching decisions. The sim-plest decisions are based on the planned timetable or-der, or static priorities (di�erentiating between classesof train services); however, in general, better decisionsare made based on actual data of the trains, real-time

M. Shakibayifar et al./Scientia Iranica, Transactions A: Civil Engineering 25 (2018) 646{662 647

information of the disturbance, as well as operationalconstraints. Furthermore, the exact time and locationof the disturbances may not be known in advance [3].These facts bring many di�culties in designing traindispatching actions or policies.

The present research is motivated by the situationwhere the recovery of the train services is of ourconcern. In Iranian railway network, the importantreasons for train delays are infrastructure failure, ac-cident, engine breakdown, and unpredicted weathercondition. Because of the complexity and dynamicbehavior of the train tra�c rescheduling, simulationmodelling has become an e�ective method to assessthe e�ectiveness of train rescheduling strategies. Sim-ulation models are powerful tools to support resolvingpath con icts in train rescheduling problem [4]. The in-tegrated simulation models and optimization methodsare able to address the complexity of real-time trainrescheduling problems [5]. We argue that the stochasticfactors, pertaining to small variations, as much aslarge disruptions, should be instead studied in moredetail. To this end, we propose a simulation modelingin combination with an optimization procedure, whichsolves the train-rescheduling problem under uncertainoperating conditions and in case of facing large disrup-tions.

Simulation modeling approaches have been usedextensively in transportation applications as a exibleand powerful method to evaluate the robustness andreliability of the system (see [2,6-14]). However, despitethe fact that the train-rescheduling problem has beenanalyzed extensively, a limited research has been di-rected to the combination of simulation platforms withadvanced search techniques to solve train-reschedulingproblems under uncertainty. By using advanced and exible simulation systems to control trains, improvedmanagement of the rail transportation will be easy.Optimization models are also trying to minimize thecost of delay, �nding solutions to repair and restorethe disrupted scenarios and improve tra�c ow oncongested bottlenecks in the rail networks. A solutionhas to respect railway operational rules and capacityconstraints, partial or full blockage during the disrup-tion, and minimum headway constraints. The objectiveis to minimize the total average delay time of trains atrail stations. The main contributions of this study lie,therefore, in the subject of microscopic disruption man-agement under uncertain conditions. First, we developa exible stochastic simulation model, which we usefor generating disposition schedules following principlesacceptable to the local dispatchers (priorities) in avery short time. Secondly, a dynamic priority ruleis proposed to accelerate the performance in terms ofspeed and convergence of the search algorithm. Third,a two-stage optimization method is proposed basedon meta-heuristic search, which further minimizes the

delays, with particular focus on the disrupted areas.We also show that the combination of the dynamicpriority rule with the meta-heuristic gives particularlygood results.

The remainder of the paper is organized as fol-lows. Section 2 presents a review of models andapproaches to railway tra�c rescheduling. In Section 3,the problem is described in detail. Afterward, thedetails of the methodology are presented in Section 4.The framework of the simulation method is discussed inSections 5. We describe a real case in Section 6 to setup a comprehensive experimental study in Section 7.Conclusive remarks will close the paper in Section 8.

2. Literature review

The train rescheduling problem is known to be stronglyNP-hard [15]. The management of train timetable is acomplex procedure subject to the capacity and resourceconstraints [16]. This problem belongs to a wide-range class of combinatorial optimization models andmethods being called railway disruption management.Railway disruption management mainly refers to themodels and approaches used in the railway real-timetra�c management [17]. A variety of approacheshave been proposed, ranging from mathematical opti-mization (mixed-integer linear programs) to simulationtechniques, heuristic and meta-heuristic methods. Allthose methods have shown their value in practiceto evaluate the stability of the disturbance recoverystrategies, or to generate near-to-optimal solutions ina reasonable computation time. Coverage surveys ofrailway disturbance management practice and theorycan be found in [18-21]. In what follows, we discuss themost related contributions in this area of the research,according to the general structure proposed in thislatter survey paper.

Cheng [22] proposed a new integrated approach ofa knowledge-based system with an operation researchtechnique to solve train rescheduling problems. Thecritical path method was used to �nd near-to-optimumsolutions. In order to reach a global optimum, afeedback control function was designed to managethe delay and resolve the resource con icts. Theproblem of controlling and coordinating rail tra�cin a whole railway network is too hard to tacklein a reasonable time. Higgins et al. [23] applied alocal search heuristic with an improved neighborhoodstructure, genetic algorithms, tabu search and twohybrid algorithms for train-scheduling problem. Thecomputational result indicates that both hybrid algo-rithms provide better results compared with the otherheuristics. A decision support system called ROMAwas designed and implemented by D'Ariano [24] basedon Alternative Graph (AG) techniques to cope withreal-time train rescheduling problem with multiple

648 M. Shakibayifar et al./Scientia Iranica, Transactions A: Civil Engineering 25 (2018) 646{662

delays more e�ciently. The aim was to improvepunctuality through better utilization of the railwayinfrastructure. The applicability of the ROMA wasveri�ed through extensive computational tests on in-stances of the Dutch railways. ROMA system was�rst implemented to optimize railway tra�c within asingle dispatching area. The system was extended byCorman et al. [25] to present an innovative distributedapproach to manage train movements more e�ectivelyin a multi-area dispatching setting. The performanceof the distributed approach was compared with theexisting models in terms of computation time andreduction of total delay.

Corman et al. [26] proposed a novel approachto deal with multiple train classes in train reschedul-ing problem. An e�cient scheduling procedure wasadopted in order to generate feasible train timeta-bles according to a set of priority classes. In eachstep, an advanced branch and bound algorithm wasused to solve the sub-problems optimality. D�undarand S�ahin [27] designed a decision support systemusing Genetic Algorithms (GAs) and Arti�cial Neu-ral Networks (ANNs) for real-time con ict resolutionproblem. The methodology was tested with actualdata extracted from train operations in Turkish StateRailways. Hassannayebi and Kiaynfar [28] proposedthree meta-heuristic algorithms based on Greedy Ran-domized Adaptive Search Procedure (GRASP) for�nding a near-optimal train timetable in double-trackrailway lines. The output results show the e�ectivenessof the proposed meta-heuristic algorithm in solvinglarge-sized instances of the train-timetabling problem.Dollevoet et al. [29] proposed an optimization methodthat solves a macroscopic delay management problemas well as a microscopic train scheduling model. Theheadway constraints were captured in the model withfull details of the railway infrastructure, especiallywithin the stations. The resulting disposition timetablewas evaluated thoroughly for a bottleneck segment ofthe rail network. Some studies integrate the conceptof priorities, easily understood and accepted by practi-tioners. Hassannayebi and Zegordi [30] proposed vari-able and adaptive local search algorithms to minimizethe total and maximum waiting time of the passengersfor urban rail transit systems. Narayanaswami andRangaraj [3] designed a multi-agent system model witha learning mechanism for real-time train reschedulingin a bi-directional railway tra�c on a single-track route.The developed framework employs a dynamic schemeof priority assignment procedure that allows for dy-namically dispatching the disturbed trains in real-timeand constructs a deadlock-free disposition schedule.Hassannayebi and Zegordi [31] proposed linear andnonlinear mathematical models for train schedulingproblem. In order to tackle large-sized instances ofthe problem, variable neighborhood search approaches

were designed. The e�ciency of the meta-heuristicalgorithms was veri�ed through its application to theTehran metropolitan network.

The topic of railway rescheduling has attracted at-tention mostly concerning small delays, while the studyof large disruptions and inclusion of many stochas-tic factors have been limited so far. The dynamicchanges over time, in those situations, are quite strong;there needs to be an inherently dynamic environment,proposing adjustments such as rescheduling and par-tial reordering during operations, which is currentlyto be found in simulation environments. Therefore,despite the interesting scienti�c results reached byoptimization models, there is a need to develop exiblesimulation systems able to evaluate di�erent partialreordering possibilities. Furthermore, the trade-o� be-tween delivered schedule quality and the reschedulingprocess time is of critical importance in the practicalimplementation of a train-rescheduling tool. On theother hand, even though several simulation modelshave been developed for rail operation managementformerly, an acceptable solution with regard to inclu-sion of optimized asynchronous choices has not beenattained in this aspect. To the best of our knowledge,a direct application of the exible simulation-basedoptimization approaches to train rescheduling problemhas not been found in the literature; if so, it has notbeen addressed to the same extent that accounted inthe present study.

With particular regards to uncertain e�ects ofsmall delays and large disruptions, we merge thedescriptive power of stochastic simulations with theeasily-accepted priority-based scheduling for disruptionmanagement. We present an advanced discrete-eventobject-oriented simulation model, implemented on acommercial event-driven simulation package. In orderto optimize the performance measures, a variableneighborhood search technique is proposed to improvesolutions under the strong capacity limitations dueto the disruption. The developed simulation-basedoptimization approach has the exibility of adjustingtrain operations under time and resource constraintsin an e�cient way.

3. Problem statement and formulation

This section provides the problem statement and thenotations used for the train-rescheduling model. Themain assumptions and characteristics of the problemare given in Table 1. It is assumed that an initialtimetable for trains on the network or by the sim-ulation model presented in this study is given. Atthe starting moment of the disruption, the trains arein a position, considered known, and set as datainputs for the simulation model. The considered railinfrastructure is illustrated in Figure 1. It includes a


Table 1. Assumptions and characteristics of the problem.

Assumptions Description

Rail infrastructure A corridor with single or double-track segmentsDisruption Temporary partial or full blockage

Disturbance management strategies The sequence of trains at the disruption site and elsewhere is changedOvertaking is permitted at stations with available capacity

Train types Passenger railwayPriority of trains Di�erent and variable over timeTravel time function per train ProbabilisticRail capacity at stations Limited (taking into account the number of tracks and platforms)Signaling systems Absolute �xed block signaling system between stations

Figure 1. The considered rail infrastructure.

set of stations (k = 1; 2; � � � ;m) and a set of operatingtrains (i = 1; 2; � � � ; n). The segments between eachpair of stations are single/double-track block sections.We consider absolute �xed block operations betweenstations by which block sections begin and end only atstations. Only one train is allowed on a track betweentwo stations. An overtaking operation is allowed onlyat stations.

During the normal operations, a train can movefrom the current station if the successor block sectionis available and there is at least one free track segmentin the next station (absolute �xed block operationsbetween stations). When a disruption occurs in ablock section, the train tra�c is heavily perturbed.At that moment, the main goal is to provide a newdisposition schedule for all operating trains at the endof the scheduling horizon, so that the total delay cost isminimized. The model proposed in this study producesnew disposition schedule from a combination of thefollowing actions (in the vicinity of the disruption, orelsewhere): reordering (changing the sequence of trainson the block sections), adjusting the departure times,and changing the stop times at stations.

A main constraint is that at stations, a train is notpermitted to depart, in any case, before its scheduleddeparture time. A con ict happens when at least twotrains request to use the same block section at the sametime. In this case, a con ict resolution procedure isrequired to decide on the ordering of the trains. Thisprocedure aims locally (or globally) to decrease thetotal delay of the trains. The total delay is de�ned

as the di�erence between the actual train arrival timeand the scheduled time at a set of prede�ned stations inthe network. Total delay of a train consists of two partstermed as initial delay and secondary delay. The initialdelay is triggered by disruptions and longer travellingtime and cannot be recovered by rescheduling model.The secondary delay is the extra delay needed to resolvethe potential con icts during a planning time horizon.In this study, the train-rescheduling model considersdynamic priority of trains during disturbed operationsin order to minimize the total delay of the trainservices. The next section provides the assumptionsmade on the train operations during both normaland degraded modes. Before the disturbance occurs(normal condition), the railway capacity utilizationis at the regular level. In the �rst state (normal-to-disrupted situation), the utilization necessities tobe reduced to achieve a utilization level that can bereserved during the disturbance. During the secondtransition state (disrupted situation), the disruptionrecovery actions should start. In this state, the newtimetable is functioned and the utilization level issteady. The third state (disrupted-to-normal) changesthe utilization level to the normal condition. In ourresearch, the focus is on the second and third transitionstates.

3.1. Train operation modeling during normaloperation

This section provides the assumptions made on thetrain operation during the simulation experiments.


The stochastic parameters here are train-running timeson block segments. We consider a stochastic simulationmodel to account for the inherent and relevant proba-bility distribution of the running time. In this regard,a stochastic distribution of train running times isestimated and used instead of the commonly considereddeterministic running time. The normal distribution,thus, proved to be a good model for the large arrayof phenomena, which can be found in real-life opera-tions [32]. The probabilistic train-running time distri-butions are �tted at a given level of signi�cance (95%).From the statistical analysis, we conclude a good �tof the experimental data with the normal distribution.All the data sets show that the running times betweenconsecutive stations �t the normal distribution at thelevel of signi�cance of 0.05 according to Kolmogorov-Smirnov (KS) statistical tests. Thus, the hypothesis ofnormal distribution is not rejected at the desired levelof signi�cance. However, in order to make the runningtime distribution more practical, we truncated thetravel time function using the maximum train speed.

In order to formulate the running time function,we consider distances between any consecutive stationsk and k+1(Lk). Let � and � be the mean and standarddeviation of the running time distribution. We assumethat the running time of train i between consecutivestations k and k + 1(tik) follows a normal distributionwith average � = Lk

V avei

and variance �2 (minutes2),where V ave

i and V maxi are de�ned as average and max-

imum speeds of train i, respectively. The variance canbe determined through sampling methods. It should benoted that the running times between stations cannotbe less than the minimum technically feasible. Thus,to ensure that all trains cannot exceed their maximumtechnically speed, the minimum running time ( Lk

V maxi

)is de�ned in Eq. (1). A similar running time functionwas proposed by Nie and Hansen [33]:

tik=max�

Normal�LkV avei

; �2�;LkV maxi

�8 i; k:

(1)

3.2. Train operations during disruptionsAn infrastructure failure occurring in the route istermed disruption, or degraded mode. Without lossof generality, consider a single-track segment of arailroad line between two major intersections as shownin Figure 2. The dispatching rules on this single-track segment manage the movement of trains for both

directions. Di�erent dispatching policies will causedi�erent amounts of delays for trains. In this research,the length of the train is not considered. The e�ectof train length on train delay would be insigni�cantif the distance of the track segment is much lengthierthan the length of the train. It is assumed that thedisruption occurs at one block section and degradesthe tra�c in partial or in full. According to railwaysafety rules, no more than one train at a time ispermitted to dwell in any block section (referring tothe con ict-free situation). In this article, we focuson two frequent degraded modes in railway systems.In the �rst degraded mode (full blockage), the normaloperation of a single-track block section is disrupteddue to an incident between two neighboring stationsas illustrated in Figure 2. In this �gure, the tra�c ow under normal condition and the location of servicedisturbance are depicted. As can be seen, there is nopossibility of passing during the disturbance. However,during the normal condition, the tra�c between twoconsecutive stations is bi-directional. After recoveryof the disturbance, trains start normal operation onthe single-track segment. According to the acceptedoperational rules in Iran, the allowed control actions inthis case consist of retiming or re-routing the incomingtrains toward the disturbance location, while there is nopossibility for cancelling or short-turning trains. Thus,in the �rst degraded mode, the main decision variablesare which train should be reordered, or delayed at whatlocations.

The second degraded mode is a blockage of onetrack out of a double-track block segment (Figure 3). Inthis situation, trains moving toward the disrupted areacan bypass the blockage and after traversing a numberof switch points, they go back to the original route. Thereordering policy (as illustrated in Figure 3) enables thewaiting train to switch to the bypass direction track.Crossover tracks allow trains to be transferred from onetrack to another, enabling trains to bypass the incidentlocation. During the disruption, the system e�ectivelybecomes a single-track between two consecutive switchpoints, and the trains requesting to pass through thispart of route wait at stations until the single line issuitable for their trips. After the blocked track isrepaired (which might take a long time), the systemagain becomes a two-parallel-track line, and tra�c owreturns to normal. The con ict resolution of trainon the single-track segment involves sequencing the

Figure 2. The line blockage in the degraded mode #1 .


Figure 3. Train services on the single-track segment during degraded mode #2.

inbound and outbound trains. Thus, the optimizationmodel aims to �nd the best crossing order of thewaiting trains and the related times of operations. Wefocus particularly on �nding the order of crossing thedisrupted area, as we experimentally found out that ithas a major in uence. To this end, we de�ne meta-heuristic procedures, explained in the remainder of thepaper.

4. An object-oriented event-driven simulationframework for train rescheduling

Discrete event simulation systems are extensively usedfor modeling the behavior of a complex dynamic systemwithin a discrete time framework based on an event list.An event indicates the occurrence of a change in thestatus of the rail system at a speci�c time. Di�erentmodeling approaches, e.g. process-oriented [9,34] andobject-oriented [35,36], can be used for railway sys-

tems. The object-oriented simulation model providesa exible build-in framework that supports the designprocess of railway network layout. In the presentstudy, we use Enterprise Dynamics (ED) simulationsoftware as a simulation platform due to its capabilityof designing customized rail objects and ability toimplement optimization algorithms. Enterprise Dy-namics is a leading object-oriented simulation platformto design and implement simulation models [37]. It hasalso a built-in programming language called 4DScript,which can be used for advanced modeling purposes.Another application of the 4DScript is the capabilityof programming, which allows us to include the meta-heuristic optimization approaches right into the simu-lation system [38].

The main procedure of the simulation optimiza-tion of the train dispatching is presented in Table 2.When a train enters a waiting queue, a dispatchingalgorithm is applied to check the operational and safety

Table 2. The main procedure of the simulation-optimization.

Step 1: Initialize necessary simulation parameters(Con�dence level 1� �, number of replications)Set simulation clock (t = 0)Initialize system statePrepare event list (ascending order of time)

Step 2: Perform several simulation runs using dynamic dispatching rulesStep 3: Use a look-ahead procedure to �nd out a new event (either stop at the

current station or move to the next station)Step 4: Update the priority of the train according to the accumulated delay when

it arrives at a stationStep 5: Aggregate simulation results and store them in the databasewhile stopping criteria is not met do

Load aggregated parameters into simulation systemSolve the optimization model using VNSWrite new decision variables corresponded to the re-ordering and adjustedpriority to the databaseLoad new decision rules into simulation modelPerform several simulation runs to evaluate the solutionAggregate simulation results and store them in the database

end-whileLoad the best found solutionsGenerate output reports� New rescheduled train graphs (time-station diagrams)� Estimate the expected value and the variance of the train delays

at destinations.


constraints. If all conditions are satis�ed, then thetrain is allowed to move to the successor block sectionaccording to its route. Else, an event is created toexecute dispatching algorithm and the involved trainwaits in the current position until all conditions aremet. The conditions are the available free track on thenext segment and a free platform for the train that hasa stopping plan at the next station.

5. Simulation-based optimization approach

The proposed two-stage simulation-based optimizationframework for train rescheduling problem is illustratedin Figure 4. As can be seen, it follows a kindof black-box approach to tackle large and complexsimulation-based optimization problems. We considersolutions based on either the static timetable orderor priority based. Furthermore, the priorities canbe static or dynamic. The latter is generally more exible and can deliver better solutions with regardto delays. Concerning dynamic priorities, we restrictourselves to dispatching algorithms that calculate andassign priorities based on time-based parameters. Ourprocedure works in two stages. In the �rst stage,the initial random solutions are generated based onheuristic dispatching rules based on dynamic priority.At this point, the goal is to reach a relatively good newdisposition schedule in order to handle the disruptedtra�c conditions on the route in a short period of time.In the second stage ,the initial generated schedules areevaluated by their total average delays (considered areliability index) via simulations' experiments. Thebest solution from this stage is regarded as a startingpoint for further optimization. A meta-heuristic algo-rithm (variable neighborhood search) is used in order toimprove the solution to the train rescheduling problemalgorithm in terms of mean and variance of delaytimes. During stage 1, due to time constraints, thenumber of simulation replication must be determinedcarefully for solving train-rescheduling problem. The

updated values of the decision variables refer to controlactions such as retiming and reordering of train at railsegments. At each iterative step of the meta-heuristicoptimization algorithm, a set of new departure times isdecided, and a new tentative schedule is tested by thesimulation model. Given a train scheduling solution,the simulation model obtains statistical bounds on theobjective value, and the optimization model iterativelyimproves the expected value until the time limit isreached. At the end of each simulation run, the currentsolution is evaluated based on the quality and reliabilitycriteria. The process continues to achieve a desiredresponse plan with respect to time constraint. Theobjective function is de�ned as the total average delayof train services at all visiting stations.

5.1. Dynamic priority rule-based heuristicThis sub-section gives the explanation regarding howto resolve the con icts and generate good-quality initialrescheduled plans rapidly by means of dynamic priorityscheduling. For this purpose, heuristic dispatchingrules are proposed that change the priorities of theoperating trains dynamically in order to reduce the sec-ondary delays. As we observe, train dispatchers in dif-ferent railway companies mostly perform a preference-based process of con ict detection and resolution. Thetraditional dispatching rules do not take into accountthe updated information of the trains and may fail to�nd appropriate solutions. Consequently, it is essentialto recognize the decision-making process in order todevelop innovative con ict resolution models. Theapplication of the dynamic priority rule-based modelpresented in this study seems to be an e�ective methodto meet this objective. In what follows, we explainour method of train con ict resolution. As mentionedearlier, an initial static priority class is assigned to eachtrain before the implementation of the reschedulingprocedure. In the simulation experiments, the staticpriority class is then updated in order to further adjustthe importance and urgency of the train service to-

Figure 4. The proposed two-stage simulation-based optimization framework for train rescheduling problem.


Table 3. Notations used in dynamic priority rule-based heuristic method.

Symbol De�nitionpi The initial priority of train ifi The accumulated delay of train iai The allowed (maximum) delay of train i�i The surplus delay regarding the maximum allowed delayU The utility functiona0i; a1i The start and end break points of the utility functionL The total number of train con icts in the schedule

wards the objective value. Our dynamic priority-basedtrain rescheduling is a type of scheduling algorithmin which the train priorities are computed during theexecution of the simulation model. The main goalof dynamic scheduling is to adjust to dynamicallydispatching order and design a good quality solutionin an adaptive approach. The proposed frameworkis an iterative probabilistic procedure for determiningthe dispatching priorities. The dynamic priority of aspeci�c train is calculated as a function of the initialpriority class, the actual (accumulated) delay, and theallowed (maximum) delay time. Notations of dynamicpriority rule-based heuristic are summarized in Table 3.Every time a con ict happens, one train should bedelayed to resolve the con ict. The resolving of thecon icts is mainly based on train priorities. Theproposed dynamic priority rule preserves the overalldelay of the trains and resolves the train con icts in ashort period.

The initial values of the train priorities are basedon the train classes. The adjusted priorities imposeadditional challenges on the optimization problem sothat the priority of a particular train may changeseveral times during a single simulation run. In the�rst step of the heuristic method, a new con ict-freedisposition schedule is constructed through a con ictresolution model by the adjusted priorities. An initialtrain schedule is represented by a set of potentialcon icts (C). Cj represents the jth con ict as it occursin time. Train con icts are resolved according to therelative priority ratio chronologically. The adjustedpriorities are calculated according to the calculatedvalues of accumulative delay of trains. A piecewiselinear utility function (U) is used to determine theadjusted train priority in terms of the deviation fromthe allowed delay. The train priorities update wheneverthey depart from or arrive at stations according toEq. (3). U(x) consists of K linear pieces joinedtogether at breakpoints 0 � di � 1. The priorityof the trains increases when the accumulated delayexceeds the allowed delay. Using the initial set of trainweights or initial priority, it is possible to calculatedynamic priority, pi, of any train, i; a con ict isresolved according to their value with a higher valueresulting in a higher priority to reserve the path. In

the second step, the objective function of the generatedsolution is measured by the reliability criteria. Oncethe limit is reached, the heuristic algorithm terminatesand provides the best solution found by the heuristicmethod. We consider a time limit of 10 minutes toexecute the algorithms:

C = fC1; C2; � � � ; CLg; (2)

pi pi+U(maxffi�ai; 0g)=pi+U(maxf�i; 0g);(3)

U(x) = a0k + a1kx; (4)

dk�1 � x � dk; k = 1; 2; � � � ;K: (5)

5.2. Variable neighborhood search algorithmIn this section, we explain the proposed variableneighborhood search algorithm. This is speci�callyintroduced to deal with the strong shortage of capacitynear the blockage, which asks for more sophisticatedoptimization approaches. The Variable NeighborhoodSearch implemented here �xes the full order for trainsgoing on the disrupted area, possibly overriding (dy-namic) priorities. In the improvement stage of theproposed two-stage simulation-based optimization ap-proach, a local search algorithm is required to performa sequence of local moves in neighborhood N(x) ofinitial solution x to improve the performance valueuntil a local optimum solution (x0) is obtained. Thebasic function of the local search algorithm can be im-proved in order to avoid trapping in local optima. Oneof the most practical extensions of the local search isVariable Neighborhood Search (VNS). In this method,the systematic changes in neighborhood structure areperformed to escape from the local optima. VNSmethod was originally introduced by Mladenovi�c andHansen [39]; after that, it received increasing attentionboth in theoretic extension and large-scale optimizationproblems [40]. VNS has been applied to a wide-range of combinatorial optimization problems includingcapacitated vehicle routing problems [41].

The notations are given in Table 4 to betterexplain the method. Moreover, the pseudo codeof the proposed variable neighborhood (a Variable


Table 4. Notations of the proposed VND method.

Symbol De�nition

k The counter of the neighborhood structures (k = 1; 2; � � � ; kmax)kmax The total number of neighborhood structuresx The candidate solution for local searchxo The initial solutionxbest The best incumbent solutionNk(x) The set of solutions in the kth neighborhood structuresF (x) The �tness functionRp The number of simulation replications to evaluate the objective functioni The index of algorithm iterationItermax The maximum algorithm iterations

Table 5. Pseudo code of the proposed variableneighborhood search method for train rescheduling.

1 Input (kmax; xo; Itermax; Rp)2 x := xo;3 i := 1;4 k := 1;5 While i � Itermax do6 While k <= kmax do7 x0 := BestImprovement (x; k);8 F (x0) := simulation (Rp; x0);9 i := i+ 1;10 If F (x0) < F (x) then11 xbest := x0;12 k := 1;13 Else14 k := k + 1;15 EndWhile16 k := 1;17 EndWhile18 Return (xbest);19 End.

Neighborhood Descent (VND)) method, in the termi-nology of Mladenovi�c and Hansen [39], is provided inTable 5. In our implementation, the search methodchanges the neighborhoods in a deterministic way. TheVNS algorithm starts with the best-found solutionsfrom the �rst stage optimization. VNS algorithmsstart with iteratively changing the properties of anincumbent solution. A neighborhood search heuristic isperformed by picking initial solution, xo, determininga search direction of descent from this solution withina neighborhood, N(x), and continuing to the minimumof F (x) within neighborhood space, N(x). In Step 7,neighborhood N(x) of x is explored completely. Thehighest direction of descent is related to be the best

Table 6. Pseudo code of best improvement (highestdescent) heuristic.

Function BestImprovement (x)1 repeat2 x0 x3 x argminfF (y)g; y 2 N(x)4 until (F (x) � F (x0))5 return x

improvement that is summarized in Table 6. Theprocess of a move from a basic solution to a possiblybetter one is guided by the evaluation of the �tnessfunction value. Since the problem considered in thisstudy has a stochastic nature, each potential solutionof the problem is evaluated using the discrete-eventsimulation model. In Step 8, the simulation function isemployed to evaluate each solution like x. The result isthe average �tness value of the solution that is storedin F (x).

In what follows, the neighborhood structuresproposed in this paper are described in detail. Amove alters the current solution to the neighboringone by shifting the relative order of some trains. Wepropose a combined remove-insertion with a variablestep-size mechanism to alter the order of trains. Inorder to explain better the way that the search methodperforms, we provide an illustrative example. In thisexample, six trains approach the disrupted location.We report them along a time axis (horizontal) andspace axis (vertical), with two stations; trains canovertake each other only at stations. Thus, each train(a � f) is a line crossing the diagram from top tobottom, or vice versa. The blockage has occurred ona single-track segment between stations k and k+ 1 asillustrated with a shaded rectangular block in time andspace. Let fa; b; c; d; e; fg be the initial order of trainincoming to the disturbance location. Each of themhas an origin and an initial priority (P0). If there isno change in the train orders, then the resulting time-


Figure 5. The disposition schedule based on the static train order.

Figure 6. The disposition schedule associated to one neighbor with k = 1 (train b).

Figure 7. The disposition schedule associated to one neighbor with k = 3 (train a).

station graph is illustrated in Figure 5. In this graph,the train departs with the same order and follows theFirst-Come, First-Serve (FCFS) dispatching rule.

Now, consider the case that train order changes byinsertion operators. The kth neighborhood structureis de�ned as the neighbors described by k shiftsperformed in the train orders. For example, the �rstneighborhood structure only performs one shift in thesequence. In this case, a single train is selected ran-domly, removed from the sequence, and inserted eitherimmediately before or immediately after its originalposition. For example, an adjusted sequence using one-step move operator is fa; c; b; d; e; fg where train b isselected and inserted after train c (Figure 6). Anotherexample is to perform a three-step (k = 3) move.Assume that train a is removed from the sequenceand inserted after train d. The adjusted train orderis fb; c; d; a; e; fg as illustrated in Figure 7. As can beseen, train a faces with the highest delay after the orderadjustment.

In the cases presented in Figures 5 to 7, each sta-tion (between segments k and k+1) hosts three trains.

In longer blockage periods, station capacities may beinsu�cient to host all the visiting trains. We explainhow simulation model deals with these occasions. Incase of higher tra�c volume, the trains must wait atthe former stations to be ready to dispatch when thenext station has a free track (or a free platform in caseof passenger load/unloading). The main objective ofapplying the above-mentioned moves is the attempt torecover the train schedule in terms of reducing totalaverage delay time. In this regard, the validity of theproposed solution method is demonstrated in the nextsection.

6. Test case description: Tehran-Razi corridor

6.1. InfrastructureTehran-Razi corridor is considered as a case study.This corridor is one of the most congested ones in Iran.The infrastructure considered is a main part of therailway network in the west of the Iran. As presentedin Figure 8, the network is composed of three majorstations with dense tra�c: Tehran, Tabriz, and Razi.


Figure 8. The considered Iranian railway network (Tehran-Tabriz-Razi corridor).

Table 7. The priority classes of static priority set S.

Priorityclass(wi)

Train typedescription

Numberof trains

1 Local 122 Intercity 163 Express 18

Other intermediate stations in the network are alsoconsidered in our simulation model. The line betweenTehran and Razi (eastbound route) serves the two maintra�c directions to Tehran (westbound route). Thenetwork comprises a combination of single and doubletracks of di�erent length, with a maximum distancebetween two end stations of about 930 km. Tehran-Razi corridor consists of 62 stations, 57 single-trackblocks, and 4 double-track block sections. The totalnumber of daily operating trains is 46. Overall, thereare more than 202 track segment and 90 platforms(i.e., track segments and platforms are actually usedat stations). The networks operate based on absoluteblock operations, i.e. only one train is allowed at alltimes in the segment between two stations for eachtrack. The prede�ned classes of the static priority setare given in Table 7.

6.2. Disruptions scenariosDue to the unknown nature of the disruptions, di�erentpossibilities for the start time and location of thedisturbance are probable. We consider the moste�ective disruption scenarios, which start before themost congested period of the day, in the bottleneckswith the highest tra�c. Formally, we identi�ed thoselocations and times by computing a Congestion Factor

(CF) as the number of train con icts in a scheduleduring a speci�ed interval. Because of the high den-sity of tra�c through bottleneck segments, the bu�ertimes added in the initial timetables are de�cient toabsorb train delays caused by unpredicted disruptions.According to the above explanation, the identi�ed testcases are summarized in Table 8. The disruptionscenarios are characterized by the location, type of thedegraded mode, the expected duration, and hours ofthe blockage.

7. Computational results

7.1. PerformanceThis section provides the computational results on thesimulation model and the meta-heuristic technique pro-posed in this study. The simulation runs are executedvia Enterprise Dynamics 8.2.5. All the experiments areperformed on an Intel(R) Core2 Due personal computerwith 3.3 GHz and 4 GB of RAM.

We report the performance of the proposedVNS method compared with those obtained fromthe simulation-optimization methods embedded in Op-tQuest package. OptQuest is a well-known registeredoptimization solution of OptTek Systems, Inc. (avail-able in www.opttek.com). OptQuest works iterativelyusing a black-box approach as a general-purpose opti-mizer that performs a series of simulation experimentsto �nd optimal or near-optimal solutions. OptQuestutilizes a mix of meta-heuristics algorithms, includingScatter Search (SS), Genetic Algorithm (GA), TabuSearch (TS), and neural network learning algorithms,to �nd the global optimum [42]. In the present study,OptQuest is employed which takes advantage of thedecision-support features of the Enterprise Dynamics


Table 8. The disruption scenarios and the associated speci�cations.

Disruptionscenario #

Location Degraded modeExpectedduration(hour)

Blockageinterval

1 Qazvin-Kohandezh Full blockage 1 7:00-8:002 Qazvin-Kohandezh Full blockage 2 7:00-9:003 Qazvin-Kohandezh Full blockage 3 7:00-10:004 Zanjan-Khorram pey Full blockage 1 2:00-3:005 Zanjan-Khorram pey Full blockage 2 2:00-4:006 Zanjan-Khorram pey Full blockage 3 2:00-5:007 Karaj-Rabet One out of two tracks 2 7:00-9:008 Karaj-Rabet-Aprin One out of two tracks 3 6:00-9:009 Abyek-Ziaran Full blockage 1 20:00-21:0010 Abyek-Ziaran Full blockage 2 20:00-22:00

Table 9. Result of the proposed two-stage simulation-based optimization method versus FCFS and OptQuest solver.

Disruptionscenario

Total average delay (hours) Total traveling time (hours)

FCFS�VNS withdynamicpriority

OptQuest FCFSVNS withdynamicpriority

OptQuest

1 43.01 27.16 32.72 391.43 388.71 393.912 54.32 38.83 42.69 398.19 392.95 397.233 65.83 42.34 47.51 410.58 394.70 398.024 36.38 29.86 33.62 370.42 365.52 370.465 54.73 45.02 47.09 353.62 348.04 358.906 76.17 62.30 71.77 382.66 380.17 383.477 37.05 24.33 29.02 394.98 385.46 391.068 44.00 23.75 32.55 396.45 389.13 386.249 39.23 28.31 31.76 391.61 390.99 394.1210 66.54 44.41 49.82 381.83 394.06 399.77

Average 51.73 36.63 41.86 387.18 382.97 387.32

simulation software with the use of global optimizationalgorithms. The experimental results of the proposedtwo-stage simulation-based optimization method andOptQuest solver are given in Table 9. In this table,two performance metrics are calculated:

1. Total average travelling time;

2. Total average delay.

The cumulative delay time is de�ned as the sum oftotal delays at all relevant locations. It measures forall train the positive arrival time with the due dateemployed to measure the train delay with respect tothe time at which the operation is planned, i.e. thearrival of a train at a planned stop or its plannedexit from a relevant point. The best-found solutionswith 10 minutes of execution are reported in this table.As can be seen in this graph, disruption scenario #6

has the most disruptive impact on the performancemeasure compared with the other disruption scenarios.To compare the computation e�ciencies of the VNSand OptQuest, we recorded the computation time ofthe two methods when solving the train-reschedulingproblem. Both the solution quality and computationalperformance are compared to the OptQuest. Accordingto the data in Table 9, the total average delay time ofall trains at all stops is reduced by almost 12.48% and29.18% compared with the FCFS and the OptQuest,respectively. Furthermore, the total average travellingtime of all trains is decreased by nearly 1.12% and1.09% compared with FCFS and OptQuest, corre-spondingly. It should be noted that the total travellingtime averaged over all test instances is nearly similarfor VNS and OptQuest as well as FCFS.

As mentioned earlier, a two-stage simulation-based optimization method was proposed that incor-


Table 10. Computational results of two-stage VNS versus single-stage and static priority-driven scheduling methods.

DisruptionScenario

Single-stage:VNS+plannedtimetable order

Two-stage:VNS+orders updated

on static priority

Two-stage:VNS with orders updated

by dynamic priority1 29.71 30.98 27.532 44.90 43.82 39.323 45.12 48.66 42.724 32.84 33.29 30.325 47.31 45.48 45.206 67.38 69.01 63.057 26.35 25.58 24.408 28.98 26.39 24.179 29.34 31.18 28.7310 47.75 46.36 44.85

porates a dynamic priority rule-based algorithm to �ndthe initial solutions. In what follows, we analyze theperformance of the VNS without heuristic method, i.e.considering as initial solution the train order speci�edo�ine in the original timetable. This approach isbeing called single-stage VNS throughout the article.Furthermore, it is worth showing the signi�cance ofour contribution by testing the performance of two-stage VNS, i.e. with a starting solution optimized. Inthis case, we refer to a static priority-driven schedulingmethod against the proposed dynamic priority schedul-ing approach. The computational results of two-stageVNS versus single-stage VNS and a static priority-driven scheduling method are given in Table 10. Thistable provides the objective value (the expected valueof the total average delay in hours) of the best-found so-lutions obtained for each algorithm within 10 minutes.The outcomes indicate that the average improvementgained by the dynamic priority method is about 7.6%compared with the single-stage VNS and the two-stageVNS with static priority. As can be seen, the two-stage VNS outperforms the single-stage VNS and staticpriority-driven scheduling methods in all disruptionscenarios. This �nding veri�es the applicability andimprovement of the dynamic scheduling method overthe single-stage VNS and static priority-driven trainrescheduling.

7.2. Convergence analysisIn case of an unexpected disruption, it is vital thatdispatchers speedily provide a good solution in order toreduce the annoyance for the travelers. Thus, a fasterconvergence rate results in a better and more realisticsolution to the real-time train-rescheduling problem.We provide the plot of solution quality against time,which accounts for the convergence analysis of theproposed as well as benchmark algorithms. The searchpro�les of the VNS and OptQuest, which are both

Figure 9. The search pro�les of the two-stage VNS,single-stage VNS, and OptQuest (scenario #6).

iterative procedures, are illustrated in Figure 9. Thegraph shows the best objective value over search timefor scenario No. 6. We remark that the computationtime is analogous to considering the iterations, as eachsimulation replication takes a nearly constant time.The computation result of the proposed VNS plusheuristic method (dynamic priority) illustrates that itcould �nd better solutions with improved computa-tional e�ciency compared with OptQuest. The VNSplus heuristic method (dynamic priority) convergesfaster than the pure VNS as well as the algorithmsof OptQuest to �nd the solution of train reschedulingproblem. It can be seen that the proposed two-stagesimulation-based optimization method is superior interms of solution quality and convergence performance.

7.3. Statistical analysisThis section provides a reliability-oriented evaluationof the generated solutions. As mentioned earlier,the designed system can stochastically evaluate trainschedules by means of simulation. It is important todraw attention to the fact that while train-reschedulingstrategies will aim at optimizing e�ciency, the impactof stochastic variables during a rescheduling procedure


Table 11. Statistical analysis of the best-found solution by VNS under di�erent disruption scenarios.


Total averagedelay time

(hour)

Standarddeviation

(hour)

LBa

(95%)UBb

(95%)

Minimumvalue(hour)

Maximumvalue(hour)

1 27.53 1.14 26.53 28.53 24.09 30.212 39.32 1.81 37.73 40.91 35.93 44.513 42.72 0.57 42.22 43.22 37.83 45.314 30.32 1.41 29.08 31.56 25.51 33.085 45.2 0.69 44.60 45.80 44.55 50.126 63.05 0.59 62.53 63.57 58.89 67.667 24.4 2.83 21.91 26.89 18.35 29.348 24.17 0.14 24.05 24.29 20.87 26.919 28.73 1.18 27.69 29.77 23.79 33.9910 44.85 1.77 43.29 46.41 41.07 49.56

aLB: Lower bound, bUB: Upper bound.

is mostly neglected. In the present study, by applyingdiscrete-event simulations, the solutions are analyzedstatistically in a test environment. The result ofstatistical analysis of the best-found solution underdi�erent disruption scenarios is summarized in Ta-ble 11. The reported results include the expected value,standard deviation, minimum and maximum values,and the value of the (lower and upper) 95% con�denceintervals (reported as LB and UB, respectively). Thereliability of the result is represented by con�denceinterval that indicates the probability (e.g., 95%) thatthe response variable is within the range speci�ed. Forevery performance measure (PFM), observation wi iscollected after each observation period i. Each statisticis estimated based on raw data w1; w2; � � � ; wn, where nis the number of replications [43]. The lower and upperbounds of the Con�dence Interval (CI) are obtained byEq. (6). Values tn�1;1�1=2� and �1�1=2� are obtainedfrom a table of t-values where � = 1� Reliability:

CI =

8><>:�w � tn�1;1�1=2�: spn n � 30

�w � �1�1=2�: spn n > 30(6)

For example, in the �rst scenario, the standard devi-ation of delay time is reduced by 60% compared tothe OptQuest best-found solution. For the secondscenario, the blockage takes 2 hours, and the standarddeviation of delay time decreases by 47% comparedto the OptQuest best-found solution. In the thirdcase, which imposes longer duration of disruption,the standard deviation of the delay time decreasesby more than 40% compared to the OptQuest best-found solution. The result of the simulation modelindicates that the average and standard deviations ofthe delay times are a�ected by the duration of theblockage. Compared to the results in Table 12, the

standard deviation of the delay times calculated withthe proposed VNS method is on average 1.95 hoursless than that with the OptQuest package. It can beconcluded that the approach proposed in this paper hasmore dominant optimizing capability compared withthe OptQuest. From the computational results, wealso conclude that the performance of the proposedsimulation-based optimization method is robust be-cause of the less variance of delays. We also remarkthat the performance of FCFS is much less attractivecompared to the other two; therefore, we skip reportingit in full.

8. Conclusion

Railway systems operate growingly at maximum ca-pacity, timetables are becoming further at risk ofinstabilities, and delays propagate and reduce theservice level perceived by the passengers. This makesreal-time train tra�c planning become more and morechallenging as a result motivating the developing rail-way decision support systems. The procedure ofdisturbance management in rail transportation systemsfaces di�erent challenges, e.g. the irregular occurrencetime, the strong limitation of capacity for long period,and the presence of many other stochastic phenomenaof smaller magnitude occurring in the network. Thisstudy developed an object-oriented discrete-event sim-ulation model, which is able to model heavy disruptionand small stochastic variations due to smaller delays,which optimizes tra�c by means of dynamic prioritiesrules and further employs a variable neighborhoodsearch algorithm as a global con ict resolution methodin order to decrease the total delays after line blockagedisruptions. The computational experiments alongwith a discussion about practical strengths and limi-tations of the proposed simulation-based optimization


Table 12. Statistical analysis of the best-found solution by OptQuest under di�erent disruption scenarios.


Total averagedelay time

(hour)

Standarddeviation

(hour)

LB(95%)

UB(95%)

Minimumvalue(hour)

Maximumvalue(hour)

1 31.31 2.89 28.74 33.88 26.61 38.88

2 40.88 3.45 37.81 43.95 35.86 44.64

3 45.57 0.95 44.72 46.42 39.15 49.96

4 32.71 3.33 29.74 35.68 27.69 40.20

5 46.97 4.94 42.58 51.36 38.86 53.53

6 70.33 2.26 68.32 72.34 66.94 77.42

7 27.92 4.89 23.57 32.27 22.23 37.83

8 30.82 2.64 28.47 33.17 25.25 34.54

9 30.42 2.79 27.93 32.91 28.59 32.41

10 49.59 3.46 46.51 52.67 43.44 57.43

approach were conducted on real-world test cases ofthe Iranian railway network. The outcomes indicatethat the proposed variable neighborhood search meta-heuristic outperforms the commercial OptQuest opti-mization toolbox in both solution quality (delays andtheir deviation) and computational time. Computa-tional results of the developed model on an importantpart of the Iranian railway network illustrate that thesimulation-based optimization approach is capable of�nding near-optimal solutions in a reasonable compu-tation time.

As accounted for the future research, many ofthe modeling characteristics can be adapted to morerealistic situation. One important extension of thecurrent study is to consider the network case. Thedetermination of train priority can be handled througha comprehensive predictive model, or a more abstractoptimization approach could be implemented, based,for instance, on robust or stochastic programming. Inaddition, it is worth mentioning that the simulationmodel can be extended to analysis of other performancemeasures such as punctuality and robustness. Finally,a still open challenge for the railway community is thedevelopment of exact algorithms for scheduling tra�cunder stochastic factors.

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Biographies

Masoud Shakibayifar is a PhD candidate at the De-partment of Transportation Engineering and Planning,School of Civil Engineering, Iran University of Science& Technology (IUST).

He is doing his PhD thesis entitled: \Train Re-Scheduling model for Reducing Delay under Distur-bances". This research focuses on designing simulation-optimization methods for train tra�c rescheduling inrailways systems.

His research interests are railway electri�cation,railway scheduling and rescheduling, and optimiza-tion of transportation systems under uncertainty. Heobtained BSc (1997-2001) and MSc (2004-2006) de-grees in Civil Engineering at Sharif University ofTechnology, Tehran, Iran. He has managed morethan 15 transportation-planning projects in IranianRailway Company and the Ministry of Roads andUrban Development. Recently, he has managed aresearch project related to the design of railwaytra�c simulation software for Iranian Railway Com-pany.

Abdorreza Sheikholeslami is an Associate Professorat the Department of Transportation Engineering and

Planning, School of Civil Engineering, Iran Universityof Science & Technology (IUST). He received his BScand MSc degrees from IUST. He received his PhDdegree in Transportation Engineering and Planningfrom Iran University of Science and Technology in 2006.

His research interests are transportation plan-ning, transportation economics, railway scheduling,disturbance management, mathematical models andoptimization techniques for designing transportationsystems.

He was elected as the top student in technical andengineering group in Iran in 2001. He has teachingexperience of more than 20 years at IUST. He haspublished more than 80 scienti�c papers in ISI journalsand international conferences.

Francesco Corman is an Assistant Professor inTransport Engineering and Logistics, TUDelft, and aGuest Professor at KULeuven.

His research interest relates to optimization oftransport networks under uncertainty. This substan-tiates optimization and automation in supply chainnetworks and logistic systems, especially with intercon-nected systems and modes, mathematical models andoptimization techniques for tra�c control in railwayssystems, optimal coordination strategies, equity issuesin logistics; robustness, reliability, and resilience oftransport networks under stochastic phenomena; ana-lytics, information, and uncertainty dynamics; a-prioriand online data collection and assessment of quality ofinformation.

He has more than 25 high-impact articles injournals and book chapters, and more than 100 scien-ti�c papers in journals or peer-reviewed internationalconferences; he received numerous awards and nomina-tions.

He has been involved in organizing and chairingof the International Conference on Computational Lo-gistics 2015, among others. He has been the Gen-eral Chair of Problem Solving Competition, INFORMRailway Application Section 2015 and 2016. He is aguest editor in major transportation journals (TRC,TRE, Public Transport), and participates actively inTRB and Informs community. He is the initiator ofmany international research exchange and coordinationnetworks.

a simulation-based optimization approach to...

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