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38
Solution of RealWorld Train Timetabling Problems
 In Proc. HICSS 34. IEEE
, 2001
"... The Train Timetabling Problem (TTP) aims at determining a timetable for a set of trains which does not violate track capacities and satises some operational constraints. We concentrate on the problem of a single, oneway track linking two major stations, with a number of intermediate stations in ..."
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The Train Timetabling Problem (TTP) aims at determining a timetable for a set of trains which does not violate track capacities and satises some operational constraints. We concentrate on the problem of a single, oneway track linking two major stations, with a number of intermediate stations in between.
Periodic Railway Timetabling with Event Flexibility
, 2007
"... This paper addresses the problem of generating conflictfree periodic train timetables for large railway networks. We follow a two level approach, where a simplified track topology is used to obtain a macrolevel schedule, and the detailed topology is considered locally on the micro level. To increa ..."
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Cited by 8 (4 self)
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This paper addresses the problem of generating conflictfree periodic train timetables for large railway networks. We follow a two level approach, where a simplified track topology is used to obtain a macrolevel schedule, and the detailed topology is considered locally on the micro level. To increase the solution space in the interface of the two levels, we propose an extension of the wellknown Periodic Event Scheduling Problem (PESP) such that it allows to generate flexible time slots for the departure and arrival times instead of exact times. This Flexible Periodic Event Scheduling Problem (FPESP) formulation considerably increases the chance to obtain feasible solutions (exact train routings) subsequently on the micro level, in particular for stations with dense peak traffic. Total trip time and the time slot sizes are used as multiple objectives and weighted and/or constrained to allocate the flexibility where it is most useful. Tests on a medium size instance of the Swiss Federal Railways 2007 service intention demonstrate the advantage of the FPESP model, while it only moderately increases its solution time in most cases.
An Auctioning Approach to Railway Slot Allocation
, 2005
"... We present an approach to implement an auction of railway slots. Railway network, train driving characteristics, and safety requirements are described by a simplified, but still complex macroscopic model. In this environment, slots are modelled as combinations of scheduled track segments. The auctio ..."
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Cited by 7 (2 self)
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We present an approach to implement an auction of railway slots. Railway network, train driving characteristics, and safety requirements are described by a simplified, but still complex macroscopic model. In this environment, slots are modelled as combinations of scheduled track segments. The auction design builds on the iterative combinatorial auction. However, combinatorial bids are restricted to some types of slot bundles that realize positive synergies between slots. We present a bidding language that allows bidding for these slot bundles. An integer programming approach is proposed to solve the winner determination problem of our auction. Computational results for auction simulations in the HannoverFuldaKassel area of the German railway network give evidence that auction approaches can induce a more efficient use of railway capacity.
An Exact Solution Procedure to Determine the Optimal Dispatching Times for
 Complex Rail Networks,” IEE Transactions
"... Abstract: Trains operating in densely populated metropolitan areas typically encounter complex trackage configurations. To make optimal use of the available rail capacity, some portions of the rail network may consist of singletrack lines while other locations may consist of double or tripletrack ..."
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Cited by 6 (2 self)
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Abstract: Trains operating in densely populated metropolitan areas typically encounter complex trackage configurations. To make optimal use of the available rail capacity, some portions of the rail network may consist of singletrack lines while other locations may consist of double or tripletrack lines. This paper develops a branchandbound procedure for determining the optimal dispatching times for trains traveling in complex rail networks. We demonstrate the efficiency of our branchandbound algorithm by comparing it to CPLEX, a commercially available integer program solver, on an actual rail network in Los Angeles County. 1
Models for Railway Track Allocation
, 2007
"... The optimal track allocation problem (OPTRA) is to find, in a given railway network, a conflict free set of train routes of maximum value. We study two types of integer programming formulations for this problem: a standard formulation that models block conflicts in terms of packing constraints, and ..."
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Cited by 5 (0 self)
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The optimal track allocation problem (OPTRA) is to find, in a given railway network, a conflict free set of train routes of maximum value. We study two types of integer programming formulations for this problem: a standard formulation that models block conflicts in terms of packing constraints, and a novel formulation of the ‘extended ’ type that is based on additional ‘configuration ’ variables. The packing constraints in the standard formulation stem from an interval graph and can therefore be separated in polynomial time. It follows that the LPrelaxation of a strong version of this model, including all clique inequalities from block conflicts, can be solved in polynomial time. We prove that the LPrelaxation of the extended formulation can also be solved in polynomial time, and that it produces the same LPbound. Albeit the two formulations are in this sense equivalent, the extended formulation has advantages from a computational point of view. It features a constant number of rows and is amenable to standard column generation techniques. Results of an empirical model comparison on mesoscopic data for the HanoverFuldaKassel region of the German long distance railway network involving up to 570 trains are reported.
Fast approaches to improve the robustness of a railway timetable
 Transportation Science
"... Abstract. The Train Timetabling Problem (TTP) consists in finding a train schedule on a railway network that satisfies some operational constraints and maximizes some profit function which counts for the efficiency of the infrastructure usage. In practical cases, however, the maximization of the obj ..."
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Abstract. The Train Timetabling Problem (TTP) consists in finding a train schedule on a railway network that satisfies some operational constraints and maximizes some profit function which counts for the efficiency of the infrastructure usage. In practical cases, however, the maximization of the objective function is not enough and one calls for a robust solution that is capable of absorbing as much as possible delays/disturbances on the network. In this paper we propose and analyze computationally four different methods to improve the robustness of a given TTP solution for the aperiodic (non cyclic) case. The approaches combine Linear Programming (LP) and adhoc Stochastic Programming/Robust Optimization techniques. We compare computationally the effectiveness and practical applicability of the four techniques under investigation on realworld test cases from the Italian railway company (Trenitalia). The outcome is that two of the proposed techniques are very fast and provide robust solutions of comparable quality with respect to the standard (but very time consuming) Stochastic Programming approach.
Towards Solving Very Large Scale Train Timetabling Problems by Lagrangian Relaxation
 ATMOS
, 2008
"... The train timetabling problem considered is to find conflict free routes for a set of trains in a given railway network so that certain time window conditions are satisfied. We deal with the very large scale problem of constructing such timetables for the German railway network. A number of restric ..."
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Cited by 4 (0 self)
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The train timetabling problem considered is to find conflict free routes for a set of trains in a given railway network so that certain time window conditions are satisfied. We deal with the very large scale problem of constructing such timetables for the German railway network. A number of restrictions on different train types like freight trains or passenger trains have to be observed, e.g., sequence dependent headway times, station capacities, and stopping times. In order to handle the enormous number of variables and constraints we employ Lagrangian relaxation of the conflict constraints combined with a cutting plane approach. The model is solved by a bundle method; its primal aggregate is used for separation and as starting point for rounding heuristics. We present some promising results towards handling a test instance comprising ten percent of the entire network.
A Genetic Algorithm for Railway Scheduling Problems
, 2008
"... This work is focused on the application of evolutionary algorithms to solve very complex realworld problems. For this purpose a Genetic Algorithm is designed to solve the Train Timetabling Problem. Optimizing train timetables on a single line track is known to be NPhard with respect to the number ..."
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Cited by 3 (1 self)
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This work is focused on the application of evolutionary algorithms to solve very complex realworld problems. For this purpose a Genetic Algorithm is designed to solve the Train Timetabling Problem. Optimizing train timetables on a single line track is known to be NPhard with respect to the number of conflicts in the schedule. This makes it difficult to obtain good solutions to real life problems in a reasonable computational time and raises the need for good heuristic scheduling techniques. The railway scheduling problem considered in this work implies the optimization of trains on a railway line that is occupied (or not) by other trains with fixed timetables. The timetable for the new trains is obtained with a Genetic Algorithm (GA) that includes a guided process to build the initial population. The proposed GA is tested using real instances obtained from the Spanish Manager of Railway Infrastructure (ADIF). The results of the computational experience, point out that GA is an appropriate method to explore the search space of this complex problems and able to lead to good solutions in a short amount of time.
Almost 20 Years of Combinatorial Optimization for Railway Planning: from Lagrangian Relaxation to Column Generation
"... We summarize our experience in solving combinatorial optimization problems arising in railway planning, illustrating all of these problems as integer multicommodity flow ones and discussing the main features of the mathematical programming models that were successfully used in the 1990s and in recen ..."
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Cited by 3 (0 self)
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We summarize our experience in solving combinatorial optimization problems arising in railway planning, illustrating all of these problems as integer multicommodity flow ones and discussing the main features of the mathematical programming models that were successfully used in the 1990s and in recent years to solve them.