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12
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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Cited by 10 (0 self)
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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 3 (3 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.
The Periodic Service Intention as a Conceptual Frame for Generating Timetables with Partial Periodicity
, 2009
"... Many railway companies in Europe operate periodic timetables. Yet, most timetables are not entirely periodic but have a mixture of different periodicity and many exceptions to cope with changing demand. Current approaches for automatic timetable generation are not able to deal with such partially pe ..."
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Cited by 1 (0 self)
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Many railway companies in Europe operate periodic timetables. Yet, most timetables are not entirely periodic but have a mixture of different periodicity and many exceptions to cope with changing demand. Current approaches for automatic timetable generation are not able to deal with such partially periodic structure, but consider only fully periodic inputs. We therefore introduce the periodic Service Intention (pSI) as a framework where the customerrelevant information about train services can be described, including their periodicity information. We then address the problem of finding a feasible timetable that fulfills the requirements specified in a pSI without the need of manual postprocessing. We solve this problem by projecting intended train runs over equivalence classes and thereby reducing the pSI to an augmented instance for periodic timetabling. Thus it is possible to use existing models for periodic scheduling, such as the PESP, to generate periodic timetables with partial periodicity, which are finally rolled out to obtain the desired daily schedule according to the commercial requirements of the pSI. Results for a test case from the timetable of central Switzerland in 2008 show that this approach needs only slighly longer computation time than for a fully periodic instance, but the additional time is compensated by the fact that postprocessing becomes unnecessary and by the better quality of the solution. The approach is particularly well suited for offers with a strong periodicity but some irregularities, which could not be treated properly by existing methods.
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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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 Robust Railway Timetabling
"... Abstract. The Train Timetabling Problem (TTP) consists in finding a train schedule on a railway network that satisfies some operational constraints and maximizes a profit function which counts for the efficiency of the infrastructure usage. In practical cases, however, the maximization of the object ..."
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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 a 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 find robust TTP solutions for the aperiodic (non cyclic) case, that combine Mixed Integer Programming (MIP) 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.
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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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.
Optimal Scheduling of Mixed Speed Trains on a Single Track Line
, 2006
"... Market demands for different classes of rail transportation service are not served because of the inability to assess the cost to the network of disparate services, as well as the inability to determine optimal scheduling. A new scheduling model is presented, based on a multicommodity flow and discr ..."
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Market demands for different classes of rail transportation service are not served because of the inability to assess the cost to the network of disparate services, as well as the inability to determine optimal scheduling. A new scheduling model is presented, based on a multicommodity flow and discrete time, that both selects an optimal set of trains and schedules these trains over a time horizon according to a linear value function, and calculates a total flow value for a scheduled set of trains. The model is validated against analytical capacity measures and demonstrated with an example of mixed speed train scheduling.
KonradZuseZentrum
"... 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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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. 1
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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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.