Integral cycle bases for cyclic timetabling

Liebchen, Christian; Peeters, Leon

doi:10.1016/j.disopt.2008.09.003

Cited by 44 publications

(21 citation statements)

References 19 publications

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“…The number of cycles in a graph can be exponential in the number of nodes, but it can be shown that it is sufficient to require Eq. (6) to hold for an integral cycle basis B of G Rizzi 2007, Liebchen andPeeters 2009). Such a basis has the property that each cycle C in G is a linear combination with integer coefficients of the cycles in B.…”

Section: Transportation Planning and Technology 327mentioning

confidence: 98%

The periodic service intention as a conceptual framework for generating timetables with partial periodicity

Caimi

Laumanns

Schüpbach

et al. 2011

Transportation Planning and Technology

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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 periodicities and many exceptions to cope with changing demand. Current approaches for automatic timetable generation are not able to deal with such partially periodic structures but consider only fully periodic inputs. We therefore introduce the periodic Service Intention (pSI) as a framework where customer-relevant 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 for manual postprocessing. We solve this problem by projecting intended train runs over equivalence classes and thereby reducing the pSI to an augmented instance of periodic timetabling. Thus it is possible to use existing models for periodic scheduling, such as Periodic Event Scheduling Problem, 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 for central Switzerland in 2008 show that this approach needs only slightly 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.

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Section: Transportation Planning and Technology 327mentioning

confidence: 98%

The periodic service intention as a conceptual framework for generating timetables with partial periodicity

Caimi

Laumanns

Schüpbach

et al. 2011

Transportation Planning and Technology

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show abstract

“…An overview of the theory concerning cycle bases is given in Liebchen and Peeters [2009]. An advantage of this model is that it uses fewer integer variables and equality constraints instead of inequality constraints.…”

Section: Solving Conflicts By Extending the Cycle Periodicity Formumentioning

confidence: 99%

Resolving Infeasibilities in Railway Timetabling Instances

Polinder

Kroon²,

Aardal

et al. 2018

SSRN Journal

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One of the key assumptions of timetabling algorithms is that a solution exists that meets the pre-specified constraints, like driving times, transfer constraints and headway constraints. If this assumption is satisfied, in most cases a timetable can be found rapidly. Nowadays, railways are being used more intensively, which leads to a higher utilization of the network. Due to this increased utilisation, capacity conflicts occur, so that no feasible solution to the timetabling models can be found, without making subtle but non-trivial changes to the initial input. Resolving these conflicts is essential for railway companies with high utilization of infrastructure. In this paper, we consider infeasible timetabling instances together with a list of allowed modifications of the constraints. We iteratively identify local conflicts in these instances and resolve them by adapting some of the constraints, until there are no more conflicts. The adaptations of the constraints are changes in the right-hand sides that we try to make as small as possible but that resolve the infeasibility. We empirically show that our method can be improved by enriching the initial minimal conflicts found with more constraints. In order to keep the problems tractable, an iterative procedure is used to find solutions to subproblems corresponding to conflicts in the complete timetabling instance. In a case study on instances from the Dutch railway network, we show that these instances can be made feasible within a few minutes.

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“…Equation (5) imposes constraints on each cycle in the graph. The number of cycles in a graph can be exponential in the number of nodes, but it can be shown that it is sufficient to require (5) to hold for an integral cycle bases B of G [13,14]. Such a basis has the property that each cycle C in G is a linear combination with integer coefficients of the cycles in B.…”

Section: Cycle Periodicity Formulationmentioning

confidence: 99%

Periodic railway timetabling with event flexibility

et al. 2010

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Abstract. This paper addresses the problem of generating conflict-free periodic train timetables for large railway networks. We follow a two level approach, where a simplified track topology is used to obtain a macro-level 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 well-known 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.

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Integral cycle bases for cyclic timetabling

Cited by 44 publications

References 19 publications

The periodic service intention as a conceptual framework for generating timetables with partial periodicity

The periodic service intention as a conceptual framework for generating timetables with partial periodicity

Resolving Infeasibilities in Railway Timetabling Instances

Periodic railway timetabling with event flexibility

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