90B06 Transportation, logistics
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Institute
This paper provides a generic formulation for rolling stock planning
problems in the context of intercity passenger traffic. The main contributions
are a graph theoretical model and a Mixed-Integer-Programming
formulation that integrate all main requirements of the considered
Vehicle-Rotation-Planning problem (VRPP). We show that it is
possible to solve this model for real-world instances provided by our
industrial partner DB Fernverkehr AG using modern algorithms and
computers.
Rapid Branching
(2012)
We propose rapid branching (RB) as a general branch-and-bound heuristic
for solving large scale optimization problems in traffic and transport.
The key idea is to combine a special branching rule and a greedy node selection
strategy in order to produce solutions of controlled quality rapidly
and efficiently. We report on three successful applications of the method
for integrated vehicle and crew scheduling, railway track allocation, and
railway vehicle rotation planning.
Duty Scheduling Templates
(2012)
We propose duty templates as a novel concept to produce similar duty
schedules for similar days of operation in public transit. Duty templates
can conveniently handle various types of similarity requirements, and
they can be implemented with ease using standard algorithmic techniques.
They have produced good results in practice.
Vehicle rotation planning is a fundamental problem in
rail transport. It decides how the railcars, locomotives, and
carriages are operated in order to implement the trips of the
timetable. One important planning requirement is operational
regularity, i.e., using the rolling stock in the same way on every
day of operation. We propose to take regularity into account by
modeling the vehicle rotation planning problem as a minimum cost
hyperassignment problem (HAP). Hyperassignments are generalizations
of assignments from directed graphs to directed hypergraphs.
Finding a minimum cost hyperassignment is
NP-hard.
Most instances arising from regular vehicle rotation planning, however, can
be solved well in practice. We show that, in particular, clique
inequalities strengthen the canonical LP relaxation substantially.
Im Zuge der Übernahme von 6 Linien der Havelbus Verkehrsgesellschaft
mbH durch die ViP Verkehr in Potsdam GmbH ergab sich 2009 die Notwendigkeit der
Entwicklung eines neuen Linien- und Taktplans für das Jahr 2010.
Das Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB)
entwickelt in einem Projekt des DFG-Forschungszentrums Matheon ein Verfahren zur mathematischen Linienoptimierung. Dieses Tool wurde bei der Optimierung des ViP Linienplans 2010 in
einer projektbegleitenden Studie eingesetzt, um Alternativen bei
verschiedenen Planungs- und Zielvorgaben auszuloten.
In dem Artikel wird eine Auswertung der Ergebnisse mit dem Verkehrsanalysesystem Visum der PTV AG beschrieben. Die Auswertungen bestätigen, dass mit Hilfe von mathematischer Optimierung eine weitere Verkürzung der Reisezeit um 1%, eine
als um 6% verkürzt empfundene Reisezeit, 10% weniger Fahrzeit im
Fahrzeug und eine gleichzeitige Kostenreduktion um 5% möglich sind.
This paper proposes the first model for toll enforcement optimization
on German motorways. The enforcement is done by mobile control teams and our
goal is to produce a schedule achieving network-wide control, proportional to
spatial and time-dependent traffic distributions. Our model consists of two
parts. The first plans
control tours using a vehicle routing approach with profits and some side
constraints. The second plans feasible rosters for the control teams. Both
problems can be modeled as Multi-Commodity Flow Problems. Adding additional
coupling constraints produces a large-scale integrated integer programming
formulation. We show that this model can be solved to optimality for real
world instances associated with a control area in East Germany.
This cumulative thesis collects the following six papers for obtaining the
habilitation at the Technische Universität Berlin, Fakultät II – Mathematik
und Naturwissenschaften:
(1) Set packing relaxations of some integer programs.
(2) Combinatorial packing problems.
(3) Decomposing matrices into blocks.
(4) A bundle method for integrated multi-depot vehicle and duty scheduling
in public transit.
(5) Models for railway track allocation.
(6) A column-generation approach to line planning in public transport.
Some changes were made to the papers compared to the published versions.
These pertain to layout unifications, i.e., common numbering, figure, table,
and chapter head layout. There were no changes with respect to notation or
symbols, but some typos have been eliminated, references updated, and some
links and an index was added. The mathematical content is identical.
The papers are about the optimization of public transportation systems,
i.e.,
bus networks, railways, and airlines, and its mathematical foundations,
i.e.,
the theory of packing problems. The papers discuss mathematical models,
theoretical analyses, algorithmic approaches, and computational aspects of
and to problems in this area.
Papers 1, 2, and 3 are theoretical. They aim at establishing a theory of
packing problems as a general framework that can be used to study traffic
optimization problems. Indeed, traffic optimization problems can often be
modelled as path packing, partitioning, or covering problems, which lead
directly to set packing, partitioning, and covering models. Such models are
used in papers 4, 5, and 6 to study a variety of problems concerning the
planning
of line systems, buses, trains, and crews. The common aim is always
to exploit as many degrees of freedom as possible, both at the level of the
individual problems by using large-scale integer programming techniques, as
well as on a higher level by integrating hitherto separate steps in the
planning
process.
This paper presents a case study on a railway timetable optimization for the very dense Simplon corridor, a major railway connection in the Alps between Switzerland and Italy. Starting from a detailed microscopic network as it is used in railway simulation, the data is transformed by an automatic procedure to a less detailed macroscopic network, that is sufficient for the purpose of capacity planning and amenable to state-of-the-art integer programming optimization methods. In this way, the macroscopic railway network is saturated with trains. Finally, the corresponding timetable is re-transformed to the microscopic level in such a way that it can be operated without any conflicts among the slots. Using this integer programming based micro-macro aggregation-disaggregation approach, it becomes for the first time possible to generate a profit maximal and conflict free timetable for the complete Simplon corridor over an entire day by a simultaneous optimization of all trains requests. This also allows to to undertake a sensitivity analysis of various problem parameters.
In this paper a bottom-up approach of automatic simplification of a railway network is presented. Starting from a very detailed, microscopic level, as it is used in railway simulation, the network is transformed by an algorithm to a less detailed level (macroscopic network), that is sufficient for long-term planning and optimization. In addition running and headway times are rounded to a pre-chosen time discretization by a special cumulative method, which we will present and analyse in this paper. After the transformation we fill the network with given train requests to compute an optimal slot allocation. Then the optimized schedule is re-transformed into the microscopic level and can be simulated without any conflicts occuring between the slots. The algorithm is used to transform the network of the very dense Simplon corridor between Swiss and Italy. With our aggregation it is possible for the first time to generate a profit maximal and conflict free timetable for the corridor across a day by a simultaneously optimization run.
The track allocation problem, also known as train routing problem or train timetabling problem, is to find a conflict-free set of train routes of maximum value in a railway network. Although it can be modeled as a standard path packing problem, instances of sizes relevant for real-world railway applications could not be solved up to now. We propose a rapid branching column generation approach that integrates the solution of the LP relaxation of a path coupling formulation of the problem with a special rounding heuristic. The approach is based on and exploits special properties of the bundle method for the approximate solution of convex piecewise linear functions. Computational results for difficult instances of the benchmark library TTPLIB are reported.