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  • 2020-2023  (29)
  • 2010-2014  (75)
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  • 1
    Publication Date: 2020-08-05
    Description: We propose an efficient column generation method to minimize the probability of delay propagations along aircraft rotations. In this way, delay resistant schedules can be constructed. Computational results for large-scale real-world problems demonstrate substantial punctuality improvements. The method can be generalized to crew and integrated scheduling problems.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 2
    Publication Date: 2020-08-05
    Description: We propose a novel integer programming approach to transfer minimization for line planning problems in public transit. The idea is to incorporate penalties for transfers that are induced by “connection capacities” into the construction of the passenger paths. We show that such penalties can be dealt with by a combination of shortest and constrained shortest path algorithms such that the pricing problem for passenger paths can be solved efficiently. Connection capacity penalties (under)estimate the true transfer times. This error is, however, not a problem in practice. We show in a computational comparison with two standard models on a real-world scenario that our approach can be used to minimize passenger travel and transfer times for large-scale line planning problems with accurate results.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 3
    Publication Date: 2020-08-05
    Description: 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.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 4
    Publication Date: 2020-08-05
    Description: 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.
    Language: English
    Type: doctoralthesis , doc-type:doctoralThesis
    Format: application/pdf
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  • 5
    Publication Date: 2020-08-05
    Description: 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.
    Language: German
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 6
    Publication Date: 2020-08-05
    Description: 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.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 7
    Publication Date: 2020-08-05
    Description: 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.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 8
    Publication Date: 2020-08-05
    Description: 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.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 9
    Publication Date: 2020-08-05
    Description: 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.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 10
    Publication Date: 2020-08-05
    Description: The hypergraph assignment problem (HAP) is the generalization of assignments from directed graphs to directed hypergraphs. It serves, in particular, as a universal tool to model several train composition rules in vehicle rotation planning for long distance passenger railways. We prove that even for problems with a small hyperarc size and hypergraphs with a special partitioned structure the HAP is NP-hard and APX-hard. Further, we present an extended integer linear programming formulation which implies, e. g., all clique inequalities.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
    Format: application/pdf
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