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  • 2010-2014  (43)
  • 1995-1999  (14)
  • 2014  (17)
  • 2012  (26)
  • 1999  (3)
  • 1997  (11)
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  • 2010-2014  (43)
  • 1995-1999  (14)
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  • 1
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    Matrix Decomposition by Branch-and-Cut (1997)
    Details
    Publication Date: 2020-03-09
    Description: In this paper we investigate whether matrices arising from linear or integer programming problems can be decomposed into so-called {\em bordered block diagonal form}. More precisely, given some matrix $A$, we try to assign as many rows as possible to some number of blocks of limited size such that no two rows assigned to different blocks intersect in a common column. Bordered block diagonal form is desirable because it can guide and speed up the solution process for linear and integer programming problems. We show that various matrices from the %LP- and MIP-libraries \Netlib{} and MIPLIB can indeed be decomposed into this form by computing optimal decompositions or decompositions with proven quality. These computations are done with a branch-and-cut algorithm based on polyhedral investigations of the matrix decomposition problem.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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    OPUS
  • 2
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    Set Packing Relaxations of Some Integer Programs (1997)
    Details
    Publication Date: 2020-08-05
    Description: This paper is about {\em set packing relaxations\/} of combinatorial optimization problems associated with acyclic digraphs and linear orderings, cuts and multicuts, and vertex packings themselves. Families of inequalities that are valid for such a relaxation as well as the associated separation routines carry over to the problems under investigation.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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    OPUS
  • 3
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    Der Schnellste Weg zum Ziel (1999)
    Details
    Publication Date: 2020-08-05
    Description: Wir geben eine Einführung in die Mathematik von und mit Wegen. Nicht auf dem kürzesten, aber auf einem hoffentlich kurzweiligen Weg!
    Keywords: ddc:000
    Language: German
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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    OPUS
  • 4
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    Optimierung des Linienplans 2010 in Potsdam (2012)
    Details
    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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    OPUS
  • 5
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    Minimum Cost Hyperassignments with Applications to ICE/IC Rotation Planning (2012)
    Details
    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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    OPUS
  • 6
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    Duty Scheduling Templates (2012)
    Details
    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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    OPUS
  • 7
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    Rapid Branching (2012)
    Details
    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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    OPUS
  • 8
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    Vehicle Rotation Planning for Intercity Railways (2012)
    Details
    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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    OPUS
  • 9
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    The Hypergraph Assignment Problem (2012)
    Details
    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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    OPUS
  • 10
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    A Stackelberg game to optimize the distribution of controls in transportation networks (2012)
    Details
    Publication Date: 2020-08-05
    Description: We propose a game theoretic model for the spatial distribution of inspectors on a transportation network. The problem is to spread out the controls so as to enforce the payment of a transit toll. We formulate a linear program to find the control distribution which maximizes the expected toll revenue, and a mixed integer program for the problem of minimizing the number of evaders. Furthermore, we show that the problem of finding an optimal mixed strategy for a coalition of $N$ inspectors can be solved efficiently by a column generation procedure. Finally, we give experimental results from an application to the truck toll on German motorways.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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    OPUS
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