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  • English  (11)
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  • 1
    Book
    Book
    New York ; Berlin ; Heidelberg ; Hong Kong ; London ; Milan ; Pa :Springer,
    Title: Convex polytopes /; 221
    Author: Grünbaum, Branko
    Contributer: Kaibel, Volker
    Edition: 2. ed. / prepared by Volker Kaibel ...
    Publisher: New York ; Berlin ; Heidelberg ; Hong Kong ; London ; Milan ; Pa :Springer,
    Year of publication: 2003
    Pages: XVI, 466 S.
    Series Statement: Graduate texts in mathematics 221
    ISBN: 0-387-00424-6 , 0-387-40409-0
    Type of Medium: Book
    Language: English
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  • 2
    Title: Mixed-integer programming subject to uncertain data /
    Author: Pfeuffer, Frank Martin
    Contributer: Kaibel, Volker
    Edition: 1. Aufl.
    Publisher: Göttingen :Cuvillier,
    Year of publication: 2012
    Pages: X, 123 S. : , graph. Darst. ; , 21 cm
    Dissertation note: Zugl.: Magdeburg, Otto-von-Guericke-Univ., Fak. für Mathematik., Diss., 2012
    ISBN: 978-3-9540423-9-5
    Type of Medium: Book
    Language: English
    Note: Zsfassungen in engl. und dt. Sprache
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  • 3
    Publication Date: 2020-02-11
    Language: English
    Type: article , doc-type:article
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  • 4
    Publication Date: 2020-08-05
    Language: English
    Type: article , doc-type:article
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  • 5
    Publication Date: 2020-08-05
    Language: English
    Type: article , doc-type:article
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  • 6
    Publication Date: 2020-12-15
    Description: The topic of this paper are integer programming models in which a subset of 0/1-variables encode a partitioning of a set of objects into disjoint subsets. Such models can be surprisingly hard to solve by branch-and-cut algorithms if the permutation of the subsets of the partition is irrelevant. This kind of symmetry unnecessarily blows up the branch-and-cut tree. We present a general tool, called orbitopal fixing, for enhancing the capabilities of branch-and-cut algorithms in solving this kind of symmetric integer programming models. We devise a linear time algorithm that, applied at each node of the branch-and-cut tree, removes redundant parts of the tree produced by the above mentioned permutations. The method relies on certain polyhedra, called orbitopes, which have been investigated in (Kaibel and Pfetsch (2006)). However, it does not add inequalities to the model, and thus, it does not increase the difficulty of solving the linear programming relaxations. We demonstrate the computational power of orbitopal fixing at the example of a graph partitioning problem motivated from frequency planning in mobile telecommunication networks.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
    Format: application/pdf
    Format: application/postscript
    Format: application/postscript
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  • 7
    Publication Date: 2020-08-05
    Description: We consider polytopes associated with cardinality constrained path and cycle problems defined on a directed or undirected graph. We present integer characterizations of these polytopes by facet defining linear inequalities for which the separation problem can be solved in polynomial time. Moreover, we give further facet defining inequalities, in particular those that are specific to odd/even paths and cycles.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
    Format: application/postscript
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  • 8
    Publication Date: 2020-12-15
    Description: We introduce orbitopes as the convex hulls of 0/1-matrices that are lexicographically maximal subject to a group acting on the columns. Special cases are packing and partitioning orbitopes, which arise from restrictions to matrices with at most or exactly one 1-entry in each row, respectively. The goal of investigating these polytopes is to gain insight into ways of breaking certain symmetries in integer programs by adding constraints, e.g., for a well-known formulation of the graph coloring problem. We provide a thorough polyhedral investigation of packing and partitioning orbitopes for the cases in which the group acting on the columns is the cyclic group or the symmetric group. Our main results are complete linear inequality descriptions of these polytopes by facet-defining inequalities. For the cyclic group case, the descriptions turn out to be totally unimodular, while for the symmetric group case, both the description and the proof are more involved. The associated separation problems can be solved in linear time.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
    Format: application/postscript
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  • 9
    Publication Date: 2014-11-21
    Description: The standard computational methods for computing the optimal value functions of Markov Decision Problems (MDP) require the exploration of the entire state space. This is practically infeasible for applications with huge numbers of states as they arise, e.\,g., from modeling the decisions in online optimization problems by MDPs. Exploiting column generation techniques, we propose and apply an LP-based method to determine an $\varepsilon$-approximation of the optimal value function at a given state by inspecting only states in a small neighborhood. In the context of online optimization problems, we use these methods in order to evaluate the quality of concrete policies with respect to given initial states. Moreover, the tools can also be used to obtain evidence of the impact of single decisions. This way, they can be utilized in the design of policies.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
    Format: application/postscript
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  • 10
    Publication Date: 2014-11-21
    Description: The Bottleneck Shortest Path Problem is a basic problem in network optimization. The goal is to determine the limiting capacity of any path between two specified vertices of the network. This is equivalent to determining the unsplittable maximum flow between the two vertices. In this note we analyze the complexity of the problem, its relation to the Shortest Path Problem, and the impact of the underlying machine/computation model.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
    Format: application/postscript
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