Orbitopal Fixing

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 order of the subsets of the partition is irrelevant, since this kind of symmetry unnecessarily blows up the search tree. We present a general tool, called orbitopal fixing, for enhancing the capabilities of branch-and-cut algorithms in solving such symmetric integer programming models. We devise a linear time algorithm that, applied at each node of the search tree, removes redundant parts of the tree produced by the above mentioned symmetry. The method relies on certain polyhedra, called orbitopes, which have been introduced bei Kaibel and Pfetsch (Math. Programm. A, 114 (2008), 1-36). It does, however, not explicitly add inequalities to the model. Instead, it uses certain fixing rules for variables. We demonstrate the computational power of orbitopal fixing at the example of a graph partitioning problem.Comment: 22 pages, revised and extended version of a previous version that has appeared under the same title in Proc. IPCO 200

On the Bottleneck Shortest Path Problem

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

Orbitopal fixing

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 order 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 such 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 symmetry. The method relies on certain polyhedra, called orbitopes, which have been investigated in [11]. It does, however, 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

LP-Based Local Approximation for Markov Decision Problems

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 ε-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

67. International investment arbitration: Winning, losing and why

This second edition of this publication provides an overview of important contemporary issues relating to foreign direct investment (FDI) and multinational enterprises for all those who are interested in this subject, but are not always in a position to follow diverse perspectives and what is being written in the various corners of this field. The contributions are grouped under the following headings: attracting FDI and its impact; the rise of emerging market investors; national policies; sustainable international investment; and international investment treaties and arbitration. The volume brings together all Perspectives published since the inception of this series until 2012.https://digitalcommons.wcl.american.edu/facsch_bk_contributions/1391/thumbnail.jp

67. International investment arbitration: Winning, losing and why

This second edition of this publication provides an overview of important contemporary issues relating to foreign direct investment (FDI) and multinational enterprises for all those who are interested in this subject, but are not always in a position to follow diverse perspectives and what is being written in the various corners of this field. The contributions are grouped under the following headings: attracting FDI and its impact; the rise of emerging market investors; national policies; sustainable international investment; and international investment treaties and arbitration. The volume brings together all Perspectives published since the inception of this series until 2012.https://digitalcommons.wcl.american.edu/facsch_bk_contributions/1391/thumbnail.jp