Solving Network Design Problems via Decomposition, Aggregation and Approximation

1. Front Matter

   Pages I-XV

   PDF

2. Introduction

   • Andreas Bärmann

   Pages 1-5

3. Decomposition Algorithms for Multi-Period Network Design

   1. Front Matter

      Pages 7-9

      PDF

   2. Motivation

      • Andreas Bärmann

      Pages 11-14

   3. Strategic Infrastructure Planning in Railway Networks

      • Andreas Bärmann

      Pages 15-47

   4. Modelling the Expansion Problem

      • Andreas Bärmann

      Pages 49-66

   5. Model Analysis and Solution Approaches

      • Andreas Bärmann

      Pages 67-84

   6. Case Study for the German Railway Network

      • Andreas Bärmann

      Pages 85-102

4. Iterative Aggregation Procedures for Network Design Problems

   1. Front Matter

      Pages 103-105

      PDF

   2. Motivation

      • Andreas Bärmann

      Pages 107-109

   3. An Iterative Aggregation Algorithm for Optimal Network Design

      • Andreas Bärmann

      Pages 111-121

   4. Integration of Routing Costs into the Aggregation Scheme

      • Andreas Bärmann

      Pages 123-134

   5. The Computational Impact of Aggregation

      • Andreas Bärmann

      Pages 135-153

5. Approximate Second-Order Cone Robust Optimization

   1. Front Matter

      Pages 155-156

      PDF

   2. Motivation

      • Andreas Bärmann

      Pages 159-162

   3. Polyhedral Approximation of Second-Order Cone Robust Counterparts

      • Andreas Bärmann

      Pages 163-177

   4. Computational Assessment of Approximate Robust Optimization

      • Andreas Bärmann

      Pages 179-188

   5. Conclusions and Outlook

      • Andreas Bärmann

      Pages 189-191

6. Back Matter

   Pages 193-203

   PDF

Andreas Bärmann develops novel approaches for the solution of network design problems as they arise in various contexts of applied optimization. At the example of an optimal expansion of the German railway network until 2030, the author derives a tailor-made decomposition technique for multi-period network design problems. Next, he develops a general framework for the solution of network design problems via aggregation of the underlying graph structure. This approach is shown to save much computation time as compared to standard techniques. Finally, the author devises a modelling framework for the approximation of the robust counterpart under ellipsoidal uncertainty, an often-studied case in the literature. Each of these three approaches opens up a fascinating branch of research which promises a better theoretical understanding of the problem and an increasing range of solvable application settings at the same time.

• Discrete Optimization
• Network Design
• Decomposition
• Aggregation
• Robust Optimization

• Dept. Mathe/Lehrstu. f. Wirtschaftsmathe, FAU Erlangen-Nürnberg, Erlangen, Germany

  Andreas Bärmann

Dr. Andreas Bärmann is currently working as a postdoctoral researcher at the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) at the chair of Economics, Discrete Optimization and Mathematics. His research is focussed on mathematical optimization, especially the optimization of logistic processes.

Policies and ethics