Solving Network Design Problems via Decomposition, Aggregation and Approximation

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Springer, Jun 2, 2016 - Mathematics - 203 pages
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.
 

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Contents

Introduction
1
Part I Decomposition Algorithms for MultiPeriod Network Design
6
Part II Iterative Aggregation Procedures for Network Design Problems
103
Part III Approximate SecondOrder Cone Robust Optimization
154
Conclusions and Outlook
189
Bibliography
192
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About the author (2016)

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.

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