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Mathematical Programming Computation

, Volume 7, Issue 2, pp 189–217 | Cite as

Solving network design problems via iterative aggregation

  • Andreas Bärmann
  • Frauke Liers
  • Alexander Martin
  • Maximilian Merkert
  • Christoph Thurner
  • Dieter Weninger
Full Length Paper

Abstract

In this work, we present an exact approach for solving network design problems that is based on an iterative graph aggregation procedure. The scheme allows existing preinstalled capacities. Starting with an initial aggregation, we solve a sequence of network design master problems over increasingly fine-grained representations of the original network. In each step, a subproblem is solved that either proves optimality of the solution or gives a directive where to refine the representation of the network in the subsequent iteration. The algorithm terminates with a globally optimal solution to the original problem. Our implementation uses a standard integer programming solver for solving the master problems as well as the subproblems. The computational results on random and realistic instances confirm the profitable use of the iterative aggregation technique. The computing time often reduces drastically when our method is compared to solving the original problem from scratch.

Keywords

Aggregation Network design Combinatorial optimization Mixed-integer programming Branch-and-cut 

Mathematics Subject Classification

90C35 90C27 90C11 90C57 

Notes

Acknowledgments

We would like to express our gratitude to Daniel Schmidt for providing us with his preferential attachment graph generator. Furthermore, we thank Andreas Bley for fruitful discussions on the topic. We gratefully acknowledge the computing resources provided by the group of Michael Jünger in Cologne. In particular, we thank Thomas Lange for technical support. We are also indebted to the anonymous reviewers for their constructive comments on this paper. We furthermore acknowledge financial support under BMBF grant 05M10WEC and thank the EnCN for support within research focus Simulation, Projects TP3 and TP6 as well as the DFG for their support within Projects A05, B06, and B07 in CRC TRR 154.

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Copyright information

© Springer-Verlag Berlin Heidelberg and The Mathematical Programming Society 2015

Authors and Affiliations

  • Andreas Bärmann
    • 1
  • Frauke Liers
    • 1
  • Alexander Martin
    • 1
  • Maximilian Merkert
    • 1
  • Christoph Thurner
    • 1
  • Dieter Weninger
    • 1
  1. 1.Department Mathematik, Lehrstuhl für WirtschaftsmathematikFriedrich-Alexander-Universität Erlangen-NürnbergErlangenGermany

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