@misc{KosterZymolkaKutschka, author = {Koster, Arie M.C.A. and Zymolka, Adrian and Kutschka, Manuel}, title = {Algorithms to Separate {0,1/2}-Chvatal-Gomory Cuts}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9531}, number = {07-10}, abstract = {Chvatal-Gomory cuts are among the most well-known classes of cutting planes for general integer linear programs (ILPs). In case the constraint multipliers are either 0 or \$\frac{1}{2}\$, such cuts are known as \$\{0,\frac{1}{2}\}\$-cuts. It has been proven by Caprara and Fischetti (1996) that separation of \$\{0,\frac{1}{2}\}\$-cuts is NP-hard. In this paper, we study ways to separate \$\{0,\frac{1}{2}\}\$-cuts effectively in practice. We propose a range of preprocessing rules to reduce the size of the separation problem. The core of the preprocessing builds a Gaussian elimination-like procedure. To separate the most violated \$\{0,\frac{1}{2}\}\$-cut, we formulate the (reduced) problem as integer linear program. Some simple heuristic separation routines complete the algorithmic framework. Computational experiments on benchmark instances show that the combination of preprocessing with exact and/or heuristic separation is a very vital idea to generate strong generic cutting planes for integer linear programs and to reduce the overall computation times of state-of-the-art ILP-solvers.}, language = {en} } @misc{KosterKutschkaRaack, author = {Koster, Arie M.C.A. and Kutschka, Manuel and Raack, Christian}, title = {Robust Network Design: Formulations, Valid Inequalities, and Computations}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-13890}, number = {11-34}, abstract = {Traffic in communication networks fluctuates heavily over time. Thus, to avoid capacity bottlenecks, operators highly overestimate the traffic volume during network planning. In this paper we consider telecommunication network design under traffic uncertainty, adapting the robust optimization approach of Bertsimas and Sim [2004]. We present three different mathematical formulations for this problem, provide valid inequalities, study the computational implications, and evaluate the realized robustness. To enhance the performance of the mixed-integer programming solver we derive robust cutset inequalities generalizing their deterministic counterparts. Instead of a single cutset inequality for every network cut, we derive multiple valid inequalities by exploiting the extra variables available in the robust formulations. We show that these inequalities define facets under certain conditions and that they completely describe a projection of the robust cutset polyhedron if the cutset consists of a single edge. For realistic networks and live traffic measurements we compare the formulations and report on the speed up by the valid inequalities. We study the "price of robustness" and evaluate the approach by analyzing the real network load. The results show that the robust optimization approach has the potential to support network planners better than present methods.}, language = {en} } @misc{BauschertBuesingD'Andreagiovannietal., author = {Bauschert, Thomas and B{\"u}sing, Christina and D'Andreagiovanni, Fabio and Koster, Arie M.C.A. and Kutschka, Manuel and Steglich, Uwe}, title = {Network Planning under Demand Uncertainty with Robust Optimization}, issn = {1438-0064}, doi = {10.1109/MCOM.2014.6736760}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-42557}, abstract = {The planning of a communication network is inevitably depending on the quality of both the planning tool and the demand forecast used. In this article, we show exemplarily how the emerging area of Robust Optimization can advance the network planning by a more accurate mathematical description of the demand uncertainty. After a general introduction of the concept and its application to a basic network design problem, we present two applications: multi-layer and mixed-line-rate network design. We conclude with a discussion of extensions of the robustness concept to increase the accuracy of handling uncertainties.}, language = {en} } @article{BauschertBuesingD'Andreagiovannietal., author = {Bauschert, Thomas and B{\"u}sing, Christina and D'Andreagiovanni, Fabio and Koster, Arie M.C.A. and Kutschka, Manuel and Steglich, Uwe}, title = {Network planning under demand uncertainty with robust optimization}, series = {IEEE Communications Magazine}, volume = {52}, journal = {IEEE Communications Magazine}, number = {2}, doi = {10.1109/MCOM.2014.6736760}, pages = {178 -- 185}, language = {en} } @inproceedings{KosterKutschkaRaack2010, author = {Koster, Arie M.C.A. and Kutschka, Manuel and Raack, Christian}, title = {Towards Robust Network Design using Integer Linear Programming Techniques}, series = {Proceedings of the NGI 2010, Paris, France}, booktitle = {Proceedings of the NGI 2010, Paris, France}, publisher = {Next Generation Internet}, address = {Paris, France}, year = {2010}, language = {en} }