@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{KosterOrlowskiRaacketal., author = {Koster, Arie M.C.A. and Orlowski, Sebastian and Raack, Christian and Bayer, Georg and Engel, Thomas}, title = {Single-layer Cuts for Multi-layer Network Design Problems}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9641}, number = {07-21}, abstract = {We study a planning problem arising in SDH/WDM multi-layer telecommunication network design. The goal is to find a minimum cost installation of link and node hardware of both network layers such that traffic demands can be realized via grooming and a survivable routing. We present a mixed-integer programming formulation that takes many practical side constraints into account, including node hardware, several bitrates, and survivability against single physical node or link failures. This model is solved using a branch-and-cut approach with problem-specific preprocessing and cutting planes based on either of the two layers. On several realistic two-layer planning scenarios, we show that these cutting planes are still useful in the multi-layer context, helping to increase the dual bound and to reduce the optimality gaps.}, language = {en} } @misc{ZymolkaKosterWessaely, author = {Zymolka, Adrian and Koster, Arie M.C.A. and Wess{\"a}ly, Roland}, title = {Transparent optical network design with sparse wavelength conversion}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7017}, number = {02-34}, abstract = {We consider the design of transparent optical networks from a practical perspective. Network operators aim at satisfying the communication demands at minimum cost. Such an optimization involves three interdependent planning issues: the dimensioning of the physical topology, the routing of lightpaths, and the wavelength assignment. Further topics include the reliability of the configuration and sparse wavelength conversion for efficient use of the capacities. In this paper, we investigate this extensive optical network design task. Using a flexible device-based model, we present an integer programming formulation that supports greenfield planning as well as expansion planning on top of an existing network. As solution method, we propose a suitable decomposition approach that separates the wavelength assignment from the dimensioning and routing. Our method in particular provides a lower bound on the total cost which allows to rate the solution quality. Computational experiments on realistic networks approve the solution approach to be appropriate.}, language = {en} } @misc{OrlowskiKosterRaacketal., author = {Orlowski, Sebastian and Koster, Arie M.C.A. and Raack, Christian and Wess{\"a}ly, Roland}, title = {Two-layer Network Design by Branch-and-Cut featuring MIP-based Heuristics}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9412}, number = {06-47}, abstract = {This paper deals with MIP-based primal heuristics to be used within a branch-and-cut approach for solving multi-layer telecommunication network design problems. Based on a mixed-integer programming formulation for two network layers, we present three heuristics for solving important subproblems, two of which solve a sub-MIP. On multi-layer planning instances with many parallel logical links, we show the effectiveness of our heuristics in finding good solutions early in the branch-and-cut search tree.}, language = {en} } @misc{Koster, author = {Koster, Arie M.C.A.}, title = {Wavelength Assignment in Multi-Fiber WDM Networks by Generalized Edge Coloring}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8478}, number = {05-13}, abstract = {In this paper, we study wavelength assignment problems in multi-fiber WDM networks. We focus on the special case that all lightpaths have at most two links. This in particular holds in case the network topology is a star. As the links incident to a specific node in a meshed topology form a star subnetwork, results for stars are also of interest for general meshed topologies. We show that wavelength assignment with at most two links per lightpath can be modeled as a generalized edge coloring problem. By this relation, we show that for a network with an even number of fibers at all links and at most two links per lightpath, all lightpaths can be assigned a wavelength without conversion. Moreover, we derive a lower bound on the number of lightpaths to be converted for networks with arbitrary numbers of fibers at the links. A comparison with linear programming lower bounds reveals that the bounds coincide for problems with at most two links per lightpath. For meshed topologies, the cumulative lower bound over all star subnetworks equals the best known solution value for all realistic wavelength assignment instances available, by this proving optimality.}, language = {en} }