@misc{WernerAurzadaBleyetal., author = {Werner, Axel and Aurzada, Frank and Bley, Andreas and Eisenbl{\"a}tter, Andreas and Geerdes, Hans-Florian and Guillemard, Mijail and Kutyniok, Gitta and Philipp, Friedrich and Raack, Christian and Scheutzow, Michael}, title = {Mathematics for telecommunications}, series = {MATHEON - Mathematics for Key Technologies}, volume = {1}, journal = {MATHEON - Mathematics for Key Technologies}, editor = {Deuflhard, Peter and Gr{\"o}tschel, Martin and H{\"o}mberg, Dietmar and Horst, Ulrich and Kramer, J{\"u}rg and Mehrmann, Volker and Polthier, Konrad and Schmidt, Frank and Sch{\"u}tte, Christof and Skutella, Martin and Sprekels, J{\"u}rgen}, edition = {EMS Series in Industrial and Applied Mathematics}, publisher = {European Mathematical Society}, doi = {10.4171/137}, pages = {75 -- 89}, language = {en} } @article{HeinzeDipankarHenkenetal., author = {Heinze, Rieke and Dipankar, Anurag and Henken, Cintia Carbajal and Moseley, Christopher and Sourdeval, Odran and Tr{\"o}mel, Silke and Xie, Xinxin and Adamidis, Panos and Ament, Felix and Baars, Holger and Barthlott, Christian and Behrendt, Andreas and Blahak, Ulrich and Bley, Sebastian and Brdar, Slavko and Brueck, Matthias and Crewell, Susanne and Deneke, Hartwig and Di Girolamo, Paolo and Evaristo, Raquel and Fischer, J{\"u}rgen and Frank, Christopher and Friederichs, Petra and G{\"o}cke, Tobias and Gorges, Ksenia and Hande, Luke and Hanke, Moritz and Hansen, Akio and Hege, Hans-Christian and Hose, Corinna and Jahns, Thomas and Kalthoff, Norbert and Klocke, Daniel and Kneifel, Stefan and Knippertz, Peter and Kuhn, Alexander and van Laar, Thriza and Macke, Andreas and Maurer, Vera and Mayer, Bernhard and Meyer, Catrin I. and Muppa, Shravan K. and Neggers, Roeland A. J. and Orlandi, Emiliano and Pantillon, Florian and Pospichal, Bernhard and R{\"o}ber, Niklas and Scheck, Leonhard and Seifert, Axel and Seifert, Patric and Senf, Fabian and Siligam, Pavan and Simmer, Clemens and Steinke, Sandra and Stevens, Bjorn and Wapler, Kathrin and Weniger, Michael and Wulfmeyer, Volker and Z{\"a}ngl, G{\"u}nther and Zhang, Dan and Quaas, Johannes}, title = {Large-eddy simulations over Germany using ICON: a comprehensive evaluation}, series = {Quarterly Journal of the Royal Meteorological Society}, volume = {143}, journal = {Quarterly Journal of the Royal Meteorological Society}, number = {702}, doi = {10.1002/qj.2947}, pages = {69 -- 100}, abstract = {Large-eddy simulations (LES) with the new ICOsahedral Non-hydrostatic atmosphere model (ICON) covering Germany are evaluated for four days in spring 2013 using observational data from various sources. Reference simulations with the established Consortium for Small-scale Modelling (COSMO) numerical weather prediction model and further standard LES codes are performed and used as a reference. This comprehensive evaluation approach covers multiple parameters and scales, focusing on boundary-layer variables, clouds and precipitation. The evaluation points to the need to work on parametrizations influencing the surface energy balance, and possibly on ice cloud microphysics. The central purpose for the development and application of ICON in the LES configuration is the use of simulation results to improve the understanding of moist processes, as well as their parametrization in climate models. The evaluation thus aims at building confidence in the model's ability to simulate small- to mesoscale variability in turbulence, clouds and precipitation. The results are encouraging: the high-resolution model matches the observed variability much better at small- to mesoscales than the coarser resolved reference model. In its highest grid resolution, the simulated turbulence profiles are realistic and column water vapour matches the observed temporal variability at short time-scales. Despite being somewhat too large and too frequent, small cumulus clouds are well represented in comparison with satellite data, as is the shape of the cloud size spectrum. Variability of cloud water matches the satellite observations much better in ICON than in the reference model. In this sense, it is concluded that the model is fit for the purpose of using its output for parametrization development, despite the potential to improve further some important aspects of processes that are also parametrized in the high-resolution model.}, language = {en} } @misc{BleyKoch, author = {Bley, Andreas and Koch, Thorsten}, title = {Optimierung in der Planung und beim Aufbau des G-WiN}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6169}, number = {00-48}, abstract = {Ende Juni diesen Jahres wurde das Gigabit-Wissenschaftsnetz offiziell gestartet. In der zweij{\"a}hrigen Vorbereitungsphase wurden nicht nur die technischen M{\"o}glichkeiten der neuen {\"U}bertragungstechniken und Dienste getestet. Es wurden auch verschiedene Fragestellungen zum effizienten Einsatz der verf{\"u}gbaren Ressourcen f{\"u}r den Betrieb des G-WiN untersucht. In diesem Artikel beschreiben wir, wie das G-WiN zu seiner jetzigen Struktur und Topologie gekommen ist.}, language = {de} } @misc{BleyKoch, author = {Bley, Andreas and Koch, Thorsten}, title = {Integer programming approaches to access and backbone IP-network planning}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7081}, number = {02-41}, abstract = {In this article we study the problem of designing a nation-wide communication network. Such networks usually consist of an access layer, a backbone layer, and maybe several intermediate layers. The nodes of each layer must be connected to those of the next layer in a tree-like fashion. The backbone layer has to satisfy certain survivability and routing constraints. Given the node locations, the demands between them, the possible connections and hardware configurations, and various other technical and administrational constraints, the goal is to decide, which node is assigned to which network level, how the nodes are connected, what hardware must be installed, and how traffic is routed in the backbone. Mixed integer linear programming models and solution methods are presented for both the access and the backbone network design problem. The focus is on the design of IP-over-SDH networks, but the access network design model and large parts of the backbone network design models are general and also applicable for other types of communication networks. Results obtained with these methods in the planning of the German research network are presented.}, language = {en} } @misc{Bley, author = {Bley, Andreas}, title = {Inapproximability Results for the Inverse Shortest Paths Problem with Integer Length and Unique Shortest Paths}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8388}, number = {05-04}, abstract = {We study the complexity of two Inverse Shortest Paths (ISP) problems with integer arc lengths and the requirement for uniquely determined shortest paths. Given a collection of paths in a directed graph, the task is to find positive integer arc lengths such that the given paths are uniquely determined shortest paths between their respective terminals. The first problem seeks for arc lengths that minimize the length of the longest of the prescribed paths. In the second problem, the length of the longest arc is to be minimized. We show that it is \$np-hard\$ to approximate the minimal longest path length within a factor less than \$8/7\$ or the minimal longest arc length within a factor less than \$9/8\$. This answers the (previously) open question whether these problems are \$np-hard\$ or not. We also present a simple algorithm that achieves an \$\mathcal{O}(|V|)\$-approximation guarantee for both variants. Both ISP problems arise in the planning of telecommunication networks with shortest path routing protocols. Our results imply that it is \$\mathcal{NP}\$-hard to decide whether a given path set can be realized with a real shortest path routing protocol such as OSPF, IS-IS, or RIP.}, language = {en} } @misc{BleyKochNiu, author = {Bley, Andreas and Koch, Thorsten and Niu, Lingfeng}, title = {Experiments with nonlinear extensions to SCIP}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8300}, number = {08-28}, abstract = {This paper describes several experiments to explore the options for solving a class of mixed integer nonlinear programming problems that stem from a real-world mine production planning project. The only type of nonlinear constraints in these problems are bilinear equalities involving continuous variables, which enforce the ratios between elements in mixed material streams. A branch-and-bound algorithm to handle the integer variables has been tried in another project. However, this branch-and-bound algorithm is not effective for handling the nonlinear constraints. Therefore state-of-the-art nonlinear solvers are utilized to solve the resulting nonlinear subproblems in this work. The experiments were carried out using the NEOS server for optimization. After finding that current nonlinear programming solvers seem to lack suitable preprocessing capabilities, we preprocess the instances beforehand and use an heuristic approach to solve the nonlinear subproblems. In the appendix, we explain how to add a polynomial constraint handler that uses IPOPT as embedded nonlinear programming solver for the constraint programming framework SCIP. This is one of the crucial steps for implementing our algorithm in SCIP. We briefly described our approach and give an idea of the work involved.}, language = {en} } @misc{BleyPattloch, author = {Bley, Andreas and Pattloch, Marcus}, title = {Modellierung und Optimierung der X-WiN Plattform}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8551}, number = {05-21}, abstract = {In diesem Artikel werden die Optimierungsmodelle und -verfahren beschrieben, die bei der Planung des Kernnetzes und der Zugangsinfrastruktur des X-WiN verwendet wurden.}, language = {de} } @misc{Bley, author = {Bley, Andreas}, title = {A Lagrangian Approach for Integrated Network Design and Routing in IP Networks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7515}, number = {03-29}, abstract = {We consider the problem of designing a network that employs a non-bifurcated shortest path routing protocol. The network's nodes and the set of potential links are given together with a set of forecasted end-to-end traffic demands. All relevant hardware components installable at links or nodes are considered. The goal is to simultaneously choose the network's topology, to decide which hardware components to install on which links and nodes, and to find appropriate routing weights such that the overall network cost is minimized. In this paper, we present a mathematical optimization model for this problem and an algorithmic solution approach based on a Lagrangian relaxation. Computational results achieved with this approach for several real-world network planning problems are reported.}, language = {en} } @misc{BleyKosterKroelleretal., author = {Bley, Andreas and Koster, Arie M.C.A. and Kr{\"o}ller, Alexander and Wess{\"a}ly, Roland and Zymolka, Adrian}, title = {Kosten- und Qualit{\"a}tsoptimierung in Kommunikationsnetzen}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7537}, number = {03-31}, abstract = {Der scharfe Wettbewerb innerhalb der Telekommunikationsbranche zwingt die Netzbetreiber dazu, ihre Investitionen genau zu planen und immer wieder Einsparungsmanahmen durchzuf{\"u}hren. Gleichzeitig ist es jedoch wichtig, die Qualit{\"a}t der angebotenen Dienste zu verbessern, um neue Kunden zu gewinnen und langfristig an sich zu binden. Die mathematische Optimierung bietet sich f{\"u}r viele solcher Aufgabenstellungen als hervorragend geeignetes Planungswerkzeug an. Ziel dieses Artikels ist es, ihre Methodik und ihre Anwendung speziell zur Kosten- und Qualit{\"a}tsoptimierung in Kommunikationsnetzen vorzustellen. Anhand von vier konkreten Planungsaufgaben aus dem Bereich der Festnetzplanung wird aufgezeigt, wie sich komplexe Zusammenh{\"a}nge in flexiblen mathematischen Modellen abbilden lassen und welche Verfahren zur automatisierten Bearbeitung der Probleme eingesetzt werden k{\"o}nnen. Die hier vorgestellten Methoden zeichnen sich insbesondere dadurch aus, dass sie neben hochwertigen L{\"o}sungen auch eine Qualittsgarantie liefern, mit der sich die Lsungen fundiert bewerten lassen. Die dokumentierten Ergebnisse aus verschiedenen Industrieprojekten belegen die Eignung und G{\"u}te der mathematischen Optimierung f{\"u}r die Praxis.}, language = {de} } @misc{BleyZymolka, author = {Bley, Andreas and Zymolka, Adrian}, title = {Planung kostenoptimaler Informations- und Kommunikations-Infrastrukturen}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7591}, number = {03-37}, abstract = {Beim Entwurf und Ausbau von Informations- und Kommunikationsnetzwerken m{{\"u}}ssen zahlreiche interdependente Entscheidungen getroffen und gleichzeitig mannigfaltige Bedingungen ber{{\"u}}cksichtigt werden. Die verf{{\"u}}gbaren technischen und organisatorischen Alternativm{{\"o}}glichkeiten sind normalerweise so vielf{{\"a}}ltig und komplex, dass eine manuelle Planung praktisch nicht m{{\"o}}glich ist. In diesem Artikel wird das Potential und die Methodik der mathematischen Optimierung bei der kostenoptimalen Planung von Kommunikationsnetzen vorgestellt. Als Ausgangspunkt wird exemplarisch eine typische praktische Aufgabe, die Struktur- und Konfigurationsplanung mehrstufiger Telekommunikationsnetzwerke, dargestellt. Anschließend werden kurz die wesentlichen Modellierungstechniken und Verfahrensans{{\"a}}tze der mathematischen Optimierung skizziert. Abschließend gehen wir auf die Planung einer ad{{\"a}}quaten Informations- und Kommunikations- Infrastruktur f{{\"u}}r ein dezentrales Energieversorgungsnetz ein.}, language = {de} } @misc{BleyKochWessaely, author = {Bley, Andreas and Koch, Thorsten and Wess{\"a}ly, Roland}, title = {Large-scale hierarchical networks: How to compute an optimal architecture?}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7799}, number = {04-04}, abstract = {In this article, we present a mathematical model and an algorithm to support one of the central strategic planning decisions of network operators: How to organize a large number of locations into a hierarchical network? We propose a solution approach that is based on mixed-integer programming and Lagrangian relaxation techniques. As major advantage, our approach provides not only solutions but also worst-case quality guarantees. Real-world scenarios with more than 750 locations have been solved within 30 minutes to less than 1\\% off optimality.}, language = {en} } @misc{Bley, author = {Bley, Andreas}, title = {On the Hardness of Finding Small Shortest Path Routing Conflicts}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11276}, number = {09-15}, abstract = {Nowadays most data networks use shortest path protocols such as OSPF or IS-IS to route traffic. Given administrative routing lengths for the links of a network, all data packets are sent along shortest paths with respect to these lengths from their source to their destination. One of the most fundamental problems in planning shortest path networks is to decide whether a given set of routing paths forms a valid routing and, if this is not the case, to find a small subset of the given paths that cannot be shortest paths simultaneously for any routing lengths. In this paper we show that it is NP-hard to approximate the size of the smallest shortest path conflict by a factor less than 7/6.}, language = {en} } @misc{BleyGleixnerKochetal., author = {Bley, Andreas and Gleixner, Ambros and Koch, Thorsten and Vigerske, Stefan}, title = {Comparing MIQCP solvers to a specialised algorithm for mine production scheduling}, organization = {ZIB}, issn = {1438-0064}, doi = {10.1007/978-3-642-25707-0}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11507}, number = {09-32}, abstract = {In this paper we investigate the performance of several out-of-the box solvers for mixed-integer quadratically constrained programmes (MIQCPs) on an open pit mine production scheduling problem with mixing constraints. We compare the solvers BARON, Couenne, SBB, and SCIP to a problem-specific algorithm on two different MIQCP formulations. The computational results presented show that general-purpose solvers with no particular knowledge of problem structure are able to nearly match the performance of a hand-crafted algorithm.}, language = {en} } @misc{Bley, author = {Bley, Andreas}, title = {An Integer Programming Algorithm for Routing Optimization in IP Networks}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10814}, number = {08-30}, abstract = {Most data networks nowadays use shortest path protocols to route the traffic. Given administrative routing lengths for the links of the network, all data packets are sent along shortest paths with respect to these lengths from their source to their destination. In this paper, we present an integer programming algorithm for the minimum congestion unsplittable shortest path routing problem, which arises in the operational planning of such networks. Given a capacitated directed graph and a set of communication demands, the goal is to find routing lengths that define a unique shortest path for each demand and minimize the maximum congestion over all links in the resulting routing. We illustrate the general decomposition approach our algorithm is based on, present the integer and linear programming models used to solve the master and the client problem, and discuss the most important implementational aspects. Finally, we report computational results for various benchmark problems, which demonstrate the efficiency of our algorithm.}, language = {en} } @misc{Bley, author = {Bley, Andreas}, title = {Approximability of Unsplittable Shortest Path Routing Problems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8968}, number = {06-02}, abstract = {In this paper, we discuss the relation of unsplittable shortest path routing (USPR) to other routing schemes and study the approximability of three USPR network planning problems. Given a digraph \$D=(V,A)\$ and a set \$K\$ of directed commodities, an USPR is a set of flow paths \$\Phi_{(s,t)}\$, \$(s,t)\in K\$, such that there exists a metric \$\lambda=(\lambda_a)\in \mathbb{Z}^A_+\$ with respect to which each \$\Phi_{(s,t)}\$ is the unique shortest \$(s,t)\$-path. In the \textsc{Min-Con-USPR} problem, we seek for an USPR that minimizes the maximum congestion over all arcs. We show that this problem is hard to approximate within a factor of \$\mathcal{O}(|V|^{1-\epsilon})\$, but easily approximable within min\$(|A|,|K|)\$ in general and within \$\mathcal{O}(1)\$ if the underlying graph is an undirected cycle or a bidirected ring. We also construct examples where the minimum congestion that can be obtained by USPR is a factor of \$\Omega(|V|^2)\$ larger than that achievable by unsplittable flow routing or by shortest multi-path routing, and a factor of \$\Omega(|V|)\$ larger than by unsplittable source-invariant routing. In the CAP-USPR problem, we seek for a minimum cost installation of integer arc capacities that admit an USPR of the given commodities. We prove that this problem is \$\mathcal{NP}\$-hard to approximate within \$2-\epsilon\$ (even in the undirected case), and we devise approximation algorithms for various special cases. The fixed charge network design problem \textsc{Cap-USPR}, where the task is to find a minimum cost subgraph of \$D\$ whose fixed arc capacities admit an USPR of the commodities, is shown to be \$\mathcal{NPO}\$-complete. All three problems are of great practical interest in the planning of telecommunication networks that are based on shortest path routing protocols. Our results indicate that they are harder than the corresponding unsplittable flow or shortest multi-path routing problems.}, language = {en} } @phdthesis{Bley, author = {Bley, Andreas}, title = {Routing and Capacity Optimization for IP Networks}, isbn = {978-3-86727-281-0}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:83-opus-15530}, abstract = {This thesis is concerned with dimensioning and routing optimization problems for communication networks that employ a shortest path routing protocol such as OSPF, IS-IS, or RIP. These protocols are widely used in the Internet. With these routing protocols, all end-to-end data streams are routed along shortest paths with respect to a metric of link lengths. The network administrator can configure the routing only by modifying this metric. In this thesis we consider the unsplittable shortest path routing variant, where each communication demand must be sent unsplit through the network. This requires that all shortest paths are uniquely determined. The major difficulties in planning such networks are that the routing can be controlled only indirectly via the routing metric and that all routing paths depend on the same routing metric. This leads to rather complicated and subtle interdependencies among the paths that comprise a valid routing. In contrast to most other routing schemes, the paths for different communication demands cannot be configured independent of each other. Part I of the thesis is dedicated to the relation between path sets and routing metrics and to the combinatorial properties of those path sets that comprise a valid unsplittable shortest path routing. Besides reviewing known approaches to find a compatible metric for a given path set (or to prove that none exists) and discussing some properties of valid path sets, we show that the problem of finding a compatible metric with integer lengths as small as possible and the problem of finding a smallest possible conflict in the given path set are both NP-hard to approximate within a constant factor. In Part II of the thesis we discuss the relation between unsplittable shortest path routing and several other routing schemes and we analyze the computational complexity of three basic unsplittable shortest path routing problems. We show that the lowest congestion that can be obtained with unsplittable shortest path routing may significantly exceed that achievable with other routing paradigms and we prove several non-approximability results for unsplittable shortest path routing problems that are stronger than those for the corresponding unsplittable flow problems. In addition, we derive various polynomial time approximation algorithms for general and special cases of these problems. In Part III of the thesis we finally develop an integer linear programming approach to solve these and more realistic unsplittable shortest path routing problems to optimality. We present alternative formulations for these problems, discuss their strength and computational complexity, and show how to derive strong valid inequalities. Eventually, we describe our implementation of this solution approach and report on the numerical results obtained for real-world problems that came up in the planning the German National Research and Education Networks G-WiN and X-WiN and for several benchmark instances.}, language = {en} } @misc{Bley, author = {Bley, Andreas}, title = {On the Complexity of Vertex-Disjoint Length-Restricted Path Problems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3639}, number = {SC-98-20}, abstract = {Let \$G=(V,E)\$ be a simple graph and \$s\$ and \$t\$ be two distinct vertices of \$G\$. A path in \$G\$ is called \$\ell\$-bounded for some \$\ell\in\mathbb{N}\$, if it does not contain more than \$\ell\$ edges. We study the computational complexity of approximating the optimum value for two optimization problems of finding sets of vertex-disjoint \$\ell\$-bounded \$s,t\$-paths in \$G\$. First, we show that computing the maximum number of vertex-disjoint \$\ell\$-bounded \$s,t\$-paths is \$\mathcal{AP\kern-1pt X}\$--complete for any fixed length bound \$\ell\geq 5\$. Second, for a given number \$k\in\mathbb{N}\$, \$1\leq k \leq |V|-1\$, and non-negative weights on the edges of \$G\$, the problem of finding \$k\$ vertex-disjoint \$\ell\$-bounded \$s,t\$-paths with minimal total weight is proven to be \$\mathcal{NPO}\$--complete for any length bound \$\ell\geq 5\$. Furthermore, we show that, even if \$G\$ is complete, it is \$\mathcal{NP}\$--complete to approximate the optimal solution value of this problem within a factor of \$2^{\langle\phi\rangle^\epsilon}\$ for any constant \$0<\epsilon<1\$, where \$\langle\phi\rangle\$ denotes the encoding size of the given problem instance \$\phi\$. We prove that these results are tight in the sense that for lengths \$\ell\leq 4\$ both problems are polynomially solvable, assuming that the weights satisfy a generalized triangle inequality in the weighted problem. All results presented also hold for directed and non-simple graphs. For the analogous problems where the path length restriction is replaced by the condition that all paths must have length equal to \$\ell\$ or where vertex-disjointness is replaced by edge-disjointness we obtain similar results.}, language = {en} } @misc{BleyGroetschelWessaely, author = {Bley, Andreas and Gr{\"o}tschel, Martin and Wess{\"a}ly, Roland}, title = {Design of Broadband Virtual Private Networks: Model and Heuristics for the B-WiN}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3565}, number = {SC-98-13}, abstract = {We investigate the problem of designing survivable broadband virtual private networks that employ the Open Shortest Path First (OSPF) routing protocol to route the packages. The capacities available for the links of the network are a minimal capacity plus multiples of a unit capacity. Given the directed communication demands between all pairs of nodes, we wish to select the capacities in a such way, that even in case of a single node or a single link failure a specified percentage of each demand can be satisfied and the costs for these capacities are minimal. We present a mixed--integer linear programming formulation of this problem and several heuristics for its solution. Furthermore, we report on computational results with real-world data.}, language = {en} } @misc{BienstockBley, author = {Bienstock, Daniel and Bley, Andreas}, title = {Capacitated Network Design with Multicast Commodities}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5823}, number = {00-14}, abstract = {This paper addresses the problem of designing a minimum cost network whose capacities are sufficiently large to allow a feasible routing of a given set of multicast commodities. A multicast commodity consists of a set of two or mo re terminals that need to be connected by a so called broadcast tree, which consumes on all of its edges a capacity as large as the demand value associated with that commodity. We model the network design problem with multicast commodities as the problem of packing capacitated Steiner trees in a graph. In the first part of the paper we present three mixed-integer programming formulations for this problem. The first natural formulation uses only one integer capacity variable for each edge and and one binary tree variable for each commodity-edge pair. Applying well-known techniques from the Steiner tree problem, we then develop a stronger directed and a multicommodity flow based mixed-integer programming formulation. In the second part of the paper we study the associated polyhedra and derive valid and even facet defining inequalities for the natural formulation. Finally, we describe separation algorithms for these inequalities and present computational results that demonstrate the strength of our extended formulations.}, language = {en} } @misc{Bley, author = {Bley, Andreas}, title = {Routing and Capacity Optimization for IP networks}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10323}, number = {07-33}, abstract = {This article describes the main concepts and techniques that have been developed during the last year at ZIB to solve dimensioning and routing optimization problems for IP networks. We discuss the problem of deciding if a given path set corresponds to an unsplittable shortest path routing, the fundamental properties of such path sets, and the computational complexity of some basic network planning problems for this routing type. Then we describe an integer-linear programming approach to solve such problems in practice. This approach has been used successfully in the planning of the German national education and research network for several years.}, language = {en} } @inproceedings{BleyGroetschelWessaely2000, author = {Bley, Andreas and Gr{\"o}tschel, Martin and Wess{\"a}ly, Roland}, title = {Design of broadband virtual private networks: Model and Heuristics for the B-WiN}, series = {Robust communication networks: Interconnection and survivability. DIMACS workshop, Princeton, NJ, USA, 1998 at Rutgers University}, volume = {53}, booktitle = {Robust communication networks: Interconnection and survivability. DIMACS workshop, Princeton, NJ, USA, 1998 at Rutgers University}, editor = {Dean, Nathaniel and Hsu, D. and Ravi, R.}, publisher = {American Mathematical Society}, address = {Providence, RI}, pages = {1 -- 16}, year = {2000}, language = {en} } @inproceedings{BleyMenneKlaehneetal.2008, author = {Bley, Andreas and Menne, Ulrich and Kl{\"a}hne, Roman and Raack, Christian and Wess{\"a}ly, Roland}, title = {Multi-layer network design - A model-based optimization approach}, series = {Proceedings of the PGTS 2008, Berlin, Germany}, booktitle = {Proceedings of the PGTS 2008, Berlin, Germany}, publisher = {Polish-German Teletraffic Symposium}, address = {Berlin, Germany}, pages = {107 -- 116}, year = {2008}, language = {en} } @misc{BleyD'AndreagiovanniKarch, author = {Bley, Andreas and D'Andreagiovanni, Fabio and Karch, Daniel}, title = {Scheduling technology migration in WDM Networks}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-42654}, abstract = {The rapid technological evolution of telecommunication networks demands service providers to regularly update their technology, with the aim of remaining competitive in the marketplace. However, upgrading the technology in a network is not a trivial task. New hardware components need to be installed in the network and during the installation network connectivity may be temporarily compromised. The Wavelength Division Multiplexing (WDM) technology, whose upgrade is considered in here, shares fiber links among several optical connections and tearing down a single link may disrupt several optical connections at once. When the upgrades involve large parts of a network, typically not all links can be upgraded in parallel, which may lead to an unavoidable longer disruption of some connections. A bad scheduling of the overall endeavor, however, can dramatically increase the disconnection time of parts of the networks, causing extended service disruption. In this contribution, we study the problem of finding a schedule of the fiber link upgrades that minimizes the total service disruption time. To the best of our knowledge, this problem has not yet been formalized and investigated. The aim of our work is to close this gap by presenting a mathematical optimization model for the problem and an innovative solution algorithm that tackles the intrinsic difficulties of the problem. Computational experience on realistic instances completes our study. Our original investigations have been driven by real needs of DFN, operator of the German National Research and Education Network and our partner in the BMBF research project ROBUKOM (http://www.robukom.de/).}, language = {en} } @inproceedings{BleyGleixnerKochetal.2012, author = {Bley, Andreas and Gleixner, Ambros and Koch, Thorsten and Vigerske, Stefan}, title = {Comparing MIQCP Solvers to a Specialised Algorithm for Mine Production Scheduling}, series = {Modeling, Simulation and Optimization of Complex Processes. Proceedings of the Fourth International Conference on High Performance Scientific Computing, March 2-6, 2009, Hanoi, Vietnam}, booktitle = {Modeling, Simulation and Optimization of Complex Processes. Proceedings of the Fourth International Conference on High Performance Scientific Computing, March 2-6, 2009, Hanoi, Vietnam}, doi = {10.1007/978-3-642-25707-0_3}, pages = {25 -- 39}, year = {2012}, abstract = {In this paper we investigate the performance of several out-of-the box solvers for mixed-integer quadratically constrained programmes (MIQCPs) on an open pit mine production scheduling problem with mixing constraints. We compare the solvers BARON, Couenne, SBB, and SCIP to a problem-specific algorithm on two different MIQCP formulations. The computational results presented show that general-purpose solvers with no particular knowledge of problem structure are able to nearly match the performance of a hand-crafted algorithm.}, language = {en} } @inproceedings{Bley, author = {Bley, Andreas}, title = {On the Hardness of Finding Small Shortest Path Routing Conflicts}, series = {Proceedings of 4th International Network Optimization Conference (INOC2009)}, booktitle = {Proceedings of 4th International Network Optimization Conference (INOC2009)}, abstract = {Nowadays most data networks use shortest path protocols such as OSPF or IS-IS to route traffic. Given administrative routing lengths for the links of a network, all data packets are sent along shortest paths with respect to these lengths from their source to their destination. One of the most fundamental problems in planning shortest path networks is to decide whether a given set of routing paths forms a valid routing and, if this is not the case, to find a small subset of the given paths that cannot be shortest paths simultaneously for any routing lengths. In this paper we show that it is NP-hard to approximate the size of the smallest shortest path conflict by a factor less than 7/6.}, language = {en} } @inproceedings{BleyD'AndreagiovanniKarch, author = {Bley, Andreas and D'Andreagiovanni, Fabio and Karch, Daniel}, title = {Scheduling technology migration in WDM Networks}, series = {Photonic Networks, 14. 2013 ITG Symposium. Proceedings}, booktitle = {Photonic Networks, 14. 2013 ITG Symposium. Proceedings}, pages = {1 -- 5}, language = {en} } @inproceedings{BleyD'AndreagiovanniKarch, author = {Bley, Andreas and D'Andreagiovanni, Fabio and Karch, Daniel}, title = {WDM Fiber Replacement Scheduling}, series = {Proceedings of INOC 2013}, volume = {41}, booktitle = {Proceedings of INOC 2013}, doi = {10.1016/j.endm.2013.05.092}, pages = {189 -- 196}, language = {en} } @inproceedings{BleyKoch2008, author = {Bley, Andreas and Koch, Thorsten}, title = {Integer programming approaches to access and backbone IP-network planning}, series = {Modeling, Simulation and Optimization of Complex Processes, Proceedings of the 3rd International Conference on High Performance Scientific Computing, March 6-10, Hanoi, Vietnam}, booktitle = {Modeling, Simulation and Optimization of Complex Processes, Proceedings of the 3rd International Conference on High Performance Scientific Computing, March 6-10, Hanoi, Vietnam}, publisher = {Springer}, pages = {87 -- 110}, year = {2008}, language = {en} } @article{BleyKoch2000, author = {Bley, Andreas and Koch, Thorsten}, title = {Optimierung des G-WiN}, series = {DFN-Mitteilungen}, journal = {DFN-Mitteilungen}, number = {54}, pages = {13 -- 15}, year = {2000}, language = {en} } @inproceedings{BleyKochWessaely2004, author = {Bley, Andreas and Koch, Thorsten and Wess{\"a}ly, Roland}, title = {Large-Scale hierarchical networks: How to compute an optimal architecture?}, series = {Networks 2004}, booktitle = {Networks 2004}, editor = {Kaindl, H.}, publisher = {VDE Verlag}, address = {Berlin}, isbn = {3-8007-2840-0}, pages = {429 -- 434}, year = {2004}, language = {en} } @inproceedings{MatuschkeBleyMueller, author = {Matuschke, Jannik and Bley, Andreas and M{\"u}ller, Benjamin}, title = {Approximation Algorithms for Facility Location with Capacitated and Length-Bounded Tree Connections}, volume = {Algorithms -- ESA 2013}, editor = {Bodlaender, Hans L. and Italiano, Giuseppe F.}, publisher = {Springer}, doi = {10.1007/978-3-642-40450-4_60}, pages = {707 -- 718}, abstract = {We consider a generalization of the uncapacitated facility location problem that occurs in planning of optical access networks in telecommunications. Clients are connected to open facilities via depth-bounded trees. The total demand of clients served by a tree must not exceed a given tree capacity. We investigate a framework for combining facility location algorithms with a tree-based clustering approach and derive approximation algorithms for several variants of the problem, using techniques for approximating shallow-light Steiner trees via layer graphs, simultaneous approximation of shortest paths and minimum spanning trees, and greedy coverings.}, language = {en} }