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Ende Juni diesen Jahres wurde das Gigabit-Wissenschaftsnetz offiziell gestartet. In der zweijährigen Vorbereitungsphase wurden nicht nur die technischen Möglichkeiten der neuen Übertragungstechniken und Dienste getestet. Es wurden auch verschiedene Fragestellungen zum effizienten Einsatz der verfügbaren Ressourcen für den Betrieb des G-WiN untersucht. In diesem Artikel beschreiben wir, wie das G-WiN zu seiner jetzigen Struktur und Topologie gekommen ist.
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.
A model for the optimisation of the location and configuration of base stations in a UMTS network is described. The focus is primarily on modelling the configuration problem sufficiently accurate using mixed-integer variables and (essentially) linear constraints. These constraints reflect the limited downlink code capacity in each cell, the interference limitations for successful up- and downlink transmissions, the need for sufficiently strong (cell) pilot signals, and the potential gain for mobiles from being in soft(er) hand-over. It is also explained how to use the model as a basis for rating network configurations.
Mixed integer programs ($MIPs$) are commonly solved with branch and bound algorithms based on linear programming. The success and the speed of the algorithm strongly depends on the strategy used to select the branching variables. Today's state-of-the-art strategy is called \emph{pseudocost branching} and uses information of previous branchings to determine the current branching. We propose a modification of \emph{pseudocost branching} which we call \emph{history branching}. This strategy has been implemented in $SIP$, a state-of-the-art $MIP$ solver. We give computational results that show the superiority of the new strategy.
ZIMPL User Guide
(2001)
The thesis deals with the implementation and application of out-of-the-box tools in linear and mixed integer programming. It documents the lessons learned and conclusions drawn from five years of implementing, maintaining, extending, and using several computer codes to solve real-life industrial problems. By means of several examples it is demonstrated how to apply algebraic modeling languages to rapidly devise mathematical models of real-world problems. It is shown that today's MIP solvers are capable of solving the resulting mixed integer programs, leading to an approach that delivers results very quickly. Even though, problems are tackled that not long ago required the implementation of specialized branch-and-cut algorithms. In the first part of the thesis the modeling language Zimpl is introduced. Chapter 2 contains a complete description of the language. In the subsequent chapter details of the implementation are described. Both theoretical and practical considerations are discussed. Aspects of software engineering, error prevention, and detection are addressed. In the second part several real-world projects are examined that employed the methodology and the tools developed in the first part. Chapter 4 presents three projects from the telecommunication industry dealing with facility location problems. Chapter 5 characterizes questions that arise in UMTS planning. Problems, models, and solutions are discussed. Special emphasis is put on the dependency of the precision of the input data and the results. Possible reasons for unexpected and undesirable solutions are explained. Finally, the Steiner tree packing problem in graphs, a well-known hard combinatorial problem, is revisited. A formerly known, but not yet used model is applied to combine switchbox wire routing and via minimization. All instances known from the literature are solved by this approach, as are some newly generated bigger problem instances.
In this article, strategical infrastructure planning problems in the design of large-scale telecommunication networks are discussed based on experiences from three projects with industrial partners: The access network planning of the German Gigabit-Wissenschaftsnetz (G-WiN) for DFN (Verein zur Förderung eines Deutschen Forschungsnetzes e.V.), the mobile network switching center location planning project for E-Plus Mobilfunk, and the fixed network switching center location planning project for TELEKOM AUSTRIA. We introduce a mathematical model for a hierarchical multi-commodity capacitated facility location problem, present adaptions of this basic model to the specific requirements within the different projects and discuss the individual peculiarities and model decisions made. Eventually, we present and discuss computational results of three associated case studies, illustrating '"how we did the job`` with mathematical methods.
The final NETLIB-LP results
(2003)
The NETLIB has now served for 18 years as a repository of LP problem instances. From the beginning to the present day there was some uncertainness about the precise values of the optimal solutions. We implemented a program using exact rational arithmetic to compute proofs for the feasibility and optimality of an LP solution. This paper reports the \emph{exact} optimal objective values for all NETLIB problems.
We present publicly available data sets related to research on wireless networks. The scenarios contain a wide range of data and are detailed in all aspects. To our knowledge, this is the most realistic, comprehensive, and detailed \emph{public} data collection on mobile networking. We indicate example uses of this data collection in applications related tu UMTS.
Branching rules revisited
(2004)
Mixed integer programs are commonly solved with linear programming based branch-and-bound algorithms. The success of the algorithm strongly depends on the strategy used to select the variable to branch on. We present a new generalization called {\sl reliability branching} of today's state-of-the-art {\sl strong branching} and {\sl pseudocost branching} strategies for linear programming based branch-and-bound algorithms. After reviewing commonly used branching strategies and performing extensive computational studies we compare different parameter settings and show the superiority of our proposed newstrategy.
This paper is concerned with UMTS radio network design. Our task is to reconfigure antennas and the related cells as to improve network quality. In contrast to second generation GSM networks, \emph{interference} plays a paramount role when designing third generation radio networks. A known compact formulation for assessing the interference characteristics of a radio network as coupling relations between cells based on user snapshots is generalized to statistical average load. This enables us to overcome the notorious difficulties of snapshot-based network optimization approaches. We recall a mixed-integer programming model for the network design problem that is based on user snapshots and contrast it with a new network design model based on the average coupling formulation. Exemplarily focusing on the important problem of optimizing antenna tilts, we give computational results for a fast local search algorithm and the application of a MIP solver to both models. These results demonstrate that our new average-based approaches outperform state-of-the-art snapshot models for UMTS radio network optimization.
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.
The UMTS radio network planning problem poses the challenge of designing a cost-effective network that provides users with sufficient coverage and capacity. We describe an optimization model for this problem that is based on comprehensive planning data of the EU project MOMENTUM. We present heuristic mathematical methods for this realistic model, including computational results.
"`Volkssport Sudoku"' titelt der Stern in seiner Ausgabe vom 24. Mai2006. In der Tat traut sich derzeit kaum noch eine Zeitung, ohne Sudoku zu erscheinen. Die Begeisterung am Lösen dieser Zahlenrätsel offenbart eine unvermutete Freude am algorithmischen Arbeiten. Mathematisch kann man Sudokus als lineare diophantische Gleichungssysteme mit Nichtnegativitätsbedingungen formulieren. Solche ganzzahligen linearen Programme sind die wichtigsten Modellierungswerkzeuge in zahlreichen Anwendungsgebieten wie z.B. der Optimierung von Telekommunikations- und Verkehrsnetzen. Moderne Verfahren zur Lösung dieser Optimierungsprobleme sind durch Sudokus allerdings deutlich weniger zu beeindrucken als Zeitungsleser.
This paper concerns the problem of operating a landside container exchange area that is serviced by multiple semi-automated rail mounted gantry cranes (RMGs) that are moving on a single bi-directional traveling lane. Such a facility is being built by Patrick Corporation at the Port Botany terminal in Sydney. The gantry cranes are a scarce resource and handle the bulk of container movements. Thus, they require a sophisticated analysis to achieve near optimal utilization. We present a three stage algorithm to manage the container exchange facility, including the scheduling of cranes, the control of associated short-term container stacking, and the allocation of delivery locations for trucks and other container transporters. The key components of our approach are a time scale decomposition, whereby an integer program controls decisions across a long time horizon to produce a balanced plan that is fed to a series of short time scale online subproblems, and a highly efficient space-time divisioning of short term storage areas. A computational evaluation shows that our heuristic can find effective solutions for the planning problem; on real-world data it yields a solution at most~8\% above a lower bound on optimal RMG utilization.
Modern applications of mathematical programming must take into account a multitude of technical details, business demands, and legal requirements. Teaching the mathematical modeling of such issues and their interrelations requires real-world examples that are well beyond the toy sizes that can be tackled with the student editions of most commercial software packages. We present a new tool, which is freely available for academic use including complete source code. It consists of an algebraic modeling language and a linear mixed integer programming solver. The performance and features of the tool are in the range of current state-of-the-art commercial tools, though not in all aspects as good as the best ones. Our tool does allow the execution and analysis of large real-world instances in the classroom and can therefore enhance the teaching of problem solving issues. Teaching experience has been gathered and practical usability was tested in classes at several universities and a two week intensive block course at TU Berlin. The feedback from students and teachers has been very positive.
MIPLIB 2003
(2005)
This paper reports on the fourth version of the Mixed Integer Programming Library. Since ({\sc miplib}) is to provide a concise set of challenging problems, it became necessary to purge instances that became too easy. We present an overview of the 27 new problems and statistical data for all 60 instances.
In this paper we present the implementation of a branch-and-cut algorithm for solving Steiner tree problems in graphs. Our algorithm is based on an integer programming formulation for directed graphs and comprises preprocessing, separation algorithms and primal heuristics. We are able to solve all problem instances discussed in literature to optimality, including one to our knowledge not yet solved problem. We also report on our computational experiences with some very large Steiner tree problems arising from the design of electronic circuits. All test problems are gathered in a newly introduced library called {\em SteinLib} that is accessible via World Wide Web.
In this paper we present the {\em SteinLib}, a library of data sets for the Steiner tree problem in graphs. This library extends former libraries on Steiner tree problems by many new interesting and difficult instances, most of them arising from real-world applications. We give a survey on the difficulty of these problem instances by giving references to state-of-the-art software packages that were the first or are currently among the best to solve these instances.