TY - THES A1 - Zymolka, Adrian T1 - Design of Survivable Optical Networks by Mathematical Optimization N2 - Abstract The cost-efficient design of survivable optical telecommunication networks is the topic of this thesis. In cooperation with network operators, we have developed suitable concepts and mathematical optimization methods to solve this comprehensive planning task in practice. Optical technology is more and more employed in modern telecommunication networks. Digital information is thereby transmitted as short light pulses through glass fibers. Moreover, the optical medium allows for simultaneous transmissions on a single fiber by use of different wavelengths. Recent optical switches enable a direct forwarding of optical channels in the network nodes without the previously required signal retransformation to electronics. Their integration creates ongoing optical connections,which are called lightpaths. We study the problem of finding cost-efficient configurations of optical networks which meet specified communication requirements. A configuration comprises the determination of all lightpaths to establish as well as the detailed allocation of all required devices and systems. We use a flexible modeling framework for a realistic representation of the networks and their composition. For different network architectures, we formulate integer linear programs which model the design task in detail. Moreover, network survivability is an important issue due to the immense bandwidths offered by optical technology. Operators therefore request for designs which perpetuate protected connections and guarantee for a defined minimum throughput in case of malfunctions. In order to achieve an effective realization of scalable protection, we present a novel survivability concept tailored to optical networks and integrate several variants into the models. Our solution approach is based on a suitable model decomposition into two subtasks which separates two individually hard subproblems and enables this way to compute cost-efficient designs with approved quality guarantee. The first subtask consists of routing the connections with corresponding dimensioning of capacities and constitutes a common core task in the area of network planning. Sophisticated methods for such problems have already been developed and are deployed by appropriate integration. The second subtask is characteristic for optical networks and seeks for a conflict-free assignment of available wavelengths to the lightpaths using a minimum number of involved wavelength converters. For this coloring-like task, we derive particular models and study methods to estimate the number of unavoidable conversions. As constructive approach, we develop heuristics and an exact branch-and-price algorithm. Finally, we carry out an extensive computational study on realistic data, provided by our industrial partners. As twofold purpose, we demonstrate the potential of our approach for computing good solutions with quality guarantee, and we exemplify its flexibility for application to network design and analysis. KW - network design KW - optical networks KW - integer programming KW - mathematical optimization Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10408 ER - TY - THES A1 - Koch, Thorsten T1 - Rapid Mathematical Programming N2 - 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. T3 - ZIB-Report - 04-58 KW - Modelling Languages KW - Mixed Integer Programming KW - Steiner Tree Packing in Graphs KW - Location Planning in Telecommunications KW - UMTS Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8346 ER - TY - THES A1 - Bley, Andreas T1 - Routing and Capacity Optimization for IP Networks N2 - 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. N2 - Die Arbeit befasst sich mit der Kapazitäts- und Routenplanung für Kommunikationsnetze, die ein kürzeste-Wege Routingprotokoll verwenden. Diese Art von Protokollen ist im Internet weit verbreitet. Bei diesen Routingverfahren wird für jede Verbindung im Netz ein Längenwert festgelegt, diese Längen formen die sogenannte Routingmetrik. Die Routingwege der Kommunikationsbedarfe sind dann die jeweiligen kürzesten Wege bezüglich dieser Metrik. Bei der in der Arbeit untersuchten Variante dieser Routingprotokolle wird zusätzlich verlangt, dass es je Kommunikationsbedarf genau einen eindeutigen kürzesten Weg gibt. Die Schwierigkeit bei der Planung solcher Netze besteht darin, dass sich die Routingwege einerseits nur indirekt über die Routingmetrik beeinflussen lassen, andererseits aber alle Routingwege von der gleichen Metrik abhängen. Dadurch können die Wege verschiedener Kommunikationsanforderungen nicht wie bei anderen Routingverfahren unabhängig voneinander gewählt werden. Im erstem Teil der Arbeit werden der Zusammenhang zwischen gegebenen Wegesystemen und kompatiblen Routingmetriken sowie die Beziehungen der Wege eines zulässigen eindeutige-kürzeste-Wege-Routings untereinander untersucht. Dabei wird unter Anderem gezeigt, dass es NP-schwer ist, eine kompatible Metrik mit kleinstmöglichen Routinglängen zu einem gegebenen Wegesystem zu finden. Es wird auch bewiesen, dass das Finden eines kleinstmöglichen Konfliktes in einem gegebenen Wegesystem, zu dem keine kompatible Metrik existiert, NP-schwer ist. Im zweiten Teil der Arbeit wird die Approximierbarkeit von drei grundlegenden Netz- und Routenplanungsproblemen mit eindeutige-kürzeste-Wege-Routing untersucht. Für diese Probleme werden stärkere Nichtapproximierbarkeitsresultate als für die entsprechenden Einwege-Routing Probleme bewiesen und es werden verschiedene polynomiale Approximationsverfahren für allgemeine und Spezialfälle entworfen. Ausserdem wird die Beziehung zwischen eindeutige-kürzeste-Wege-Routing und anderen Routingverfahren diskutiert. Im dritten und letzten Teil der Arbeit wird ein (gemischt-) ganzzahliger Lösungsansatz für Planungsprobleme mit eindeutige-kürzeste-Wege-Routing vorgestellt. Für die im zweiten Teil diskutierten grundlegenden Netz- und Routenplanungsprobleme werden verschiedene (gemischt-) ganzzahlige lineare Modelle vorgestellt und es wird deren Lösbarkeit und die Stärke ihrer LP Relaxierungen untersucht. Es wird auch gezeigt, wie sich starke gültig Ungleichungen aus den in diesen Modellen enthalten Substrukturen ableiten lassen. Schlielich werden am Ende der Arbeit die Software-Implementierung dieses Lösungsverfahrens für eine praxisrelevante Verallgemeinerung der Planungsprobleme sowie die damit erzielten numerischen Ergebnisse vorgestellt und diskutiert. KW - kombinatorische Optimierung KW - gemischt-ganzzahlige Programmierung KW - kürzeste-Wege Routing KW - Approximationsalgorithmen KW - combinatorial optimization KW - mixed-integer programming KW - shortest path routing KW - approximation algorithms Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:83-opus-15530 SN - 978-3-86727-281-0 ER -