TY - GEN A1 - Bley, Andreas A1 - Grötschel, Martin A1 - Wessäly, Roland T1 - Design of Broadband Virtual Private Networks: Model and Heuristics for the B–WiN N2 - 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. T3 - ZIB-Report - SC-98-13 KW - Telecommunication Network Design KW - Survivable Networks KW - Network Capacity Planning KW - OSPF Routing KW - Shortest Path Routing KW - Heuristics Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3565 ER - TY - GEN A1 - Bley, Andreas A1 - Gleixner, Ambros A1 - Koch, Thorsten A1 - Vigerske, Stefan T1 - Comparing MIQCP solvers to a specialised algorithm for mine production scheduling N2 - 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. T3 - ZIB-Report - 09-32 Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11507 SN - 1438-0064 ER - TY - GEN A1 - Bley, Andreas T1 - A Lagrangian Approach for Integrated Network Design and Routing in IP Networks N2 - 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. T3 - ZIB-Report - 03-29 KW - Network Planning KW - Routing KW - IP Routing KW - Lagrangian relaxation Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7515 ER - TY - GEN A1 - Bley, Andreas A1 - Koch, Thorsten T1 - Integer programming approaches to access and backbone IP-network planning N2 - 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. T3 - ZIB-Report - 02-41 KW - Network design KW - Traffic enineering KW - Internet routing KW - Mixed-integer programming Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7081 ER - TY - GEN A1 - Bienstock, Daniel A1 - Bley, Andreas T1 - Capacitated Network Design with Multicast Commodities N2 - 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. T3 - ZIB-Report - 00-14 KW - multicast network design KW - Steiner tree packing Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5823 ER - TY - GEN A1 - Bley, Andreas T1 - An Integer Programming Algorithm for Routing Optimization in IP Networks N2 - 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. T3 - ZIB-Report - 08-30 KW - Shortest Path Routing KW - Integer Programming Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10814 SN - 1438-0064 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 - TY - GEN A1 - Bley, Andreas T1 - Routing and Capacity Optimization for IP networks N2 - 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. T3 - ZIB-Report - 07-33 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:0297-zib-10323 SN - 1438-0064 ER -