Mixed integer programming approaches to problems combining network design and facility location

Viele heutzutage über das Internet angebotene Dienstleistungen benötigen wesentlich höhere Bandbreiten als von bestehenden lokalen Zugangsnetzen bereitgestellt werden. Telekommunikationsanbieter sind daher seit einigen Jahren bestrebt, ihre zum Großteil auf Kupferkabeln basierenden Zugangsnetze entsprechend zu modernisieren. Die gewünschte Erweiterung der bereitgestellten Bandbreiten wird oftmals erzielt, indem ein Teil des Kupfernetzes durch Glasfaser ersetzt wird. Dafür sind Versorgungsstandorte notwendig, an welchen die optischen und elektrischen Signale jeweils in einander umgewandelt werden. In der Praxis gibt es mehrere Strategien für die Installation von optischen Zugangsnetzen. Fiber-to-the-Home bezeichnet Netze, in denen jeder Haushalt direkt per Glasfaser angebunden wird. Wird je Wohngebäude eine optische Verbindung bereitgestellt, nennt man dies Fiber-to-the-Building. Endet die Glasfaserverbindung an einem Versorgungsstandort, welcher die Haushalte eines ganzen Wohnviertels durch Kupferkabel versorgt, bezeichnet man dies als Fiber-to-the-Curb. Inhalt dieser Dissertation sind mathematische Optimierungsmodelle für die kosteneffiziente Planung von auf Glasfaser basierenden lokalen Zugangsnetzen. Diese Modelle decken mehrere Aspekte der Planung ab, darunter die Fiber-to-the-Curb-Strategie mit zusätzlichen Restriktionen betreffend Ausfallssicherheit, gemischte Fiber-to-the-Home und Fiber-to-the-Curb-Netze sowie die Kapazitätenplanung von Fiber-to-the-Curb-Netzen. Ergebnis dieser Dissertation sind die theoretische Analyse der beschriebenen Modelle sowie effiziente Lösungsalgorithmen. Es kommen Methoden der kombinatorischen Optimierung zum Einsatz, darunter Umformulierungen auf erweiterten Graphen, zulässige Ungleichungen und Branch-and-Cut-Verfahren.In recent years, telecommunication service providers started to adapt their local access networks to the steadily growing demand for bandwidth of internet-based services. Most existing local access networks are based on copper cable and offer a limited bandwidth to customers. A common approach to increase this bandwidth is to replace parts of the network by fiber-optic cable. This requires the installation of facilities, where the optical signal is transformed into an electrical one and vice versa. Several strategies are commonly used to deploy fiber-optic networks. Connecting each customer via a fiber-optic link is referred to as Fiber-to-the-Home. If there is a fiber-optic connection for every building this is commonly referred to as Fiber-to-the-Building. If a fiber-optic connection leads to each facility that serves an entire neighborhood, this is referred to as Fiber-to-the-Curb. In this thesis we propose mathematical optimization models for the cost-efficient design of local access networks based on fiber-optic cable. These models cover several aspects, including the Fiber-to-the-Curb strategy under additional reliability constraints, mixed Fiber-to-the-Home and Fiber-to-the-Curb strategies and capacity planning of links and facilities for Fiber-to-the-Curb networks. We provide a theoretical analysis of the proposed models and develop efficient solution algorithms. We use state-of-the-art methods from combinatorial optimization including polyhedral comparisons, reformulations on extended graphs, valid inequalities and branch-and-cut procedures

Fiber to the home

In den letzten Jahren gab es zunehmenden Bedarf für breitbandige Telekommunikations Netzwerke. Eine von Telekommunikationsunternehmen angewandte Strategie um die Bandbreite entlang der last-mile des Netzwerks zu erhöhen ist, Glasfaserkabel direkt bis zum Endkunden zu verlegen. Diese Strategie wird fiber to the home (FTTH) genannt. In der vorliegenden Arbeit wird das local access network design problem (LAN) und die Variante mit prize-collecting (PC-LAN) verwendet, um das Problem der FTTH Planung zu modellieren. Das LAN Problem zielt darauf ab eine kostenminimale Lösung zu finden und gestattet es sowohl verschiedene Kabeltechnologien und existierende Infrastruktur, als auch die Zusatzkosten zu modellieren, die anfallen wenn neue Verbindungen hergestellt werden. Darüber hinaus, erlaubt das PC-LAN Problem den Aspekt zu modellieren, dass nicht unbedingt alle Kunden mit FTTH versorgt werden müssen. Stattdessen wird eine Teilmenge der Kunden versorgt mit dem Ziel den Profit zu maximieren. Um LAN und PC-LAN Problem Instanzen zu lösen, werden folgende Methoden des Operations Research angewandt: Preprocessing, ganzzahlige Programmierung, Stärkung der mathematischen Modelle durch Disaggregation der Variablen, Benders' Dekomposition und adaptive Multi-Start-Heuristiken. In einem Projekt von Universität Wien und Telekom Austria wurden große FTTH Datensätze untersucht und die hier vorgestellten Methoden entworfen. Diese Lösungsansätze wurden als Computerprogramme implementiert und ihre Tauglichkeit zur Behandlung von FTTH Planungsfragen konnte gezeigt werden.Within recent years the request for broadband telecommunication networks has been constantly increasing. A strategy employed by telecommunication companies to increase the bandwidth on the last mile of the network is to lay optical fiber directly to the end customer. This strategy is denoted as fiber to the home (FTTH). In this thesis the local access network design problem (LAN) and its prize-collecting variant (PC-LAN) are used to formalize the planning of FTTH networks. The LAN problem asks for a cost minimal solution and allows to model different cable technologies, existing infrastructure and the overhead cost incurred by building new connections. In addition, the PC-LAN problem covers the aspect, that not all customers must necessarily be connected with FTTH, but instead we search for a subset of customers in order to maximize profits. To solve LAN and PC-LAN instances, the following operations research methods are employed: Preprocessing, mixed integer programming, model strengthening by variable disaggregation, Benders' decomposition and adaptive multi-start heuristics. In a project between University of Vienna and Telekom Austria, large real world data sets for FTTH planning were investigated and the methods presented in this thesis have been designed. These solution methods have been implemented as computer programs and empirically verified to be reasonable approaches to FTTH network design problems

Operational Research: Methods and Applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes

Model-Based Heuristics for Combinatorial Optimization

Many problems arising in several and different areas of human knowledge share the characteristic of being intractable in real cases. The relevance of the solution of these problems, linked to their domain of action, has given birth to many frameworks of algorithms for solving them. Traditional solution paradigms are represented by exact and heuristic algorithms. In order to overcome limitations of both approaches and obtain better performances, tailored combinations of exact and heuristic methods have been studied, giving birth to a new paradigm for solving hard combinatorial optimization problems, constituted by model-based metaheuristics. In the present thesis, we deepen the issue of model-based metaheuristics, and present some methods, belonging to this class, applied to the solution of combinatorial optimization problems

Operational Research: Methods and Applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order

Operational research:methods and applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order

Efficient Algorithms for Infrastructure Networks: Planning Issues and Economic Impact

Mei, R.D. van der [Promotor]Bhulai, S. [Copromotor

Parallel algorithms for two-stage stochastic optimization

We develop scalable algorithms for two-stage stochastic program optimizations. We propose performance optimizations such as cut-window mechanism in Stage 1 and scenario clustering in Stage 2 of benders method for solving two-stage stochastic programs. A naive implementation of benders method has slow convergence rate and does not scale well to large number of processors especially when the problem size is large and/or there are integer variables in Stage 1. Parallelization of stochastic integer programs pose very unique characteristics that make them very challenging to parallelize. We develop a Parallel Stochastic Integer Program Solver (PSIPS) that exploits nested parallelism by exploring the branch-and-bound tree vertices in parallel along with scenario parallelization. PSIPS has been shown to have high parallel efficiency of greater than 40% at 120 cores which is significantly greater than the parallel efficiency of state-of-the-art mixed-integer program solvers. A significant portion of the time in this branch-and-bound solver is spent in optimizing the stochastic linear program at the root vertex. Stochastic linear programs at other vertices of the branch-and-bound tree take very less iterations to converge because they can inherit benders cut from their parent vertices and/or the root. Therefore, it is important to reduce the optimization time of the stochastic linear program at the root vertex. We propose two decomposition schemes namely the Split-and-Merge (SAM) method and the Lagrangian Decomposition and Merge (LDAM) method that significantly increase the convergence rate of benders decomposition. SAM method gives up to 64% reduction in solution time while also giving significantly higher parallel speedups as compared to the naive benders method. LDAM method, on the other hand, has made it possible to solve otherwise intractable stochastic programs. We further provide a computational engine for many real-time and dynamic problems faced by US Air Mobility Command. We first propose a stochastic programming solution to the military aircraft allocation problem with consideration for disaster management. Then, we study US AMC's dynamic mission re-planning problem and propose a mathematical formulation that is computationally feasible and leads to significant savings in cost as compared to myopic and deterministic optimization. It is expected that this work will provide the springboard for more robust problem solving with HPC in many logistics and planning problems

Operational Research: methods and applications

This is the final version. Available on open access from Taylor & Francis via the DOI in this recordThroughout its history, Operational Research has evolved to include methods, models and algorithms that have been applied to a wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first summarises the up-to-date knowledge and provides an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion and used as a point of reference by a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes