Layered graph approaches for combinatorial optimization problems

Extending the concept of time-space networks, layered graphs associate information about one or multiple resource state values with nodes and arcs. While integer programming formulations based on them allow to model complex problems comparably easy, their large size makes them hard to solve for non-trivial instances. We detail and classify layered graph modeling techniques that have been used in the (recent) scientific literature and review methods to successfully solve the resulting large-scale, extended formulations. Modeling guidelines and important observations concerning the solution of layered graph formulations by decomposition methods are given together with several future research directions

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

Benders decomposition for network design covering problems

Article number 105417We consider two covering variants of the network design problem. We are given a set of origin/destination pairs, called O/D pairs, and each such O/D pair is covered if there exists a path in the network from the origin to the destination whose length is not larger than a given threshold. In the first problem, called the Maximal Covering Network Design problem, one must determine a network that maximizes the total fulfilled demand of the covered O/D pairs subject to a budget constraint on the design costs of the network. In the second problem, called the Partial Covering Network Design problem, the design cost is minimized while a lower bound is set on the total demand covered. After presenting formulations, we develop a Benders decomposition approach to solve the problems. Further, we consider several stabilization methods to determine Benders cuts as well as the addition of cut-set inequalities to the master problem. We also consider the impact of adding an initial solution to our methods. Computational experiments show the efficiency of these different aspects.Feder (UE) PID2019- 106205GB-I00FEDER(UE) MTM2015-67706-PFonds de la Recherche Scientifique PDR T0098.1

The Steiner Tree Problem with Delays: A compact formulation and reduction procedures

This paper investigates the Steiner Tree Problem with Delays (STPD), a variation of the classical Steiner Tree problem that arises in multicast routing. We propose an exact solution approach that is based on a polynomial-size formulation for this challenging NP-hard problem. The LP relaxation of this formulation is enhanced through the derivation of new lifted Miller-Tucker-Zemlin subtour elimination constraints. Furthermore, we present several preprocessing techniques for both reducing the problem size and tightening the LP relaxation. Finally, we report the results of extensive computational experiments on instances with up to 1000 nodes. These results attest to the efficacy of the combination of the enhanced formulation and reduction techniques