Extended formulation for hop constrained distribution network configuration problems

International audienceA distribution network is a system aiming to transfer a certain type of resource from feeders to customers. Feeders are producers of a resource and customers have a certain demand in this resource that must be satisfied. Distribution networks can be represented on graphs and be subject to constraints that limit the number of intermediate nodes between some elements of the network (hop constraints) because of physical constraints. This paper uses layered graphs for hop constrained problems to build extended formulations. Preprocessing techniques are also presented to reduce the size of the layered graphs used. The presented model is studied on the hop-constrained minimum margin problem in an electricity network. This problem consists of designing a connected electricity distribution network, and to assign customers to electricity feeders at a maximum number of hops H so as to maximize the minimum capacity margin over the feeders to avoid an overload for any feeder. Numerical results of our model are compared with those of state-of-the-art solution techniques of the minimum margin problem form Rossi et al. [20]. Variations of the initial problem are also presented, considering losses due to transportation or by replacing hop constraints by distance constraints, a variation arising in the context of multicast transmission in telecommunications

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

Estimating the efficacy of mass rescue operations in ocean areas with vehicle routing models and heuristics

Tese de doutoramento, Estatística e Investigação Operacional (Optimização), Universidade de Lisboa, Faculdade de Ciências, 2018Mass rescue operations (MRO) in maritime areas, particularly in ocean areas, are a major concern for the authorities responsible for conducting search and rescue (SAR) activities. A mass rescue operation can be defined as a search and rescue activity characterized by the need for immediate assistance to a large number of persons in distress, such that the capabilities normally available to search and rescue are inadequate. In this dissertation we deal with a mass rescue operation within ocean areas and we consider the problem of rescuing a set of survivors following a maritime incident (cruise ship, oil platform, ditched airplane) that are drifting in time. The recovery of survivors is performed by nearby ships and helicopters. We also consider the possibility of ships capable of refuelling helicopters while hovering which can extend the range to which survivors can be rescued. A linear binary integer formulation is presented along with an application that allows users to build instances of the problem. The formulation considers a discretization of time within a certain time step in order to assess the possibility of travelling along different locations. The problem considered in this work can be perceived as an extension of the generalized vehicle routing problem (GVRP) with a profit stance since we may not be able to recover all of the survivors. We also present a look ahead approach, based on the pilot method, to the problem along with some optimal results using state of the art Mixed-integer linear programming solvers. Finally, the efficacy of the solution from the GVRP is estimated for a set of scenarios that combine incident severity, location, traffic density for nearby ships and SAR assets availability and location. Using traffic density maps and the estimated MRO efficacy, one can produce a combined vulnerability map to ascertain the quality of response to each scenario.Marinha Portuguesa, Plano de Atividades de Formação Nacional (PAFN