Extended Cutset Inequalities for the Network Power Consumption Problem

International audienceIn this paper, we enhance the MIP formulation for the Network Power Consumption problem, proposed by Giroire et al. We derive cutting planes, extending the well-known cutset inequalities, and report on preliminary computations

Lecture Notes on Network Information Theory

These lecture notes have been converted to a book titled Network Information Theory published recently by Cambridge University Press. This book provides a significantly expanded exposition of the material in the lecture notes as well as problems and bibliographic notes at the end of each chapter. The authors are currently preparing a set of slides based on the book that will be posted in the second half of 2012. More information about the book can be found at http://www.cambridge.org/9781107008731/. The previous (and obsolete) version of the lecture notes can be found at http://arxiv.org/abs/1001.3404v4/

Energy management in communication networks: a journey through modelling and optimization glasses

The widespread proliferation of Internet and wireless applications has produced a significant increase of ICT energy footprint. As a response, in the last five years, significant efforts have been undertaken to include energy-awareness into network management. Several green networking frameworks have been proposed by carefully managing the network routing and the power state of network devices. Even though approaches proposed differ based on network technologies and sleep modes of nodes and interfaces, they all aim at tailoring the active network resources to the varying traffic needs in order to minimize energy consumption. From a modeling point of view, this has several commonalities with classical network design and routing problems, even if with different objectives and in a dynamic context. With most researchers focused on addressing the complex and crucial technological aspects of green networking schemes, there has been so far little attention on understanding the modeling similarities and differences of proposed solutions. This paper fills the gap surveying the literature with optimization modeling glasses, following a tutorial approach that guides through the different components of the models with a unified symbolism. A detailed classification of the previous work based on the modeling issues included is also proposed

Synthesizing Robust Networks for Engineering Applications with Resource Constraints

This dissertation deals with the following simpler version of an open problem in system realization theory which has several important engineering applications: Given a collection of masses and a set of linear springs with a specified cost and stiffness, a resource constraint in terms of a budget on the total cost, the problem is to determine an optimal connection of masses and springs so that the resulting structure is as stiff as possible, i.e., the structure is connected and its smallest nonzero natural frequency is as large as possible. One often encounters variants of this problem in deploying Unmanned Aerial Vehicles (UAVs) for civilian and military applications. In such problems, one must determine the pairs of UAVs that must maintain a communication link so that constraints on resources and performance, such as a limit on the maximum number of communication links deployed, power consumed and maximum latency in routing information from one UAV to the other, are met and a performance objective is maximized. In this dissertation, algebraic connectivity, or its mechanical analog - the smallest non-zero natural frequency of a connected structure was chosen as a performance objective. Algebraic connectivity determines the convergence rate of consensus protocols and error attenuation in UAV formations and is chosen to be a performance objective as it can be viewed as a measure of robustness in UAV communication networks to random node failures. Underlying the mechanical and UAV network synthesis problems is a Mixed Integer Semi-Definite Program (MISDP), which was recently shown to be a NP-hard problem. There has not been any systematic procedure in the literature to solve this problem. This dissertation is aimed at addressing this void in the literature. The novel contributions of this dissertation to the literature are as follows: a) An iterative primal-dual algorithm and an algorithm based on the outer approximation of the semi-definite constraint utilizing a cutting plane technique were developed for computing optimal algebraic connectivity. These algorithms are based on a polyhedral approximation of the feasible set of MISDP, b) A bisection algorithm was developed to reduce the MISDP to a Binary Semi-Definite Program (BSDP) to achieve better computational efficiency, c) The feasible set of the MISDP was efficiently relaxed by replacing the positive semi-definite constraint with linear inequalities associated with a family of Fiedler vectors to compute a tighter upper bound for algebraic connectivity, d) Efficient neighborhood search heuristics based on greedy methods such as the k-opt and improved k-opt heuristics were developed, e) Variants of the problem occurring in UAV backbone networks and Air Transportation Management were considered in the dissertation along with numerical simulations corroborating the methodologies developed in this dissertation

Design of robust networks. Application to the design of wind farm cabling networks.

RÉSUMÉ: Aujourd’hui, la conception de réseaux est une problématique cruciale qui se pose dans beaucoup de domaines tels que le transport ou l’énergie. En particulier, il est devenu nécessaire d’optimiser la façon dont sont conçus les réseaux permettant de produire de l’énergie. On se concentre ici sur la production électrique produite à travers des parcs éoliens. Cette énergie apparait plus que jamais comme une bonne alternative à la production d’électricité via des centrales thermiques ou nucléaires. Nous nous intéressons dans cette thèse à la conception du câblage collectant l’énergie dans les parcs éoliens. On connaît alors la position de l’ensemble des éoliennes appartenant au parc ainsi que celle du site central collecteur vers laquelle l’énergie doit être acheminée. On connaît également la position des câbles que l’on peut construire, leurs capacités, et la position des noeuds d’interconnexion possibles. Il s’agit de déterminer un câblage de coût minimal permettant de relier l’ensemble des éoliennes à la sous-station, tel que celui-ci soit résistant à un certain nombre de pannes sur le réseau. Mots clés: Recherche opérationnelle, Optimisation combinatoire, Conception de réseaux robustes, Théorie des graphes, Programmation en nombres entiers, Câblage de parcs éoliens.----------ABSTRACT: Nowadays, the design of networks has become a decisive problematic which appears in many fields such as transport or energy. In particular, it has become necessary and important to optimize the way in which networks used to produce, collect or transport energy are designed. We focus in this thesis on electricity produced through wind farms. The production of energy by wind turbines appears more than ever like a good alternative to the electrical production of thermal or nuclear power plants, giving that both of those production can have harmful consequences on the environment. It has then become necessary to optimize the design and construction of such networks. We focus in this thesis on the design of the cabling network which allows to collect and route the energy from the wind turbines to a sub-station, linking the wind farm to the electrical network. In this problem, we know the location of each wind turbine of the farm and the one of the sub-station. We also know the location of possible inter-connection nodes which allow to connect different cables between them. Each wind turbine produces a known quantity of energy and with each cable are associated a cost and a capacity (the maximum amount of energy that can be routed through this cable). The optimization problem that we consider is to select a set of cables of minimum cost such that the energy produced from the wind turbines can be routed to the sub-station in the network induced by this set of cables, without exceeding the capacity of each cable. We focus on cabling networks resilient to breakdowns. Keywords : Operations Research, Combinatorial optimization, Robust networks design, Graph theory, Mixed integer programming, Wind farm cabling networks

Some Applications of the Weighted Combinatorial Laplacian

The weighted combinatorial Laplacian of a graph is a symmetric matrix which is the discrete analogue of the Laplacian operator. In this thesis, we will study a new application of this matrix to matching theory yielding a new characterization of factor-criticality in graphs and matroids. Other applications are from the area of the physical design of very large scale integrated circuits. The placement of the gates includes the minimization of a quadratic form given by a weighted Laplacian. A method based on the dual constrained subgradient method is proposed to solve the simultaneous placement and gate-sizing problem. A crucial step of this method is the projection to the flow space of an associated graph, which can be performed by minimizing a quadratic form given by the unweighted combinatorial Laplacian.Andwendungen der gewichteten kombinatorischen Laplace-Matrix Die gewichtete kombinatorische Laplace-Matrix ist das diskrete Analogon des Laplace-Operators. In dieser Arbeit stellen wir eine neuartige Charakterisierung von Faktor-Kritikalität von Graphen und Matroiden mit Hilfe dieser Matrix vor. Wir untersuchen andere Anwendungen im Bereich des Entwurfs von höchstintegrierten Schaltkreisen. Die Platzierung basiert auf der Minimierung einer quadratischen Form, die durch eine gewichtete kombinatorische Laplace-Matrix gegeben ist. Wir präsentieren einen Algorithmus für das allgemeine simultane Platzierungs- und Gattergrößen-Optimierungsproblem, der auf der dualen Subgradientenmethode basiert. Ein wichtiger Bestandteil dieses Verfahrens ist eine Projektion auf den Flussraum eines assoziierten Graphen, die als die Minimierung einer durch die Laplace-Matrix gegebenen quadratischen Form aufgefasst werden kann