Approximation Algorithms for Survivable Multicommodity Flow Problems with Applications to Network Design

Multicommodity flow (MF) problems have a wide variety of applications in areas such as VLSI circuit design, network design, etc., and are therefore very well studied. The fractional MF problems are polynomial time solvable while integer versions are NP-complete. However, exact algorithms to solve the fractional MF problems have high computational complexity. Therefore approximation algorithms to solve the fractional MF problems have been explored in the literature to reduce their computational complexity. Using these approximation algorithms and the randomized rounding technique, polynomial time approximation algorithms have been explored in the literature. In the design of high-speed networks, such as optical wavelength division multiplexing (WDM) networks, providing survivability carries great significance. Survivability is the ability of the network to recover from failures. It further increases the complexity of network design and presents network designers with more formidable challenges. In this work we formulate the survivable versions of the MF problems. We build approximation algorithms for the survivable multicommodity flow (SMF) problems based on the framework of the approximation algorithms for the MF problems presented in [1] and [2]. We discuss applications of the SMF problems to solve survivable routing in capacitated networks.

Efficient Forest Data Structure for Evolutionary Algorithms Applied to Network Design

The design of a network is a solution to several engineering and science problems. Several network design problems are known to be NP-hard, and population-based metaheuristics like evolutionary algorithms (EAs) have been largely investigated for such problems. Such optimization methods simultaneously generate a large number of potential solutions to investigate the search space in breadth and, consequently, to avoid local optima. Obtaining a potential solution usually involves the construction and maintenance of several spanning trees, or more generally, spanning forests. To efficiently explore the search space, special data structures have been developed to provide operations that manipulate a set of spanning trees (population). For a tree with n nodes, the most efficient data structures available in the literature require time O(n) to generate a new spanning tree that modifies an existing one and to store the new solution. We propose a new data structure, called node-depth-degree representation (NDDR), and we demonstrate that using this encoding, generating a new spanning forest requires average time O(root n). Experiments with an EA based on NDDR applied to large-scale instances of the degree-constrained minimum spanning tree problem have shown that the implementation adds small constants and lower order terms to the theoretical bound.

Algorithms for network design and routing problems

In this thesis we study three combinatorial optimization problems belonging to the classes of Network Design and Vehicle Routing problems that are strongly linked in the context of the design and management of transportation networks: the Non-Bifurcated Capacitated Network Design Problem (NBP), the Period Vehicle Routing Problem (PVRP) and the Pickup and Delivery Problem with Time Windows (PDPTW). These problems are NP-hard and contain as special cases some well known difficult problems such as the Traveling Salesman Problem and the Steiner Tree Problem. Moreover, they model the core structure of many practical problems arising in logistics and telecommunications. The NBP is the problem of designing the optimum network to satisfy a given set of traffic demands. Given a set of nodes, a set of potential links and a set of point-to-point demands called commodities, the objective is to select the links to install and dimension their capacities so that all the demands can be routed between their respective endpoints, and the sum of link fixed costs and commodity routing costs is minimized. The problem is called non- bifurcated because the solution network must allow each demand to follow a single path, i.e., the flow of each demand cannot be splitted. Although this is the case in many real applications, the NBP has received significantly less attention in the literature than other capacitated network design problems that allow bifurcation. We describe an exact algorithm for the NBP that is based on solving by an integer programming solver a formulation of the problem strengthened by simple valid inequalities and four new heuristic algorithms. One of these heuristics is an adaptive memory metaheuristic, based on partial enumeration, that could be applied to a wider class of structured combinatorial optimization problems. In the PVRP a fleet of vehicles of identical capacity must be used to service a set of customers over a planning period of several days. Each customer specifies a service frequency, a set of allowable day-combinations and a quantity of product that the customer must receive every time he is visited. For example, a customer may require to be visited twice during a 5-day period imposing that these visits take place on Monday-Thursday or Monday-Friday or Tuesday-Friday. The problem consists in simultaneously assigning a day- combination to each customer and in designing the vehicle routes for each day so that each customer is visited the required number of times, the number of routes on each day does not exceed the number of vehicles available, and the total cost of the routes over the period is minimized. We also consider a tactical variant of this problem, called Tactical Planning Vehicle Routing Problem, where customers require to be visited on a specific day of the period but a penalty cost, called service cost, can be paid to postpone the visit to a later day than that required. At our knowledge all the algorithms proposed in the literature for the PVRP are heuristics. In this thesis we present for the first time an exact algorithm for the PVRP that is based on different relaxations of a set partitioning-like formulation. The effectiveness of the proposed algorithm is tested on a set of instances from the literature and on a new set of instances. Finally, the PDPTW is to service a set of transportation requests using a fleet of identical vehicles of limited capacity located at a central depot. Each request specifies a pickup location and a delivery location and requires that a given quantity of load is transported from the pickup location to the delivery location. Moreover, each location can be visited only within an associated time window. Each vehicle can perform at most one route and the problem is to satisfy all the requests using the available vehicles so that each request is serviced by a single vehicle, the load on each vehicle does not exceed the capacity, and all locations are visited according to their time window. We formulate the PDPTW as a set partitioning-like problem with additional cuts and we propose an exact algorithm based on different relaxations of the mathematical formulation and a branch-and-cut-and-price algorithm. The new algorithm is tested on two classes of problems from the literature and compared with a recent branch-and-cut-and-price algorithm from the literature.

Numerical coupling of thermal-electric network models and energy-transport equations including optoelectronic semiconductor devices

In this work the numerical coupling of thermal and electric network models with model equations for optoelectronic semiconductor devices is presented. Modified nodal analysis (MNA) is applied to model electric networks. Thermal effects are modeled by an accompanying thermal network. Semiconductor devices are modeled by the energy-transport model, that allows for thermal effects. The energy-transport model is expandend to a model for optoelectronic semiconductor devices. The temperature of the crystal lattice of the semiconductor devices is modeled by the heat flow eqaution. The corresponding heat source term is derived under thermodynamical and phenomenological considerations of energy fluxes. The energy-transport model is coupled directly into the network equations and the heat flow equation for the lattice temperature is coupled directly into the accompanying thermal network. The coupled thermal-electric network-device model results in a system of partial differential-algebraic equations (PDAE). Numerical examples are presented for the coupling of network- and one-dimensional semiconductor equations. Hybridized mixed finite elements are applied for the space discretization of the semiconductor equations. Backward difference formluas are applied for time discretization. Thus, positivity of charge carrier densities and continuity of the current density is guaranteed even for the coupled model.

Decomposition Methods and Network Design Problems

Decomposition based approaches are recalled from primal and dual point of view. The possibility of building partially disaggregated reduced master problems is investigated. This extends the idea of aggregated-versus-disaggregated formulation to a gradual choice of alternative level of aggregation. Partial aggregation is applied to the linear multicommodity minimum cost flow problem. The possibility of having only partially aggregated bundles opens a wide range of alternatives with different trade-offs between the number of iterations and the required computation for solving it. This trade-off is explored for several sets of instances and the results are compared with the ones obtained by directly solving the natural node-arc formulation. An iterative solution process to the route assignment problem is proposed, based on the well-known Frank Wolfe algorithm. In order to provide a first feasible solution to the Frank Wolfe algorithm, a linear multicommodity min-cost flow problem is solved to optimality by using the decomposition techniques mentioned above. Solutions of this problem are useful for network orientation and design, especially in relation with public transportation systems as the Personal Rapid Transit. A single-commodity robust network design problem is addressed. In this, an undirected graph with edge costs is given together with a discrete set of balance matrices, representing different supply/demand scenarios. The goal is to determine the minimum cost installation of capacities on the edges such that the flow exchange is feasible for every scenario. A set of new instances that are computationally hard for the natural flow formulation are solved by means of a new heuristic algorithm. Finally, an efficient decomposition-based heuristic approach for a large scale stochastic unit commitment problem is presented. The addressed real-world stochastic problem employs at its core a deterministic unit commitment planning model developed by the California Independent System Operator (ISO).

Hierarchical Approach for Survivable Network Design

A central design challenge facing network planners is how to select a cost-effective network configuration that can provide uninterrupted service despite edge failures. In this paper, we study the Survivable Network Design (SND) problem, a core model underlying the design of such resilient networks that incorporates complex cost and connectivity trade-offs. Given an undirected graph with specified edge costs and (integer) connectivity requirements between pairs of nodes, the SND problem seeks the minimum cost set of edges that interconnects each node pair with at least as many edge-disjoint paths as the connectivity requirement of the nodes. We develop a hierarchical approach for solving the problem that integrates ideas from decomposition, tabu search, randomization, and optimization. The approach decomposes the SND problem into two subproblems, Backbone design and Access design, and uses an iterative multi-stage method for solving the SND problem in a hierarchical fashion. Since both subproblems are NP-hard, we develop effective optimization-based tabu search strategies that balance intensification and diversification to identify near-optimal solutions. To initiate this method, we develop two heuristic procedures that can yield good starting points. We test the combined approach on large-scale SND instances, and empirically assess the quality of the solutions vis-à-vis optimal values or lower bounds. On average, our hierarchical solution approach generates solutions within 2.7% of optimality even for very large problems (that cannot be solved using exact methods), and our results demonstrate that the performance of the method is robust for a variety of problems with different size and connectivity characteristics.

Multibeam Network Design and Measurement for Triangular Array of Three Radiating Elements

Nowadays, more a more base stations are equipped with active conformal antennas. These antenna designs combine phase shift systems with multibeam networks providing multi-beam ability and interference rejection, which optimize multiple channel systems. GEODA is a conformal adaptive antenna system designed for satellite communications. Operating at 1.7 GHz with circular polarization, it is possible to track and communicate with several satellites at once thanks to its adaptive beam. The antenna is based on a set of similar triangular arrays that are divided in subarrays of three elements called `cells'. Transmission/Receiver (T/R) modules manage beam steering by shifting the phases. A more accurate steering of the antenna GEODA could be achieved by using a multibeam network. Several multibeam network designs based on Butler network will be presented

Designing Rapid Transit Network Design with Alternative routes

The aim of this paper is to propose a model for the design of a robust rapid transit network. In this paper, a network is said to be robust when the effect of disruption on total trip coverage is minimized. The proposed model is constrained by three different kinds of flow conditions. These constraints will yield a network that provides several alternative routes for given origin–destination pairs, therefore increasing robustness. The paper includes computational experiments which show how the introduction of robustness influences network design

Aspects of a phased array radar feed and bias network design

Radar technologies have been developed to improve the efficiency when detecting targets. Radar is a system composed by several devices connected and working together. Depending on the type of radar, the improvements are focused on different functionalities of the radar. One of the most important devices composing a radar is the antenna, that sends the radio-frequency signal to the space in order to detect targets. This project is focused on a specific type of radar called phased array radar. This type of radar is characterized by its antenna, which consist on a linear array of radiating elements, in this particular case, eight dipoles working at the frequency band S. The main advantage introduced by the phased array antenna is that using the fundamentals of arrays, the directivity of the antenna can change by shifting the phase of the signal at the input of each radiating element. This can be done using phase shifters. Phase shifter consists on a device which produces a phase shift in the radio-frequency input signal depending on a control DC voltage. Using a phased array antenna allows changing the directivity of the antenna without a mechanical rotating system. The objective of this project is to design the feed network and the bias network of the phased antenna. The feed network consists on a parallel-fed network composed by power dividers that sends the radio-frequency signal from the source to each radiating element of the antenna. The bias network consists on a system that generates the control DC voltages supplied to the phase shifters in order to change the directivity. The architecture of the bias network is composed by a software, implemented in Matlab and run in a laptop which is connected to a micro-controller by a serial communication port. The software calculates the control DC voltages needed to obtain a determined directivity or scan angle. These values are sent by the serial communication port to the micro-controller as data. Then the micro-controller generates the desired control DC voltages and supplies them to the phase shifters. In this project two solutions for bias network are designed. Each one is tested and final conclusions are obtained to determine the advantages and disadvantages. Finally a graphic user interface is developed in order to make the system easy to use. RESUMEN. Las tecnologías empleadas por lo dispositivos radar se han ido desarrollando para mejorar su eficiencia y usabilidad. Un radar es un sistema formado por varios subsistemas conectados entre sí. Por lo que dependiendo del tipo de radar las mejoras se centran en los subsistemas correspondientes. Uno de los elementos más importantes de un radar es la antena. Esta se emplea para enviar la señal de radiofrecuencia al espacio y así poder detectar los posibles obstáculos del entorno. Este proyecto se centra en un tipo específico de radar llamado phased array radar. Este tipo de radar se caracteriza por la antena que es un array de antenas, en concreto para este proyecto se trata de un array lineal de ocho dipolos en la banda de frequencia S. El uso de una antena de tipo phased array supone una ventaja importante. Empleando los fundamentos de radiación aplicado a array de antenas se obtiene que la directividad de la antena puede ser modificada. Esto se consigue aplicando distintos desfasajes a la señal de radiofrecuencia que alimenta a cada elemento del array. Para aplicar los desfasajes se emplea un desplazador de fase, este dispositivo aplica una diferencia de fase a su salida con respecto a la señal de entrada dependiendo de una tensión continua de control. Por tanto el empleo de una antena de tipo phased array supone una gran ventaja puesto que no se necesita un sistema de rotación para cambiar la directividad de la antena. El objetivo principal del proyecto consiste en el diseño de la red de alimentación y la red de polarización de la antena de tipo phased array. La red de alimentación consiste en un circuito pasivo que permite alimentar a cada elemento del array con la misma cantidad de señal. Dicha red estará formada por divisores de potencia pasivos y su configuración será en paralelo. Por otro lado la red de polarización consiste en el diseño de un sistema automático que permite cambiar la directividad de la antena. Este sistema consiste en un programa en Matlab que es ejecutado en un ordenador conectado a un micro-controlador mediante una comunicación serie. El funcionamiento se basa en calcular las tensiones continuas de control, que necesitan los desplazadores de fase, mediante un programa en Matlab y enviarlos como datos al micro-controlador. Dicho micro-controlador genera las tensiones de control deseadas y las proporciona a cada desplazador de fase, obteniendo así la directividad deseada. Debido al amplio abanico de posibilidades, se obtienen dos soluciones que son sometidas a pruebas. Se obtienen las ventajas y desventajas de cada una. Finalmente se implementa una interfaz gráfica de usuario con el objetivo de hacer dicho sistema manejable y entendible para cualquier usuario.

Truck lane needs methodology: a heuristic approach to solve a five option discrete network design problem. Interim report.

Texas State Department of Highways and Public Transportation, Transportation Planning Division, Austin

Topics in MOSFET network design /

Thesis--University of Illinois at Urbana-Champaign.

NOR (NAND) network design : error-compensation procedures for fan-in and fan-out restricted networks (NETTRA-E1-FIFO and NETTRA-E2-FIFO /

Thesis (M. S.)--University of Illinois at Urbana-Champaign.

Optimum network design using NOR-OR gates by integer programming.

"Supported in part by ... Grant no. NSF GJ-503."

Privacy in the Smart City: Implications of Sensor Network Design, Law, and Policy for Locational Privacy

Thesis (Master's)--University of Washington, 2016-06