Polyhedral analysis for concentrator location problems

The concentrator location problem is to choose a subset of a given terminal set to install concentrators and to assign each remaining terminal node to a concentrator to minimize the cost of installation and assignment. The concentrators may have capacity constraints. We study the polyhedral properties of concentrator location problems with different capacity structures. We develop a branch and cut algorithm and present computational results. © 2006 Springer Science + Business Media, Inc

Concentrator location in telecommunications

We survey the main results in the author's PhD Thesis presented in December 2002 at the Université Libre de Bruxelles and supervised by Prof. Martine Labbé. The dissertation is written in English and is available at smg.ulb.ac.be. Several versions of concentrator location problems in telecommunication networks are studied. The thesis presents a list of polyhedral results for these problems and a branch and cut algorithm for the most general problem introduced. © Springer-Verlag 2004

Optimal Trees

Not Availabl

Star p-hub median problem with modular arc capacities

Cataloged from PDF version of article.We consider the hub location problem, where p hubs are chosen from a given set of nodes, each nonhub node is connected to exactly one hub and each hub is connected to a central hub. Links are installed on the arcs of the resulting network to route the traffic. The aim is to find the hub locations and the connections to minimize the link installation cost.We propose two formulations and a heuristic algorithm to solve this problem. The heuristic is based on Lagrangian relaxation and local search.We present computational results where formulations are compared and the quality of the heuristic solutions are tested. 2007 Elsevier Ltd. All rights reserved

Survivability in hierarchical telecommunications networks

Abstract We consider the problem of designing a two level telecommunications network at minimum cost. The decisions involved are the locations of concentrators, the assignments of user nodes to concentrators and the installation of links connecting concentrators in a reliable backbone network. We define a reliable backbone network as one where there exist at least 2-edge disjoint paths between any pair of concentrator nodes. We formulate this problem as an integer program and propose a facial study of the associated polytope. We describe valid inequalities and give sufficient conditions for these inequalities to be facet defining. We also propose some reduction operations in order to speed up the separation procedures for these inequalities. Using these results, we devise a branch-and-cut algorithm and present some computational results

A decomposition algorithm for local access telecommunications network expansion planning

Includes bibliographical references.Supported by a grant from GTE Laboratories, Inc., Waltham, Mass., and by a research award from the AT&T Foundation. Supported by a NATO Collaborative research grant. CRG 900281Anantaram Balakrishnan, Thomas L. Magnanti, Richard T. Wong

Development of a high concentration solar flux mapping system.

Masters Degree. University of KwaZulu-Natal, Durban.The Group for Solar Energy Thermodynamics (GSET) is in the process of commissioning the Solar Energy Research Amplified Flux Facility (SERAFF), which is South Africa’s first solar furnace facility. SERAFF is situated at the University of KwaZulu-Natal’s Howard College campus and assumes an on-axis optical configuration, comprising a 9 m2 non-focusing heliostat reflector, a 3 m diameter paraboloidal dish concentrator and a test article platform. The facility was designed to aid research in the fields of high temperature materials testing, concentrating solar energy and solar thermochemistry. The concentrated radiative energy output of a solar furnace establishes the energy input to prototype receivers, reactors or materials that aim to be tested using the facility. The challenge is compounded by the temporal and spatial variation of SERAFF’s radiative energy output, influenced by weather-related and geometric factors. In this study, an indirect spatial flux mapping system is developed to characterise SERAFF’s spatial radiative energy output. SERAFF’s theoretical spatial radiative energy output is estimated through Monte Carlo ray-tracing techniques to provide benchmark performance parameters including total thermal power output, peak concentration ratio and focal spot size. The indirect system uses optical measurement techniques, in which spatial solar flux is measured via diffuse reflection off a Lambertian target using a digital CMOS camera through a neutral density filter and lens. Pixel intensities are calibrated against reference measurements acquired from a circular-foil Gardon gauge heat flux transducer. The calibrated CMOS camera can be used to measure values of radiative flux, incident at the focal plane from 0 kW/m2 - 468.19 kW/m2. Measurements were restricted to a brief testing period and are not representative of SERAFF’s peak operating conditions. Spatial flux measurements indicated a thermal power output of 3.83 kW, with a corresponding peak solar flux of 227.8 kW/m2 within a focal diameter of 250 mm. The study demonstrated successful integration of an indirect spatial flux mapping system into the SERAFF solar furnace

Robust Branch-Cut-and-Price for the Capacitated Minimum Spanning Tree Problem over a Large Extended Formulation

This paper presents a robust branch-cut-and-price algorithm for the Capacitated Minimum Spanning Tree Problem (CMST). The variables are associated to q-arbs, a structure that arises from a relaxation of the capacitated prize-collecting arbores- cence problem in order to make it solvable in pseudo-polynomial time. Traditional inequalities over the arc formulation, like Capacity Cuts, are also used. Moreover, a novel feature is introduced in such kind of algorithms. Powerful new cuts expressed over a very large set of variables could be added, without increasing the complexity of the pricing subproblem or the size of the LPs that are actually solved. Computational results on benchmark instances from the OR-Library show very signi¯cant improvements over previous algorithms. Several open instances could be solved to optimalityNo keywords;

A branch and cut algorithm for hub location problems with single assignment

The hub location problem with single assignment is the problem of locating hubs and assigning the terminal nodes to hubs in order to minimize the cost of hub installation and the cost of routing the traffic in the network. There may also be capacity restrictions on the amount of traffic that can transit by hubs. The aim of this paper is to investigate polyhedral properties of these problems and to develop a branch and cut algorithm based on these results. © Springer-Verlag 2004