Robust network design under polyhedral traffic uncertainty

Ankara : The Department of Industrial Engineering and The Institute of Engineering and Science of Bilkent Univ., 2007.Thesis (Ph.D.) -- Bilkent University, 2007.Includes bibliographical references leaves 160-166.In this thesis, we study the design of networks robust to changes in demand estimates. We consider the case where the set of feasible demands is defined by an arbitrary polyhedron. Our motivation is to determine link capacity or routing configurations, which remain feasible for any realization in the corresponding demand polyhedron. We consider three well-known problems under polyhedral demand uncertainty all of which are posed as semi-infinite mixed integer programming problems. We develop explicit, compact formulations for all three problems as well as alternative formulations and exact solution methods. The first problem arises in the Virtual Private Network (VPN) design field. We present compact linear mixed-integer programming formulations for the problem with the classical hose traffic model and for a new, less conservative, robust variant relying on accessible traffic statistics. Although we can solve these formulations for medium-to-large instances in reasonable times using off-the-shelf MIP solvers, we develop a combined branch-and-price and cutting plane algorithm to handle larger instances. We also provide an extensive discussion of our numerical results. Next, we study the Open Shortest Path First (OSPF) routing enhanced with traffic engineering tools under general demand uncertainty with the motivation to discuss if OSPF could be made comparable to the general unconstrained routing (MPLS) when it is provided with a less restrictive operating environment. To the best of our knowledge, these two routing mechanisms are compared for the first time under such a general setting. We provide compact formulations for both routing types and show that MPLS routing for polyhedral demands can be computed in polynomial time. Moreover, we present a specialized branchand-price algorithm strengthened with the inclusion of cuts as an exact solution tool. Subsequently, we compare the new and more flexible OSPF routing with MPLS as well as the traditional OSPF on several network instances. We observe that the management tools we use in OSPF make it significantly better than the generic OSPF. Moreover, we show that OSPF performance can get closer to that of MPLS in some cases. Finally, we consider the Network Loading Problem (NLP) under a polyhedral uncertainty description of traffic demands. After giving a compact multicommodity formulation of the problem, we prove an unexpected decomposition property obtained from projecting out the flow variables, considerably simplifying the resulting polyhedral analysis and computations by doing away with metric inequalities, an attendant feature of most successful algorithms on NLP. Under the hose model of feasible demands, we study the polyhedral aspects of NLP, used as the basis of an efficient branch-and-cut algorithm supported by a simple heuristic for generating upper bounds. We provide the results of extensive computational experiments on well-known network design instances.Altın, AyşegülPh.D

Reformulation and Decomposition Approaches for Traffic Routing in Optical Networks

International audienceWe consider a multi-layer network design model arising from a real-life telecommunication application where traffic routingdecisions imply the installation of expensive nodal equipment. Customer requests come in the form of bandwidthreservations for a given origin destination pair. Bandwidth demands are expressed as multiples of nominal granularities. Each request must be single-path routed. Grooming several requests on the same wavelength and multiplexing wavelengths in the same optical stream allow a more efficient use of network capacity. However, each addition or withdrawal of a request from a wavelength requires optical to electrical conversion and the use of cross-connect equipment with expensive ports of high densities. The objective is to minimize the number of required ports of the cross-connect equipment. We deal with backbone optical networks, therefore with networks with a moderate number of nodes (14 to 20) but thousands of requests. Further difficulties arise from the symmetries in wavelength assignment and traffic loading. Traditional multi-commodity network flowapproaches are not suited for this problem. Instead, four alternative models relying on Dantzig-Wolfe and/or Benders' decomposition areintroduced and compared. The formulations are strengthened using symmetry breaking restrictions, variable domain reduction, zero-onediscretization of integer variables, and cutting planes. The resulting dual bounds are compared to the values of primal solutions obtained through hierarchical optimization and rounding procedures. For realistic size instances, our best approaches provide solutions with optimality gap of approximately 5% on average in around two hours of computing time

Reformulation and Decomposition Approaches for Traffic Routing in Optical Networks

International audienceWe consider a multi-layer network design model arising from a real-life telecommunication application where traffic routingdecisions imply the installation of expensive nodal equipment. Customer requests come in the form of bandwidthreservations for a given origin destination pair. Bandwidth demands are expressed as multiples of nominal granularities. Each request must be single-path routed. Grooming several requests on the same wavelength and multiplexing wavelengths in the same optical stream allow a more efficient use of network capacity. However, each addition or withdrawal of a request from a wavelength requires optical to electrical conversion and the use of cross-connect equipment with expensive ports of high densities. The objective is to minimize the number of required ports of the cross-connect equipment. We deal with backbone optical networks, therefore with networks with a moderate number of nodes (14 to 20) but thousands of requests. Further difficulties arise from the symmetries in wavelength assignment and traffic loading. Traditional multi-commodity network flowapproaches are not suited for this problem. Instead, four alternative models relying on Dantzig-Wolfe and/or Benders' decomposition areintroduced and compared. The formulations are strengthened using symmetry breaking restrictions, variable domain reduction, zero-onediscretization of integer variables, and cutting planes. The resulting dual bounds are compared to the values of primal solutions obtained through hierarchical optimization and rounding procedures. For realistic size instances, our best approaches provide solutions with optimality gap of approximately 5% on average in around two hours of computing time

Thirty years of heterogeneous vehicle routing

It has been around thirty years since the heterogeneous vehicle routing problem was introduced, and significant progress has since been made on this problem and its variants. The aim of this survey paper is to classify and review the literature on heterogeneous vehicle routing problems. The paper also presents a comparative analysis of the metaheuristic algorithms that have been proposed for these problems

A survey on OFDM-based elastic core optical networking

Orthogonal frequency-division multiplexing (OFDM) is a modulation technology that has been widely adopted in many new and emerging broadband wireless and wireline communication systems. Due to its capability to transmit a high-speed data stream using multiple spectral-overlapped lower-speed subcarriers, OFDM technology offers superior advantages of high spectrum efficiency, robustness against inter-carrier and inter-symbol interference, adaptability to server channel conditions, etc. In recent years, there have been intensive studies on optical OFDM (O-OFDM) transmission technologies, and it is considered a promising technology for future ultra-high-speed optical transmission. Based on O-OFDM technology, a novel elastic optical network architecture with immense flexibility and scalability in spectrum allocation and data rate accommodation could be built to support diverse services and the rapid growth of Internet traffic in the future. In this paper, we present a comprehensive survey on OFDM-based elastic optical network technologies, including basic principles of OFDM, O-OFDM technologies, the architectures of OFDM-based elastic core optical networks, and related key enabling technologies. The main advantages and issues of OFDM-based elastic core optical networks that are under research are also discussed

The development of a mathematical programming technique as a design tool for traffic management

In urban areas, competition for road space at junctions is one of the major causes of congestion and accidents. Routes chosen to avoid conflict at junctions have a mutually beneficial effect which should improve circulation and reduce accidents. A prototype design tool has been developed to provide for traffic management based on such routes. The mathematical model behind the design tool works with a given road network and a given O-D demand matrix to produce feasible routes for all drivers in such a way that the weighted sum of potential conflicts is minimised. The result is a route selection in which all journeys from origin i to destination j follow the same route. The method which works best splits the problem into single commodity problems and solves these repeatedly by the Out-of-Kilter algorithm. Good locally optimal solutions can be produced by this method, even though global optimality cannot be guaranteed. Software for a microcomputer presented here as part of the design tool is capable of solving problems on realistic networks in a reasonable time. This method is embedded in a suite of computer programs which makes the input and output straightforward. Used as a design tool in the early stages of network design it gives a network-wide view of the possibilities for reducing conflict and indicates a coherent set of traffic management measures. The ideal measure would be automatic route guidance, such as the pilot scheme currently being developed for London. Other measures include a set of one-way streets and banned turns. The resulting turning flows could be used as input to the signal optimiser TRANSYT to determine signal settings favouring the routeing pattern. The project was funded by the S. E. R. C. and carried out at Middlesex Polytechnic in collaboration with MVA Systematica

Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization

International audienceThe Cologne-Twente Workshop (CTW) on Graphs and Combinatorial Optimization started off as a series of workshops organized bi-annually by either Köln University or Twente University. As its importance grew over time, it re-centered its geographical focus by including northern Italy (CTW04 in Menaggio, on the lake Como and CTW08 in Gargnano, on the Garda lake). This year, CTW (in its eighth edition) will be staged in France for the first time: more precisely in the heart of Paris, at the Conservatoire National d’Arts et Métiers (CNAM), between 2nd and 4th June 2009, by a mixed organizing committee with members from LIX, Ecole Polytechnique and CEDRIC, CNAM

Optimization Methods Applied to Power Systems Ⅱ

Electrical power systems are complex networks that include a set of electrical components that allow distributing the electricity generated in the conventional and renewable power plants to distribution systems so it can be received by final consumers (businesses and homes). In practice, power system management requires solving different design, operation, and control problems. Bearing in mind that computers are used to solve these complex optimization problems, this book includes some recent contributions to this field that cover a large variety of problems. More specifically, the book includes contributions about topics such as controllers for the frequency response of microgrids, post-contingency overflow analysis, line overloads after line and generation contingences, power quality disturbances, earthing system touch voltages, security-constrained optimal power flow, voltage regulation planning, intermittent generation in power systems, location of partial discharge source in gas-insulated switchgear, electric vehicle charging stations, optimal power flow with photovoltaic generation, hydroelectric plant location selection, cold-thermal-electric integrated energy systems, high-efficiency resonant devices for microwave power generation, security-constrained unit commitment, and economic dispatch problems