11 research outputs found
A hybrid polyhedral uncertainty model for the robust network loading problem
[No abstract available
Multicommodity capacitated network design
Network design models have wide applications in telecommunications and transportation planning; see, for example, the survey articles by Magnanti and Wong (1984), Minoux (1989), Chapter 16 of the book by Ahuja, Magnanti and Orlin (1993), Section 13 of Ahuja et al. (1995). In particular, Gavish (1991) and Balakrishnan et al. (1991) present reviews of important applications in telecommunications. In many of these applications, it is required to send flows (which may be fractional) to satisfy demands given arcs with existing capacities, or to install, in discrete amounts, additional facilities with fixed capacities. In doing so, one pays a price not only for routing flows, but also for using an arc or installing additional facilities. The objective is then to determine the optimal amounts of flows to be routed and the facilities to be installed.
Document type: Part of book or chapter of boo
MĂ©thode de gĂ©nĂ©ration de colonnes pour les problĂšmes de conception de rĂ©seaux avec coĂ»ts dâajout de capacitĂ©
Les problĂšmes de conception de rĂ©seaux ont reçu un intĂ©rĂȘt particulier et ont Ă©tĂ© largement Ă©tudiĂ©s de par leurs nombreuses applications dans diffĂ©rents domaines, tels que les transports et les tĂ©lĂ©communications.
Nous nous intĂ©ressons dans ce mĂ©moire au problĂšme de conception de rĂ©seaux avec coĂ»ts dâajout de capacitĂ©. Il sâagit dâinstaller un ensemble dâĂ©quipements sur un rĂ©seau en vue de satisfaire la demande, tout en respectant les contraintes de capacitĂ©, chaque arc pouvant admettre plusieurs Ă©quipements. Lâobjectif est de minimiser les coĂ»ts variables de transport des produits et les coĂ»ts fixes dâinstallation ou dâaugmentation de capacitĂ© des Ă©quipements.
La méthode que nous envisageons pour résoudre ce problÚme est basée sur les techniques utilisées en programmation linéaire en nombres entiers, notamment celles de génération de colonnes et de coupes. Ces méthodes sont introduites dans un algorithme général de branch-and-bound basé sur la relaxation linéaire.
Nous avons testĂ© notre mĂ©thode sur quatre groupes dâinstances de tailles diffĂ©rentes, et nous lâavons comparĂ©e Ă CPLEX, qui constitue un des meilleurs solveurs permettant de rĂ©soudre des problĂšmes dâoptimisation, ainsi quâĂ une mĂ©thode existante dans la littĂ©rature combinant des mĂ©thodes exactes et heuristiques. Notre mĂ©thode a Ă©tĂ© plus performante que ces deux mĂ©thodes, notamment pour les instances de trĂšs grandes tailles.Network design problems received a particular interest and have been widely studied because of their many applications in different areas, such as logistics and telecommunications.
We focus in this work on the multicommodity capacitated network design problem with capacity expansion costs. It consists in opening a set of facilities on a network in order to meet the demand of some commodities, while respecting the capacity constraints. Each arc can admit several facilities. The objective is to minimize the commodities transportation costs, and the fixed costs of opening or increasing the capacity of the facilities.
The method we are using to solve this problem is based on techniques used in integer programming, including column generation and cutting-plane methods. These methods are introduced into a general branch-and-bound algorithm, based on linear relaxation.
We test our method on four groups of instances of different sizes, and we compare it with CPLEX, which is one of the best solvers available for optimization problems. We compare it also with an existing method in the literature, combining exact and heuristic methods.
Numerical results show that our method was able to outperform both methods, especially when tested on large scale instances
Placement of express links in a DWDM optical network
Cataloged from PDF version of article.With the introduction of DWDM technology in telecommunication network systems,
important advancements have been achieved in the problem of routing the increasing
signal traffic between demand-supply nodes. The choice of the links to open, the number
of links and routing of current traffic on these links in such an optical network system are
important in terms of decreasing the complexity of the network and cost savings. The
study in this thesis firstly introduces the use of express links, which enables those
objectives, and then determines the appropriate network structure and routing. The study
introduces two mathematical models as well as a lagrangian based heuristic for the
solution of the problem.Ćöhret, OÄuzM.S
Logistics service network design : models, algorithms, and applications
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2004.Includes bibliographical references (leaves 177-186).Service network design is critical to the profitability of express shipment carriers. In this thesis, we consider two challenging problems associated with designing networks for express shipment service. The first problem is to design an integrated network for premium and deferred services simultaneously. Related existing models adapted to this problem are intractable for realistic instances of this problem: computer memory requirements and solution times are excessive. We introduce a disaggregate information-enhanced column generation approach for this problem that reduces the number of variables to be considered in the integer program from hundreds of thousands to only thousands, allowing us to solve previously unsolvable problem instances. The second problem is to determine the express package service network design in its entirety, including aircraft routings, fleet assignments, and package flow routings, including hub assignments. Existing models applied to this problem have weak associated linear programming bounds and hence, fail to produce quality feasible solutions. For example, for a small network design problem instance it takes days to produce a feasible solution that is provably near- optimal using the best performing existing model. To overcome these tractability challenges, we introduce a new model, referred to as the gateway cover and flow formulation. Applying our new formulation to the same network design instance, it takes only minutes to find an optimal solution.(cont.) Applying our disaggregate information-enhanced column generation approach and gateway cover and flow formulation and solution approach to the network design problems of a large express package service provider, we demonstrate tens of millions of dollars in potential annual operating cost savings and reductions in the numbers of aircraft needed to perform the service. Moreover, we illustrate that, though designed for tactical planning, our new model and solution approach can provide insights for strategic decision-making, such as hub opening/closure, hub capacity expansion, and fleet composition and size.by Su Shen.Ph.D
Fiber to the home
In den letzten Jahren gab es zunehmenden Bedarf fĂŒr breitbandige Telekommunikations Netzwerke. Eine von Telekommunikationsunternehmen angewandte Strategie um die Bandbreite entlang der last-mile des Netzwerks zu erhöhen ist, Glasfaserkabel direkt bis zum Endkunden zu verlegen. Diese Strategie wird fiber to the home (FTTH) genannt.
In der vorliegenden Arbeit wird das local access network design problem (LAN) und die Variante mit prize-collecting (PC-LAN) verwendet, um das Problem der FTTH Planung zu modellieren. Das LAN Problem zielt darauf ab eine kostenminimale Lösung zu finden und gestattet es sowohl verschiedene Kabeltechnologien und existierende Infrastruktur, als auch die Zusatzkosten zu modellieren, die anfallen wenn neue Verbindungen hergestellt werden. DarĂŒber hinaus, erlaubt das PC-LAN Problem den Aspekt zu modellieren, dass nicht unbedingt alle Kunden mit FTTH versorgt werden mĂŒssen. Stattdessen wird eine Teilmenge der Kunden versorgt mit dem Ziel den Profit zu maximieren.
Um LAN und PC-LAN Problem Instanzen zu lösen, werden folgende Methoden des Operations Research angewandt: Preprocessing, ganzzahlige Programmierung, StÀrkung der mathematischen Modelle durch Disaggregation der Variablen, Benders' Dekomposition und adaptive Multi-Start-Heuristiken.
In einem Projekt von UniversitĂ€t Wien und Telekom Austria wurden groĂe FTTH DatensĂ€tze untersucht und die hier vorgestellten Methoden entworfen. Diese LösungsansĂ€tze wurden als Computerprogramme implementiert und ihre Tauglichkeit zur Behandlung von FTTH Planungsfragen konnte gezeigt werden.Within recent years the request for broadband telecommunication networks has been constantly increasing. A strategy employed by telecommunication companies to increase the bandwidth on the last mile of the network is to lay optical fiber directly to the end customer. This strategy is denoted as fiber to the home (FTTH).
In this thesis the local access network design problem (LAN) and its prize-collecting variant (PC-LAN) are used to formalize the planning of FTTH networks. The LAN problem asks for a cost minimal solution and allows to model different cable technologies, existing infrastructure and the overhead cost incurred by building new connections. In addition, the PC-LAN problem covers the aspect, that not all customers must necessarily be connected with FTTH, but instead we search for a subset of customers in order to maximize profits.
To solve LAN and PC-LAN instances, the following operations research methods are employed: Preprocessing, mixed integer programming, model strengthening by variable disaggregation, Benders' decomposition and adaptive multi-start heuristics.
In a project between University of Vienna and Telekom Austria, large real world data sets for FTTH planning were investigated and the methods presented in this thesis have been designed. These solution methods have been implemented as computer programs and empirically verified to be reasonable approaches to FTTH network design problems
Satellite Network, Design, Optimization, and Management
We introduce several network design and planning problems that arise in the context of commercial satellite networks. At the heart of most of these problems we deal with a traffic routing problem over an extended planning horizon. In satellite networks route changes are associated with significant monetary penalties that are usually in the form of discounts (up to 40%) offered by the satellite provider to the customer that is affected. The notion of these rerouting penalties requires the network planners to consider management problems over multiple time periods and introduces novel challenges that have not been considered previously in the literature.
Specifically, we introduce a multiperiod traffic routing problem and a multiperiod network design problem that incorporate rerouting penalties. For both of these problems we present novel path-based reformulations and develop branch-and-price-and-cut approaches to solve them. The pricing problems in both cases present new challenges and we develop special purpose approaches that can deal with them. We also show how these results can be extended to deal with traffic routing and network design decisions in other settings with much more general rerouting penalties. Our computational work demonstrates the benefits of using the branch-and-price-and-cut procedure developed that can deal with the multiperiod nature of the problem as opposed to straightforward, myopic period-by-period optimization approaches.
In order to deal with cases in which future demand is not known with certainty we present the stochastic version of the multiperiod traffic routing problem and formulate it as a stochastic multistage recourse problem with integer variables at all stages. We demonstrate how an appropriate path-based reformulation and an associated branch-and-price-and-cut approach can solve this problem and other more general multistage stochastic integer multicommodity flow problems.
Finally, we motivate the notion of reload costs that refer to variable (i.e., per unit of flow) costs for the usage of pairs of edges, as opposed to single edges. We highlight the practical and theoretical significance of these cost structures and present two extended graphs that allow us to easily capture these costs and generate strong formulations
Robust Design of Single-Commodity Networks
The results in the present work were obtained in a collaboration with Eduardo Ălvarez-
Miranda, Valentina Cacchiani, Tim Dorneth, Michael JĂŒnger, Frauke Liers, Andrea Lodi
and Tiziano Parriani.
The subject of this thesis is a robust network design problem, i.e., a problem of the type
âdimension a network such that it has sufficient capacity in all likely scenarios.â In our case,
we model the network with an undirected graph in which each scenario defines a supply or
demand for each node. We say that a flow in the network is feasible for a scenario if it can
balance out its supplies and demands. A scenario polytope B defines which scenarios are
relevant. The task is now to find integer capacities that minimize the total installation costs
while allowing for a feasible flow in each scenario. This problem is called Single-Commodity
Robust Network Design Problem (sRND) and was introduced by Buchheim, Liers and SanitĂ
(INOC 2011). The problem contains the Steiner Tree Problem (given an undirected graph
and a terminal set, find a minimum cost subtree that connects all terminals) and therefore
is N P-hard. The problem is also a natural extension of minimum cost flows.
The network design literature treats the case that the scenario polytope B is given as
the finite set of its extreme points (finite case) and that it is given as the feasible region
of finitely many linear inequalities (polyhedral case). Both descriptions are equivalent,
however, an efficient transformation is not possible in general.
Buchheim, Liers and SanitĂ (INOC 2011) propose a Branch-and-Cut algorithm for the
finite case. In this case, there exists a canonical problem formulation as a mixed integer
linear program (MIP). It contains a set of flow variables for every scenario. Buchheim, Liers
and SanitĂ enhance the formulation with general cutting planes that are called target cuts.
The first part of the dissertation considers the problem variant where every scenario has
exactly two terminal nodes. If the underlying network is a complete, unweighted graph,
then this problem is the Network Synthesis Problem as defined by Chien (IBM Journal of
R&D 1960). There exist polynomial time algorithms by Gomory and Hu (SIAM J. of Appl.
Math 1961) and by Kabadi, Yan, Du and Nair (SIAM J. on Discr. Math.) for this special
case. However, these algorithms are based on the fact that complete graphs are Hamiltonian.
The result of this part is a similar algorithm for hypercube graphs that assumes a special
distribution of the supplies and demands. These graphs are also Hamiltonian.
The second part of the thesis discusses the structure of the polyhedron of feasible sRND
solutions. Here, the first result is a new MIP-based capacity formulation for the sRND
problem. The size of this formulation is independent of the number of extreme points
of B and therefore, it is also suited for the polyhedral case. The formulation uses so-called
cut-set inequalities that are known in similar form from other network design problems. By
adapting a proof by Mattia (Computational Optimization and Applications 2013), we show
that cut-set inequalities induce facets of the sRND polyhedron. To obtain a better linear
programming relaxation of the capacity formulation, we interpret certain general mixed
integer cuts as 3-partition inequalities and show that these inequalities induce facets as well.
The capacity formulation has exponential size and we therefore need a separation algorithm
for cut-set inequalities. In the finite case, we reduce the cut-set separation problem to
a minimum cut problem that can be solved in polynomial time. In the polyhedral case,
however, the separation problem is N P-hard, even if we assume that the scenario polytope
is basically a cube. Such a scenario polytope is called Hose polytope. Nonetheless, we can
solve the separation problem in practice: We show a MIP based separation procedure for
the Hose scenario polytope. Additionally, the thesis presents two separation methods for
3-partition inequalities. These methods are independent of the encoding of the scenario
polytope. Additionally, we present several rounding heuristics.
The result is a Branch-and-Cut algorithm for the capacity formulation. We analyze the
algorithm in the last part of the thesis. There, we show experimentally that the algorithm
works in practice, both in the finite and in the polyhedral case. As a reference point, we
use a CPLEX implementation of the flow based formulation and the computational results by
Buchheim, Liers and SanitĂ . Our experiments show that the new Branch-and-Cut algorithm
is an improvement over the existing approach. Here, the algorithm excels on problem
instances with many scenarios. In particular, we can show that the MIP separation of the
cut-set inequalities is practical