205 research outputs found
Valid Inequalities and Facets for Multi-Module (Survivable) Capacitated Network Design Problem
In this dissertation, we develop new methodologies and algorithms to solve the multi-module (survivable) network design problem. Many real-world decision-making problems can be modeled as network design problems, especially on networks with capacity requirements on arcs or edges. In most cases, network design problems of this type that have been studied involve different types of capacity sizes (modules), and we call them the multi-module capacitated network design (MMND) problem. MMND problems arise in various industrial applications, such as transportation, telecommunication, power grid, data centers, and oil production, among many others.
In the first part of the dissertation, we study the polyhedral structure of the MMND problem. We summarize current literature on polyhedral study of MMND, which generates the family of the so-called cutset inequalities based on the traditional mixed integer rounding (MIR). We then introduce a new family of inequalities for MMND based on the so-called n-step MIR, and show that various classes of cutset inequalities in the literature are special cases of these inequalities. We do so by studying a mixed integer set, the cutset polyhedron, which is closely related to MMND. We We also study the strength of this family of inequalities by providing some facet-defining conditions. These inequalities are then tested on MMND instances, and our computational results show that these classes of inequalities are very effective for solving MMND problems. Generalizations of these inequalities for some variants of MMND are also discussed.
Network design problems have many generalizations depending on the application. In the second part of the dissertation, we study a highly applicable form of SND, referred to as multi-module SND (MM-SND), in which transmission capacities on edges can be sum of integer multiples of differently sized capacity modules. For the first time, we formulate MM-SND as a mixed integer program (MIP) using preconfigured-cycles (p-cycles) to reroute flow on failed edges. We derive several classes of valid inequalities for this MIP, and show that the valid inequalities previously developed in the literature for single-module SND are special cases of our inequalities. Furthermore, we show that our valid inequalities are facet-defining for MM-SND in many cases. Our computational results, using a heuristic separation algorithm, show that these inequalities are very effective in solving MM-SND. In particular they are more effective than compared to using single-module inequalities alone.
Lastly, we generalize the inequalities for MMND for other mixed integer sets relaxed from MMND and the cutset polyhedron. These inequalities also generalize several valid inequalities in the literature. We conclude the dissertation by summarizing the work and pointing out potential directions for future research
Strong Formulations for Network Design Problems with Connectivity Requirements
The network design problem with connectivity requirements (NDC) models a wide variety of celebrated combinatorial optimization problems including the minimum spanning tree, Steiner tree, and survivable network design problems. We develop strong formulations for two versions of the edge-connectivity NDC problem: unitary problems requiring connected network designs, and nonunitary problems permitting non-connected networks as solutions. We (i) present a new directed formulation for the unitary NDC problem that is stronger than a natural undirected formulation, (ii) project out several classes of valid inequalities-partition inequalities, odd-hole inequalities, and combinatorial design inequalities-that generalize known classes of valid inequalities for the Steiner tree problem to the unitary NDC problem, and (iii) show how to strengthen and direct nonunitary problems. Our results provide a unifying framework for strengthening formulations for NDC problems, and demonstrate the strength and power of flow-based formulations for network design problems with connectivity requirements
A comparison of different routing schemes for the robust network loading problem: polyhedral results and computation
International audienceWe consider the capacity formulation of the Robust Network Loading Problem. The aim of the paper is to study what happens from the theoretical and from the computational point of view when the routing policy (or scheme) changes. The theoretical results consider static, volume, affine and dynamic routing, along with splittable and unsplittable flows. Our polyhedral study provides evidence that some well-known valid inequalities (the robust cutset inequalities) are facets for all the considered routing/flows policies under the same assumptions. We also introduce a new class of valid inequalities, the robust 3-partition inequalities, showing that, instead, they are facets in some settings, but not in others. A branch-and-cut algorithm is also proposed and tested. The computational experiments refer to the problem with splittable flows and the budgeted uncertainty set. We report results on several instances coming from real-life networks, also including historical traffic data, as well as on randomly generated instances. Our results show that the problem with static and volume routing can be solved quite efficiently in practice and that, in many cases, volume routing is cheaper than static routing, thus possibly representing the best compromise between cost and computing time. Moreover, unlikely from what one may expect, the problem with dynamic routing is easier to solve than the one with affine routing, which is hardly tractable, even using decomposition methods
The k-edge connected subgraph problem: Valid inequalities and Branch-and-Cut
International audienceIn this paper we consider the k-edge connected subgraph problem from a polyhedral point of view. We introduce further classes of valid inequalities for the associated polytope, and describe sufficient conditions for these inequalities to be facet defining. We also devise separation routines for these inequalities, and discuss some reduction operations that can be used in a preprocessing phase for the separation. Using these results, we develop a Branch-and-Cut algorithm and present some computational results
Optimization in Telecommunication Networks
Network design and network synthesis have been the classical optimization problems intelecommunication for a long time. In the recent past, there have been many technologicaldevelopments such as digitization of information, optical networks, internet, and wirelessnetworks. These developments have led to a series of new optimization problems. Thismanuscript gives an overview of the developments in solving both classical and moderntelecom optimization problems.We start with a short historical overview of the technological developments. Then,the classical (still actual) network design and synthesis problems are described with anemphasis on the latest developments on modelling and solving them. Classical results suchas Mengerâs disjoint paths theorem, and Ford-Fulkersonâs max-flow-min-cut theorem, butalso Gomory-Hu trees and the Okamura-Seymour cut-condition, will be related to themodels described. Finally, we describe recent optimization problems such as routing andwavelength assignment, and grooming in optical networks.operations research and management science;
Hub & regenerator location and survivable network design
Ankara : The Department of Industrial Engineering and the Institute of Engineering and Science of Bilkent University, 2010.Thesis (Ph. D.) -- Bilkent University, 2010.Includes bibliographical references leaves 180-184.With the vast development of the Internet, telecommunication networks are employed
in numerous different outlets. In addition to voice transmission, which is
a traditional utilization, telecommunication networks are now used for transmission
of different types of data. As the amount of data transmitted through the
network increases, issues such as the survivability and the capacity of the network
become more imperative. In this dissertation, we deal with both design and routing
problems in telecommunications networks. Our first problem is a two level
survivable network design problem. The topmost layer of this network consists of
a backbone component where the access equipments that enable the communication
of the local access networks are interconnected. The second layer connects
the users on the local access network to the access equipments, and consequently
to the backbone network. To achieve a survivable network, one that stays operational
even under minor breakdowns, the backbone network is assumed to be
2-edge connected while local access networks are to have the star connectivity.
Within the literature, such a network is referred to as a 2-edge connected/star
network. Since the survivability requirements of networks may change based on
the purposes they are utilized for, a variation of this problem in which local access
networks are also required to be survivable is also analyzed. The survivability of
the local access networks is ensured by providing two connections for every component
of the local access networks to the backbone network. This architecture
is known as dual homing in the literature. In this dissertation, the polyhedral
analysis of the two versions of the two level survivable network design problem is
presented; separation problems are analyzed; and branch-and-cut algorithms are
developed to find exact solutions.
The increased traffic on the telecommunications networks requires the use of high capacity components. Optical networks, composed of fiber optical cables,
offer solutions with their higher bandwidths and higher transmission speeds. This
makes the optical networks a good alternative to handle the rapid increase in the
data traffic. However, due to signal degradation which makes signal regeneration
necessary introduces the regenerator placement problem as signal regeneration is
a costly process in optical networks. In the regenerator placement problem, we
study a location and routing problem together on the backbone component of a
given telecommunications network. Survivability is also considered in this problem
simultaneously. Exact solution methodologies are developed for this problem:
mathematical models and some valid inequalities are proposed; separation problems
for the valid inequalities are analyzed and a branch-and-cut algorithm is
devised.ĂzkĂśk, OnurPh.D
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