Optimal expansion of an existing network

Christofides, Nicos; Brooker, Philip A. H.

doi:10.1007/bf01580236

Cited by 30 publications

(9 citation statements)

References 2 publications

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“…There has been intense research on multi-period network design problems since publication of the seminal articles by [6], [7] and [17]. Optimization methods have been used for designing networks for telecommunication, transportation [16], distribution of gas or water [14] and many others.…”

Section: Related Multi-period Optimization Problemsmentioning

confidence: 99%

MIP Modeling of Incremental Connected Facility Location

Arulselvan

Bley

Gollowitzer

et al. 2011

Lecture Notes in Computer Science

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We consider the incremental connected facility location problem, in which we are given a set of potential facilities, a set of interconnection nodes, a set of customers with demands, and a planning horizon. For each time period, we have to select a set of facilities to open, a set of customers to be served, the assignment of these customers to the open facilities, and a network that connects the open facilities. Once a customer is served, it must also be served in subsequent periods. Furthermore, in each time period the total demand of all customers served must be at least equal to a given minimum coverage requirement for that period. The objective is to maximize the net present value of the network, which is given by the discounted revenues of serving the customers and by the discounted investments and maintenance costs for the facilities and the network. We study different MIP models for this problem, discuss some valid inequalities to strengthen these formulations, and present a branch and cut algorithm for finding its solution. Finally, we report (preliminary) computational results of our implementation of this algorithm.

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Section: Related Multi-period Optimization Problemsmentioning

confidence: 99%

MIP Modeling of Incremental Connected Facility Location

Arulselvan

Bley

Gollowitzer

et al. 2011

Lecture Notes in Computer Science

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“…This is an iterative algorithm comprising two main steps as in [15]. Typically, during an iteration we first solve the relaxed MILPM problem with a subset of constraints (9). At this stage, if the solution is feasible, we have reached the optimal solution and the algorithm stops.…”

Section: Solution Approach and Implementationmentioning

confidence: 99%

“…In practice, adding one valid inequality at a time to the master program is not efficient. On the basis of the theoretical results presented in the previous section, we have generated and added other valid inequalities of type (9). Their integration in the master program allows the model to be strengthened and significantly reduces the computation time.…”

Section: Solution Approach and Implementationmentioning

confidence: 99%

“…A variant of the network design problem studied in the literature is the MPND problem. Although this problem has been around since the 1970s (see [9] and [27]), the network design expansion is limited in these models, because no links or nodes can be added from one period to the next. The topology remains the same from the first to the last period.…”

Section: Introductionmentioning

confidence: 99%

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Multiperiod network design with incremental routing

2007

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In this paper, we study a special case of multiperiod network design (MPND) problems, multiperiod network design with incremental routing (MPNDI), as applied to the transmission layer of an optical network. We optimize simultaneously the network architecture and the link dimensioning under discrete cost functions in order to route all traffic demands in line with traffic growth over a discrete time horizon. Because of operational requirements, routing paths used at a given period to route some traffic demands have to be preserved over subsequent periods; this is called incremental routing with respect to incremental flow. To handle the high dimensionality, a compact formulation omitting explicitly written flow variables is given. We examine the dominant polyhedron of the incremental multicommodity flow and provide a polyhedral study of it. Finally, a solution approach taking advantage of the polyhedral structure of MPNDI is proposed, and computational results for a range of instances with 8 and 10 nodes are provided.

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“…They include Zadeh [34], Christofides and Brooker [6], Doulliez and Rao [7], Minoux [29], and Parrish et al [31]. They include Zadeh [34], Christofides and Brooker [6], Doulliez and Rao [7], Minoux [29], and Parrish et al [31].…”

Section: Topological Design and Capacity Expansion Problemsmentioning

confidence: 99%

Configuring wide area computer networks

Gavish

1992

OR Spektrum

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Modern computer networks consist of wide area backbone networks which serve as major highways to transfer large volumes of communication traffic between access points, and local access networks which feed traffic between the backbone network and end user nodes. The topological design of wide area computer communication networks consists of selecting a set of locations for network control processors (NCPs) placement, deciding on backbone links and their capacities to connect the NCPs, linking end user nodes to the NCPs and selecting routes for routing messages between communicating end user pairs. This paper presents some of the problems faced by network designers starting from the capacity assignment problem, moving to routing and capacity assignment, followed by the topological design and capacity assignment problem; the last problem presented is the topological design and capacity expansion over time. The problems are complex combinatorial optimization problems, which require developing new solution procedures. The paper presents the problems and discusses models and solution procedures. The paper concludes with a discussion and directions for further research.Zusammenfassung. In dieser Arbeit behandeln wir einige Probleme die als Schritte beim Design yon Weitverkehrsnetzen (WAN) auftreten: Kapazit/itsplanung und -zuordnung, Wegebestimmung, Wahl der Netztopologie sowie Kapazit~itserweiterung. Diese Problemstellungen ffihren dabei auf komplexe Kombinatorische Optimierungsprogramme, die die Entwicktung neuer L6sungstechniken verlangen.Wit beschreiben die verschiedenen Probleme und diskutieren zugeh6rige Optimierungsmodelle und L6sungsverfah.ren. Diese Arbeit schliegt mit einem Ausblick auf zukfinftige Forschungsschwerpunkte.

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Optimal expansion of an existing network

Cited by 30 publications

References 2 publications

MIP Modeling of Incremental Connected Facility Location

MIP Modeling of Incremental Connected Facility Location

Multiperiod network design with incremental routing

Configuring wide area computer networks

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