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A column generation approach for a ring network design problem
Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0001-5907-0087
Linköping University, Department of Science and Technology. Linköping University, The Institute of Technology.
##### Abstract [en]

When designing a telecommunication network, one often wish to include some kind of survivability requirement, for example that there should be at least two paths between every pair of nodes in the network. A design model who fulfills this requirement is a network build up with rings. The network design problem is to choose links from a given network, and compose them into a number of rings. The rings are connected to each other at certain transit nodes. The number of possible rings is enormous, and each possible ring is associated with a certain fixed cost. A ring has a fixed capacity, however, we model it as a linear cost depending on the traffic using the ring and the length of the ring. We describe the problem, and model it is a set covering model, where a column describes how a specific ring is used. Even with a small set of rings, number of possible columns in the model is large. Therefore, a column generation approach is used to solve the set covering model with a given set of rings. An important part of the problem is to generate new rings, were the dual solution from the set covering model gives rewards on the nodes, representing a nodes’ wish to be included in a new ring. The ring generation problem is a modification of a traveling salesman subtour problem. New rings are generated using a heuristic. We present some computational results for a real data network and a number of random generated networks.

2003. , p. 26
##### Series
LiTH-MAT-R, ISSN 0348-2960 ; 21
##### National Category
Engineering and Technology
##### Identifiers
OAI: oai:DiVA.org:liu-87193DiVA, id: diva2:587153
Available from: 2013-01-14 Created: 2013-01-14 Last updated: 2013-08-29
##### In thesis
Open this publication in new window or tab >>Ring network design in telecommunications: optimization based solution approaches
2003 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

When designing a telecommunication network, one often wish to include some kind of survivability requirement, for example that the network should be two-connected. A two-connected network fulfills the requirement that there should be at least two paths with no links in common between all pairs of nodes. One form of design model is to prescribe that the network should be composed of connected rings of links. The network design problem is then to choose links from a given network, and compose them into a number of rings. A ring is reliable in the sense that there always exist two ways of sending traffic, clockwise or counter-clockwise, which means that a ring fulfills the two-connectivity requirement. There is often a number of requirements on a ring, such as a limited length and limited number of nodes connected to the ring. This means that a ring network will include a number of rings, and traffic between rings must be possible. The traffic between rings is usually made at certain nodes, called transit nodes. Therefore all rings should be connected to at least one of the transit nodes. We focus on the case where we have two transit nodes in the network.

Each possible ring is associated with a certain fixed cost, and all links in a certain ring are given the same capacity. Reserve capacity is allocated according to certain principles. The number of possible rings in a network is an exponential function of the number of nodes in the network, so for larger networks is it impossible to a priori generate all possible rings.

We describe the problem, and model it as a linear integer programming problem, where a set of rings are assumed to be known. The usage of rings, i.e., the allocation of demand to rings, is determined. In practice, too many rings can not be included in the model. Instead we must be able to generate useful rings. A Lagrangean relaxation of the model is formulated, and the dual solution is used in order to derive reduced costs which can be used to generate new better rings. The information generated describes only the physical structure of the ring, not the usage of it. The ring generation problem is a modified traveling salesman subtour problem, which is known to be difficult to solve. Therefore, we focus on heuristic solution methods for this problem.

We also presents a column generation approach where the problem is modeled as a set covering problem. Here, a column describes both the topology of the ring and the exact usage of it. A similar ring generation problem appears as a subproblem, in order to generate new rings.

All methods are computationally tested on both real life data and randomly generated data, similar to real life problems.

##### Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 829
Mathematics
##### Identifiers
urn:nbn:se:liu:diva-22357 (URN)1563 (Local ID)91-7373-668-6 (ISBN)1563 (Archive number)1563 (OAI)
##### Opponent
Available from: 2009-10-07 Created: 2009-10-07 Last updated: 2013-01-14

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#### Authority records BETA

Henningsson, MathiasHolmberg, KajRönnqvist, MikaelVärbrand, Peter

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Cite
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