A column generation approach for a ring network design problem
2003 (English)Report (Other academic)
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.
Place, publisher, year, edition, pages
2003. , 26 p.
LiTH-MAT-R, ISSN 0348-2960 ; 21
Engineering and Technology
IdentifiersURN: urn:nbn:se:liu:diva-87193OAI: oai:DiVA.org:liu-87193DiVA: diva2:587153