The network design problem with relays
Date
2007Source Title
European Journal of Operational Research
Print ISSN
0377-2217
Electronic ISSN
1872-6860
Publisher
Elsevier
Volume
180
Issue
2
Pages
834 - 844
Language
English
Type
ArticleItem Usage Stats
229
views
views
241
downloads
downloads
Abstract
The network design problem with relays (NDPR) is defined on an undirected graph G = (V, E, K), where V = {1, ..., n} is a vertex set, E = {(i, j) : i, j ∈ V, i < j} is an edge set. The set K = {(o(k), d(k))} is a set of communication pairs (or commodities): o(k) ∈ V and d(k) ∈ V denote the origin and the destination of the kth commodity, respectively. With each edge (i, j) are associated a cost cij and a length dij. With vertex i is associated a fixed cost fi of locating a relay at i. The NDPR consists of selecting a subset over(E, -) of edges of E and of locating relays at a subset over(V, -) of vertices of V in such a way that: (1) the sum Q of edge costs and relay costs is minimized; (2) there exists a path linking the origin and the destination of each commodity in which the length between the origin and the first relay, the last relay and the destination, or any two consecutive relays does not exceed a preset upper bound λ. This article develops a lower bound procedure and four heuristics for the NPDR. These are compared on several randomly generated instances with |V| ≤ 1002 and |E| ≤ 1930.
Keywords
Column generationHeuristic
Network design
Telecommunications
Costs
Problem solving
Set theory
Telecommunication systems
Design problems
Graph theory