Abstract
In this article, we introduce the Generalized {0,1,2}-Survivable Network Design Problem ({0,1,2}-GSNDP) which has applications in the design of backbone networks. Different mixed integer linear programming formulations are derived by combining previous results obtained for the related {0,1,2}-GSNDP and Generalized Network Design Problems. An extensive computational study comparing the correspondingly developed branch-and-cut approaches shows clear advantages for two particular variants. Additional insights into individual advantages and disadvantages of the developed algorithms for different instance characteristics are given.
Highlights
The optimal design of networks has been the topic of numerous scientific articles and a variety of different combinatorial optimization problems arising in that domain have been studied in detail
To analyze the performance of the branch-and-cut algorithms developed for the different models proposed in Sects. 2.1 and 2.2 we first discuss the results obtained for the five considered variants on instances with less than 100 nodes
To gain insight into potential advantages and disadvantages of the methods, these results are grouped according to three different characteristics
Summary
The optimal design of (telecommunication) networks has been the topic of numerous scientific articles and a variety of different (classes of) combinatorial optimization problems arising in that domain have been studied in detail. For the {0, 1, 2}-GSNDP studied in this article, their result implies that each solution can be oriented based on an arbitrarily chosen “root cluster” r ∈ C2 as follows: (i) There exists a directed path Pi ⊂ A from the node chosen in Vr to a node selected in any other mandatory cluster i ∈ C1 ∪ C2; (ii) There exists a directed path Pi ⊂ A from a node selected in cluster i ∈ C2 to the chosen node in Vr that is node disjoint with Pi except for its start and end node in Vi and Vr , respectively This characterization has two important consequences for MILP formulations such as the ones introduced : (i) Instead of the need to consider paths between all pairs of (mandatory) clusters, it is sufficient to consider paths from the root cluster to all other mandatory clusters and from all redundant clusters to the root cluster. In the following we refrain from giving the details which would require to introduce undirected counterparts of our formulations
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