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Topological design of survivable meshbased transport networks
 Annals of Operations Research
, 2001
"... Abstract: The advent of Sonet and DWDM meshrestorable networks which contain explicit reservations of spare capacity for restoration presents a new problem in topological network design. On the one hand, the routing of working flows wants a sparse treelike graph for minimization of the classic fi ..."
Abstract

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Abstract: The advent of Sonet and DWDM meshrestorable networks which contain explicit reservations of spare capacity for restoration presents a new problem in topological network design. On the one hand, the routing of working flows wants a sparse treelike graph for minimization of the classic fixed charge plus routing (FCR) costs. On the other hand, restorability requires a closed (biconnected) and preferably highdegree topology for efficient sharing of spare capacity allocations (SCA) for restoration over nonsimultaneous failure scenarios. These diametrically opposed considerations underlie the determination of an optimum physical facilities graph for a broadband network provider. Standalone instances of each constituent problem are NPhard. The full problem of simultaneously optimizing meshrestorable topology, routing, and sparing is therefore very difficult computationally. Following a comprehensive survey of prior work on topological design problems, we provide a {10} MIP formulation for the complete meshrestorable design problem and also propose a novel threestage heuristic. The heuristic is based on the hypothesis that the union set of edges obtained from separate FCR and SCA subproblems constitutes an effective topology space within which to solve a restricted instance of the full problem. Where fully optimal reference solutions are obtainable the heuristic shows less than 8 % gaps but runs in minutes as opposed to days. In other test cases the reference problem cannot be solved to optimality and we can only