Topological Design of Survivable Mesh-Based Transport Networks

The advent of Sonet and DWDM mesh-restorable 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 tree-like graph for minimization of the classic fixed charge plus routing (FCR) costs. On the other hand, restorability requires a closed (bi-connected) and preferably high-degree topology for efficient sharing of spare capacity allocations (SCA) for restoration over non-simultaneous 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 NP-hard. The full problem of simultaneously optimizing mesh-restorable topology, routing, and sparing is therefore very difficult computationally. Following a comprehensive survey of prior work on topological design problems, we provide a {1–0} MIP formulation for the complete mesh-restorable design problem and also propose a novel three-stage heuristic. The heuristic is based on the hypothesis that the union set of edges obtained from separate FCR and SCA sub-problems 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 report that heuristic results obtained in minutes are not improved upon by CPLEX running the full problem for 6 to 18 hours. The computational behavior we observe gives insight for further work based on an appreciation of the problem as embodying unexpectedly difficult feasibility apects, as well as optimality aspects.