In this paper, we study a special case of multiperiod network design (MPND) problems, multiperiod network design with incremental routing (MPNDI), as applied to the transmission layer of an optical network. We optimize simultaneously the network architecture and the link dimensioning under discrete cost functions in order to route all traffic demands in line with traffic growth over a discrete time horizon. Because of operational requirements, routing paths used at a given period to route some traffic demands have to be preserved over subsequent periods; this is called incremental routing with respect to incremental flow. To handle the high dimensionality, a compact formulation omitting explicitly written flow variables is given. We examine the dominant polyhedron of the incremental multicommodity flow and provide a polyhedral study of it. Finally, a solution approach taking advantage of the polyhedral structure of MPNDI is proposed, and computational results for a range of instances with 8 and 10 nodes are provided.

In this paper we focus on the single facility capacitated survivable network design problem. We optimize simultaneously the topology, the link dimensioning for the nominal state as well as for the single link failure state when the survivable conditions are expressed by various rerouting strategies. We present an (mixed) integer mathematical approach that consists of several methodologies. To address the high dimensionality we use Benders' decomposition, and in parallel a Branch-and-Bound method and a cutting plane approach. Beyond the interest of the proposed approach itself, we have considered and compared two well known restoration technics as local rerouting and end-toend rerouting. Numerous computational results for realistic instance networks are given to compare these rerouting mechanisms in terms of installed capacities as well as overall costs with respect to topology requirements.

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