A polyhedral study of the capacity formulation of the multilayer network design problem

Abstract

A multilayer network is a hierarchical network where each layer is built using the components of the previous one. Optical networks are an example of two layered networks. The multilayer network design problem consists of installing minimum cost integer capacities on the edges of all the layers so that a set of demands can be routed on the network. In this article, two versions of the optical network design problem are studied, and polyhedral results for the corresponding capacity formulations are presented. We also show how to extend the results to a network with an arbitrary number of layers.

An optimization approach for congestion control in network routing with quality of service requirements

“…In , instead, arc capacities have already been set and the decision is to choose the arcs to be activated to ensure the routing of some traffic demands. Two‐layer networks are investigated in and references therein. For papers dealing with the survivability of a network under some failure scenarios see , where several protection and restoration techniques are analyzed.…”

The cut property under demand uncertainty

“…For additional details about metric inequalities see also [17]. For approaches that use metric inequalities to solve ND problems see [3,7,18,19,21], and references therein.…”

A polyhedral analysis of the capacitated edge activation problem with uncertain demands

“…In a complete characterization of the capacity formulation polyhedron of the splittable NL problem is given and a branch‐and‐cut approach is proposed: The tight metric inequalities are proved to completely define the capacity polyhedron. The result also applies to two‐layer networks . As for uncertain demands, in some properties about cuts and feasibility for deterministic network design are generalized to robust problems with splittable flows.…”

“…For splittable flows, capacity formulations can be obtained by the Benders decomposition approach , a popular technique with applications to many problems . Benders approaches and capacity formulations for network design problems with and without uncertainty can be found in and references therein. For unsplittable flows, capacity formulations are far less common and they are mainly obtained using (possibly modified versions of) combinatorial Benders cuts derived from the combinatorial properties, if any, of the considered problem .…”