A comparison of different routing schemes for the robust network loading problem: polyhedral results and computation

International audienceWe consider the capacity formulation of the Robust Network Loading Problem. The aim of the paper is to study what happens from the theoretical and from the computational point of view when the routing policy (or scheme) changes. The theoretical results consider static, volume, affine and dynamic routing, along with splittable and unsplittable flows. Our polyhedral study provides evidence that some well-known valid inequalities (the robust cutset inequalities) are facets for all the considered routing/flows policies under the same assumptions. We also introduce a new class of valid inequalities, the robust 3-partition inequalities, showing that, instead, they are facets in some settings, but not in others. A branch-and-cut algorithm is also proposed and tested. The computational experiments refer to the problem with splittable flows and the budgeted uncertainty set. We report results on several instances coming from real-life networks, also including historical traffic data, as well as on randomly generated instances. Our results show that the problem with static and volume routing can be solved quite efficiently in practice and that, in many cases, volume routing is cheaper than static routing, thus possibly representing the best compromise between cost and computing time. Moreover, unlikely from what one may expect, the problem with dynamic routing is easier to solve than the one with affine routing, which is hardly tractable, even using decomposition methods

Solving Survivable Two-Layer Network Design Problems by Metric Inequalities

We address the problem of designing a multi-layer network with survivability requirements. We are given a two-layer network: the lower layer represents the potential physical connections that can be activated, the upper layer is made of logical connections that can be set up using physical links. We are given origin-destination demands (commodities) to be routed at the upper layer. We are also given a set of failure scenarios and, for every scenarios, an associated subset of commodities. The goal is to install minimum cost integer capacities on the links of both layers in order to ensure that the commodities can be routed simultaneously on the network. In addition, in every failure scenario the routing of the associated commodities must be guaranteed. We consider two variants of the problem and develop a branch-and-cut scheme based on the capacity formulation. Computational results on instances derived from the SNDLib for single node failure scenarios are discussed