Optimization methods for network design under variable link capacities

This thesis summaries the work we have done in optimization of resilient communication networks. More specifically, the main goal is to propose appropriated recovery mechanisms for managing the demand traffic in a network under partial failures, i.e. when some part of the network (one or some links and/or nodes) is operational with reduced capacity. The main criterion in deciding the efficiency of the proposed recovery scheme is the dimensioning cost of the network while keeping the management cost at reasonable levels. Our main contribution is the design of two restoration strategies named Flow Thinning and Elastic Flow Rerouting. This document is organized in three main parts. In the first part, we present the problematic of the thesis. It includes an introduction on the protection and rerouting state-of-art strategies, together with their mathematical models and resolution methods. The second part presents in depth the first protection strategy named Flow Thinning. This strategy manages partial failures by decreasing appropriately the bandwidth on some flows routed through one of perturbed links. This implies overdimensionning of the network in the nominal state to ensure demand traffic in all failure states. The third and last part deals with the second rerouting strategy called Elastic Flow Rerouting. This strategy is a bit more complex than the first one because, in a failure state, we need to distinguish demands which are disturbed and the one which are not. If a demand is disturbed, it can increase the traffic on some of its paths. If it is not disturbed, it can release bandwidth on paths at the condition it remains non-disturbed. All this allows for further reducing the dimensioning cost but at a higher cost in terms of recovery process management. Note that the dimensioning problems for each strategy are shown to be NP-hard in their general form. The work of the thesis has been published in: three journal articles (Fouquet et al. (2015b), Pioro et al. (2015), Shinko et al. (2015)), two invited articles (Fouquet and Nace (2015), Fouquet et al. (2014c)) and height articles in international conferences (Fouquet et al. (2015a; 2014d;a;b;e), Pioro et al. (2013b;a), Shinko et al. (2013)). Note that Pioro et al. (2013b) has been rewarded by a "Best Paper Award" from the RNDM conference. To conclude, note that this thesis was realized in the Heudiasyc laboratory, from the Universite de Technologie de Compiegne (UTC). It was financed by the French Ministry of Higher Education and Research1 with the support of the Labex MS2T2 of the UTC.