Robust network design

A crucial assumption in many network design problems is that of knowing the traffic demands in advance. Unfortunately, measuring and predicting traffic demands are difficult problems. Moreover, often communication patterns change over time, and therefore we are not given a single static traffic demand, but instead a set of non-simultaneous traffic demands. The network should be able to support any traffic demand that is from the given set. Several methodologies have been proposed to address the traffic demand uncertainty in network design problems, such as Robust Optimization. Here we provide an overview of the main results which have been achieved in modelling and solving network design problems in the framework of robust optimization. We then display some promising avenues of research. Robust network design: an overview Let G be a communication network, and K be a set of users that wish to communicate, expressed in terms of origin-destination pairs. Usually the traffic demands associated with the origin-destination pairs are not known in advance, but can only be forecast or estimated. This situation fits perfectly into the framework of Robust Optimization, that entails modeling optimization problems with uncertain parameters to obtain a solution that is guaranteed to be ‘good’ for all possible realizations of the parameters in given uncertainty sets. Let D denote the set of the estimated uncertain demands, while cij be the non-negative cost of installing a unit of capacity along the link (i, j). The Robust network design problem (RND) then consists of determining a minimum cost capacity allocation for the links of G such that the network is able to route each demand in D. Several variants and generalizations of RND have been proposed in the literature in the last decade, with the aim of modelling and solving relevant aspects in practical applications. Concerning the routing constraints, each origindestination pair may be required to communicate through a single path (unsplittable routing), or the traffic can be split among different paths (splittable routing). In addition, the routing can be dynamic, i.e., it can change as the demand varies in D, or static, i.e., the same routing template must be used for each demand in D [1]. Static routing can be preferable in applications where migrating from one routing to another one is costly. In general, splittable routing leads to a cheaper solution than unsplittable routing, and dynamic routing leads to a cheaper solution than static routing. From a time complexity perspective, the splittable static case is polynomially solvable [1]. On the other hand, in the unsplittable case RND is coNP -Hard. RND is also difficult in the splittable dynamic case, as it is coNP -Hard even for the so-called Hose model [3]. Thus, dynamic routing is, in general, substantially more difficult than static routing. This has motivated the study of “intermediate scenarios” such as the one where the demands in D can be served by two alternative routing templates [8] [9], which allows one to obtain cheaper solutions than static routing while being computationally tractable in some cases. Another possible approach is to study special cases of RND that are solvable in polynomial time due to the special structure of the demand polyhedron D, such as the ones addressed in [6]. See [2] for a detailed survey on RND, its variants and its generalizations. Some avenues of research The research on robust network design has been essentially theoretical. In a few cases there have been computational studies on peculiar robust models, usually involving a comparison between robust and nominal approaches of the same kind. An interesting line of research is to compare robust models of different kinds, in order to assess their efficiency and the quality of the returned solutions. Some steps in this direction can be found in [7], which reports the results of a preliminary computational comparison of robust models of different kinds in a telecommunications setting. We aim to enlarge the computational analysis to additional robust models and benchmark instances. Furthermore, we plan to investigate whether the use of two (or a constant number of) alternative routing templates [8] may provide good results in practice. This aspects will be investigated in telecommunications and transportation settings.