Technical Note—Branch-and-Price-and-Cut Approach to the Robust Network Design Problem Without Flow Bifurcations

Abstract

This paper presents a robust optimization approach to the network design problem under traffic demand uncertainty. Here, we consider the specific case of the network design problem in which there are several alternatives in edge capacity installations and the traffic cannot be split over several paths. A new decomposition approach is proposed which yields a strong LP relaxation and enables traffic demand uncertainty to be addressed efficiently through localization of the uncertainty to each edge of the underlying network. A branch-and-price-and-cut algorithm is subsequently developed and tested on a set of benchmark instances.

Networks, uncertainty, applications and a crusade for optimality

“…A deviation of 5% is in the middle of the values considered in most of the literature which range from 1% up to 10%; [see Bertsimas and Sim, 2003, 2004, Fischetti and Monaci, 2012, among other papers. Almost the same criterion to generate interval data instances is also used in [Ben-Tal et al, 2004, Klopfenstein and Nace, 2012, Lee et al, 2012 and [Solyali et al, 2012].…”

Solving the bifurcated and nonbifurcated robust network loading problem with k‐adaptive routing

“…Many approaches have been presented to solve static routing network design problems, experimenting the effect of different formulations, uncertainty sets or solution methods through robust reformulation, decomposition and/or valid inequalities (as examples, see [1], [2], [23], [24], [21]) As presented, static and dynamic are two extremes routing schemes. In [20], they show that the solution for static routing RN L (splittable or unsplittable, under polyhedral uncertainty set) may be a factor of Ω(log |V |) more than the cost required when using dynamic routing.…”

Robust Optimization: Concise Review of Current Status and Issues

“…Hence if the nominal problem can be solved efficiently, the robust counterpart can also be solved efficiently. As an application of the model, Lee et al (2012) applied the result to a telecommunication network design problem with demand uncertainty.…”