Robust multiobjective optimization with application to Internet routing

Robust optimization addressing decision making under uncertainty has been very well developed for problems with a single objective function and applied to areas of human activity such as portfolio selection, investment decisions, signal processing, and telecommunication-network planning. As these decision problems typically have several decisions or goals, we extend robust single objective optimization to the multiobjective case. The column-wise uncertainty model can be carried over to the multiobjective case without any additional assumptions. For the row-wise uncertainty model, we show under additional assumptions that robust efficient solutions are efficient to specific instance problems and can be found as the efficient solutions of another deterministic problem. Being motivated by the fact that Internet traffic must be maintained in a reliable yet affordable manner in situations of complex and dynamic usage, we apply the row-wise model to an intradomain multiobjective routing problem with polyhedral traffic uncertainty. We consider traditional objective functions corresponding to link utilizations and implement the biobjective case using the parametric simplex algorithm to compute robust efficient routings. We also present computational results for the Abilene network and analyze their meaning in the context of the application.