Distributed stochastic multicommodity flow optimization

In this paper we are concerned with a class of stochastic multicommodity network flow problems, the so called capacity expansion planning problems. We consider a two-stage stochastic optimization formulation that incorporates uncertainty in the problem parameters. To address the computational complexity of these stochastic models, we propose a decomposition method to divide the original problem into smaller, tractable subproblems that are solved in parallel at the network nodes. Unlike relevant techniques in existing literature that decompose the problem with respect to the possible realizations of the random parameters, our approach can be applied to networked systems that lack a central processing unit and require autonomous decision making by the network nodes. Our method relies on the recently proposed Accelerated Distributed Augmented Lagrangians (ADAL) algorithm, a dual decomposition technique with regularization, which achieves very fast convergence rates.