Decomposable robust two-stage optimization: An application to gas network operations under uncertainty

We study gas network problems with compressors and control valves under uncertainty that can be formulated as two-stage robust optimization problems. Uncertain data are present in the physical parameters of the pipes as well as in the overall demand. We show how to exploit the special decomposable structure of the problem to reformulate the two-stage problem as a single-stage robust optimization problem. The right-hand side of the single-stage problem can be precomputed by solving a series of optimization problems and multiple elements of the right-hand side can be combined into one optimization task. The practical feasibility and effectiveness of our approach is demonstrated with benchmarks on several gas network instances, among them a realistic model of the Greek natural gas network. Overall, aggregation and preprocessing allow us to quickly solve large gas network instances under uncertainty for the price of slightly more conservative solutions.