An integrated learning and progressive hedging matheuristic for stochastic network design problem

We address the Multicommodity Capacitated Fixed-charge Network Design problem with uncertain demands, which we formulate as a two-stage stochastic program. We rely on the progressive hedging (PH) algorithm of Rockafellar and Wets where the subproblems are defined using scenario groups. To address the problem, we propose an efficient matheuristic approach which we refer to as the Integrated Learning and Progressive Hedging. The proposed method takes advantage of a specialized learning-based matheuristic that is able to quickly produce high-quality solutions to multi-scenario subproblems. Furthermore, we propose a novel reference point definition, at each aggregation step of the PH algorithm, which leverages subproblem information regarding promising design variables. Extensive computational experiments illustrate that the proposed approach should be the method of choice when high-quality solutions to large instances of stochastic network problems need to be found quickly.