An asynchronous parallel benders decomposition method for stochastic network design problems

Abstract

Benders decomposition (BD) is one of the most popular solution algorithms for stochastic integer programs. The BD method decomposes stochastic problems into one master problem and multiple disjoint subproblems. It thus lends itself readily to parallelization. In almost all studies on the parallelization of this algorithm, the master problem remains idle until every subproblem is solved and vice versa. This can clearly result in an extremely inefficient parallel algorithm due to excessive idle times. On the other hand, relaxing the synchronization requirement can yield a nonconvergent or less efficient algorithm that may even underperform when compared to the sequential version. Addressing these issues, we introduce an asynchronous parallel BD method for stochastic network design problems. We show that the proposed algorithm converges to the global optimum and suggest various acceleration strategies to enhance its performance. We conduct an extensive numerical study on benchmark instances from a generic stochastic network design problem. The results indicate that using up to 20 processors, our asynchronous algorithm is on average 1.4 times faster than the conventional low-level parallel methods.