Dynamic cut aggregation in L-shaped algorithms

We present a novel framework for dynamic cut aggregation in L-shaped algorithms. The aim is to improve the parallel performance of distributed L-shaped algorithms through reduced communication latency and load imbalance. We show how optimality cuts can be aggregated into arbitrary partitions without affecting convergence of the L-shaped algorithm. Furthermore, we give a worst-case bound for L-shaped algorithms with static cut aggregation and then extend this result for dynamic aggregation. We propose a variety of aggregation schemes that fit into our framework, and evaluate them on a collection of large-scale stochastic programming problems. All methods are implemented in our open-source framework for stochastic programming, StochasticPrograms.jl, written in the Julia programming language. In addition, we propose a granulated strategy that combines the strengths of dynamic and static cut aggregation. Major performance improvements are possible with our approach in distributed settings. Our experimental results suggest that the granulated strategy can consistently yield high performance on a range of test problems. The experimental results are supported by our worst-case bounds.