  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.
