An aggregated multi-cut decomposition algorithm for two-stage transmission expansion planning problems

Zhang, Hui; Vittal, Vijay; Heydt, Gerald

doi:10.1109/pesgm.2015.7285608

Cited by 5 publications

(2 citation statements)

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“…The partial-cut approach has since been shown to be effective in various applied problems [4,5]. Moreover, the results in [3,9,10] suggest that many problems are solved more efficiently with an aggregation level somewhere between the single-cut and multi-cut, i.e., partitioning schemes S where 1 < A L (S) < n. For instance, in [10], a uniform aggregation scheme with variable aggregation level is adopted in a distributed setting to solve a large problem instance of 1000 scenarios corresponding to 2.5 million variables and 1.4 million constraints.…”

Section: Partial Cut Aggregationmentioning

confidence: 99%

“…It was later extended to a multi-cut variant, with better convergence properties on many test examples [2]. Recent contributions have explored aggregation strategies that fall between a single-cut and multi-cut approach [3,4,5]. The aim is to preserve the convergence properties of a multi-cut algorithm, while reducing the size growth of the master problem and communication overhead in distributed implementations.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic cut aggregation in L-shaped algorithms

Biel¹,

Johansson²

2019

Preprint

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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. Our approach requires tunable parameters, where the optimal settings for any given problem are unknown. We devise a simple tuning procedure and show its effectiveness. We also propose a variety of aggregation schemes that fit into our framework, and evaluate them on two large-scale stochastic programming problems. In addition, we propose a fixing 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 uniform cut aggregation, as well as our fixing strategy, can yield high performance at low overhead cost. These results are supported by our worst-case bounds.

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