Adaptive multicut aggregation for two-stage stochastic linear programs with recourse

Trukhanov, Svyatoslav; Ntaimo, Lewis; Schaefer, Andrew J.

doi:10.1016/j.ejor.2010.02.025

Cited by 45 publications

(37 citation statements)

References 11 publications

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“…Since the standard Benders decomposition returns only one cut to the master problem in each iteration, its convergence might be slow for some computationally demanding problems (Birge & Louveaux, 1997). To address this issue, numerous researchers have proposed variants to accelerate the algorithm (Bahn et al, 1995;Escudero et al, 2007;Fragniere et al, 2000;Gerd Infanger, 1993;Latorre et al, 2009;Linderoth & Wright, 2003;Mulvey & Ruszczynski, 1995;Ruszczynski, 1993;Contreras, et al, 2010;Miller & Ruszczyński, 2010;Trukhanov et al, 2010).…”

Section: Introductionmentioning

confidence: 99%

Multicut Benders decomposition algorithm for process supply chain planning under uncertainty

You

Grossmann

2011

Ann Oper Res

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Section: Introductionmentioning

confidence: 99%

Multicut Benders decomposition algorithm for process supply chain planning under uncertainty

You

Grossmann

2011

Ann Oper Res

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“…In this method, which is applied to a stochastic UC with load and generation uncertainty, scenarios are divided into (homogeneous) groups and cuts are derived for each group, as proposed in Trukhanova et al (2010). Consequently, the dimension of the master problem is smaller in comparison with the classical multi-cut algorithm, while less information is lost compared to the single cut version.…”

Section: Benders(-like) Decompositionmentioning

confidence: 99%

Large-scale Unit Commitment under uncertainty

Ackooij²,

et al. 2015

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The Unit Commitment problem in energy management aims at finding the optimal productions schedule of a set of generation units while meeting various system-wide constraints. It has always been a large-scale, non-convex difficult problem, especially in view of the fact that operational requirements imply that it has to be solved in an unreasonably small time for its size. Recently, the ever increasing capacity for renewable generation has strongly increased the level of uncertainty in the system, making the (ideal) Unit Commitment model a large-scale, non-convex, uncertain (stochastic, robust, chance-constrained) program. We provide a survey of the literature on methods for the Uncertain Unit Commitment problem, in all its variants. We start with a review of the main contributions on solution methods for the deterministic versions of the problem, focusing on those based on mathematical programming techniques that are more relevant for the uncertain versions of the problem. We then present and categorize the approaches to the latter, also providing entry points to the relevant literature on optimization under uncertainty

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“…Trukhanov, Ntaimo, and Schaefer [35] introduce an adaptive multicut method that generalizes the single-cut (L-shaped) and multicut methods. The method dynamically adjusts the aggregation level of the optimality cuts in the master program.…”

Section: Introductionmentioning

confidence: 99%

“…In the SAA framework, the idea of adaptive aggregation has been applied to manage the optimality cuts in the master problem to enhance the computational performance of Benders decomposition for solving two-stage stochastic programs [35] and multistage stochastic programs [38]. Trukhanov, Ntaimo, and Schaefer [35] introduce an adaptive multicut method that generalizes the single-cut (L-shaped) and multicut methods.…”

Section: Introductionmentioning

confidence: 99%

An Adaptive Partition-Based Approach for Solving Two-Stage Stochastic Programs with Fixed Recourse

Song

Luedtke

2015

SIAM J. Optim.

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We study an adaptive partition-based approach for solving two-stage stochastic programs with fixed recourse. A partition-based formulation is a relaxation of the original stochastic program, and we study a finitely converging algorithm in which the partition is adaptively adjusted until it yields an optimal solution. A solution guided refinement strategy is developed to refine the partition by exploiting the relaxation solution obtained from a partition. In addition to refinement, we show that in the case of stochastic linear programs, it is possible to merge some components in a partition, without weakening the corresponding relaxation bound, thus allowing the partition size to be kept small. We also show that for stochastic linear programs with simple recourse, there exists a small partition that yields an optimal solution. The size of this partition is independent of the number of scenarios used in the model. Our computational results show that the proposed adaptive partition-based approach converges very fast to a small partition for our test instances. In particular, on our test instances the proposed approach outperforms basic versions of Benders decomposition and is competitive with the state-of-art methods such as the level method for stochastic linear programs with fixed recourse.

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Adaptive multicut aggregation for two-stage stochastic linear programs with recourse

Cited by 45 publications

References 11 publications

Multicut Benders decomposition algorithm for process supply chain planning under uncertainty

Multicut Benders decomposition algorithm for process supply chain planning under uncertainty

Large-scale Unit Commitment under uncertainty

An Adaptive Partition-Based Approach for Solving Two-Stage Stochastic Programs with Fixed Recourse

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