Quality evaluation of scenario-tree generation methods for solving stochastic programming problems

Keutchayan, Julien; Gendreau, Michel; Saucier, Antoine

doi:10.1007/s10287-017-0279-4

Cited by 9 publications

(8 citation statements)

References 28 publications

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“…This has been a tool for the further development of scenario-generation methods. The concept of extension rules for out-of-sample evaluation in multistage problems proposed by Keutchayan et al (2017) serves as a multistage counterpart. In principle, other evaluation bounds from Section 3 could also have been used to compare candidate decisions.…”

Section: Out-of-sample Evaluation Boundsmentioning

confidence: 99%

“…The simplest extension rule would be a nearest neighbour rule according to the distance from the tree to any given path ξ[t] up to its realisation at stage t where the policy must be determined. Regression procedures have been proposed by Keutchayan et al (2017), while Stochastic Dual Dynamic Programming (SDDP) can be applied to obtain piece-wise linear policies for problems of a special kind (Pereira and Pinto, 1991). Alternatively, we may incrementally optimise the decision in each stage, conditional on decisions determined in past stages.…”

Section: Bounds Based On Candidate Policiesmentioning

confidence: 99%

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On the safe side of stochastic programming: bounds and approximations

Narum,

Maggioni,

Wallace

2023

Int Trans Operational Res

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There will always be stochastic programs that are too large or complex to be solved in their basic form. In this article, we review, discuss, and compare different ways such stochastic programs can be handled using bounds and approximations, all based on manipulations of the random variables. We are particularly interested in how methods based on different underlying ideas can be combined or possibly are the same.

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Section: Out-of-sample Evaluation Boundsmentioning

confidence: 99%

Section: Bounds Based On Candidate Policiesmentioning

confidence: 99%

On the safe side of stochastic programming: bounds and approximations

Narum,

Maggioni,

Wallace

2023

Int Trans Operational Res

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“…Hence, the stochastic problem can be converted to a (larger) deterministic problem. The quality of the stochastic solution depends on the form of the scenario tree (Keutchayan et al 2017). Two stages are enough in our case, because operating rules are not anticipative.…”

Section: Literature Reviewmentioning

confidence: 99%

Optimized operating rules for short-term hydropower planning in a stochastic environment

et al. 2019

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To operate a large-scale hydropower production system in an ever-changing environment, operating rules are a convenient way of communication between short-term planners and real-time dispatchers. This articles presents a new form of operating rules, and a solution approach to solve the short-term planning problem directly in the space of rules. Our operating rules are designed to handle complex hydro-valleys and highly constrained reservoirs. Our solution approach is based on tabu search and easily implemented. Uncertainty on inflows and electrical load is represented in the mathematical model via a 2-stage scenario tree. Numerical experiments on real instances from Hydro-Québec show that our approach is able to find good stochastic solutions while respecting the operational timing, and it improves the objective value by up to 54% in instances with moderate to high inflows.

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“…When uncertainty is present in decision-making contexts, scenario generation refers to the methods used to sample the set of possible outcomes of the random parameters, see [Kaut, 2012, Keutchayan et al, 2017. Such methods are staples in the design of decision support techniques that explicitly consider the uncertainty affecting the parameters defining the informational context in which problems are to be solved.…”

Section: Introductionmentioning

confidence: 99%

Problem-Driven Scenario Clustering in Stochastic Optimization

Keutchayan¹,

Ortmann²,

Rei³

2021

Preprint

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In stochastic optimisation, the large number of scenarios required to faithfully represent the underlying uncertainty is often a barrier to finding efficient numerical solutions. This motivates the scenario reduction problem: by find a smaller subset of scenarios, reduce the numerical complexity while keeping the error at an acceptable level.In this paper we propose a novel and computationally efficient methodology to tackle the scenario reduction problem when the error to be minimised is the implementation error, i.e. the error incurred by implementing the solution of the reduced problem in the original problem. Specifically, we develop a problem-driven scenario clustering method that produces a partition of the scenario set. Each cluster contains a representative scenario that best reflects the conditional objective values in each cluster of the partition to be identified.We demonstrate the efficiency of our method by applying it to two challenging stochastic combinatorial optimization problems: the two-stage stochastic network design problem and the two-stage facility location problem. When compared to alternative clustering methods and Monte Carlo sampling, our method is shown to clearly outperform all other methods.

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Quality evaluation of scenario-tree generation methods for solving stochastic programming problems

Cited by 9 publications

References 28 publications

On the safe side of stochastic programming: bounds and approximations

On the safe side of stochastic programming: bounds and approximations

Optimized operating rules for short-term hydropower planning in a stochastic environment

Problem-Driven Scenario Clustering in Stochastic Optimization

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