Discrepancy distances and scenario reduction in two-stage stochastic mixed-integer programming

Henrion, René; Küchler, Christian; Römisch, Werner

doi:10.3934/jimo.2008.4.363

Cited by 32 publications

(11 citation statements)

References 24 publications

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“…Finally, it is worthwhile to note that stability theory for CCO is developed in [430]; stability results provide an answer to the important question of how model results (cost or even solution sets) vary with respect to changes in the underlying distribution of the random vector. An application of stability results in the context of a simple recourse model is given as early as [213,431]; for more recent research we refer to [238,239,241,242,429] and references therein. In particular, the authors explicitly consider stability results for probabilistically constrained power dispatch models, showing that the models are stable for several underlying distributions of the load, such as discrete or multi-variate Gaussian.…”

Section: Chance-constrained Optimization Approachesmentioning

confidence: 99%

Large-scale unit commitment under uncertainty: an updated literature survey

Ackooij¹,

et al. 2018

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The Unit Commitment problem in energy management aims at finding the optimal production 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, due to operational requirements, it has to be solved in an unreasonably small time for its size. Recently, growing renewable energy shares have strongly increased the level of uncertainty in the system, making the (ideal) Unit Commitment model a large-scale, non-convex and uncertain (stochastic, robust, chanceconstrained) 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, focussing 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, while providing entry points to the relevant literature on optimization under uncertainty. This is an updated version of the paper "Large-scale Unit Commitment under uncertainty: a literature survey" that appeared in 4OR 13(2), 115-171 (2015); this version has over 170 more citations, most of which appeared in the last three years, proving how fast the literature on uncertain Unit Commitment evolves, and therefore the interest in this subject.

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Section: Chance-constrained Optimization Approachesmentioning

confidence: 99%

Large-scale unit commitment under uncertainty: an updated literature survey

Ackooij¹,

et al. 2018

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“…To solve the optimal scenario reduction problem, two heuristic solution algorithms are proposed and widely adopted, namely the backward reduction and the forward selection .…”

Section: Scenario Reduction Problemmentioning

confidence: 99%

“…Further refinements and extensions for these backward and forward type reduction algorithms were given in Refs. . Although clustering approach and its combination with evolutionary particle swarm optimization (EPSO) are also used for scenario reduction in recent years, they all belong to the heuristic algorithm in their nature.…”

Section: Introductionmentioning

confidence: 99%

PSO algorithm‐based scenario reduction method for stochastic unit commitment problem

Xiong

Liu²,

Chen

et al. 2016

IEEJ Transactions Elec Engng

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This paper proposes a particle swarm optimization (PSO) algorithm-based scenario reduction method for stochastic unit commitment problems. In this method, the position of each particle is an index set of the preserved scenarios, that is, a possible solution to the optimal scenario reduction problem. The Kantorovich distance between the original scenarios and the preserved scenarios is used to calculate the fitness value of each particle. A repair procedure is carried out to ensure that there are nonrepeating index numbers in the newly generated position of each particle during the iterations. The performance of the PSO-based method is tested on two scenario sets of electricity prices in a stochastic profit/price-based unit commitment (SPBUC) problem, and is compared with backward reduction and forward selection. Test results show that the PSO-based method performs very well with respect to the relative accuracy and running times when reducing large scenario set. Impacts of scenario reduction on the expected profits of the SPBUC problem are also investigated with different numbers of the preserved scenarios of electricity prices, which are obtained by these three different reduction methods from the same original scenario set. Simulation results show that optimal solutions of the SPBUC problem are related not only to the number of the preserved scenarios but also to the scenario reduction methods. The PSO-based method can lead to less conservative solutions than the forward selection, while the backward reduction can result in nonconservative solutions.

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“…Some heuristics for solving both the inner and the outer optimization problems have been suggested in [64]. In that paper, Henrion, Küchler, and Römisch mainly regard the star discrepancy measure, but results for other distance measures are provided as well; see also the paper [63] by the same set of authors for results on minimizing the distance with respect to polyhedral discrepancies.…”

Section: Scenario Reduction In Stochastic Programmingmentioning

confidence: 99%

Calculation of Discrepancy Measures and Applications

Doerr

Gnewuch

Wahlström

2014

A Panorama of Discrepancy Theory

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In this book chapter we survey known approaches and algorithms to compute discrepancy measures of point sets. After providing an introduction which puts the calculation of discrepancy measures in a more general context, we focus on the geometric discrepancy measures for which computation algorithms have been designed. In particular, we explain methods to determine L_2-discrepancies and approaches to tackle the inherently difficult problem to calculate the star discrepancy of given sample sets. We also discuss in more detail three applications of algorithms to approximate discrepancies

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Discrepancy distances and scenario reduction in two-stage stochastic mixed-integer programming

Cited by 32 publications

References 24 publications

Large-scale unit commitment under uncertainty: an updated literature survey

Large-scale unit commitment under uncertainty: an updated literature survey

PSO algorithm‐based scenario reduction method for stochastic unit commitment problem

Calculation of Discrepancy Measures and Applications

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