Scenario Reduction Techniques in Stochastic Programming

2009 ◽  
pp. 1-14 ◽  
Author(s):  
Werner Römisch
Keyword(s):  
Stochastic Programming ◽  
Scenario Reduction ◽  
Reduction Techniques

Scenario reduction in stochastic programming

2003 ◽  
Vol 95 (3) ◽  
pp. 493-511 ◽  
Author(s):  
J. Dupa?ov� ◽  
N. Gr�we-Kuska ◽  
W. R�misch
Keyword(s):  
Stochastic Programming ◽  
Scenario Reduction

scholarly journals The energy distance for ensemble and scenario reduction

2021 ◽  
Vol 379 (2202) ◽  
pp. 20190431 ◽  
Author(s):  
Florian Ziel
Keyword(s):  
Power Systems ◽  
Real Data ◽  
Wasserstein Distance ◽  
Generative Adversarial Networks ◽  
Probabilistic Forecasting ◽  
Multivariate Distributions ◽  
Scenario Reduction ◽  
Stochastic Programs ◽  
Reduction Techniques ◽  
Energy Distance

Scenario reduction techniques are widely applied for solving sophisticated dynamic and stochastic programs, especially in energy and power systems, but are also used in probabilistic forecasting, clustering and estimating generative adversarial networks. We propose a new method for ensemble and scenario reduction based on the energy distance which is a special case of the maximum mean discrepancy. We discuss the choice of energy distance in detail, especially in comparison to the popular Wasserstein distance which is dominating the scenario reduction literature. The energy distance is a metric between probability measures that allows for powerful tests for equality of arbitrary multivariate distributions or independence. Thanks to the latter, it is a suitable candidate for ensemble and scenario reduction problems. The theoretical properties and considered examples indicate clearly that the reduced scenario sets tend to exhibit better statistical properties for the energy distance than a corresponding reduction with respect to the Wasserstein distance. We show applications to a Bernoulli random walk and two real data-based examples for electricity demand profiles and day-ahead electricity prices. This article is part of the theme issue ‘The mathematics of energy systems’.

scholarly journals Scenario reduction in stochastic programming with respect to discrepancy distances

2007 ◽  
Vol 43 (1) ◽  
pp. 67-93 ◽  
Author(s):  
René Henrion ◽  
Christian Küchler ◽  
Werner Römisch
Keyword(s):  
Stochastic Programming ◽  
Scenario Reduction

Catalogue reduction techniques

1978 ◽  
Vol 48 ◽  
pp. 389-390 ◽  
Author(s):  
Chr. de Vegt
Keyword(s):  
Adjustment Process ◽  
Proper Motions ◽  
Measuring Process ◽  
Aerial Photogrammetry ◽  
Reduction Techniques ◽  
Observational Technique ◽  
The Common ◽  
Astrometric Data

AbstractReduction techniques as applied to astrometric data material tend to split up traditionally into at least two different classes according to the observational technique used, namely transit circle observations and photographic observations. Although it is not realized fully in practice at present, the application of a blockadjustment technique for all kind of catalogue reductions is suggested. The term blockadjustment shall denote in this context the common adjustment of the principal unknowns which are the positions, proper motions and certain reduction parameters modelling the systematic properties of the observational process. Especially for old epoch catalogue data we frequently meet the situation that no independent detailed information on the telescope properties and other instrumental parameters, describing for example the measuring process, is available from special calibration observations or measurements; therefore the adjustment process should be highly self-calibrating, that means: all necessary information has to be extracted from the catalogue data themselves. Successful applications of this concept have been made already in the field of aerial photogrammetry.

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