AZEMA, M. MATHIS (2024) Comparison between Robust Optimization, Stochastic Programming and Distributionally Robust Optimization for Unit Commitment PFE - Project Graduation, ENSTA.
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Abstract
This Master's internship report, carried out at the Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS) under the supervision of Vincent LECLERE and in collaboration with Wim VAN ACKOOIJ, deals with the study of the Unit Commitment problem under uncertainty, focusing on the Robust Distribution Optimization (DRO) approach. The aim was to evaluate the potential advantages of this approach in comparison with more traditional methods. The report begins with a presentation of commonly used robust and stochastic optimization algorithms, while adapting a method from the literature to the Unit Commitment problem in a more general framework. The study then focuses on two approaches to DRO: phi-divergence and Wasserstein distance. Theoretical results and reformulations in the literature are discussed. In particular, emphasis is placed on the use of Wasserstein's L2 norm, as yet unexplored for Unit Commitment. Finally, the performance of the different methods (robust, stochastic and DRO) is compared using an out-of-sample analysis. This internship led to several contributions: a review of optimization methods under uncertainty, the adaptation of a robust method, a review of theoretical results on DRO, an in-depth study of the Wasserstein L2 distance, and a comparison of the different approaches via out-of-sample tests.
Item Type: | Thesis (PFE - Project Graduation) |
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Subjects: | Mathematics and Applications |
ID Code: | 10454 |
Deposited By: | Mathis AZEMA |
Deposited On: | 28 oct. 2024 17:01 |
Dernière modification: | 28 oct. 2024 17:01 |
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