Pujol, M Romain (2024) Scenario reduction techniques for two-stage stochastic programming PRE - Research Project, ENSTA.
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Abstract
Two-stage stochastic optimization problems become extremely large when the distributions involved have a large number of atoms. To address this issue, we can reduce the size of the distributions to decrease the number of variables and constraints in the problem, hence facilitating the resolution of the optimization problem. It is required to ensure that the reduced distribution maintains the structure and characteristics of the original distribution. The proximity between distributions is quantified using Wasserstein distances, distances that we are studying in this report. We work on algorithms that give reduced distribution with the aim of minimizing a Wasserstein distance. A new variant of the euclidean Wasserstein distances that relies on the underlying stochastic optimization problem is studied in the end of this report. In order to integrate scenario reduction techniques into the SMS++ ecosystem of the University of Pisa, attention is paid to algorithmic efficiency.
Item Type: | Thesis (PRE - Research Project) |
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Uncontrolled Keywords: | Stochastic programming, scenario reduction, Wasserstein distance, greedy algorithm, localsearch, stability |
Subjects: | Mathematics and Applications |
ID Code: | 10215 |
Deposited By: | Romain PUJOL |
Deposited On: | 04 sept. 2024 11:19 |
Dernière modification: | 04 sept. 2024 11:19 |
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