Solving Multistage Stochastic Linear Programming via Regularized Linear Decision Rules: An Application to Hydrothermal Dispatch Planning

Autor:	Nazare, Felipe, Street, Alexandre
Rok vydání:	2021
Předmět:	Mathematics - Optimization and Control Computer Science - Machine Learning Economics - Econometrics Electrical Engineering and Systems Science - Systems and Control Statistics - Machine Learning
Druh dokumentu:	Working Paper
DOI:	10.1016/j.ejor.2022.12.039
Popis:	The solution of multistage stochastic linear problems (MSLP) represents a challenge for many application areas. Long-term hydrothermal dispatch planning (LHDP) materializes this challenge in a real-world problem that affects electricity markets, economies, and natural resources worldwide. No closed-form solutions are available for MSLP and the definition of non-anticipative policies with high-quality out-of-sample performance is crucial. Linear decision rules (LDR) provide an interesting simulation-based framework for finding high-quality policies for MSLP through two-stage stochastic models. In practical applications, however, the number of parameters to be estimated when using an LDR may be close to or higher than the number of scenarios of the sample average approximation problem, thereby generating an in-sample overfit and poor performances in out-of-sample simulations. In this paper, we propose a novel regularized LDR to solve MSLP based on the AdaLASSO (adaptive least absolute shrinkage and selection operator). The goal is to use the parsimony principle, as largely studied in high-dimensional linear regression models, to obtain better out-of-sample performance for LDR applied to MSLP. Computational experiments show that the overfit threat is non-negligible when using classical non-regularized LDR to solve the LHDP, one of the most studied MSLP with relevant applications. Our analysis highlights the following benefits of the proposed framework in comparison to the non-regularized benchmark: 1) significant reductions in the number of non-zero coefficients (model parsimony), 2) substantial cost reductions in out-of-sample evaluations, and 3) improved spot-price profiles. Comment: European Journal of Operational Research, 2022. See the published version at (EJOR) through the DOI link https://doi.org/10.1016/j.ejor.2022.12.039
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2110.03146 Zobrazit plný text záznamu View this record from Arxiv