Abstract
We study different parallelization schemes for the stochastic dual dynamic programming (SDDP) algorithm. We propose a taxonomy for these parallel algorithms, which is based on the concept of parallelizing by scenario and parallelizing by node of the underlying stochastic process. We develop a synchronous and asynchronous version for each configuration. The parallelization strategy in the parallelscenario configuration aims at parallelizing the Monte Carlo sampling procedure in the forward pass of the SDDP algorithm, and thus generates a large number of supporting hyperplanes in parallel. On the other hand, the parallel-node strategy aims at building a single hyperplane of the dynamic programming value function in parallel. The considered algorithms are implemented using Julia and JuMP on a high performance computing cluster. We study the effectiveness of the methods in terms of achieving tight optimality gaps, as well as the scalability properties of the algorithms with respect to an increasing number of CPUs. In particular, we study the effects of the different parallelization strategies on performance when increasing the number of Monte Carlo samples in the forward pass, and demonstrate through numerical experiments that such an increase may be harmful. Our results indicate that a parallel-node strategy presents certain benefits as compared to a parallel-scenario configuration.
Highlights
The stochastic dual dynamic programming (SDDP) algorithm, developed by Pereira and Pinto (1991), has emerged as a scalable approximation method for tackling multistage stochastic programming problems
We present empirical evidence which indicates that increasing the number of Monte Carlo samples in the forward pass of the SDDP algorithm may undermine performance
4.1 Experimental results The computational work is performed on the Lemaitre3 cluster, which is hosted at the Consortium des Equipements de Calcul Intensif (CECI)
Summary
The stochastic dual dynamic programming (SDDP) algorithm, developed by Pereira and Pinto (1991), has emerged as a scalable approximation method for tackling multistage stochastic programming problems. Multistage stochastic programming problems are generally computationally intractable and pose serious computational challenges, even for SDDP. With an objective of limiting the complexity of the cost-to-go function, cut selection techniques are considered in De Matos et al (2015); Guigues (2017); Guigues and Bandarra (2019); Löhndorf et al (2013). The nature of the SDDP algorithm makes it suitable for parallel computing (Pereira and Pinto, 1991). This has led to parallel schemes for SDDP in past research that aim at improving the performance of the algorithm (da Silva and Finardi, 2003; Pinto et al, 2013; Helseth and Braaten, 2015; Dowson and Kapelevich, 2021; Machado et al, 2021)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
