SDDP for multistage stochastic programs: preprocessing via scenario reduction
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Even with recent enhancements, computation times for large-scale multistage problems with risk-averse objective functions can be very long. Therefore, preprocessing via scenario reduction could be considered as a way to significantly improve the overall performance. Stage-wise backward reduction of single scenarios applied to a fixed branching structure of the tree is a promising tool for efficient algorithms like stochastic dual dynamic programming. We provide computational results which show an acceptable precision of the results for the reduced problem and a substantial decrease of the total computation time.
KeywordsMultistage stochastic programs Stochastic dual dynamic programming Multiperiod CVaR Scenario reduction
Mathematics Subject Classification65C05 90C15 91G60
Jitka Dupačová has initiated this project and we have worked together till the very final form of the article, unfortunately, she passed away during the publication process. I would like to dedicate this paper to Jitka, for her restless guidance, knowledge, patience and care. The research was partly supported by the project of the Czech Science Foundation P/402/12/G097 ’DYME/Dynamic Models in Economics’.
- Bayraksan G, Morton DP (2009) Assessing solution quality in stochastic programs via sampling. In: Oskoorouchi M, Gray P, Greenberg H (eds) Tutorials in operations research. Informs, Hannover, pp 102–122, ISBN 978-1-877640-24-7Google Scholar
- Infanger G, Morton DP (1996) Cut sharing for multistage stochastic linear programs with interstage dependency. Math Progr 75:241–256Google Scholar
- Pflug GCh, Pichler A (2011) Approximations for probability distributions and stochastic optimization problems. In: Bertocchi M, Consigli G, Dempster MAH (eds) Stochastic optimization methods in finance and energy. Springer, New York, pp 343–388, ISBN 978-1-4419-9585-8Google Scholar
- Römisch W (2009) Scenario reduction techniques in stochastic programming. In: Watanabe O, Zeugmann T (eds) Stochastic algorithms: foundations and applications, vol 5792., Lecture notes in computer science. Springer, Sapporo, pp 1–14Google Scholar
- Shapiro A, Dentcheva D, Ruszczyński A (2009) Lectures on stochastic programming: modeling and theory. SIAM Society for Industrial and Applied Mathematics, Philadelphia, ISBN 978-1107025127Google Scholar