Evaluation of scenario reduction algorithms with nested distance

Markéta Horejšová (), Sebastiano Vitali (), Miloš Kopa () and Vittorio Moriggia ()
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Markéta Horejšová: Charles University
Sebastiano Vitali: Charles University
Miloš Kopa: Charles University
Vittorio Moriggia: University of Bergamo

Computational Management Science, 2020, vol. 17, issue 2, No 5, 275 pages

Abstract: Abstract Multistage stochastic optimization is used to solve many real-life problems where decisions are taken at multiple times. Such problems need the representation of stochastic processes, which are usually approximated by scenario trees. In this article, we implement seven scenario reduction algorithms: three based on random extraction, named Random, and four based on specific distance measures, named Distance-based. Three of the latter are well known in literature while the fourth is a new approach, namely nodal clustering. We compare all the algorithms in terms of computational cost and information cost. The computational cost is measured by the time needed for the reduction, while the information cost is measured by the nested distance between the original and the reduced tree. Moreover, we also formulate and solve a multistage stochastic portfolio selection problem to measure the distance between the optimal solutions and between the optimal objective values of the original and the reduced tree.

Keywords: Nested distance; Multistage stochastic optimization; Scenario tree reduction; Nodal clustering; 90C15; 60B05; 62P05 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10287-020-00375-4

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