Comparing scenario reduction methods for stochastic transmission planning

Scenario tree reduction for multistage stochastic programs

A framework for the reduction of scenario trees as inputs of (linear) multistage stochastic programs is provided such that optimal values and approximate solution sets remain close to each other. The argument is based on upper bounds of the Lr -distance and the filtration distance, and on quantitative stability results for multistage stochastic programs. The important difference from scenario r...

Scenario reduction in stochastic programming

Given a convex stochastic programming problem with a discrete initial probability distribution, the problem of optimal scenario reduction is stated as follows: Determine a scenario subset of prescribed cardinality and a probability measure based on this set that is the closest to the initial distribution in terms of a natural (or canonical) probability metric. Arguments from stability analysis ...

Optimal scenario tree reduction for stochastic streamflows in power generation planning problems

Welington Luis de Oliveira; Claudia Sagastizábal; Débora Dias Jardim Penna; Maria Elvira Piñeiro Maceira; Jorge Machado Damázio 2 Electric Power Research Center – CEPEL, CP 68007 Rio de Janeiro, Brazil. 3 IMPA – Estrada Dona Castorina 110, Jardim Botânico, Rio de Janeiro, Brazil. Research of this author is supported in part by CNPq Grant 30345-2008/9, by PRONEX-Optimization, and by FAPERJ. 4 Ri...

Scenario Reduction Algorithms in Stochastic Programming

Scenario Reduction Techniques in Stochastic Programming

Stochastic programming problems appear as mathematical models for optimization problems under stochastic uncertainty. Most computational approaches for solving such models are based on approximating the underlying probability distribution by a probability measure with finite support. Since the computational complexity for solving stochastic programs gets worse when increasing the number of atom...