scenario (version 1.0)

buildtree: Build a scenario tree with a predefined nodal structure.

Description

Uses the neural gas method to build a scenario tree.

Usage

buildtree(x, treeStruct, lambda_0 = 10, lambda_f = 0.01, e_0 = 0.5, e_f = 0.05, jMax = 40000, plot = TRUE)

Arguments

x

Matrix of initial scenarios, realizations or ensemble members. Each column stores a scenario, with number of rows equal to number of time steps.

treeStruct

Matrix defining the nodal structure of the tree (see example). This is a scenario tree nodal partition matrix.

lambda_0

Upper neighbourhood range parameter. Default = 10.

lambda_f

Lower neighborhood range paramger. Default = 0.01.

e_0

Upper adaptation step parameter. Default = 0.5.

e_f

Lower adaptation step parameter. Default = 0.05.

jMax

Number of iterations. Default = 40000.

plot

logical. If TRUE (the default) the final tree is plotted.

Value

Returns a list object containing the initial input scenarios, the input scenarios tree structure, the values of the final reduced scenario tree, and the tree branch probabilities at the end nodes.

References

Xu, B., Zhong, P.A., Zambon, R.C., Zhao, Y., Yeh, W. (2015) Scenario tree reduction in stochastic programming with recourse for hydropower operations, Water Resources Research, 51, 6359-6380.

Dupacova, Jitka, Giorgio Consigli, and Stein W. Wallace. "Scenarios for multistage stochastic programs." Annals of operations research 100.1-4 (2000): 25-53.

Examples

# Generate some 25 random realizations of length 4 and reduce to scenario tree.
scenarios <- matrix(rnorm(100),ncol=25)
treeStruct <- rbind(c(1, 1, 1, 1, 1),
                    c(2, 2, 7, 7, 11),
                    c(3, 5, 8, 8, 12),
                    c(4, 6, 9, 10, 13)
                    )
tree <- buildtree(scenarios, treeStruct, jMax = 1000)