Julia Package for Generating Scenario Trees and Scenario Lattices for Multistage Stochastic Optimization
Author kirui93
14 Stars
Updated Last
1 Year Ago
Started In
August 2019

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ScenTrees.jl is a Julia package for generating and improving scenario trees and scenario lattices for multistage stochastic optimization problems using stochastic approximation. It is totally written in the Julia programming language. This package provides functions for generating scenario trees and scenario lattices from stochastic processes and stochastic data.

We provide two important features at the moment:

  • Generation of scenario trees and scenario lattices using stochastic approximation procedure.
    • Scenario trees are used in the case of discrete time and discrete state stochastic processes.
    • Scenario lattices are a natural discretization of Markov processes and so if the stochastic process is Markovian, scenario lattices would approximate the process well.
  • Estimating trajectories from stochastic data using conditional density estimation.
    • This is a non-parametric technique for generating trajectories from a given observed data whose distribution is unknown.
    • The new trajectories estimated here can thus be used in stochastic approximation process to generate scenario trees and scenario lattices.

Stochastic approximation procedure in ScenTrees.jl library follows from the framework provided by Pflug and Pichler(2015). The two main user inputs are a fixed branching structure and a function that generates samples from a stochastic process.

N/B - This package is actively developed and therefore new improvements and new features are continuously added.


Get the latest stable release with Julia's package manager:

] add ScenTrees

To use ScenTrees.jl, you need to have Julia >= v1.0. This package was developed in Julia 1.0.4, and has been tested for Julia >= v1.0 in Linux and OSX distributions.


The STABLE documentation of ScenTrees.jl is available here. Here you can get the description of the various functions in the package and also different examples for the different features.

Example of Usage

After installing the ScenTrees.jl package, you can use it as in the following examples:

  1. Consider the Gaussian random walk process in 4 stages. This process is already available in the package and can just be called by gaussian_path1D() for 1D and gaussian_path2D() for 2D. We want to approximate 1D process with a scenario tree as follows:
julia> using ScenTrees
julia> gstree = tree_approximation!(Tree([1,2,2,2],1),gaussian_path1D,100000,2,2);
julia> tree_plot(gstree)

Scenario Tree

  1. We want to approximate running maximum process with a scenario lattice. It follows the same procedure as for scenario trees only that we use a different function as follows:
julia> using ScenTrees
julia> rmlattice = lattice_approximation([1,2,3,4],running_maximum1D,100000,2,1);
julia> plot_lattice(rmlattice)

Scenario Lattice

  1. We also provide the conditional density estimation of trajectories given data. Given an NxT dataframe, we use the kernel_scenarios() function to generate a new and similar trajectory with length equal to T. This function can thus be used to generated trajectories for creating a scenario tree and a scenario lattice. Consider a Gaussian random walk data which can be generated by calling the function gaussian_path1D() many times and saving the result in a matrix form. We can use this data and the kernel density estimation method to generate new and similar trajectories as follows:
julia> using ScenTrees
julia> using Distributions
julia> gsdata = Array{Float64}(undef,1000,4)
julia> for i = 1:1000
           gsdata[i,:] = gaussian_path1D()
julia> gsGen = kernel_scenarios(gsdata,Logistic; Markovian = true)()
4-element Array{Float64,1}:

To use the above samples for scenario trees or scenario lattice generation:

julia> kerneltree = tree_approximation!(Tree([1,2,2,2],1),kernel_scenarios(gsdata,Logistic;Markovian=false),100000,2,2);
julia> tree_plot(kerneltree)
julia> kernelLattice = lattice_approximation([1,3,4,5],kernel_scenarios(gsdata,Logistic;Markovian=true),100000,2,1);
julia> plot_lattice(kernelLattice)
Kernel Tree Kernel Lattice
Kernel Scenario Tree Kernel Scenario Lattice

Contributing to ScenTrees.jl

As in, if you believe that you have found any bugs or if you need help or any questions regarding the library and any suggestions, please feel free to file a new GitHub issue. You can also raise an issue or a pull request which fixes the issue as long as it doesn't affect performance.

Citing ScenTrees.jl

We ask that you please cite the following paper if you use ScenTrees.jl:

        author = {Kirui, Kipngeno and Pichler, Alois and Pflug, Georg {\relax Ch}.},
        title = {ScenTrees.jl: A {J}ulia Package for Generating Scenario Trees and Scenario Lattices for Multistage Stochastic Programming},
        journal = {Journal of Open Source Software},
        publisher = {The Open Journal},
        year = {2020},
        volume = {5},
        number = {46},
        pages = {1912},
        doi = {10.21105/joss.01912},
        url = {}


  • Pflug, Georg Ch., and Alois Pichler, 2012. A Distance for Multistage Stochastic Optimization Models. SIAM Journal on Optimization 22(1) Doi:

  • Pflug, Georg Ch., and Alois Pichler,2015. Dynamic Generation of Scenario Trees. Computational Optimization and Applications 62(3): Doi:

  • Pflug, Georg Ch., and Alois Pichler,2016. From Empirical Observations to Tree Models for Stochastic Optimization : Convergence Properties : Convergence of the Smoothed Empirical Process in Nested Distance. SIAM Journal on Optimization 26(3). Society for Industrial and Applied Mathematics (SIAM). Doi:

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