LatinHypercubeSampling.jl

Documentation	Build & Testing Status

LatinHypercubeSampling is a Julia package for the creation of optimised Latin Hypercube Sampling Plans. The genetic optimisation algorithm is largely based on the work by Bates et al. [1]. The package includes additional functionality for the creation of an optimised subset of an existing plan. For more details, see our paper.

Features:

• Creation of an optimised Latin Hypercube Sampling plan.
• Generate an optimised subset of an existing plan.
• Refine existing plan.
• Ability to include discrete parameters in the design.

It also has the option to optimize the sampling plans using the periodic Audze–Eglājs criteria [2].

Installation

The package is registered and can be installed with Pkg.add.

julia> Pkg.add("LatinHypercubeSampling")

Documentation

• STABLE — tagged version of the documentation.

Author

• Magnus Urquhart - @MrUrq

Example

Sampling the Rosenbrock function with an optimized Latin Hypercube sampling plan.

julia> plan, _ = LHCoptim(100,2,1000)
julia> scaled_plan = scaleLHC(plan,[(-5.0,5.0),(-5.0,5.0)])
julia> rosenbrock_2D(x) = (1.0 - x[1])^2 + 100.0 * (x[2] - x[1]^2)^2
julia> mapslices(rosenbrock_2D,scaled_plan; dims=2)

Example LHC

Example of optimised LHC plan for 120 points in 2 dimensions.

References

[1]: Stuart Bates, Johann Sienz, and Vassili Toropov. "Formulation of the Optimal Latin Hypercube Design of Experiments Using a Permutation Genetic Algorithm", 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, Structures, Structural Dynamics, and Materials and Co-located Conferences, () https://doi.org/10.2514/6.2004-2011

[2]: Jan Eliáš, Miroslav Vořechovský, Modification of the Audze–Eglājs criterion to achieve a uniform distribution of sampling points, Advances in Engineering Software, Volume 100, 2016, Pages 82-96, ISSN 0965-9978, () https://doi.org/10.1016/j.advengsoft.2016.07.004.

Citation

@article{urquhart_surrogate-based_2020,
    title = {Surrogate-based optimisation using adaptively scaled radial basis functions},
    volume = {88},
    issn = {1568-4946},
    doi = {10.1016/j.asoc.2019.106050},
    journal = {Applied Soft Computing},
    author = {Urquhart, Magnus and Ljungskog, Emil and Sebben, Simone},
    year = {2020},
}