Multi-Objective Optimal Design of Experiments

Provides functionality to generate compound optimal designs for targeting the multiple experimental objectives directly, ensuring that the full set of research questions is answered as economically as possible. Designs can be found using point or coordinate exchange algorithms combining estimation, inference and lack-of-fit criteria that account for model inadequacy. Details and examples are given by Koutra et al. (2024) .

MOODE

Multi-objective Optimal Design of experiments (MOODE) for targeting the experimental objectives directly, ensuring as such that the full set of research questions is answered as economically as possible.

Installation

Install from CRAN with:

install.packages("MOODE")

You can install the development version of MOODE from GitHub with:

# install.packages("devtools")
devtools::install_github("vkstats/MOODE")

Example

As a basic example, consider an experiment with K=2 factors, each having Levels = 3 levels. The primary (assumed) model contains first-order terms, and the potential model also contains squared terms. The experiment will have Nruns = 24 runs. An optimal compound design will be sought combining $DP_S$-, $LoF-D$- and $MSE(D)$-optimality; see Koutra et al. (2024). We define the parameters for this experiment using the mood function.

library("MOODE")
ex.mood <- mood(K = 2, Levels = 3, Nruns = 24, 
                model_terms = list(primary.terms = c("x1", "x2"), 
                                   potential.terms = c("x12", "x22")), 
                criterion.choice = "MSE.D", 
                kappa = list(kappa.DP = 1 / 3, kappa.LoF = 1 / 3, 
                             kappa.mse = 1 / 3))

The kappa list defines weights for each criterion, with $\kappa_i\ge 0$ and $\sum \kappa_i = 1$.

Optimal designs are found using a point exchange algorithm, via the Search function.

search.ex <- Search(ex.mood)

#> ✔ Design search complete. Final compound objective function value = 0.19717

The best design found is available as element X.design, ordered here by treatment number.

fd <- search.ex$X.design[order(search.ex$X1[, 1]),]
cbind(fd[1:12, ], fd[13:24, ])

#>       x1 x2 x1 x2
#>  [1,] -1 -1  0  1
#>  [2,] -1 -1  0  1
#>  [3,] -1 -1  1 -1
#>  [4,] -1  0  1 -1
#>  [5,] -1  0  1 -1
#>  [6,] -1  1  1 -1
#>  [7,] -1  1  1  0
#>  [8,] -1  1  1  0
#>  [9,] -1  1  1  1
#> [10,]  0 -1  1  1
#> [11,]  0 -1  1  1
#> [12,]  0  0  1  1

The path element records the compound objective function value from each of the (by default) 10 attempts of the algorithm from different random starting designs.

search.ex$path

#>  [1] 0.1971797 0.1971700 0.1971714 0.1971458 0.1971621 0.1971951 0.1971238
#>  [8] 0.1972105 0.1979960 0.1971959