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.

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")

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