crit_EMI | R Documentation |
Expected Maximin Improvement with respect to the current Pareto front with Sample Average Approximation. The semi-analytical formula is used in the bi-objective scale if the Pareto front is in [-2,2]^2, for numerical stability reasons. To avoid numerical instabilities, the new point is penalized if it is too close to an existing observation.
crit_EMI( x, model, paretoFront = NULL, critcontrol = list(nb.samp = 50, seed = 42), type = "UK" )
x |
a vector representing the input for which one wishes to calculate |
model |
list of objects of class |
paretoFront |
(optional) matrix corresponding to the Pareto front of size |
critcontrol |
optional list with arguments (for more than 2 objectives only):
Options for the |
type |
" |
It is recommanded to scale objectives, e.g. to [0,1]
.
If the Pareto front does not belong to [-2,2]^2, then SAA is used.
The Expected Maximin Improvement at x
.
J. D. Svenson & T. J. Santner (2010), Multiobjective Optimization of Expensive Black-Box
Functions via Expected Maximin Improvement, Technical Report.
J. D. Svenson (2011), Computer Experiments: Multiobjective Optimization and Sensitivity Analysis, Ohio State University, PhD thesis.
EI
from package DiceOptim, crit_EHI
, crit_SUR
, crit_SMS
.
#--------------------------------------------------------------------------- # Expected Maximin Improvement surface associated with the "P1" problem at a 15 points design #--------------------------------------------------------------------------- set.seed(25468) library(DiceDesign) n_var <- 2 f_name <- "P1" n.grid <- 21 test.grid <- expand.grid(seq(0, 1, length.out = n.grid), seq(0, 1, length.out = n.grid)) n_appr <- 15 design.grid <- round(maximinESE_LHS(lhsDesign(n_appr, n_var, seed = 42)$design)$design, 1) response.grid <- t(apply(design.grid, 1, f_name)) Front_Pareto <- t(nondominated_points(t(response.grid))) mf1 <- km(~., design = design.grid, response = response.grid[,1]) mf2 <- km(~., design = design.grid, response = response.grid[,2]) EMI_grid <- apply(test.grid, 1, crit_EMI, model = list(mf1, mf2), paretoFront = Front_Pareto, critcontrol = list(nb_samp = 20)) filled.contour(seq(0, 1, length.out = n.grid), seq(0, 1, length.out = n.grid), nlevels = 50, matrix(EMI_grid, nrow = n.grid), main = "Expected Maximin Improvement", xlab = expression(x[1]), ylab = expression(x[2]), color = terrain.colors, plot.axes = {axis(1); axis(2); points(design.grid[,1], design.grid[,2], pch = 21, bg = "white") } )
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