Description Usage Arguments Details Value References Examples
Multiobjective Expected Hypervolume Improvement with respect to the current
Pareto front. It's based on the crit_EHI
function of the
GParetopackage
package. However, the present implementation accounts
for inequality constrains embedded into the mkm
model.
1 
x 
a vector representing the input for which one wishes to calculate 
model 
An object of class 
control 
An optional list of control parameters, some of them passed to
the

The way that the constraints are handled are based on the probability of feasibility. The strong assumption here is that the cost functions and the constraints are uncorrelated. With that assumption in mind, a simple closedform solution can be derived that consists in the product of the probability that each constraint will be met and the expected improvement of the objective.
The constrained expected hypervolume improvement at x
.
Forrester, A., Sobester, A., & Keane, A. (2008). Engineering design via surrogate modeling: a practical guide. John Wiley & Sons.
1 2 3 4 5 6 7 8 9 10 11 12 13  # 
# The Nowacki Beam
# 
n < 10
d < 2
doe < replicate(d,sample(0:n,n))/n
res < t(apply(doe, 1, nowacki_beam, box = data.frame(b = c(10, 50), h = c(50, 250))))
model < mkm(doe, res, modelcontrol = list(objective = 1:2, lower=rep(0.1,d)))
grid < expand.grid(seq(0, 1, , 10),seq(0, 1, , 10))
ehvi < apply(grid, 1, EHVI, model)
contour(matrix(ehvi, 20))
points(model@design, col=ifelse(model@feasible,'blue','red'))
points(grid[which.max(ehvi),], col='green', pch=19)

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