crit_SUR_cst: Stepwise Uncertainty Reduction criterion
In DiceOptim: Kriging-Based Optimization for Computer Experiments

Description Usage Arguments Value Author(s) References See Also Examples

Computes the Stepwise Uncertainty Reduction (SUR) criterion at current location

crit_SUR_cst(
  x,
  model.fun,
  model.constraint,
  equality = FALSE,
  critcontrol = NULL,
  type = "UK"
)

`x`	a vector representing the input for which one wishes to calculate `SUR`,
`model.fun`	object of class `km` corresponding to the objective function, or, if the objective function is fast-to-evaluate, a `fastfun` object,
`model.constraint`	either one or a list of objects of class `km`, one for each constraint function,
`equality`	either `FALSE` if all constraints are for inequalities, else a vector of boolean indicating which are equalities
`critcontrol`	optional list with arguments: `tolConstraints` optional vector giving a tolerance (> 0) for each of the constraints (equality or inequality). It is highly recommended to use it when there are equality constraints since the default tolerance of 0.05 in such case might not be suited; `integration.points` and `integration.weights`: optional matrix and vector of integration points; `precalc.data.cst, precalc.data.obj, mn.X.cst, sn.X.cst, mn.X.obj, sn.X.obj`: useful quantities for the fast evaluation of the criterion. Options for the `checkPredict` function: `threshold` (`1e-4`) and `distance` (`covdist`) are used to avoid numerical issues occuring when adding points too close to the existing ones.
`type`	"`SK`" or "`UK`" (by default), depending whether uncertainty related to trend estimation has to be taken into account.

The Stepwise Uncertainty Reduction criterion at x.

Victor Picheny

Mickael Binois

V. Picheny (2014), A stepwise uncertainty reduction approach to constrained global optimization, Proceedings of the 17th International Conference on Artificial Intelligence and Statistics, JMLR W&CP 33, 787-795.

EI from package DiceOptim, crit_EFI, crit_AL.

#---------------------------------------------------------------------------
# Stepwise Uncertainty Reduction criterion surface with one inequality constraint
#---------------------------------------------------------------------------

set.seed(25468)
library(DiceDesign)

n_var <- 2 
fun.obj <- goldsteinprice
fun.cst <- function(x){return(-branin(x) + 25)}
n.grid <- 21
test.grid <- expand.grid(X1 = seq(0, 1, length.out = n.grid), X2 = seq(0, 1, length.out = n.grid))
obj.grid <- apply(test.grid, 1, fun.obj)
cst.grid <- apply(test.grid, 1, fun.cst)

n_appr <- 15 
design.grid <- round(maximinESE_LHS(lhsDesign(n_appr, n_var, seed = 42)$design)$design, 1)
obj.init <- apply(design.grid, 1, fun.obj)
cst.init <- apply(design.grid, 1, fun.cst)
model.fun <- km(~., design = design.grid, response = obj.init)
model.constraint <- km(~., design = design.grid, response = cst.init)

integration.param <- integration_design_cst(integcontrol =list(integration.points = test.grid),
                                            lower = rep(0, n_var), upper = rep(1, n_var))

SUR_grid <- apply(test.grid, 1, crit_SUR_cst, model.fun = model.fun,
                  model.constraint = model.constraint, critcontrol=integration.param)

filled.contour(seq(0, 1, length.out = n.grid), seq(0, 1, length.out = n.grid), nlevels = 50,
               matrix(SUR_grid, n.grid), main = "SUR criterion",
               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")
                            contour(seq(0, 1, length.out = n.grid), seq(0, 1, length.out = n.grid), 
                            matrix(obj.grid, n.grid), nlevels = 10,
                                   add=TRUE,drawlabels=TRUE, col = "black")
                            contour(seq(0, 1, length.out = n.grid), seq(0, 1, length.out = n.grid), 
                            matrix(cst.grid, n.grid), level = 0, add=TRUE,
                                   drawlabels=FALSE,lwd=1.5, col = "red")
                            }
              )

#---------------------------------------------------------------------------
# SUR with one inequality and one equality constraint
#---------------------------------------------------------------------------

set.seed(25468)
library(DiceDesign)

n_var <- 2 
fun.obj <- goldsteinprice
fun.cstineq <- function(x){return(3/2 - x[1] - 2*x[2] - .5*sin(2*pi*(x[1]^2 - 2*x[2])))}
fun.csteq <- function(x){return(branin(x) - 25)}
n.grid <- 21
test.grid <- expand.grid(X1 = seq(0, 1, length.out = n.grid), X2 = seq(0, 1, length.out = n.grid))
obj.grid <- apply(test.grid, 1, fun.obj)
cstineq.grid <- apply(test.grid, 1, fun.cstineq)
csteq.grid <- apply(test.grid, 1, fun.csteq)
n_appr <- 25 
design.grid <- round(maximinESE_LHS(lhsDesign(n_appr, n_var, seed = 42)$design)$design, 1)
obj.init <- apply(design.grid, 1, fun.obj)
cstineq.init <- apply(design.grid, 1, fun.cstineq)
csteq.init <- apply(design.grid, 1, fun.csteq)
model.fun <- km(~., design = design.grid, response = obj.init)
model.constraintineq <- km(~., design = design.grid, response = cstineq.init)
model.constrainteq <- km(~., design = design.grid, response = csteq.init)

models.cst <- list(model.constraintineq, model.constrainteq)
 
SUR_grid <- apply(test.grid, 1, crit_SUR_cst, model.fun = model.fun, model.constraint = models.cst,
                  equality = c(FALSE, TRUE), critcontrol = list(tolConstraints = c(0.05, 3), 
                  integration.points=integration.param$integration.points))

filled.contour(seq(0, 1, length.out = n.grid), seq(0, 1, length.out = n.grid), nlevels = 50,
               matrix(SUR_grid, n.grid), main = "SUR criterion",
               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")
                            contour(seq(0, 1, length.out = n.grid), seq(0, 1, length.out = n.grid), 
                            matrix(obj.grid, n.grid), nlevels = 10,
                                   add=TRUE,drawlabels=TRUE, col = "black")
                            contour(seq(0, 1, length.out = n.grid), seq(0, 1, length.out = n.grid), 
                            matrix(cstineq.grid, n.grid), level = 0, add=TRUE,
                                   drawlabels=FALSE,lwd=1.5, col = "red")
                            contour(seq(0, 1, length.out = n.grid), seq(0, 1, length.out = n.grid),
                            matrix(csteq.grid, n.grid), level = 0, add=TRUE,
                                   drawlabels=FALSE,lwd=1.5, col = "orange")
                            }
              )