# Stepwise Uncertainty Reduction criterion Computes the Stepwise Uncertainty Reduction (SUR) criterion at current location ```r crit_SUR_cst( x, model.fun, model.constraint, equality = FALSE, critcontrol = NULL, type = "UK" ) ``` ## Arguments - `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. ## Returns The Stepwise Uncertainty Reduction criterion at `x`. ## Examples ```r #--------------------------------------------------------------------------- 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") } ) ``` ## References 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. ## See Also `EI` from package DiceOptim, `crit_EFI`, `crit_AL`. ## Author(s) Victor Picheny Mickael Binois

crit_SUR_cst function