# Trust-region based EGO algorithm. Executes **nsteps** iterations of the TREGO method to an object of class `km`. At each step, a kriging model is re-estimated (including covariance parameters re-estimation) based on the initial design points plus the points visited during all previous iterations; then a new point is obtained by maximizing the Expected Improvement criterion (`EI`) over either the entire search space or restricted to a trust region. The trust region is updated at each iteration based on a sufficient decrease condition. ```r TREGO.nsteps( model, fun, nsteps, lower, upper, control = NULL, kmcontrol = NULL, trcontrol = NULL, trace = 0, n.cores = 1, ... ) ``` ## Arguments - `model`: an object of class `km`, - `fun`: the objective function to be minimized, - `nsteps`: an integer representing the desired number of iterations, - `lower, upper`: vector of lower and upper bounds for the variables to be optimized over, - `control`: an optional list of control parameters for optimization. For now only the number of `restarts` can be set. - `kmcontrol`: an optional list representing the control variables for the re-estimation of the kriging model. - `trcontrol`: an optional list of control parameters for the trust-region scheme: `sigma` the initial size of the trust region, `x0` its initial center, `beta` the contraction factor, `alpha` its dilatation factor, `kappa` the forcing factor, `crit` the criterion used inside the TR (either "EI" or "gpmean"), `GLratio` number of consecutive global and local steps, `algo` either "TREGO" or "TRIKE", `minsigma` minimal sigma value, `maxsigma` maximal sigma value, `minEI` stopping criterion for TRIKE, `local.model` Boolean; if TRUE, a local model is used within the trust region, `local.trend, local.covtype` trend and covariance for the local model, `n.local.min` minimal number of points used to build the local model, - `trace`: between -1 (no trace) and 3 (full messages) - `n.cores`: number of cores used for EI maximisation - `...`: additional parameters to be given to `fun` ## Returns A list with components: - **par**: a data frame representing the additional points visited during the algorithm, - **value**: a data frame representing the response values at the points given in `par`, - **npoints**: an integer representing the number of parallel computations (=1 here), - **nsteps**: an integer representing the desired number of iterations (given in argument), - **lastmodel**: an object of class `km` corresponding to the last kriging model fitted. If warping is true, `y` values are normalized (warped) and will not match `value`. - **all.success**: a vector of Boolean indicating the successful steps according to the sufficient decrease condtion - **all.steps**: a vector of Boolean indicating which steps were global - **all.sigma**: history of trust region size - **all.x0**: history of trust region centers - **local.model**: if trcontrol$local.model=TRUE, the latest local model ## Examples ```r set.seed(123) ############################################################### ### 10 ITERATIONS OF TREGO ON THE BRANIN FUNCTION, #### ### STARTING FROM A 9-POINTS FACTORIAL DESIGN #### ############################################################### # a 9-points factorial design, and the corresponding response d <- 2 n <- 9 design.fact <- expand.grid(seq(0,1,length=3), seq(0,1,length=3)) names(design.fact)<-c("x1", "x2") design.fact <- data.frame(design.fact) names(design.fact)<-c("x1", "x2") response.branin <- apply(design.fact, 1, branin) response.branin <- data.frame(response.branin) names(response.branin) <- "y" # model identification fitted.model1 <- km(~1, design=design.fact, response=response.branin, covtype="gauss", control=list(pop.size=50,trace=FALSE), parinit=c(0.5, 0.5)) # TREGO n steps nsteps <- 5 lower <- rep(0, d) upper <- rep(1, d) oEGO <- TREGO.nsteps(model=fitted.model1, fun=branin, nsteps=nsteps, lower=lower, upper=upper) print(oEGO$par) print(oEGO$value) # graphics n.grid <- 15 # Was 20, reduced to 15 for speeding up compilation x.grid <- y.grid <- seq(0,1,length=n.grid) design.grid <- expand.grid(x.grid, y.grid) response.grid <- apply(design.grid, 1, branin) z.grid <- matrix(response.grid, n.grid, n.grid) contour(x.grid, y.grid, z.grid, 40) title("Branin function") points(design.fact[,1], design.fact[,2], pch=17, col="blue") points(oEGO$par, pch=19, col="red") text(oEGO$par[,1], oEGO$par[,2], labels=1:nsteps, pos=3) ``` ## References Diouane, Picheny, Le Riche, Scotto Di Perrotolo (2021), **TREGO: a Trust-Region Framework for Efficient Global Optimization**, ArXiv ## See Also `EI`, `max_crit`, `EI.grad` ## Author(s) Victor Picheny

TREGO.nsteps function