Implements the efficient global optimization algorithm based on Kriging. It is a wrapper around mbo1d and additionally includes latin hypercube design generation and meta model validation of the Kriging model.
mboAll(loss_func, n_steps, initDesign, lower_bounds,
upper_bounds, x_start, isoInput=FALSE, addInfo=TRUE,
maxRunsMult=1, repMult=1, tol_input=.Machine$double.eps^0.25,
envir=parent.frame(), metaModelSelect=TRUE,
EIopt="1Dmulti", GenSAmaxCall=100, timeAlloc="constant",
EItype="EI")Loss function to be minimized.
Number of steps of the EGO algorithm.
Number of initial design points to be evaluated. The higher the number, the more function evaluations of the loss function are required, but the approximation with Kriging will be more accurate.
Vector of lower bounds of the tuning parameters. First element is the lower bound of the first tuning parameter, second element the lower bound of the next tuning parameter etc.
Vector of upper bounds of the tuning parameters. First element is the upper bound of the first tuning parameter, second element the upper bound of the next tuning parameter etc.
Starting value of the one dimensional optimization algorithm. See optimize1dMulti.
Force the covariance structure of the km to have only one range parameter. For details see km
Should additional information be displayed during optimization? (logical value). Default is TRUE.
Multiplies the base number of iterations in the conditional optimization. Default is to use the number of hyperparameters. See optimize1dMulti.
Multiplies the base number of random starting values for helping to avoid local optima. Default is the number of hyperparameters. See optimize1dMulti.
Convergence criteria of each one dimensional sub-optimization. Higher values will be more accurate, but require much more function evaluations. Default is the fourth root of the machine double accuracy. See optimize1dMulti.
Internal variable to store environments. Default is to look up in a one level higher environment. Modification is unnecessary.
Should the covariance kernel of the Kriging model be automatically selected? (logical scalar) Default is TRUE and corresponds to the 5/2 materin covariance structure.
Specifies which algorithm is used to optimize the expected improvement criterion. Two alternatives are available "1Dmulti" and "GenSA". The former uses the conditional 1D algorithm and the latter generalized, simulated annealing.
Maximum number of function calls per parameter to estimate in generalized, simulated annealing. Higher values result in more accurate estimates, but the optimization process is slowed.
Specifies how the new noise variance is influenced by iteration progress. Default is to use "constant"" allocation. The other available option is to specify "zero", which corresponds to the original expected improvement criterion.
Defines the type of the improvement criterion. The default EI corresponds to the expected improvement. As an alternative EQI the expected quantile improvement is also possible.
List with following components:
par: Best found parameter values
value: Function value at the best found parameters
MBOprogress: MBO tuning process history
In addition to the function mbo1d a latin hypercube design will be generated. The design is generated by maximizing the minimum distance between the design points (maximin criteria). For reference see maximinLHS. Then the complete initial design is evaluated with the loss function. The model validation of Kriging searches for the best covariance kernel structure between five alternative specifications (see covTensorProduct-class). The performance is evaluated with a Gaussian likelihood with leave one out estimated expectations and variances of the Kriging model.
Michael Stein, (1987), Large Sample Properties of Simulations Using Latin Hypercube Sampling, Technometrics. 29, 143-151
Carl Edward Rasmussen and Christopher K. I. Williams, (2006), Gaussian Processes for Machine Learning, Massachusetts Institute of Technology
# Example with Branin function
library(globalOptTests)
tryBranin <- mboAll (loss_func=function (x) goTest(par=x, fnName="Branin",
checkDim = FALSE), n_steps=5, initDesign=15, lower_bounds=c(-5, 0),
upper_bounds=c(10, 15), x_start=c(5, -5))
abs(tryBranin$value-getGlobalOpt("Branin"))
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