#' @title
#' Deckkers-Aarts Function
#'
#' @description
#' This continuous single-objective test function is defined by the formula
#' \deqn{f(\mathbf{x}) = 10^5\mathbf{x}_1^2 + \mathbf{x}_2^2 - (\mathbf{x}_1^2 + \mathbf{x}_2^2)^2 + 10^{-5} (\mathbf{x}_1^2 + \mathbf{x}_2^2)^4}
#' with the bounding box \eqn{-20 \leq \mathbf{x}_i \leq 20} for \eqn{i = 1, 2}.
#'
#' @return
#' An object of class \code{SingleObjectiveFunction}, representing the Deckkers-Aarts Function.
#'
#' @references M. M. Ali, C. Khompatraporn, Z. B. Zabinsky, A Numerical Evaluation
#' of Several Stochastic Algorithms on Selected Continuous Global Optimization
#' Test Problems, Journal of Global Optimization, vol. 31, pp. 635-672, 2005.
#'
#' @template ret_smoof_single
#' @export
makeDeckkersAartsFunction = function() {
makeSingleObjectiveFunction(
name = "Deckkers-Aarts Function",
id = "deckkersAarts_2d",
fn = function(x) {
checkNumericInput(x, 2L)
a = x[1]^2
b = x[2]^2
1e+05 * a + b - (a + b)^2 + 1e-05 * (a + b)^4
},
par.set = ParamHelpers::makeNumericParamSet(
len = 2L,
id = "x",
lower = c(-20, -20),
upper = c(20, 20),
vector = TRUE
),
tags = attr(makeDeckkersAartsFunction, "tags"),
global.opt.params = matrix(
c(0, 15,
0, -15),
ncol = 2L, byrow = TRUE),
global.opt.value = -24771.0937
)
}
class(makeDeckkersAartsFunction) = c("function", "smoof_generator")
attr(makeDeckkersAartsFunction, "name") = c("Deckkers-Aarts")
attr(makeDeckkersAartsFunction, "type") = c("single-objective")
attr(makeDeckkersAartsFunction, "tags") = c("single-objective", "continuous", "differentiable", "non-separable", "non-scalable", "multimodal")
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