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#' Styblinkski-Tang function
#'
#' This function is based on the defintion
#' \deqn{f(\mathbf{x}) = \frac{1}{2} \sum_{i = 1}^{2} (\mathbf{x}_i^4 - 16 \mathbf{x}_i^2 + 5\mathbf{x}_i)}
#' with box-constraints given by \eqn{\mathbf{x}_i \in [-5, 5], i = 1, 2}.
#'
#' @references Z. K. Silagadze, Finding Two-Dimesnional Peaks, Physics of
#' Particles and Nuclei Letters, vol. 4, no. 1, pp. 73-80, 2007.
#'
#' @template ret_smoof_single
#' @export
#FIXME: hmm, this can be formulated as a scalable problem
makeStyblinkskiTangFunction = function() {
makeSingleObjectiveFunction(
name = "Styblinkski-Tang Function",
id = "styblinskiTang_2d",
fn = function(x) {
assertNumeric(x, len = 2L, any.missing = FALSE, all.missing = FALSE)
a = x^2
b = a^2
return(0.5 * sum(b - 16 * a + 5 * x))
},
par.set = makeNumericParamSet(
len = 2L,
id = "x",
lower = rep(-5, 2L),
upper = rep(5, 2L),
vector = TRUE
),
tags = attr(makeStyblinkskiTangFunction, "tags"),
global.opt.params = c(-2.903534, -2.903534),
global.opt.value = -78.332
)
}
class(makeStyblinkskiTangFunction) = c("function", "smoof_generator")
attr(makeStyblinkskiTangFunction, "name") = c("Styblinkski-Tang")
attr(makeStyblinkskiTangFunction, "type") = c("single-objective")
attr(makeStyblinkskiTangFunction, "tags") = c("single-objective", "continuous", "differentiable", "non-separable", "non-scalable", "multimodal")
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