#' @title
#' Price Function N. 4
#'
#' @description
#' Fourth function by Price. The implementation is based on the definition
#' \deqn{f(\mathbf{x}) = (2\mathbf{x}_1^3 \mathbf{x}_2 - \mathbf{x}_2^3)^2 + (6\mathbf{x}_1 - \mathbf{x}_2^2 + \mathbf{x}_2)^2}
#' subject to \eqn{\mathbf{x}_i \in [-500, 500]}.
#'
#' @return
#' An object of class \code{SingleObjectiveFunction}, representing the Price N. 4 Function.
#'
#' @references W. L. Price, A Controlled Random Search Procedure for Global
#' Optimisation, Computer journal, vol. 20, no. 4, pp. 367-370, 1977.
#'
#' @seealso \code{\link{makePriceN1Function}}, \code{\link{makePriceN2Function}}
#'
#' @template ret_smoof_single
#' @export
makePriceN4Function = function() {
makeSingleObjectiveFunction(
name = "Price Function N. 4",
id = "price04_2d",
fn = function(x) {
checkNumericInput(x, 2L)
(2 * x[1]^3 * x[2] - x[2]^3)^2 + (6 * x[1] - x[2]^2 + x[2])^2
},
par.set = ParamHelpers::makeNumericParamSet(
len = 2L,
id = "x",
lower = c(-500, -500),
upper = c(500, 500),
vector = TRUE
),
tags = attr(makePriceN4Function, "tags"),
global.opt.params = matrix(
c(0, 0,
2, 4,
1.464, -2.506),
ncol = 2L, byrow = TRUE),
global.opt.value = 0
)
}
class(makePriceN4Function) = c("function", "smoof_generator")
attr(makePriceN4Function, "name") = c("Price Function N. 4")
attr(makePriceN4Function, "type") = c("single-objective")
attr(makePriceN4Function, "tags") = c("single-objective", "continuous", "differentiable", "non-separable", "non-scalable", "multimodal")
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