#' @title
#' Viennet function generator
#'
#' @description
#' The Viennet test problem VNT is designed for three objectives only. It has
#' a discrete set of Pareto fronts. It is defined by the following formulae.
#' \deqn{f(\mathbf{x}) = \left(f_1(\mathbf{x}), f_2(\mathbf{x}, f_3(\mathbf{x}\right)}
#' with
#' \deqn{f_1(\mathbf{x}) = 0.5(\mathbf{x}_1^2 + \mathbf{x}_2^2) + \sin(\mathbf{x}_1^2 + \mathbf{x}_2^2)}
#' \deqn{f_2(\mathbf{x}) = \frac{(3\mathbf{x}_1 + 2\mathbf{x}_2 + 4)^2}{8} + \frac{(\mathbf{x}_1 - \mathbf{x}_2 + 1)^2}{27} + 15}
#' \deqn{f_3(\mathbf{x}) = \frac{1}{\mathbf{x}_1^2 + \mathbf{x}_2^2 + 1} - 1.1\exp(-(\mathbf{x}_1^1 + \mathbf{x}_2^2))}
#' with box constraints \eqn{-3 \leq \mathbf{x}_1, \mathbf{x}_2 \leq 3}.
#'
#' @references
#' Viennet, R. (1996). Multi-criteria optimization using a genetic algorithm for determining the
#' Pareto set. International Journal of Systems Science 27 (2), 255-260.
#'
#' @return [\code{smoof_multi_objective_function}]
#' Returns an instance of the Viennet function as a \code{smoof_multi_objective_function} object.
#' @export
makeViennetFunction = function() {
# C implementation
fn = function(x) {
checkNumericInput(x, 2L)
.Call("mof_viennet", x)
}
makeMultiObjectiveFunction(
name = "Viennet Function",
id = "viennet",
description = "Viennet function",
fn = fn,
par.set = ParamHelpers::makeNumericParamSet(
len = 2L,
id = "x",
lower = rep(-3, 2L),
upper = rep(3, 2L),
vector = TRUE
),
n.objectives = 3L#,
#ref.point = rep(11, n.objectives)
)
}
class(makeViennetFunction) = c("function", "smoof_generator")
attr(makeViennetFunction, "name") = c("Viennet")
attr(makeViennetFunction, "type") = c("multi-objective")
attr(makeViennetFunction, "tags") = c("multi-objective")
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