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#' Sum of Different Squares Function
#'
#' Simple unimodal test function similar to the Sphere and Hyper-Ellipsoidal functions.
#' Formula:
#' \deqn{f(\mathbf{x}) = \sum_{i=1}^{n} |\mathbf{x}_i|^{i+1}.}
#'
#' @template arg_dimensions
#' @template ret_smoof_single
#' @export
makeSumOfDifferentSquaresFunction = function(dimensions) {
assertCount(dimensions)
force(dimensions)
makeSingleObjectiveFunction(
name = paste(dimensions, "-d Sum of Different Squares Function", sep = ""),
id = paste0("sumOfDifferentSquares_", dimensions, "d"),
fn = function(x) {
assertNumeric(x, len = dimensions, any.missing = FALSE, all.missing = FALSE)
n = length(x)
sum(abs(x)^(1:n + 1))
},
par.set = makeNumericParamSet(
len = dimensions,
id = "x",
lower = rep(-1, dimensions),
upper = rep(1, dimensions),
vector = TRUE
),
tags = attr(makeSumOfDifferentSquaresFunction, "tags"),
global.opt.params = rep(0, dimensions),
global.opt.value = 0
)
}
class(makeSumOfDifferentSquaresFunction) = c("function", "smoof_generator")
attr(makeSumOfDifferentSquaresFunction, "name") = c("Sum of Different Squares")
attr(makeSumOfDifferentSquaresFunction, "type") = c("single-objective")
attr(makeSumOfDifferentSquaresFunction, "tags") = c("single-objective", "unimodal", "continuous", "scalable")
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