Piecewise smooth variant of the Griewank function

R/sof.bosse.R

@@ -0,0 +1,63 @@
+#' @title
+#' Bosse's Modified Griewank Function
+#'
+#' @description
+#' Piecewise-smooth variant of the classical Griewank function.
+#' The corresponding formula is:
+#' \deqn{f(\mathbf{x}) =
+#' 1 + \frac{1}{4000} \sum_{i=1}^{n} x_i^2
+#' - \prod_{i=1}^{n} P_i(x_i)}
+#' with
+#' \deqn{P_i(x_i) =
+#' |\cos(x_i/(2\sqrt{i}))| -
+#' |\sin(x_i/(2\sqrt{i}))|}
+#' subject to \eqn{\mathbf{x}_i \in [-100, 100], i = 1, \ldots, n}.
+#'
+#' @return
+#' An object of class \code{SingleObjectiveFunction}.
+#'
+#' @references
+#' T. F. Bosse and H. M. Bücker,
+#' A piecewise smooth version of the Griewank function,
+#' Optimization Methods and Software, 2024.
+#'
+#' @template arg_dimensions
+#' @template ret_smoof_single
+#' @export
+makeBosseModifiedGriewankFunction = function(dimensions) {
+  checkmate::assertCount(dimensions)
+  force(dimensions)
+
+  makeSingleObjectiveFunction(
+    name = paste(dimensions, "-d Bosse Modified Griewank Function", sep = ""),
+    id = paste0("bosse_modified_griewank_", dimensions, "d"),
+    fn = function(x) {
+      checkNumericInput(x, dimensions)
+
+      a = sum(x^2) / 4000
+
+      i = seq_along(x)
+      Pi = abs(cos(x / (2 * sqrt(i)))) - abs(sin(x / (2 * sqrt(i))))
+      b = prod(Pi)
+
+      return(1 + a - b)
+    },
+    par.set = ParamHelpers::makeNumericParamSet(
+      len = dimensions,
+      id = "x",
+      lower = rep(-100, dimensions),
+      upper = rep(100, dimensions),
+      vector = TRUE
+    ),
+    tags = attr(makeBosseModifiedGriewankFunction, "tags"),
+    global.opt.params = rep(0, dimensions),
+    global.opt.value = 0
+  )
+}
+
+class(makeBosseModifiedGriewankFunction) = c("function", "smoof_generator")
+attr(makeBosseModifiedGriewankFunction, "name") = c("BosseModifiedGriewank")
+attr(makeBosseModifiedGriewankFunction, "type") = c("single-objective")
+attr(makeBosseModifiedGriewankFunction, "tags") =
+  c("single-objective", "continuous", "non-differentiable",
+    "non-separable", "scalable", "multimodal")