R/f_ackley.R

In soobench: Single Objective Optimization Benchmark Functions

#' Ackley test function generator
#'
#' Generator for the Ackley test function.
#' The Ackley function is defined as
#' \deqn{
#'   f(x)
#'   =
#'   -20 \exp
#'   \left(
#'     -0.2 \sqrt{\frac{1}{n}
#'                \sum_{i=1}^n \left(x_i^2\right)}
#'   \right) - \exp
#'   \left(
#'     \frac{1}{n}\sum_{i=1}^n \cos\left(2 \pi x_i \right)
#'   \right) + 20 + \exp(1)}{
#' f(x) = -20 * exp(-0.2 * sqrt(1/n * sum(x^2)))
#'        -exp(1/n * sum(cos(2 * \pi * x))) + 20 + exp(1)
#' }
#'
#' @param dimensions [\code{integer(1)}] Size of parameter space.
#' @return A \code{soo_function}.
#'
#' @examples
#' f <- generate_ackley_function(2)
#' plot(f, rank=TRUE)
#'
#' @references D. H. Ackley. A connectionist machine for genetic hillclimbing.
#' Kluwer Academic Publishers, Boston, 1987
#'
#' @export
#' @useDynLib soobench do_f_ackley
generate_ackley_function <- function(dimensions)
  soo_function(name="Ackley", id=sprintf("ackley-%id", dimensions),
               dimensions=dimensions,
               fun=function(x) .Call(do_f_ackley, x),
               lower_bounds=rep(-32.786, dimensions),
               upper_bounds=rep(32.786, dimensions),
               best_par=rep(0, dimensions),
               best_value=0)


class(generate_ackley_function) <- c("soo_function_generator", "function")
attr(generate_ackley_function, "id") <- "ackley"
attr(generate_ackley_function, "name") <- "Ackley test function"

## Pure R implementation for reference purposes:
f_ackley <- function(x) {
  a <- 20
  b <- 0.2
  c <- 2 * pi
  d <- length(x)
  c1 <- sqrt(crossprod(x) / d)
  c2 <- sum(cos(c * x)) / d
  -a * exp(-b * c1) - exp(c2) + a + exp(1)
}