R/f_batman.R

In olafmersmann/soobench: Single Objective Optimization Benchmark Functions

#' Generator for the Batman function.
#'
#' The definition used is
#'
#' \deqn{f(x) = \left[\left((x^Tx)^2 - (\sum_{i=1}^n)^2\right)^2\right]^\alpha + \frac{1}{N}\left(\frac{1}{2}x^Tx + \sum_{i=1}^n x_i\right) + \frac{1}{2}}
#'
#' @param dimensions [\code{integer(1)}] Size of parameter space.
#' @param alpha [\code{numeric(1)}] Parameter for control of groove shape
#' @return A \code{soo_function}.
#'
#' @examples
#' f <- generate_batman_function(2, 1/4)
#' plot(f)
#'
#' @references H.-G. Beyer and S. Finck. HappyCat - A Simple Function Class 
#'   Where Well-Known Direct Search Algorithms Do Fail.
#'   In: PPSN XII (Parallel Problem Solving from Nature), 367-376, 
#'   Springer, Heidelberg, 2012.
#'
#' @export
#' @useDynLib soobench do_eval_batman
generate_batman_function <- function(dimensions, alpha=0.25) {
  if(alpha <= 0) 
    stop("Alpha must be greater zero!")
  f <- function(x) {}
  body(f) <- substitute(.Call(do_eval_batman, alpha, x), 
                        list(alpha=alpha))
  soo_function(name="Batman", 
               id=sprintf("batman-%id-%5.3f", dimensions, alpha),
               dimensions=dimensions,
               fun=f,
               ## lower and upper bounds unknown until now
               lower_bounds=rep(-2, dimensions),
               upper_bounds=rep(2, dimensions),
               best_par=rep(-1, dimensions),
               best_value=0)
}

class(generate_batman_function) <- c("soo_function_generator", "function")
attr(generate_batman_function, "id") <- "batman"
attr(generate_batman_function, "name") <- "Batman test function"