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#' 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"
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