R/f_chained_LQ.R

In soobench: Single Objective Optimization Benchmark Functions

#' Chained LQ test function generator.
#'
#' The chained LQ test function is defined as
#'
#'   \deqn{f(x) = \sum_{i=1}^{n-1} \max\left\{-x_i - x_{i+1}, -x_i - x_{i+1} + (x_i^2 + x_{i+1}^2 - 1)\right\}}
#'
#' @param dimensions [\code{integer(1)}] Size of parameter space.
#' @return A \code{soo_function}.
#'
#' @references Haarala, M. and Miettinen, K. and Maekelae, M. M., New limited
#' memory bundle method for large-scale nonsmooth optimization.
#'
#' @export
generate_chained_LQ_function <- function(dimensions)
  soo_function(name="Chained_LQ",
               id=sprintf("chained-LQ-%id", dimensions),
               fun=f_chained_LQ,
               dimensions=dimensions,
               lower_bounds=rep(-Inf, dimensions),
               upper_bounds=rep(Inf, dimensions),
               #FIXME: best params unknown
               best_par=rep(0, dimensions),
               best_value=-(dimensions - 1)*sqrt(2))

class(generate_chained_LQ_function) <- c("soo_function_generator", "function")
attr(generate_chained_LQ_function, "id") <- "chained_LQ"
attr(generate_chained_LQ_function, "name") <- "Chained LQ test function"

f_chained_LQ = function(x, ...) {
	n = length(x)
	res = 0
	for (i in 1:(n-1)) {
		res = res + max(-x[i] - x[i+1], -x[i] - x[i+1] + (x[i]^2 + x[i+1]^2 - 1))
	}
	res
}