R/sof.schaffer.function.2.R

In smoof: Single and Multi-Objective Optimization Test Functions

#' Modified Schaffer Function N. 2
#'
#' Second function by Schaffer. The defintion is given by the formula
#' \deqn{f(\mathbf{x}) = 0.5 + \frac{\sin^2(\mathbf{x}_1^2 - \mathbf{x}_2^2) - 0.5}{(1 + 0.001(\mathbf{x}_1^2 + \mathbf{x}_2^2))^2}}
#' subject to \eqn{\mathbf{x}_i \in [-100, 100], i = 1, 2}.
#'
#' @references S. K. Mishra, Some New Test Functions For Global Optimization
#' And Performance of Repulsive Particle Swarm Method.
#'
#' @template ret_smoof_single
#' @export
makeSchafferN2Function = function() {
  makeSingleObjectiveFunction(
    name = "Schaffer Function N. 2",
    id = "schaffer02_2d",
    fn = function(x) {
      assertNumeric(x, len = 2L, any.missing = FALSE, all.missing = FALSE)
      a = x[1]^2
      b = x[2]^2
      0.5 + (sin(a - b)^2 - 0.5) / (1 + 0.001 * (a + b))^2
    },
    par.set = makeNumericParamSet(
      len = 2L,
      id = "x",
      lower = c(-100, -100),
      upper = c(100, 100),
      vector = TRUE
    ),
    tags = attr(makeSchafferN2Function, "tags"),
    global.opt.params = c(0, 0),
    global.opt.value = 0
  )
}

class(makeSchafferN2Function) = c("function", "smoof_generator")
attr(makeSchafferN2Function, "name") = c("Schaffer N. 2")
attr(makeSchafferN2Function, "type") = c("single-objective")
attr(makeSchafferN2Function, "tags") = c("single-objective", "continuous", "differentiable", "non-separable", "non-scalable", "unimodal")