R/cf3.R

In danielhorn/moobench: Multi Objective Optimization Benchmark Functions

# CF3 test function generator.

generateCF3 = function(in.dim = 30L, out.dim = 2L, on.infeasible) {
  
  param.set = makeParamSet(
    makeNumericVectorParam(id = "x", len = in.dim,
      lower = c(0, rep(-2, in.dim - 1)), upper = c(1, rep(2, in.dim - 1))),
    forbidden = expression({
      #FIXME: Ask someone intelligent!! This is not good!!!
      if (is.list(x))
        x = x[[1L]]
      f = cf3(x)
      f[2L] + f[1L]^2 - sin(2 * pi * (f[1L]^2 - f[2L] + 1)) - 1 >= 0
    }))
  
  paretoSet = NULL
  
  paretoFront = function(n = out.dim * 100L) {
    if (n %% 2 == 1) {
      pts1 = runif(n = floor(n / 2), min = 0.5, max = sqrt(0.5))
      pts2 = runif(n = floor(n / 2), min = sqrt(0.75), max = 1)
    } else {
      pts1 = runif(n = n / 2, min = 0.5, max = sqrt(0.5))
      pts2 = runif(n = n / 2 - 1, min = sqrt(0.75), max = 1)
    }
    
    des = cbind(c(0, pts1, pts2), 1 - c(0, pts1, pts2)^2)
    des = des[order(des[, 1L]), ]
    rownames(des) = 1:nrow(des)
    as.data.frame(des)
    
  }
  
  mooFunction(
    name = "cf3",
    id = sprintf("cf3-%id-%id", in.dim, out.dim),
    fun = cf3,
    in.dim = in.dim,
    out.dim = out.dim,
    param.set = param.set,
    paretoSet = paretoSet,
    paretoFront = paretoFront,
    on.infeasible = on.infeasible)
}

# Definition of cf3
cf3 = function(x) {
  j = 2:length(x)
  j1 = j[j %% 2 == 1L]
  j2 = j[j %% 2 == 0L]
  
  y = function(j) {
    x[j] - x[1L]^(0.5 * (1 + (3 * (j - length(x))) / (length(x) - 2)))
  }
  
  f1 = x[1L] + 2 / length(j1) * 
    (4 * sum(y(j1)^2) - 2 * prod(cos((20 * y(j1) * pi) / (sqrt(j1)))) + 2)
  f2 = 1 - x[1L]^2 + 2 / length(j2) * 
    (4 * sum(y(j2)^2) - 2 * prod(cos((20 * y(j2) * pi) / (sqrt(j2)))) + 2)
  return(c(f1, f2))
}