R/dtlz1.R

In danielhorn/moobench: Multi Objective Optimization Benchmark Functions

# DTLZ1 test function generator.

generateDTLZ1 = function(in.dim = 30L, out.dim = 2L) {

  param.set = makeNumericParamSet(id = "x", len = in.dim, lower = 0, upper = 1)
  
  paretoSet = function(n = out.dim * 100L) {
    des = generateDesign(par.set = param.set, n = n)
    des = des[order(des[, 1L]), ]
    rownames(des) = 1:nrow(des)
    
    des[, out.dim:in.dim] = 0.5
    
    des
  }
  
  paretoFront = function(n = out.dim * 100L) {
    des = matrix(runif(out.dim * n), nrow = n, ncol = out.dim)
    des = des / rowSums(des) / 2

    des = des[order(des[, 1L]), ]
    rownames(des) = 1:nrow(des)
    
    as.data.frame(des)
  }
  
  mooFunction(
    name = "dtlz1",
    id = sprintf("dtlz1-%id-%id", in.dim, out.dim),
    fun = function(x) dtlz1(x, out.dim),
    in.dim = in.dim,
    out.dim = out.dim,
    param.set = param.set,
    paretoSet = paretoSet,
    paretoFront = paretoFront)
}

# Definiton of dtlz1
dtlz1 = function(x, out.dim) {
  x.head = x[seq_len(out.dim - 1L)]
  x.tail = x[out.dim:length(x)] - 0.5
  
  rev(0.5 * c(1, cumprod(x.head)) * c(1 - x.head, 1) * 
      (1 + 100 * (length(x.tail) + sum(x.tail^2 - cos(20 * pi * x.tail)))))
}