# LZ6 test function generator.
generateLZ6 = function(in.dim = 30L, out.dim = 2L) {
param.set = makeNumericParamSet(id = "x", len = in.dim,
lower = c(0, 0, rep(-2, in.dim - 2)), upper = c(1, 1, rep(2, in.dim - 2)))
paretoSet = function(n = out.dim * 100L) {
des = generateDesign(par.set = param.set, n = n)
des = des[order(des[, 1L]), ]
rownames(des) = 1:nrow(des)
x1 = des[, 1L]
x2 = des[, 2L]
j = 3:in.dim
des[, -(1:2)] = t(sapply(seq_along(x1), function(i)
2 * x2[i] * sin(2 * pi * x1[i] + (j * pi) / in.dim)))
des
}
paretoFront = function(n = out.dim * 100L) {
des = matrix(runif(3 * n), nrow = n, ncol = 3L)
des = des / rowSums(des)
des[, 1L] = sqrt(des[, 1L])
des[, 2L] = sqrt(des[, 2L])
des[, 3L] = (des[, 3L])^(1 / 3)
des = des[order(des[, 1L]), ]
rownames(des) = 1:nrow(des)
as.data.frame(des)
}
mooFunction(
name = "lz6",
id = sprintf("lz6-%id-%id", in.dim, out.dim),
fun = lz6,
in.dim = in.dim,
out.dim = out.dim,
param.set = param.set,
paretoSet = paretoSet,
paretoFront = paretoFront)
}
# Definiton of lz6
lz6 = function(x) {
j = 3:length(x)
j1 = j[j %% 3 == 1L]
j2 = j[j %% 3 == 2L]
j3 = j[j %% 3 == 0L]
f1 = cos(0.5 * x[1L] * pi) * cos(0.5 * x[2L] * pi) + 2 / length(j1) *
sum((x[j1] - 2 * x[2L] * sin(2 * pi * x[1L] + (j1 * pi) / length(x)))^2)
f2 = cos(0.5 * x[1L] * pi) * sin(0.5 * x[2L] * pi) + 2 / length(j2) *
sum((x[j2] - 2 * x[2L] * sin(2 * pi * x[1L] + (j2 * pi) / length(x)))^2)
f3 = sin(0.5 * x[1L] * pi) + 2 / length(j3) *
sum((x[j3] - 2 * x[2L] * sin(2 * pi * x[1L] + (j3 * pi) / length(x)))^2)
return(c(f1, f2, f3))
}
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