The Augmented Tchebycheff function (KNOWLES, 2006) is a scalarizing function witch the advantages of having a non-linear term. That causes points on nonconvex regions of the Pareto front can bve minimizers of this function and, thus, nonsupported solutions can be obtained.

1 | ```
Tchebycheff(y, s = 100, rho = 0.1)
``` |

`y` |
Numerical matrix or data.frame containing the responses (on each column) to be scalarized. |

`s` |
Numerical integer (default: 100) setting the number of partitions the vector lambda has. |

`rho` |
A small positive value (default: 0.1) setting the "strenght" of the non-linear term. |

Knowles, J. (2006). ParEGO: a hybrid algorithm with on-line
landscape approximation for expensive multiobjective optimization problems.
*IEEE Transactions on Evolutionary Computation*, 10(1), 50-66.

1 2 3 4 5 6 7 8 9 | ```
grid <- expand.grid(seq(0, 1, , 50),seq(0, 1, , 50))
res <- t(apply(grid, 1, nowacki_beam))
plot(nowacki_beam_tps$x, xlim=c(0,1), ylim=c(0,1))
grid <- grid[which(as.logical(apply(res[,-(1:2)] < 0, 1, prod))),]
res <- res[which(as.logical(apply(res[,-(1:2)] < 0, 1, prod))),1:2]
for (i in 1:10){
sres <- Tchebycheff(res[,1:2], s=100, rho=0.1)
points(grid[which.min(sres),], col='green')
}
``` |

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