Tchebycheff: Augmented Tchebycheff function In moko: Multi-Objective Kriging Optimization

Description

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 be minimizers of this function and, thus, nonsupported solutions can be obtained.

Usage

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

Arguments

 `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 "strength" of the non-linear term.

References

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.

Examples

 ```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') } ```

Example output

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moko documentation built on July 2, 2020, 3:59 a.m.