Pareto front on integer control parameters can have several points with the same control parameter values

[SRFU-NN]

If you have on control parameter as an integer dimension, the Pareto front plot will show multiple points with the same value for that control parameter. Is this what we want? If not, how do we handle it?

Th easiest place to see this is in the Pareto front plot in .\examples\color_pH.ipynb, in the paragraph "Additional plots". Hover over points on the Pareto front close together, and you will see that some of them have the same values in both pct_acid and vol_indicator.

This is probably because the points are different in transformed space, but map to the same point in non-transformed space.

Do we want this? It means that there are points on the Pareto front you can't get to from non-transformed space.

If we want to handle this, one solution would be to de-transform->transform points when making the Pareto front.

Another, more complex, solution, would be to make a "transform kernel", where k'(x,y) = k(T(T^-1(x), T(T^-1(y)), for points x,y in transformed space, and k being a traditional kernel. Then transformed points that maps to the same non-transformed point would have the same surrogate function value and uncertainty.