Conditional constraints for continuous factors?Say I've got a DOE with 2 continuous factors (X1 and X2). It's pretty clear how to set up linear constraints if I want to constrain my design region to make a convex polygonal shape something like this:
How do I do a "conditional constraint" to make a convex polygon, like this?
So I've got conditional linear constraints (for X1 between 0 and 1, use this line, for 1 to 2, use that line).
I realize this presents modeling and profiling problems for the excluded region. Just anticipating a potential customer need here.
Thanks for any suggestions!
Re: Conditional constraints for continuous factors?Hi Jerry
Without being too mathematical, but your Second polygon is by Definition non-convex (aka concave). Therefore many of the optimality criteria are not valid anymore which results at least to the assumption that a found local optima is not for sure anymore also a global optima.
I have not the in depth knowledge on how this might have effect on the design and the resulting analysis but it does not surprise me that there are some issues.
I leave it to the doe cracks on answering this 
Martin
Re: Conditional constraints for continuous factors?Thank you Peter! This does indeed work.
I took one last look at the original way that I was trying (both factors continuous), and found that I had some inequality signs wrong.
(Root problem here is that Linear Constraints appear to set "allowable regions", but "Disallowed combinations" are the inverse. Always helps to read the instructions!)
So the final Disallowed Constraint Script looks like this:
(X1 >= 0 & X1 < 1 & X2 <= X1) | (X1 >= 1 & X1 <= 2 & X2 <= 2 - X1)
For an I-Optimal RSM model with 100 trials, this gives an X1 vs X2 space that looks like:
which is what I wanted.
Learned a lot, maybe posted some wisdom as well. Thanks much Peter Hersh for the assist! Wouldn't have gotten there without your help.
Re: Conditional constraints for continuous factors?OK I was able to get it to work by making X1 a discrete numeric with 3 level 0,1,2. If you add in a dissallowed combination filter for X1 does not include the value 0 or 2 then you can specify that X2<1 then you should get a cludged together way to make this happen. Maybe someone else has another idea.
Re: Conditional constraints for continuous factors?I am getting the same problem as you
Re: Conditional constraints for continuous factors?Try this in dissallowed combination script
If(
0 <= :X1 < 1, :X2 >= :X1,
1 <= :X1 < 2, :X2 >= 2 - :X1
)
Re: Conditional constraints for continuous factors?It appears that "Use Disallowed Combinations Script" might get the job done, but I'm not able to get it to work. For the concave polygon shape shown in the original post, the script I used was:
(X1 >= 0 & X1 < 1 & X2 >= X1) & (X1 >= 1 & X1 <= 2 & X2 >= 2 - X1)
But the resulting I-Optimal design space looks (RSM model, 20 trials) like this:
Also, when I go back to the Script, I notice that the first set of parens have been removed so the script now looks like:
X1 >= 0 & X1 < 1 & X2 >= X1 & (X1 >= 1 & X1 <= 2 & X2 >= 2 - X1)
Anybody know what's up?
