Problem to find optimal settings for a mixture with Bayesian Optimisation

[#1]

With a 24 run mixture DOE I could find very good models and optimal settings for a ternary mixture and one categorical effect, this was presented in foregoing discussion; find in attachment again the analysis and below screenshots of the desirability results. 

With Isomer 2 desirability result is worse; below the settings when locking Isomer 2

Starting with a 9 run candidate space filling set (see attachment Succesful 9 run) set or a 12 run Kowalski set the optimal settings with Isomer 1 can be detected. 

However starting from a 6 run space filling candidate set I always get the poorer optimal settings with Isomer 2, even after several added space filling runs! What did I do wrong and how to get from this 6 run candidate the optimal Isomer 1 settings? 

[#2]

Hi @frankderuyck,

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@frankderuyck wrote:

Hi Victor in your succeful 6 run initial abov I only see 2 outputs Column 6.1 and Column 6.2 see below. There i a 3rd one Y, I don't see it 

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In my first post, I have already mentioned that I forgot the Y column, but the BayesOpt platform was able to optimize all 3 responses since Y seemed to be negatively correlated with  Column 6 2. So at the end, even when only optimizing with 2 responses instead of 3, I was able to find an optimum close to yours for all 3 responses. The other tests I have done were realized with all 3 responses.

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@frankderuyck wrote:

Incuding Y I can't detect the right optimal settings also not with 10 run see attachment (I recoded the 3 outputs as Y1, Y2 and Y3)

What did I do wrong? It is important for us to understand.

With 9 intial runs it always works perfect, why?

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I won't repeat all my previous post, sorry, you'll find all infos about how to succeed in your optimization starting with 6 or 9 space filling runs in my previous answers, about the diagnostics of your model, the choice of acquisition function, etc... I physically can't evaluate all the scenarii you provide.

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@frankderuyck wrote:

"Space filling runs to ensure a good coverage of the design space --> I have used fast flexible space filling, OK? Is assessment of the initial starting DOE is necessary? I saw a number of webinars where one  starts from just a vey limited #initial runs, sometimes even from an OFAT; guess this will only work when model is simple and when data are not too noisy, correct? This is not always the case and we don't know in advance.

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Yes, starting from a space filling fast flexible design is often a good idea, as this space filling design type is able to handle many constraints and factors types, so it's a good choice. See my previous comment about the number of runs related to the quantity, precision of information depending on the complexity of the response surface.

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@frankderuyck wrote:

Make sure the model is able to generalize the learned behavior, and that this behavior is representative of the real phenomenon in the design space" --> In my examples models have R² > 0,8, are there other criteria?

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R² is one model metric, but there are many others. I would recommend graphical analysis first, looking at the actual vs. predicted plot as they are much more informative, you can check if the general tendancy is learned by the model, if the imprecision of the model is local (in high or low response values) or global, etc...

[#3]

Could you please just send me your BO results with the three responses. Thanks

[#4]

See my first answer ! I have attached two files, one done with the optimization of two responses (but works for the three responses), and the other done for the three responses : https://community.jmp.com/t5/Discussions/Problem-to-find-optimal-settings-for-a-mixture-with-Bayesia...