topic Re: mixture experiment and cost function in Discussions

mixture experiment and cost function

MarkovVaribles1 — Wed, 16 Oct 2024 18:11:29 GMT

Hello,

I have a mixture data with ingredients I_1, I_2, ... I_9. They add up to 1 as this is a mixture data. The response is y. Of the 9 ingredients 6 of them have cost associated with them, say I_1 - I_6. I creates a new column: C = p1*I_1 + p2*I_2 + ... + p6*I_6. This gives the total cost per unit weight. Now I run a mixture response surface model for y. But when I go to optimize it, I like to take into account the cost column C and find the optimal solution while also minimizing the cost C.

How would I do this?

Thanks,

Re: mixture experiment and cost function

Mark_Bailey — Wed, 16 Oct 2024 18:39:08 GMT

Save the prediction formula for the fitted model. Select Graph > Profiler and select the model and cost formula columns. Now they both appear in the profiler for joint optimization.

Re: mixture experiment and cost function

MarkovVaribles1 — Thu, 17 Oct 2024 06:07:41 GMT

Thank you very much Mark!

Re: mixture experiment and cost function

MarkovVaribles1 — Thu, 17 Oct 2024 11:54:37 GMT

I have a question regarding the joint optimization as instructed in this post.

1. what if we have 10 responses that need to be jointly optimized? Can JMP handle this?

2. The reason for question 1, is that when I run 6 optimize 6 responses jointly using Graph > Profiler, the values of some responses are grossly out of the range as specified in Column Property > Response Limit. For example when one response has limit (47, 52) the optimized value is 15298 while in other cases the value is negative which is not acceptable at all.

Thanks,

Re: mixture experiment and cost function

Mark_Bailey — Thu, 17 Oct 2024 15:47:06 GMT

1. Yes.

2. The Response Limits column property defines the desirability of the response. It does not constrain the optimization; it guides it. If the response with a desirable range of (47,52) aims to maximize the response, the solution can exceed 52. Sometimes, the unexpected range of the response is because the linear regression model assumes that the response can range from negative infinity to positive infinity without constraint. Is your example of (47,52) a case where you want to match a target?

Re: mixture experiment and cost function

MarkovVaribles1 — Fri, 18 Oct 2024 15:41:03 GMT

Yes that is correct. here is an example of one response:

I do the same for other responses with their own limits. But when I click on maximize desirability, I get negative values for some of the response for the choice of the ingredients settings. some other responses become extreme positive.

Re: mixture experiment and cost function

Mark_Bailey — Fri, 18 Oct 2024 17:24:01 GMT

First, I recommend establishing the Lower and Upper Desirability values using the Goal drop-down menu. This is a quirk of the Profiler. It would be best not to change them to 0 or 1. Doing so can defeat the internal algorithm that optimizes the factor settings. It is OK to change the Middle value if the target is not centered in the interval.

Your example of a response with a goal of matching a target is helpful. These values are a goal. They are not guaranteed. When you have multiple responses, the optimization may not be able to achieve the goal for every response.

You changed the Importance value from the default of 1. This value can be helpful to emphasize one or more responses. The joint desirability uses this value as a power in the product of the individual desirabilities, so a large number is unnecessary. A large number might allow a single response to hijack the optimization.

As to the unrealistic high predictions, that is a matter of the model that you fit and the fact that the response limits do not actually limit the range of the response here. A linear regression model assumes that the response can range from negative to positive infinity. Setting a goal of maximizing and a range of (lower, upper) means that the high limit is good enough if another response can be satisfied, but otherwise, it does not limit the response.

With your domain expertise, you might be able to manually adjust one or more factor settings to bring such a response down to a reasonable level. You can then lock this factor so that JMP may not change it during optimization. This approach forces JMP to only use the unlocked factors during optimization.

Re: mixture experiment and cost function

MarkovVaribles1 — Mon, 21 Oct 2024 07:06:44 GMT

Thank you so much!

Re: mixture experiment and cost function

MarkovVaribles1 — Tue, 22 Oct 2024 15:57:06 GMT

Hi Mark,

In regards to the discussion of mixture modeling, I am having hard time with JMP's consistency!

The attached table is what I am using. The attached model is the mixture response surface after step-wise selection. You will notice the profiler looks unreasonable, and way out of bound. Each component has it's own limits. I am hoping I am doing something wrong and easily fixed.

In advance I appreciate your assistance.

Re: mixture experiment and cost function

Mark_Bailey — Tue, 22 Oct 2024 17:09:23 GMT

I have not seen this behavior before. I recommend sending your problem to JMP Technical Support (support@jmp.com) for resolution. Please report any solution they can give you here.

Re: mixture experiment and cost function

statman — Tue, 22 Oct 2024 20:21:21 GMT

Sorry to interrupt the discussion, but why are you using stepwise for a mixture design? You should have a model in mind á priori. All analysis are contingent on the model. If you change what is or is not in the model, the analysis will change.

Re: mixture experiment and cost function

Dan_Obermiller — Wed, 23 Oct 2024 00:19:09 GMT

I noticed that not every row in the data table added to 1. They are close, but not exact. I am wondering if this is causing the issues that you see. For example, the column properties have X1 ranging from 0.3 to 0.7. But the actual ranges are from approximately 0.32 to 0.73489.

These differences might seem small, but I do wonder if it is causing some of the issues that you are finding. If a row does not add to 1, then JMP will automatically rescale the values so that they do (I believe that is what is happening now). Therefore the ranges may be different than what you provided.