Decision making : which formula is closest to ideal

[#1]

I have a number of shortlisted formulas, all of them are in specifications. Now the challenge is to rank them and identify the best.

Each formula has about a dozen properties. So far I have tried TOPSIS ranking (Euclidean distance basis). It works somehow, but I believe there may be a better approach of decision makind with data.

Are there other methods you would recommend for ranking based on multiple properties ?

I would be happy to learn from your experience !

[#2]

Hi @RikkiTikkiTavi,

Ranking based on euclidian distances are a good idea. However, when you have competing responses/properties, there might be some tradeoffs to consider, and euclidian distances may "shrink" and hide these tradeoffs.

For this reason, I tend to prefer using Pareto front to detect optimal solutions/formulations based on different emphasis between responses/properties. There is no dedicated JMP platform, but there may be several options to do this:

• You can create a large candidate dataset thanks to the models fitted to the responses using the Simulator (Simulation Experiment) or by creating a large space filling design and adding the responses formula to your table. Then, you can Select Rows in Data Tables and choose the option Select Dominant . The resultant set of rows is called the Pareto Frontier.
• You can try to check if some responses/properties are not correlated with each others, to reduce the output space dimensionality. Then, using Principal Components analysis or non-linear dimension reduction techniques like Multivariate Embedding (UMAP), you can reduce your multivariate space in a 2D or 3Dimensional space. Plotting the formula in this reduced responses space really helps visualizing the best candidates and tradeoffs.
• You can also do the previous options but instead of using directly the responses, you can use the normalized euclidian distances to avoid that a response may have a too strong influence on the others, and check the correlations between the responses distances to optimum. If you can reduce the dimensionality, the visualization is again greatly facilitated:
  
  

Hope this other approach and few tricks may help you,

[#3]

Thank you @Victor_G ! I should probably clarify my problem because my 1st description was too general.

I have 11 shortlisted formulations, each formulation has 16 measured properties, this is the original data set. Important: all 11 formulations are already within their specification ranges. The goal is to rank the formulations according to how close their overall property profile is to an ideal profile. The ideal profile needs to be defined as well. I do not really see how Pareto could be applied in that case..

So for each property, I derived an Ideal Best and an Ideal Worst from the specification limits. For a property where higher is preferred, the upper reference is Best and the lower reference is Worst, for a property where lower is preferred, this is reversed.

I then transform every property onto the same scale: z = (x - Worst) / (Best - Worst), z  [0, 1]. 0 means performance at the Worst reference and 1 means performance at the Best reference.

After this normalization criterion weights (user defined) are applied and I calculate the weighted Euclidean distances to the Ideal Best profile (all z = 1) and the Ideal Worst profile (all z = 0). The final score is: Diw / (Dib + Diw).

Your comment about Euclidean distance hiding trade offs makes me think that maybe adding a "sensitivity analysis" for the criterion weights could help reveal important trade offs. For example I could vary weights within (user defined - 20%) and (user defined + 20%). Then check how much the ranking changes. Large changes in rank could indicate properties that need special attention

I also absolutely like your suggestions about reducing the output space dimensionality, the tools you listed are very useful :)

[#4 · Accepted solution]

Another option to compare the "overall" optimality of the 11 formula on the 16 measured properties could be to plot on a spider plot (or something similar) the different formula with each property being an axis (using your normalized scale from 0 to 1), and then calculating the area of each formula to see if the overall optimality is comparable or if there are differences among them.

Using weights looks similar to specifying different importances in desirability profiles: it can really help if the user has a fixed idea about which attribute matters and how much comparatively to other attributes, but if not, it can be difficult to evaluate which weights make sense to define for the different properties. I highly recommend reading "The attraction and limitations of desirability functions" (https://doi.org/10.1080/08982112.2026.2671710) by Christine Anderson Cook, as she describes really well the pros and cons of such situation. You can read it here: 264 - QE 2026 CACLL DFs.pdf - Google Drive

Hope this answer will help you,