How can I find the Pareto optimal boundary for three sets of data?

How can I find the Pareto optimal boundary for three sets of data that are not functions and just values? Every data set (matrix) has 3500 rows and one column. I do have the 3D scatter plot and want to see the Pareto optimal boundary (surface) on either the same scatter plot or a different plot.

Thank you!!

Answer 1

[Alan Weiss]

I am not sure of the most efficient way to do this. However, in principle all you need to do is to compare the 3-D values pairwise, and eliminate every point that is not a Pareto optimum. I mean, if point A has components A1, A2, and A3, and point B has components B1, B2, and B3, and A1 <= B1, A2 <= B2, and A3 <= B3, then for a minimizing problem you can eliminate point B. After doing this you have the 3-D points that are not eliminated, and you can use any plotting technique that you want to visualize them.

Alan Weiss

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