I’m struggling with this problem where there’re families of features and each VC chooses one feature in every family (shown in the tables). enter image description here enter image description here

And the constraint is that we need 1000 VC in total. I’m trying to find how many VCs I need based on the ratio (scale) of the features. (By ratio I meant that every feature in a family adds up to 10, which means 100%). I first found how many features I need according to the info given, i.e. enter image description here

Then, I tried to solve this by finding the minimal deviation of all VCs that have the same features and that particular feature i.e. f_ij=x_a+x_b+…-F_ij

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I get a solution after running my program in python. But I don’t know if it’s the best solution since python only gives the solution that it finds first. I don’t know if there’re better ways to do this without listing out all the solutions.

Another problem that I’m facing right now is that there’s a ratio for the VCs as well. Like based on historical data, some VCs are more popular than others. So we want to optimize the scale of the VCs at the same time. I thought of putting weights into my functions but that would change the functions as a whole. The other way I thought of doing this is to repeat what I did before with the features. So far, I can’t find any other ways to solve the problem. Can anyone please help me with these 2 problems or give me some insights? Thank you so much in advance!!!