Disclaimer As a quick disclaimer, I am approaching this problem from a programming point of view, since it is a practical problem I am trying to solve, and I do not have a background in Mathematics and may not formulate the problem in ideal terms, but I'll try.
Any help for tags for this question would be welcome too.
Problem I have a set of objects (which we can name $A, B, C,$ etc), and a matrix representing all combinations (same object pairs ($AA$ for example) are not available). For each combination there is a numerical score. Permutations do not matter: $AB$'s score = $BA$'s score, so the matrix is like a triangle in practice.
I am trying to figure out, how to make a subset, of a specified size, where the average of the score of all the pairs formed by that subset would be the highest possible.
The average score is important, because it would avoid situations where $AB$ has a very high score and $BC$ and $AC$ would have smaller ones.
To put in context, the score represent co-integration factors and I am trying to build a subset where the pairs in that subset would be as little co-integrated, with one another, as possible.
The set has a practical limit of $\approx 80-90$ elements, so an iterative solution is possible.
Since I do not know how to approach this problem, anything that points me toward the right direction would be helpful.