How would you quickly iterate over every combination of an array with 80 elements where each element is used a maximum of once in the combination? To make it faster, I've already determined the optimal solution will use at least 7 of the elements and no more than 25.

As others have pointed out, that's still an unfeasibly massive number of combinations. Perhaps a considered read through The 10**21 Problem (Part I) (and the subsequent parts) will prove instructive?