Algorithm to maximize function of subsets Let's say I have a finite set S with, say, 1000 elements, and a function f on some subset of S. Suppose that f has no useful mathematical properties.

What algorithm is most relevant in finding the subset of S that maximizes f?
The algorithm that iterates through every $2^{1000}$ subsets.  Sorry, but stated like this, the answer is that there is no solution.

For every algorithm you come up with, I can come up with a subset $T \subseteq S$ such that $T$ is the last of all sets to be tested, and be the max of $f$.