my given problem is:

choose n-vectors from n-sets (one vector from each set) so that the biggest element in the sum of the chosen vectors is minimal. Unfortunately the problem is NP-hard. So I'm looking for a heuristic. However i don't know a name for that kind of problem so i couldn't find anything in literature.

Do you have any idea for a good heuristic solution?

Edit

The vectors can contain negative numbers, have the same size and are bounded