Ant Colony optimisation for finding subsets with ~0 sum
Your problem is no harder and no easier than the approximate subset-sum problem.  There is a natural approach for your problem:


Find any subset that sums to something close to zero, and output it.  Remove those numbers from the set $A$.
Go back to step 1 and repeat, until the set $A$ is empty.


This requires a way to find a subset that sums to approximately zero, i.e., an approximation algorithm for the subset-sum problem.  That problem is well-studied and can be solved in polynomial time using an approach based on rounding and dynamic programming.

I don't see any reason to expect ant colony programming to be better than the standard approaches; and I wouldn't be surprised if it is worse.