# Would an optimization version of the 3-partition problem also be strongly np-complete / np-hard?

Anyone know if an optimization variant of the 3-partition problem (as explained there) would also be strongly np-complete?

This would be where the goal is to group a multiset whose size is evenly divisible by 3 into triplets that sum to as close to a target as possible and to produce this grouping. This would not be a decision problem but an actual optimization problem.

The objective function $$f$$ (to minimize) is not completely formalized in the question. It is written that the groups should "sum to as close to a target as possible", so it seems natural to assume that $$f$$ is $$0$$ if the sum of the elements in each group is equal to the target, and greater than $$0$$ otherwise.
Under this assumptions, the above optimization problem is strongly NP-hard since the answer to the decision problem is "yes" if and only if an optimal solution $$S$$ to the optimization problem satisfies $$f(S)=0$$.