complexity of dividing set of number with constraints

I've been thinking about a division problem for groups that I haven't found a dynamic programming solution and I'm trying to analyze the complexity of the problem.

There is a set of $$n$$ positive numbers ($$S$$), a vector of group sizes (let's call it $$Sizes$$), and a parameter $$Y$$. Find a way for divide the $$n$$ numbers into groups that their size describes in $$Sizes$$ s.t. the $$constraint$$ in close as possible to $$Y$$.

For example, $$S = \{1,1,2,2,3,4,4,7,9,11\}$$, $$Sizes = [2,2,3,3]$$, $$Y=2$$ and $$constraint =$$ the variance of the group. Of course that the $$constraint$$ could be changed in other cases. But this is representative example.

Has this problem any dynamic programming solution? or that the complexity is exponential (which means $$NP$$ problem)?

Which approximation approaches can help me in this case?

For example if $$n=3k$$, $$\text{size}=[\underbrace{3,3,3,...}_{k\text{ times}}]$$, and the constraint is that the sum of the numbers each group must be equal, then your problem is strongly NP-hard since it is exactly $$3$$-partition.
The same problem with groups of size $$2$$ is polynomial.
Notice that both problems are in $$\mathsf{NP}$$ and that being in $$\mathsf{NP}$$ does not mean that the complexity to solve it is exponential.