Branch & Bound: Avoiding equivalent solutions

Question

There is a certain family of typical branch & bound problems in which we have to put $n$ objects into $m$ indistinguishable bags.

Usually solutions are represented by $n$-size vectors in which $V[i]$ means that the $i$-th element is in the $V[i]$-th bag.

Is there a way to avoid generating equivalent solutions without performing an $\mathcal{O}(n)$ time check once the potentially equivalent solution has been built?

I was trying to do something similar as when avoiding circular permutations, but no adaptations seems to work.