Sorting: minimize number of swaps

In this post, I want to delve further into sorting. In a question on or.stackexchange.com [1], the subject was minimizing the number of swaps in sorting algorithms. A swap, i.e., an interchange of two items, is a basic operation in sorting. We usually don't pay much attention to this. First, we assume swaps are cheap. If they are not, we can sort not the real data (which can be complex, and thus more complicated and expensive to swap), but rather pointers to the data or keys. But what if we really have to reorder physical things? Then the number of swaps is a more meaningful thing. Can we minimize the work to reorder say \(n\) boxes (or containers to make it more dramatic) by minimizing the number of swaps (assuming interchanging the position of two boxes is the way reordering works).