Minimum number of swaps in sorting sequence
This problem is known as "sorting strings by interchanges". Amir et al [1] proved that the problem is NP-complete and admits a 1.5-approximation. They also obtain other results for transforming two strings into one another (which is not equivalent to the sorting problem) and using several other cost functions for each transformation.

[1]: Amihood Amir, Tzvika Hartman, Oren Kapah, Avivit Levy, Ely Porat:
On the Cost of Interchange Rearrangement in Strings. SIAM J. Comput. 39(4): 1444-1461 (2009) -- https://epubs.siam.org/doi/10.1137/080712969