Some Local Moves

The k-OPT class of moves takes the tour and removes k edges from it, then reglues the pieces in some other way.

• 2-OPT: flips a half tour. Pretty fast, can get badly stuck.
• 3-OPT: shuffles thirds. Slower, less prone to sticking.

Picture...

Theoretically, even in metric TSPs, ratio between and in the worst case.

Furthermore, it can take moves to get there!

Good performance in practice, though.