Or-opt Local Search

Or-opt relocates segments of 1–3 consecutive cities to a better position elsewhere in the tour — a cut-and-paste move, unlike 2-opt's edge reversal. Each pass scans every segment size (Or-1, Or-2, Or-3) and every insertion point, applying the single best-improving relocation (reversed insertions are also tried for Or-2/Or-3). Repeats until no relocation improves the tour.