		@@ -0,0 +1,12 @@
	1	+---
	2	+issue: 2
	3	+status: working
	4	+tags: search
	5	+---
	6	+# or-opt
	7	+
	8	+2-opt and Or-opt in turn: Or-opt moves a run of one to three cities to a better place in the tour.
	9	+
	10	+## Next
	11	+
	12	+Try restarts from random tours, or 3-opt moves.

+1 −0 routes/or-opt/metrics.json added View file

		@@ -0,0 +1 @@
	1	+{"score": 0.85, "cost": 1.9}

+52 −0 routes/or-opt/solve.py added View file

		@@ -0,0 +1,52 @@
	1	+"""2-opt and Or-opt in turn, until neither shortens the tour. Or-opt moves a run of one to three cities, either way
	2	+round, to the place in the tour where it adds the least."""
	3	+import json
	4	+import math
	5	+import sys
	6	+
	7	+p = json.load(sys.stdin)
	8	+n = len(p)
	9	+
	10	+
	11	+def d(i, j):
	12	+ return math.dist(p[i], p[j])
	13	+
	14	+
	15	+def two_opt(t):
	16	+ moved, better = False, True
	17	+ while better:
	18	+ better = False
	19	+ for i in range(1, n - 1):
	20	+ for j in range(i + 1, n):
	21	+ a, b, c, e = t[i - 1], t[i], t[j], t[(j + 1) % n]
	22	+ if d(a, c) + d(b, e) < d(a, b) + d(c, e) - 1e-12:
	23	+ t[i:j + 1] = reversed(t[i:j + 1])
	24	+ better = moved = True
	25	+ return moved
	26	+
	27	+
	28	+def or_opt(t):
	29	+ for k in (1, 2, 3):
	30	+ for i in range(1, n - k):
	31	+ run = t[i:i + k]
	32	+ a, b = t[i - 1], t[(i + k) % n]
	33	+ saved = d(a, run[0]) + d(run[-1], b) - d(a, b)
	34	+ rest = t[:i] + t[i + k:]
	35	+ for j in range(1, len(rest) + 1):
	36	+ x, y = rest[j - 1], rest[j % len(rest)]
	37	+ for r in (run, run[::-1]):
	38	+ if d(x, r[0]) + d(r[-1], y) - d(x, y) < saved - 1e-12:
	39	+ t[:] = rest[:j] + r + rest[j:]
	40	+ return True
	41	+ return False
	42	+
	43	+
	44	+left, tour = set(range(1, n)), [0]
	45	+while left:
	46	+ nxt = min(left, key=lambda j: d(tour[-1], j))
	47	+ left.remove(nxt)
	48	+ tour.append(nxt)
	49	+two_opt(tour)
	50	+while or_opt(tour):
	51	+ two_opt(tour)
	52	+print(json.dumps(tour))