Add spaceship solutions based on LKH-based reordering

scripts/spaceship_reorder_by_tsp_lkh.py

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+# Install [LKH-3](http://webhotel4.ruc.dk/~keld/research/LKH-3/)
+# This script uses "./LKH-3.0.10/LKH".
+
+import argparse
+import math
+import subprocess
+
+
+def reorder(points):
+    par_filename = "spaceship_tsp.tmp.par"
+    tsp_filename = "spaceship_tsp.tmp.tsp"
+    out_filename = "spaceship_tsp.tmp.out"
+
+    nodes = [(0, 0)] + points + [None, None]
+    dim = len(nodes)
+    start_node_id = 0  # 始点
+    sink_node_id = dim - 2  # 終点
+    dummy_node_id = dim - 1  # 終点と始点を繋いでサイクルにするためのダミーのノード
+
+    def dist(i, j):
+        # ダミーのノードは始点と終点にはコスト0で繋がっているが他には繋がっていない
+        if i == dummy_node_id:
+            if j == start_node_id or j == sink_node_id:
+                return 0
+            else:
+                return None
+        if j == dummy_node_id:
+            if i == start_node_id or i == sink_node_id:
+                return 0
+            else:
+                return None
+        # 終点は始点とダミー以外の全てのノードにコスト0で繋がっている
+        if i == sink_node_id:
+            if j == start_node_id:
+                return None
+            else:
+                return 0
+        if j == sink_node_id:
+            if i == start_node_id:
+                return None
+            else:
+                return 0
+
+        p1 = nodes[i]
+        p2 = nodes[j]
+        return math.sqrt((p1[0] - p2[0]) ** 2 + (p1[1] - p2[1]) ** 2)
+
+    edge_weights = [[dist(i, j) for j in range(i)] for i in range(len(nodes))]
+
+    precision = 100
+    int_max = 2**31
+
+    # LKH は重みは整数である必要があり、
+    # また w <= <= int_max // 2 // precision を満たす必要があるので、
+    # 適当にスケーリング。
+    #
+    # 後述の inf と他の値に差が出るように 10 倍だけ余裕を持っておく
+    max_w = max(w for ws in edge_weights for w in ws if w is not None)
+    s = 1
+    if round(10 * s * max_w) <= int_max // 2 // precision // 10:
+        while round(10 * s * max_w) <= int_max // 2 // precision // 10:
+            s *= 10
+    else:
+        while round(10 * s * max_w) > int_max // 2 // precision // 10:
+            s /= 10
+    edge_weights = [
+        [None if w is None else round(s * w) for w in ws] for ws in edge_weights
+    ]
+    for ws in edge_weights:
+        for w in ws:
+            if w is not None:
+                assert w <= int_max // 2 // precision // 10
+
+    # EDGE_DATA_FORMAT を指定するとうまくいかないので、
+    # その代わりにエッジがない場所には大きな値を入れておく。
+    inf = int_max // 2 // precision
+
+    with open(tsp_filename, "w") as f:
+        print("NAME: hoge", file=f)
+        print("TYPE: TSP", file=f)
+        print(f"DIMENSION: {dim}", file=f)
+        print(f"EDGE_WEIGHT_TYPE: EXPLICIT", file=f)
+        print(f"EDGE_WEIGHT_FORMAT: LOWER_ROW", file=f)
+        # print("EDGE_DATA_FORMAT: ADJ_LIST", file=f)
+        # print("EDGE_DATA_SECTION:", file=f)
+        # for i, ws in enumerate(edge_weights):
+        #     print(' '.join(map(str, [i+1] + [j+1 for (j, w) in enumerate(ws) if w is not None] + [-1])), file=f)
+        # print(f"-1", file=f)
+        print(f"EDGE_WEIGHT_SECTION:", file=f)
+        for ws in edge_weights:
+            print(" ".join(map(str, [inf if w is None else w for w in ws])), file=f)
+        print(f"EOF", file=f)
+
+    with open(par_filename, "w") as f:
+        print(f"PROBLEM_FILE = {tsp_filename}", file=f)
+        print(f"OUTPUT_TOUR_FILE = {out_filename}", file=f)
+        print("MOVE_TYPE = 5", file=f)
+        print("PATCHING_C = 3", file=f)
+        print("PATCHING_A = 2", file=f)
+        print("RUNS = 10", file=f)
+
+    subprocess.run(
+        [
+            "./LKH-3.0.10/LKH",
+            par_filename,
+        ],
+        text=True,
+        check=True,
+    )
+
+    tour = []
+    in_tour_section = False
+    with open(out_filename) as f:
+        for line in f:
+            if in_tour_section:
+                if int(line) == -1:
+                    break
+                else:
+                    tour.append(int(line))
+            elif line.startswith("TOUR_SECTION"):
+                in_tour_section = True
+    assert len(tour) == dim
+
+    # 1-origin to 0-origin
+    tour = [i - 1 for i in tour]
+
+    start_node_index = tour.index(start_node_id)
+    tour = tour[start_node_index:] + tour[:start_node_index]
+    assert tour[0] == start_node_id
+
+    if tour[-1] == dummy_node_id:
+        assert tour[-2] == sink_node_id
+        tour.pop()
+        tour.pop()
+    elif tour[1] == dummy_node_id:
+        assert tour[2] == sink_node_id
+        tour = [start_node_id] + list(reversed(tour[3:]))
+    else:
+        assert False
+
+    return [points[i - 1] for i in tour[1:]]
+
+
+parser = argparse.ArgumentParser()
+parser.add_argument("file", type=str, metavar="FILE", help="spaceship problem file")
+parser.add_argument(
+    "--output", "-o", type=str, metavar="FILE", required=True, help="output png file"
+)
+args = parser.parse_args()
+
+points = []
+with open(args.file) as f:
+    for line in f:
+        x, y = line.split()
+        points.append((int(x), int(y)))
+
+points2 = reorder(points)
+with open(args.output, "w") as f:
+    for p in points2:
+        print(f"{p[0]} {p[1]}", file=f)

solutions/spaceship1/prob_reordered_by_tsp_lkh

@@ -0,0 +1,5 @@
+1 -1
+1 -3
+2 -5
+2 -8
+3 -10

solutions/spaceship1/sol_reordered_by_tsp_lkh.txt

@@ -0,0 +1 @@
+34826725582672

solutions/spaceship10/prob_reordered_by_tsp_lkh

@@ -0,0 +1,100 @@
+1 -2
+2 -8
+3 -16
+-3 -22
+-9 -22
+-8 -27
+-9 -33
+-9 -38
+-13 -43
+-24 -43
+-31 -50
+-38 -56
+-41 -60
+-50 -60
+-56 -70
+-67 -73
+-74 -79
+-86 -91
+-95 -97
+-109 -112
+-127 -122
+-139 -130
+-156 -139
+-169 -146
+-189 -153
+-210 -167
+-227 -171
+-246 -179
+-262 -190
+-281 -204
+-298 -219
+-316 -229
+-335 -243
+-353 -257
+-373 -265
+-394 -277
+-421 -293
+-442 -300
+-469 -317
+-497 -328
+-521 -340
+-546 -350
+-570 -361
+-592 -369
+-615 -377
+-631 -388
+-661 -403
+-684 -405
+-705 -420
+-727 -429
+-755 -440
+-780 -452
+-805 -459
+-831 -470
+-854 -478
+-870 -482
+-890 -495
+-905 -501
+-921 -514
+-938 -528
+-948 -542
+-963 -549
+-975 -562
+-990 -572
+-1000 -579
+-1014 -590
+-1018 -598
+-1030 -605
+-1038 -606
+-1048 -609
+-1055 -607
+-1060 -606
+-1069 -610
+-1078 -603
+-1084 -603
+-1090 -604
+-1095 -602
+-1096 -604
+-1101 -600
+-1106 -603
+-1107 -600
+-1114 -598
+-1113 -596
+-1106 -587
+-1109 -580
+-1112 -574
+-1117 -568
+-1119 -562
+-1128 -560
+-1134 -560
+-1145 -551
+-1157 -548
+-1171 -544
+-1189 -535
+-1201 -535
+-1212 -537
+-1228 -536
+-1242 -531
+-1258 -522
+-1272 -526

solutions/spaceship10/sol_reordered_by_tsp_lkh.txt

@@ -0,0 +1 @@
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