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  1.                                                       TIME      TOUR   PERCENT
  2.                                              TOUR   IN TICKS  IMPROVED  FROM
  3.                                             LENGTH (.055 SEC)    BY    OPTIMUM
  4.                                             ──────   ──────   ──────   ──────
  5. 10 Cities   Optimum = 378           N.N.  |    417 |      1 |    ─── |   10.3 |
  6.    Karg and Thompson (6)            P─Opt |    395 |      2 |     22 |    4.5 |
  7.                                     2─Opt |    381 |      1 |     36 |    0.8 |
  8.    Input in 10 ticks.               Hybrid|    378 |      5 |     39 | OPTIMAL|
  9.                                     3─Opt |    378 |      6 |     39 | OPTIMAL|
  10.                                           |        |        |        |        |
  11.                                     Rev.  |    417 |      1 |    ─── |   10.3 |
  12.                                     P─Opt |    378 |      4 |     39 | OPTIMAL|
  13.                                     2─Opt |    381 |      2 |     36 |    0.8 |
  14.                                     Hybrid|    378 |      4 |     39 | OPTIMAL|
  15.                                     3─Opt |    381 |      6 |     36 |    0.8 |
  16.                                           |        |        |        |        |
  17.                                     F.N.  |    582 |      2 |    ─── |   54.0 |
  18.                                     P─Opt |    395 |      2 |    187 |    4.5 |
  19.                                     2─Opt |    381 |      2 |    201 |    0.8 |
  20.                                     Hybrid|    378 |      3 |    204 | OPTIMAL|
  21.                                     3─Opt |    387 |     12 |    195 |    2.4 |
  22.                                           |        |        |        |        |
  23. 20 Cities   Optimum = 246           N.N.  |    367 |      7 |    ─── |   49.2 |
  24.    G.A. Croes                       P─Opt |    313 |     13 |     54 |   27.2 |
  25.    Found in Roberts and Flores (9)  2─Opt |    246 |     16 |    121 | OPTIMAL|
  26.                                     Hybrid|    255 |     23 |    112 |    3.7 |
  27.    Input in 36 ticks.               3─Opt |    246 |    260 |    121 | OPTIMAL|
  28.                                           |        |        |        |        |
  29.                                     Rev.  |    367 |      7 |    ─── |   49.2 |
  30.                                     P─Opt |    304 |     13 |     63 |   23.6 |
  31.                                     2─Opt |    267 |      7 |    100 |    8.5 |
  32.                                     Hybrid|    265 |     28 |    102 |    7.7 |
  33.                                     3─Opt |    258 |    148 |    109 |    4.9 |
  34.                                           |        |        |        |        |
  35.                                     F.N.  |   1668 |      7 |    ─── |  578.0 |
  36.                                     P─Opt |    306 |     27 |   1362 |   24.4 |
  37.                                     2─Opt |    276 |     14 |   1392 |   12.2 |
  38.                                     Hybrid|    260 |     40 |   1408 |    5.7 |
  39.                                     3─Opt |    246 |    140 |   1422 | OPTIMAL|
  40.                                           |        |        |        |        |
  41. 25 Cities   Optimum = 1,711         N.N.  |   2037 |     11 |    ─── |   19.1 |
  42.    Held and Karp (5)                P─Opt |   1873 |     24 |    164 |    9.5 |
  43.                                     2─Opt |   1711 |     19 |    326 | OPTIMAL|
  44.    Input in 58 ticks.               Hybrid|   1736 |     33 |    301 |    1.5 |
  45.                                     3─Opt |   1763 |    293 |    274 |    3.0 |
  46.                                           |        |        |        |        |
  47.                                     Rev.  |   2037 |     11 |    ─── |   19.1 |
  48.                                     P─Opt |   1763 |     36 |    274 |    3.0 |
  49.                                     2─Opt |   1711 |     18 |    326 | OPTIMAL|
  50.                                     Hybrid|   1748 |     35 |    289 |    2.2 |
  51.                                     3─Opt |   1719 |    300 |    318 |    0.5 |
  52.                                           |        |        |        |        |
  53.                                     F.N.  |   6445 |     12 |    ─── |  276.7 |
  54.                                     P─Opt |   1940 |     26 |   4505 |   13.4 |
  55.                                     2─Opt |   1719 |     24 |   4726 |    0.5 |
  56.                                     Hybrid|   1886 |     45 |   4559 |   10.2 |
  57.                                     3─Opt |   1780 |    394 |   4665 |    4.0 |
  58.  
  59.  
  60.  
  61.                                                       TIME      TOUR   PERCENT
  62.                                              TOUR   IN TICKS  IMPROVED  FROM
  63.                                             LENGTH (.055 SEC)    BY    OPTIMUM
  64.                                             ──────   ──────   ──────   ──────
  65. 33 Cities   Optimum = 10,861        N.N.  |  11994 |     20 |    ─── |   10.4 |
  66.    Karg and Thompson (6)            P─Opt |  10929 |     56 |   1065 |    0.6 |
  67.                                     2─Opt |  11231 |     25 |    763 |    3.4 |
  68.    Input in 107 ticks.              Hybrid|  10861 |     62 |   1133 | OPTIMAL|
  69.                                     3─Opt |  11015 |    755 |    979 |    1.4 |
  70.                                           |        |        |        |        |
  71.                                     Rev.  |  11994 |     20 |    ─── |   10.4 |
  72.                                     P─Opt |  10929 |     61 |   1065 |    0.6 |
  73.                                     2─Opt |  11271 |     20 |    723 |    3.8 |
  74.                                     Hybrid|  10929 |     63 |   1065 |    0.6 |
  75.                                     3─Opt |  11158 |    935 |    836 |    2.7 |
  76.                                           |        |        |        |        |
  77.                                     F.N.  |  62166 |     19 |    ─── |  472.4 |
  78.                                     P─Opt |  13466 |     82 |  48700 |   24.0 |
  79.                                     2─Opt |  11182 |     35 |  50984 |    3.0 |
  80.                                     Hybrid|  11142 |     81 |  51024 |    2.6 |
  81.                                     3─Opt |  10894 |   1514 |  51272 |    0.3 |
  82.                                           |        |        |        |        |
  83. 42 Cities   Optimum = 699           N.N.  |    956 |     31 |    ─── |   36.7 |
  84.    Dantzig, Fulkerson, and Johnson  P─Opt |    780 |    116 |    176 |   11.6 |
  85.    Found in Karg and Thompson (6)   2─Opt |    737 |     44 |    219 |    5.4 |
  86.                                     Hybrid|    709 |    105 |    247 |    1.4 |
  87.    Input in 153 ticks.              3─Opt |    712 |   2440 |    244 |    1.9 |
  88.                                           |        |        |        |        |
  89.                                     Rev.  |    956 |     31 |    ─── |   36.7 |
  90.                                     P─Opt |    742 |    113 |    214 |    6.2 |
  91.                                     2─Opt |    738 |     49 |    218 |    5.6 |
  92.                                     Hybrid|    731 |    149 |    225 |    4.6 |
  93.                                     3─Opt |    719 |   2409 |    237 |    2.9 |
  94.                                           |        |        |        |        |
  95.                                     F.N.  |   4193 |     31 |    ─── |  499.9 |
  96.                                     P─Opt |    772 |    149 |   3421 |   10.4 |
  97.                                     2─Opt |    724 |     74 |   3469 |    3.6 |
  98.                                     Hybrid|    704 |    134 |   3489 |    0.7 |
  99.                                     3─Opt |    752 |   3204 |   3441 |    7.6 |
  100.                                           |        |        |        |        |
  101. 48 Cities   Optimum = 11,461        N.N.  |  14241 |     41 |    ─── |   24.3 |
  102.    Held and Karp (5)                P─Opt |  11987 |     74 |   2254 |    4.6 |
  103.                                     2─Opt |  11872 |     58 |   2369 |    3.4 |
  104.    Input in 221 ticks.              Hybrid|  11569 |    141 |   2672 |    0.9 |
  105.