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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.                    Figure 2. ─ 10, 20, and 25 City Results.
  59.