Research Article
An Improved Ant Colony Optimization Based on an Adaptive Heuristic Factor for the Traveling Salesman Problem
Table 1
Performance comparison among ACO, VTPSO, DSMO, and AHACO on TSPs.
| | SL | Instance | Best solution (deviation %) | | ACO | VTPSO | ABCSS | DSMO | AHACO |
| | 1 | burma14 | 31.21 (1.1) | 30.87 (0) | 30.87 (0) | 30.87 (0) | 30.87 (0) | | 2 | ulysses16 | 77.13 (4.24) | 73.99 (0) | 73.99 (0) | 73.99 (0) | 73.99 (0) | | 3 | ulysses22 | 84.78 (12.57) | 75.31 (0) | 75.31 (0) | 75.31 (0) | 75.31 (0) | | 4 | eil51 | 499.92 (16.57) | 429.51 (0.15) | 428.98 (0.03) | 428.86 (0) | 428.87 (0) | | 5 | berlin52 | 7870.45 (4.32) | 7544.37 (0) | 7544.37 (0) | 7544.37 (0) | 7544.37 (0) | | 6 | st70 | 734.19 (8.43) | 682.57 (0.81) | 682.57 (0.81) | 677.11 (0) | 677.11 (0) | | 7 | eil76 | 581.42 (6.61) | 559.25 (2.54) | 550.24 (0.89) | 558.68 (2.44) | 545.39 (0) | | 8 | pr76 | 127025.9 (17.44) | 109586.1 (1.32) | 108879.7 (0.67) | 108159.4 (0) | 108159 (0) | | 9 | gr96 | 563.77 (10.31) | 515.27 (0.82) | 512.2 (0.22) | 518.38 (1.43) | 511.06 (0) | | 10 | rat99 | 1366.3 (12.06) | 1256.25 (3.04) | 1242.32 (1.89) | 1225.56 (0.52) | 1219.24 (0) | | 11 | kroA100 | 24504.9 (15.13) | 21307.44 (0.1) | 21299 (0.06) | 21298.21 (0.06) | 21285.4 (0) | | 12 | kroB100 | 24664.13 (10.95) | 22475.67 (1.11) | 22229.71 (0) | 22308 (0.35) | 22234.5 (0.02) | | 13 | rd100 | 9120.92 (15.3) | 8094.75 (2.33) | 7944.32 (0.43) | 8041.3 (1.65) | 7910.39 (0) | | 14 | eil101 | 715.35 (11.22) | 653.16 (1.55) | 646.05 (0.45) | 648.66 (0.85) | 643.17 (0) | | 15 | lin105 | 15364.58 (6.82) | 14581.58 (1.38) | 14406.12 (0.16) | 14383 (0) | 14383 (0) | | 16 | pr107 | 46317.71 (4.37) | 44436.25 (0.13) | 44525.68 (0.33) | 44385.86 (0.02) | 44379.1 (0) | | 17 | pr124 | 65145.25 (10.36) | 61076.73 (3.47) | 59030.74 (0) | 60285.21 (2.13) | 59074.8 (0.07) | | 18 | pr136 | 110872.2 (14.39) | 99247.01 (2.4) | 97853.91 (0.96) | 97538.68 (0.63) | 96925.5 (0) | | 19 | gr137 | 896.07 (26.42) | 714.18 (0.76) | 713.91 (0.72) | 709.48 (0.1) | 708.79 (0) | | 20 | kroA150 | 30546.06 (14.12) | 27232.1 (1.74) | 26981.98 (0.81) | 27591.44 (3.09) | 26765.7 (0) | | 21 | kroB150 | 29124.59 (11.24) | 26579.73 (1.52) | 26760.79 (2.21) | 26601.94 (1.6) | 26175.4 (0) | | 22 | pr152 | 79153.02 (7.42) | 74414.17 (0.99) | 74337.62 (0.89) | 74243.91 (0.76) | 73683.6 (0) | | 23 | u159 | 47514.43 (12.93) | 43579.82 (3.57) | 42862.51 (1.87) | 42598.3 (1.24) | 42075.7 (0) | | 24 | rat195 | 2534.83 (8.09) | 2452.92 (4.6) | 2469.31 (5.3) | 2372.89 (1.19) | 2345.09 (0) | | 25 | d198 | 17301.47 (8.86) | 16066.44 (1.09) | 16270.22 (2.38) | 15978.13 (0.54) | 15892.6 (0) | | 26 | kroA200 | 34547.69 (17.27) | 30602.81 (3.88) | 30701.86 (4.22) | 30481.35 (3.47) | 29460 (0) | | 27 | kroB200 | 34207.79 (15.04) | 30767.52 (3.47) | 31508.85 (5.97) | 30716.5 (3.3) | 29734.7 (0) | | 28 | gr202 | 545.33 (11.36) | 497.02 (1.5) | 507.27 (3.59) | 501.83 (2.48) | 489.69 (0) | | 29 | tsp225 | 4396.39 (13.01) | 4095.01 (5.26) | 4140.24 (6.42) | 4013.68 (3.17) | 3890.32 (0) | | 30 | pr226 | 90501.46 (12.59) | 81050.23 (0.83) | 82266 (2.34) | 83587.98 (3.99) | 80382.5 (0) | | 31 | gr229 | 1865.63 (11.87) | 1676.46 (0.53) | 1713.54 (2.75) | 1683.45 (0.95) | 1667.62 (0) | | 32 | gil262 | 2730.52 (13.22) | 2547.16 (5.61) | 2713.75 (12.52) | 2543.15 (5.45) | 2406.84 (0) | | 33 | pr299 | 56700.65 (16.99) | 50571.83 (4.34) | 64464.76 (33.01) | 50579.82 (4.36) | 48466 (0) | | 34 | lin318 | 47442.95 (12.29) | 44724.38 (5.85) | 55744.52 (31.94) | 44118.66 (4.42) | 42250.7 (0) | | 35 | linhp318 | 47577.77 (12.61) | 44337.02 (4.94) | 56834.19 (34.52) | 43831.44 (3.74) | 42250.7 (0) | | 36 | fl417 | 13296.85 (10.47) | 12376.53 (2.82) | 22253.99 (84.89) | 12218.98 (1.52) | 12036.6 (0) | | 37 | gr431 | 2334.63 (17.76) | 2021.95 (1.99) | 3284.99 (65.7) | 1993.15 (0.54) | 1982.46 (0) | | 38 | pr439 | 127228 (17.05) | 112088 (3.12) | 206233.14 (89.74) | 112105.2 (3.14) | 108679 (0) | | 39 | d493 | 39254 (6.99) | 37132.09 (1.21) | 68556.68 (86.86) | 36844.63 (0.43) | 36440.6 (0) | | Optimal number/ratio | 0/0 | 4/10.26 | 6/15.38 | 7/17.95 | 36/92.31 | | Deviation/average | 459.79/11.79 | 80.77/2.07 | 485.55/12.45 | 59.56/1.53 | 0.09/0.002 |
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