Research Article
Dynamic Reduction-Expansion Operator to Improve Performance of Genetic Algorithms for the Traveling Salesman Problem
Table 1
Results on main set of 41 TSP instances: errors on assessment scenarios.
| | TSP Library | Instance | Size | Optimal Value | TSP Distance Values of Solutions Obtained with the Genetic Algorithm (GA) | Error Values E=[(GA-optimal)/optimal]×100% | Minimum Error | | | RedExp | _ | _RedExp | _RedExp | | | RedExp | _ | _RedExp | _RedExp |
| | TSPLIB95 | a280 | 280 | 2579.0 | 3063.3 | 2736.0 | 2709.9 | 2769.9 | 2910.3 | 2711.6 | 18.8 | 6.1 | 5.1 | 7.4 | 12.8 | 5.1 | 5.1 | | | berlin52 | 52 | 7542.0 | 8105.2 | 7850.8 | 7841.4 | 8000.8 | 7959.6 | 7850.8 | 7.5 | 4.1 | 4.0 | 6.1 | 5.5 | 4.1 | 4.0 | | | bier127 | 127 | 118282.0 | 126507.8 | 123003.7 | 121705.6 | 123034.1 | 122001.9 | 121312.1 | 7.0 | 4.0 | 2.9 | 4.0 | 3.1 | 2.6 | 2.6 | | | ch150 | 150 | 6528.0 | 7268.4 | 6842.4 | 6708.3 | 6746.0 | 6786.2 | 6783.0 | 11.3 | 4.8 | 2.8 | 3.3 | 4.0 | 3.9 | 2.8 | | | d198 | 198 | 15780.0 | 16996.7 | 17019.6 | 16086.1 | 17111.6 | 16227.2 | 16990.3 | 7.7 | 7.9 | 1.9 | 8.4 | 2.8 | 7.7 | 1.9 | | | d493 | 493 | 35002.0 | 38900.8 | 37190.3 | 36609.2 | 36807.4 | 36581.6 | 36749.3 | 11.1 | 6.3 | 4.6 | 5.2 | 4.5 | 5.0 | 4.5 | | | d657 | 657 | 48912.0 | 55426.9 | 52830.9 | 51372.5 | 52469.4 | 52094.2 | 52395.7 | 13.3 | 8.0 | 5.0 | 7.3 | 6.5 | 7.1 | 5.0 | | | dsj1000 | 1000 | 18659688.0 | 20991643.2 | 20760980.1 | 20454938.6 | 20923295.9 | 20545095.0 | 20156541.3 | 12.5 | 11.3 | 9.6 | 12.1 | 10.1 | 8.0 | 8.0 | | | eil51 | 51 | 426.0 | 454.4 | 437.4 | 435.4 | 438.3 | 437.4 | 439.7 | 6.7 | 2.7 | 2.2 | 2.9 | 2.7 | 3.2 | 2.2 | | | eil76 | 76 | 538.0 | 582.7 | 591.2 | 556.7 | 571.6 | 580.2 | 564.7 | 8.3 | 9.9 | 3.5 | 6.2 | 7.8 | 5.0 | 3.5 | | | fl417 | 417 | 11861.0 | 12764.2 | 13015.7 | 12874.6 | 12796.3 | 12809.8 | 12651.8 | 7.6 | 9.7 | 8.5 | 7.9 | 8.0 | 6.7 | 6.7 | | | gil262 | 262 | 2378.0 | 2616.3 | 2589.0 | 2539.3 | 2527.5 | 2493.4 | 2503.0 | 10.0 | 8.9 | 6.8 | 6.3 | 4.9 | 5.3 | 4.9 | | | kroB100 | 100 | 22141.0 | 24484.7 | 22437.5 | 22896.9 | 22496.7 | 22971.3 | 22399.5 | 10.6 | 1.3 | 3.4 | 1.6 | 3.8 | 1.2 | 1.2 | | | kroC100 | 100 | 20749.0 | 22221.5 | 22144.8 | 22093.7 | 21913.6 | 22531.1 | 21883.5 | 7.1 | 6.7 | 6.5 | 5.6 | 8.6 | 5.5 | 5.5 | | | kroD100 | 100 | 21294.0 | 23996.3 | 23030.8 | 22298.0 | 22719.1 | 22255.6 | 21903.7 | 12.7 | 8.2 | 4.7 | 6.7 | 4.5 | 2.9 | 2.9 | | kroA150 | 150 | 26524.0 | 28772.8 | 29162.2 | 27208.4 | 28820.5 | 29100.3 | 27748.1 | 8.5 | 9.9 | 2.6 | 8.7 | 9.7 | 4.6 | 2.6 | | kroB150 | 150 | 26130.0 | 29195.1 | 27739.2 | 27178.0 | 27593.8 | 27412.4 | 27464.8 | 11.7 | 6.2 | 4.0 | 5.6 | 4.9 | 5.1 | 4.0 | | kroA200 | 200 | 29368.0 | 32293.2 | 29968.2 | 29790.0 | 29920.6 | 30537.1 | 30035.5 | 10.0 | 2.0 | 1.4 | 1.9 | 4.0 | 2.3 | 1.4 | | kroB200 | 200 | 29437.0 | 32004.6 | 31324.0 | 31348.9 | 32099.6 | 31124.8 | 30900.6 | 8.7 | 6.4 | 6.5 | 9.0 | 5.7 | 5.0 | 5.0 | | lin105 | 105 | 14379.0 | 15108.6 | 14930.6 | 14633.7 | 15029.9 | 14643.5 | 14578.2 | 5.1 | 3.8 | 1.8 | 4.5 | 1.8 | 1.4 | 1.4 | | lin318 | 318 | 42029.0 | 47687.1 | 44509.1 | 43973.7 | 46097.5 | 45226.4 | 44504.0 | 13.5 | 5.9 | 4.6 | 9.7 | 7.6 | 5.9 | 4.6 | | nrw1379 | 1379 | 56638.0 | 64651.8 | 61695.0 | 61192.2 | 61373.3 | 61211.2 | 61340.3 | 14.1 | 8.9 | 8.0 | 8.4 | 8.1 | 8.3 | 8.0 | | | pcb1173 | 1173 | 56892.0 | 67114.3 | 62582.5 | 62004.2 | 62532.9 | 61903.0 | 61824.0 | 18.0 | 10.0 | 9.0 | 9.9 | 8.8 | 8.7 | 8.7 | | | pr107 | 107 | 44303.0 | 49850.8 | 45179.0 | 45123.2 | 45512.6 | 45318.3 | 45033.2 | 12.5 | 2.0 | 1.9 | 2.7 | 2.3 | 1.6 | 1.6 | | | pr124 | 124 | 59030.0 | 61408.4 | 61554.7 | 60595.2 | 61329.9 | 61281.3 | 60300.7 | 4.0 | 4.3 | 2.7 | 3.9 | 3.8 | 2.2 | 2.2 | | | pr136 | 136 | 96772.0 | 103518.4 | 105707.1 | 104396.2 | 103833.5 | 103417.9 | 104568.2 | 7.0 | 9.2 | 7.9 | 7.3 | 6.9 | 8.1 | 6.9 | | | pr264 | 264 | 49135.0 | 54992.3 | 53304.4 | 52560.5 | 52336.5 | 51673.2 | 53139.5 | 11.9 | 8.5 | 7.0 | 6.5 | 5.2 | 8.1 | 5.2 | | | pr439 | 439 | 107217.0 | 121892.8 | 114895.1 | 113016.7 | 116812.5 | 116505.1 | 115850.4 | 13.7 | 7.2 | 5.4 | 8.9 | 8.7 | 8.1 | 5.4 | | | pr1002 | 1002 | 259045.0 | 296309.0 | 282091.6 | 280868.3 | 280048.9 | 278721.5 | 276725.7 | 14.4 | 8.9 | 8.4 | 8.1 | 7.6 | 6.8 | 6.8 | | | rat195 | 195 | 2323.0 | 2638.2 | 2424.7 | 2405.9 | 2448.1 | 2409.4 | 2393.4 | 13.6 | 4.4 | 3.6 | 5.4 | 3.7 | 3.0 | 3.0 | | | rat575 | 575 | 6773.0 | 7606.9 | 7315.9 | 7178.1 | 7255.8 | 7264.9 | 7316.1 | 12.3 | 8.0 | 6.0 | 7.1 | 7.3 | 8.0 | 6.0 | | | rat783 | 783 | 8806.0 | 10285.2 | 9644.8 | 9510.9 | 9547.1 | 9507.9 | 9457.4 | 16.8 | 9.5 | 8.0 | 8.4 | 8.0 | 7.4 | 7.4 | | | st70 | 70 | 675.0 | 739.3 | 688.1 | 682.6 | 688.1 | 678.1 | 678.4 | 9.5 | 1.9 | 1.1 | 1.9 | 0.5 | 0.5 | 0.5 | | | u724 | 724 | 41910.0 | 47136.2 | 44735.9 | 44448.6 | 44490.1 | 44644.2 | 44892.4 | 12.5 | 6.7 | 6.1 | 6.2 | 6.5 | 7.1 | 6.1 | | | u1432 | 1432 | 152970.0 | 175842.4 | 166679.9 | 167534.6 | 165992.8 | 164462.7 | 166085.7 | 15.0 | 9.0 | 9.5 | 8.5 | 7.5 | 8.6 | 7.5 |
| | VLSITSP | dca1389 | 1389 | 5085.0 | 6125.2 | 5591.0 | 5670.7 | 5557.8 | 5608.9 | 5521.5 | 20.5 | 10.0 | 11.5 | 9.3 | 10.3 | 8.6 | 8.6 | | VLSITSP | dka1376 | 1376 | 4666.0 | 5467.6 | 5138.2 | 5121.5 | 5146.0 | 5124.6 | 5143.6 | 17.2 | 10.1 | 9.8 | 10.3 | 9.8 | 10.2 | 9.8 | | VLSITSP | pbm436 | 436 | 1443.0 | 1694.7 | 1536.2 | 1539.1 | 1547.3 | 1527.9 | 1561.0 | 17.4 | 6.5 | 6.7 | 7.2 | 5.9 | 8.2 | 5.9 |
| | NTSP | LU980 | 980 | 11340.0 | 12843.2 | 12180.7 | 12245.9 | 12281.0 | 12042.7 | 12146.6 | 13.3 | 7.4 | 8.0 | 8.3 | 6.2 | 7.1 | 6.2 | | NTSP | UY734 | 734 | 79114.0 | 91652.3 | 85269.0 | 84715.4 | 85487.5 | 86227.1 | 85230.5 | 15.8 | 7.8 | 7.1 | 8.1 | 9.0 | 7.7 | 7.1 | | NTSP | ZI929 | 929 | 95345.0 | 107284.6 | 103768.2 | 102227.8 | 103170.9 | 102125.1 | 101745.0 | 12.5 | 8.8 | 7.2 | 8.2 | 7.1 | 6.7 | 6.7 |
| | | | | | | | | | Average Errors = | 11.7 | 6.9 | 5.5 | 6.7 | 6.3 | 5.7 | 4.9 |
|
|
