The Scientific World Journal / 2014 / Article / Tab 2

Research Article

Crossover versus Mutation: A Comparative Analysis of the Evolutionary Strategy of Genetic Algorithms Applied to Combinatorial Optimization Problems

Table 2

Results and runtimes of the nine techniques applied to the TSP. For each instance, the results, average runtime, and their standard deviations are shown.

TSP
Instance Results Time (s) Results Time (s) Results Time (s)
Instance Optimum Avg. St.d. Avg. St.d. Avg. St.d. Avg. St.d. Avg. St.d. Avg. St.d.

St70 675 711.1 25.5 8.9 2.3 714.4 18.3 4.6 1.3 705.0 13.9 1.5 0.5
Eilon75 535 574.7 11.8 12.2 3.1 580.9 14.0 7.5 2.2 570.1 10.9 2.2 0.6
Eil76 538 575.6 11.4 13.0 3.0 586.1 13.1 6.7 1.9 574.0 11.2 2.0 0.7
KroA100 21282 22129.5 557.5 22.5 6.0 22376.5 546.5 14.3 4.3 22117.0 454.2 3.9 0.8
KroB100 22140 23133.2 561.3 24.5 5.6 23332.5 420.9 13.1 4.0 23098.1 401.6 4.0 0.8
KroC100 20749 21822.5 706.7 21.1 3.4 21924.4 479.2 15.4 4.4 21642.5 544.7 4.1 1.2
KroD100 21294 22347.9 573.2 24.4 7.5 22550.2 463.5 15.9 5.2 22239.8 383.4 4.2 1.0
Eil101 629 680.1 11.3 42.6 9.9 685.8 13.2 22.8 6.5 680.0 9.2 4.4 0.9
Pr107 44303 46282.2 1528.9 36.4 13.7 46470.5 1401.2 23.1 7.9 45587.8 936.4 5.8 1.8
Pr124 59030 60407.6 722.2 47.0 11.0 60678.3 1170.1 26.4 6.5 60384.6 927.8 7.5 1.2

Instance

St70 675 744.6 21.9 3.6 1.1 725.2 20.5 3.4 0.8 713.0 10.9 0.5 0.1
Eilon75 535 604.2 26.6 4.6 1.1 603.9 16.5 4.9 1.2 579.6 14.1 0.7 0.1
Eil76 538 619.5 19.9 4.8 0.9 597.5 26.1 5.4 1.1 583.7 8.5 0.7 0.1
KroA100 21282 22416.4 518.4 13.3 3.0 22375.6 533.5 10.0 2.6 22202.0 539.4 1.7 0.3
KroB100 22140 23425.4 421.7 11.8 2.6 23542.6 612.1 10.1 1.9 23024.2 458.9 1.7 0.3
KroC100 20749 22304.0 634.9 11.8 2.5 22302.1 733.7 10.2 3.3 21539.1 468.3 1.8 0.3
KroD100 21294 22592.3 434.4 13.0 2.6 22797.8 629.6 8.9 2.1 22370.8 525.3 1.6 0.2
Eil101 629 718.9 17.6 16.4 3.7 712.7 15.3 17.7 3.9 687.4 11.1 1.6 0.3
Pr107 44303 46810.9 1100.7 17.1 3.1 46661.2 1242.7 13.2 3.4 45319.4 694.5 2.4 0.5
Pr124 59030 61421.5 1500.9 27.1 6.1 61148.1 1286.2 18.0 3.0 60380.6 669.8 3.6 0.5

Instance

St70 675 716.1 19.8 2.8 0.6 712.4 11.6 4.9 1.0 705.3 10.3 1.3 0.2
Eilon75 535 582.8 11.9 4.0 1.1 576.2 9.9 7.7 1.5 569.0 7.4 1.9 0.6
Eil76 538 582.0 12.9 4.0 1.2 576.5 13.4 8.5 2.7 572.7 10.3 1.8 0.3
KroA100 21282 22366.4 522.9 5.5 1.5 22279.4 614.0 13.9 5.7 21838.6 294.3 3.6 0.6
KroB100 22140 23123.7 371.7 7.0 2.8 23134.9 375.8 12.7 3.9 22964.2 529.3 3.6 0.5
KroC100 20749 22005.9 584.2 6.0 1.8 21718.2 456.8 10.7 2.4 21468.0 400.8 3.8 0.8
KroD100 21294 22404.3 317.7 7.7 2.6 22163.7 356.9 13.3 4.2 22039.1 441.6 3.5 0.5
Eil101 629 696.9 16.3 11.4 2.1 689.5 12.1 24.6 5.1 675.3 9.8 4.3 0.6
Pr107 44303 46276.0 1153.6 10.5 4.2 45542.7 1053.5 25.5 9.4 45145.4 590.4 4.9 1.2
Pr124 59030 60450.1 675.1 13.7 3.2 60020.6 564.1 26.7 8.3 59962.0 740.7 6.9 0.9