The Scientific World Journal / 2014 / Article / Tab 5

Research Article

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

Table 5

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

CVRP
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.

En22k4 375 389.0 9.8 1.8 0.5 410.9 23.2 2.5 1.1 404.8 19.5 1.1 0.3
En23k3 569 622.7 28.9 2.1 0.9 629.9 41.6 2.3 1.0 602.7 30.8 1.6 0.6
En30k3 534 559.6 29.2 3.9 1.2 582.7 43.3 5.0 2.0 545.8 41.6 2.0 0.7
En33k4 835 907.4 31.9 6.0 1.8 932.8 30.6 7.0 2.3 911.9 24.9 2.2 0.7
En51k5 521 641.0 38.3 13.8 5.4 694.3 53.4 18.2 7.9 628.4 37.4 4.5 1.4
En76k7 682 850.0 45.7 44.4 16.4 899.5 63.3 55.1 16.5 822.3 42.9 10.0 3.3
En76k8 735 920.6 59.3 40.9 19.1 952.2 44.6 52.3 17.5 886.9 37.6 8.3 2.8
En76k14 1021 1186.9 35.6 33.4 14.0 1219.6 47.4 38.1 12.6 1171.0 36.2 6.5 2.2
En101k8 815 1061.4 54.8 107.5 33.9 1110.9 71.6 126.3 35.3 1016.7 49.9 15.7 5.1
Pr101k14 1071 1320.0 46.5 88.1 29.6 1370.7 73.1 114.9 34.3 1270.6 41.4 14.8 4.6

Instance

En22k4 375 388.0 14.8 1.6 0.4 386.1 10.3 2.3 0.4 392.8 13.9 0.8 0.1
En23k3 569 622.5 31.1 2.7 1.1 615.7 37.9 2.5 1.2 601.8 38.4 0.9 0.2
En30k3 534 608.1 58.0 3.3 1.3 557.6 18.3 4.0 1.0 547.0 28.9 1.4 0.4
En33k4 835 917.0 24.9 3.4 1.3 901.3 29.2 3.1 1.0 903.4 23.7 1.2 0.4
En51k5 521 716.0 50.1 8.6 2.8 631.7 34.3 8.5 3.2 623.9 31.1 2.4 0.9
En76k7 682 847.8 48.5 35.1 13.5 835.4 56.3 26.0 10.8 809.6 40.8 4.8 1.5
En76k8 735 914.8 54.4 32.4 13.9 895.2 37.9 24.4 7.0 870.2 54.4 5.1 1.5
En76k14 1021 1198.9 46.1 24.3 8.7 1188.8 45.1 33.8 10.5 1167.9 28.8 4.5 1.9
En101k8 815 1034.2 57.8 86.9 24.3 1021.6 72.9 67.2 26.0 1007.0 49.4 8.0 2.1
Pr101k14 1071 1309.8 51.0 75.6 16.7 1288.5 45.3 59.3 25.0 1253.2 36.5 8.7 2.4

Instance

En22k4 375 400.2 29.6 1.9 0.3 411.8 31.0 1.9 0.4 390.4 15.0 1.7 0.2
En23k3 569 604.2 37.8 2.9 0.8 608.9 32.8 2.9 1.2 613.5 40.9 2.1 0.8
En30k3 534 550.6 37.9 3.4 1.3 573.5 42.0 4.0 1.8 549.8 36.2 2.0 0.9
En33k4 835 914.9 33.3 3.8 1.4 904.8 24.7 3.9 1.4 901.2 24.8 1.6 0.3
En51k5 521 655.9 43.9 7.9 3.6 668.0 52.6 9.3 3.2 636.9 41.2 4.9 1.6
En76k7 682 833.1 42.0 23.2 8.1 821.8 38.5 28.8 9.5 815.2 29.2 7.7 3.7
En76k8 735 907.3 31.9 23.0 6.2 908.0 30.3 24.3 7.3 895.1 29.5 8.3 2.5
En76k14 1021 1188.3 43.8 19.0 8.3 1171.3 23.9 22.6 7.6 1178.1 32.5 7.5 3.0
En101k8 815 1001.4 57.2 71.9 23.9 1031.2 53.7 59.6 17.7 1006.9 57.7 14.1 4.8
Pr101k14 1071 1309.8 55.3 44.3 14.0 1320.0 47.2 48.2 19.2 1285.2 53.9 12.3 4.6