The Scientific World Journal / 2014 / Article / Tab 7

Research Article

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

Table 7

-test for CVRP. “+” indicates that EA is better. “−” depicts that it is worse. “*” indicates that the difference between the two algorithms is not significant (at 95% confidence level).

CVRP versus versus
Instance Results Convergence Time Results Convergence Time

En22k4 − (−5.09) * (1.61) + (7.96) * (1.41) + (4.15) + (8.64)
En23k3 + (3.35) * (1.01) + (2.76) + (3.71) * (0.43) + (3.99)
En30k3 * (1.91) * (1.55) + (9.45) + (4.33) * (1.30) + (9.88)
En33k4 * (−0.78) + (8.01) + (13.24) + (3.73) + (7.90) + (13.69)
En51k5 * (1.65) + (4.54) + (11.63) + (7.14) + (5.50) + (12.09)
En76k7 + (3.12) + (5.64) + (14.47) + (7.14) + (8.60) + (18.90)
En76k8 + (3.42) + (5.03) + (11.89) + (7.90) + (9.06) + (17.45)
En76k14 + (2.20) + (4.61) + (13.36) + (5.76) + (7.13) + (17.44)
En101k8 + (4.26) + (9.29) + (18.86) + (7.63) + (11.83) + (21.88)
En101k14 + (5.60) + (8.17) + (17.26) + (8.42) + (11.37) + (20.43)

Instance versus versus

En22k4 * (−1.67) + (2.31) + (13.71) − (−2.73) * (0.71) + (25.72)
En23k3 + (2.96) + (5.65) + (11.38) * (1.83) * (1.83) + (9.29)
En30k3 + (6.66) * (0.19) + (9.87) + (2.19) * (0.21) + (17.06)
En33k4 + (2.80) + (2.57) + (11.43) * (−0.33) + (3.32) + (12.47)
En51k5 + (11.04) * (0.74) + (14.90) * (1.19) + (3.57) + (12.97)
En76k7 + (4.26) + (4.16) + (15.77) + (2.62) + (3.19) + (13.74)
En76k8 + (4.09) + (3.31) + (13.80) + (2.66) + (2.78) + (19.06)
En76k14 + (4.03) + (3.19) + (15.72) + (2.76) + (3.68) + (19.41)
En101k8 + (2.52) + (8.45) + (22.87) * (1.17) + (5.26) + (16.04)
En101k14 + (6.38) + (8.19) + (28.03) + (4.29) + (3.94) + (14.24)

Instance versus versus

En22k4 + (2.08) + (2.92) + (3.92) + (4.39) * (1.84) + (3.16)
En23k3 * (−1.18) * (0.34) * (1.87) * (−0.62) * (1.50) * (1.47)
En30k3 * (0.10) * (0.13) + (6.26) + (3.02) * (0.61) + (7.02)
En33k4 + (2.33) + (3.78) + (10.86) * (0.72) + (3.28) + (11.35)
En51k5 + (2.23) * (1.08) + (5.38) + (3.29) + (2.50) + (8.69)
En76k7 + (2.47) + (3.39) + (12.30) * (0.96) + (4.11) + (14.63)
En76k8 + (1.98) + (3.79) + (15.54) + (2.15) + (3.31) + (14.66)
En76k14 * (1.32) * (1.79) + (9.21) * (−1.19) + (3.51) + (13.06)
En101k8 * (−0.47) + (6.29) + (16.76) + (2.17) + (7.56) + (17.54)
En101k14 + (2.25) + (3.52) + (15.35) + (3.44) + (3.27) + (12.85)