The Scientific World Journal / 2014 / Article / Tab 4

Research Article

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

Table 4

-test for TSP. “+” 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).

TSP versus versus
Instance Results Convergence Time Results Convergence Time

St70 * (1.46) * (−0.19) + (21.61) + (4.76) * (−1.51) + (14.99)
Eilon75 + (2.00) * (−0.56) + (22.02) + (4.30) * (−1.26) + (16.53)
Eil76 * (0.69) * (1.70) + (24.85) + (4.93) * (−1.86) + (16.53)
KroA100 * (0.12) − (−4.58) + (21.72) + (2.58) − (−3.69) + (16.48)
KroB100 * (0.36) − (−4.95) + (25.63) + (2.84) − (−5.08) + (15.57)
KroC100 * (1.42) − (−5.86) + (28.95) + (2.74) − (−5.61) + (17.57)
KroD100 * (1.10) − (−4.72) + (18.89) + (3.64) − (−4.09) + (15.73)
Eil101 * (0.05) + (3.97) + (26.94) + (2.56) * (0.21) + (19.56)
Pr107 + (2.73) − (−4.07) + (15.56) + (3.70) − (−4.92) + (14.90)
Pr124 * (0.13) − (−5.76) + (25.15) * (1.39) − (−9.92) + (20.12)

Instance versus versus

St70 + (9.13) + (2.23) + (25.43) + (3.71) − (−10.08) + (19.84)
Eilon75 + (5.77) * (0.42) + (24.66) + (7.91) − (−2.13) + (24.96)
Eil76 + (11.61) * (1.01) + (30.08) + (3.55) − (−6.12) + (32.01)
KroA100 + (2.02) * (−0.64) + (22.42) * (1.61) * (−1.68) + (27.20)
KroB100 + (4.55) − (−4.66) + (30.87) + (4.55) − (−5.60) + (27.28)
KroC100 + (6.85) − (−5.00) + (17.92) + (6.19) − (−20.79) + (28.08)
KroD100 + (2.29) * (−1.81) + (24.46) + (3.68) − (−4.00) + (30.91)
Eil101 + (10.70) + (3.10) + (29.10) + (9.46) − (−3.89) + (28.19)
Pr107 + (8.10) − (−6.76) + (22.22) + (6.66) − (−15.90) + (33.10)
Pr124 + (4.47) − (−6.47) + (33.47) + (3.74) − (−8.76) + (27.14)

Instance versus versus

St70 + (3.42) − (−7.30) + (16.77) + (3.23) − (−5.20) + (24.96)
Eilon75 + (6.96) − (−5.63) + (11.85) + (4.11) − (−3.39) + (25.38)
Eil76 + (3.98) * (0.21) + (12.57) * (1.58) * (0.21) + (17.43)
KroA100 + (6.21) − (−17.59) + (8.31) + (4.57) − (−6.12) + (12.7)
KroB100 + (1.74) − (−9.10) + (8.45) * (1.85) − (−9.89) + (16.36)
KroC100 + (5.36) − (−14.78) + (7.89) + (2.91) − (−15.00) + (19.28)
KroD100 + (4.74) − (−7.34) + (11.21) * (1.55) − (−7.74) + (16.38)
Eil101 + (8.03) − (−6.41) + (22.98) + (6.44) * (0.06) + (27.85)
Pr107 + (6.16) − (−9.59) + (9.06) + (2.32) − (−2.00) + (15.37)
Pr124 + (3.44) − (−16.72) + (14.46) * (0.44) − (−11.33) + (16.77)