The Scientific World Journal / 2014 / Article / Tab 10

Research Article

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

Table 10

-test for NQP. “+” 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).

NQP versus versus
Instance Results Convergence Time Results Convergence Time

8-queens * (0.00) * (0.80) * (0.00) * (1.41) + (2.70) * (0.00)
20-queens + (5.08) * (−0.57) + (15.00) + (5.07) * (−0.75) + (6.32)
50-queens + (4.76) + (2.84) + (10.00) + (4.03) + (2.10) + (2.16)
75-queens + (9.60) − (−2.19) + (4.14) + (7.88) * (−1.58) * (1.06)
100-queens + (8.23) + (3.69) + (13.04) + (7.37) + (3.63) + (7.82)
125-queens + (12.98) * (0.26) + (6.30) + (10.85) * (0.52) * (1.10)
150-queens + (13.86) * (1.71) + (5.40) + (13.86) * (1.25) + (2.61)
200-queens + (16.48) − (−6.45) + (23.56) + (13.64) − (−2.50) + (3.39)
250-queens + (14.54) * (−1.72) + (6.67) + (14.54) * (1.20) * (1.29)
300-queens + (18.06) − (−3.39) + (4.44) + (16.47) − (−2.72) + (3.27)

Instance versus versus

8-queens * (0.00) + (3.92) * (0.00) * (0.00) * (1.19) * (0.00)
20-queens + (3.63) − (−2.54) * (0.00) + (3.53) − (−2.81) * (0.00)
50-queens + (3.93) * (1.27) + (5.00) + (3.56) * (1.74) + (5.00)
75-queens + (5.89) * (−0.21) + (10.00) + (3.09) − (−2.43) + (15.00)
100-queens + (4.76) + (2.09) + (7.37) + (6.57) − (−4.30) + (3.63)
125-queens + (4.80) * (1.61) + (6.43) + (2.11) * (−0.43) + (9.94)
150-queens + (3.56) + (2.09) + (5.64) + (1.45) * (1.13) + (11.06)
200-queens + (6.94) * (1.93) + (6.86) + (3.84) + (2.10) + (8.14)
250-queens + (6.29) * (−1.23) + (3.66) + (4.62) − (4.22) + (5.14)
300-queens + (11.19) * (1.30) + (3.81) + (3.92) * (−0.21) + (8.36)

Instance versus versus

8-queens * (0.00) * (0.86) * (0.00) * (0.00) + (3.42) * (0.00)
20-queens + (4.16) * (0.05) * (0.00) + (2.71) * (0.33) * (0.00)
50-queens + (3.32) * (−0.29) + (5.00) + (2.68) * (−1.66) + (5.00)
75-queens + (5.56) * (−1.37) + (15.00) + (2.60) * (−1.09) + (10.00)
100-queens * (1.86) − (−4.37) + (7.07) + (3.38) − (−0.42) + (3.92)
125-queens + (7.02) − (−9.61) + (8.40) + (2.06) − (−5.45) + (2.00)
150-queens + (2.21) * (−1.80) * (1.12) + (2.81) − (−5.15) + (2.56)
200-queens + (4.26) − (−5.93) + (6.35) + (4.36) − (−4.88) + (2.81)
250-queens + (6.14) * (−1.65) + (2.90) + (5.70) * (0.30) + (4.63)
300-queens + (3.06) * (−1.05) * (0.97) + (3.86) − (−2.89) + (4.77)