The Scientific World Journal

Research Article

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

Table 8

Results and runtime of the nine techniques applied to the NQP. For each instance, the results, average runtime, and their standard deviations are shown.
NQP
Instance Results Time (s) Results Time (s) Results Time (s)
Instance Avg. St.d. Avg. St.d. Avg. St.d. Avg. St.d. Avg. St.d. Avg. St.d.
8-queens 0.0 0.0 0.1 0.0 0.1 0.2 0.1 0.0 0.0 0.0 0.1 0.0
20-queens 1.6 0.8 0.1 0.1 1.5 0.7 0.1 0.1 0.8 0.5 0.1 0.0
50-queens 6.6 1.6 0.6 0.1 6.4 1.6 0.3 0.1 5.1 1.4 0.3 0.1
75-queens 13.7 2.2 0.8 0.3 13.1 2.5 0.7 0.4 9.2 2.3 0.6 0.1
100-queens 15.4 2.3 6.2 1.5 15.2 2.6 4.7 1.3 11.5 2.3 2.9 0.7
125-queens 25.5 3.4 5.2 1.5 24.3 3.6 3.9 1.2 17.0 3.1 3.6 0.8
150-queens 32.0 3.9 9.5 3.4 27.7 3.9 7.6 2.2 21.9 3.2 6.6 1.4
200-queens 43.2 5.9 69.9 7.9 38.2 4.5 38.0 8.1 26.6 3.9 32.5 7.9
250-queens 56.4 7.1 63.8 19.8 52.1 5.2 45.5 12.5 38.0 5.3 42.5 10.7
300-queens 69.9 7.9 123.3 41.3 65.2 6.5 109.5 25.6 45.6 5.3 94.6 19.3
Instance
8-queens0.0 0.0 0.1 0.1 0.0 0.0 0.1 0.1 0.0 0.0 0.1 0.1
20-queens 1.4 1.0 0.1 0.1 1.3 0.8 0.1 0.1 0.8 0.6 0.1 0.1
50-queens 5.9 1.8 0.2 0.1 5.6 1.3 0.2 0.1 4.6 1.5 0.1 0.1
75- queens 10.9 2.1 0.7 0.1 10.0 2.5 0.8 0.1 8.7 1.6 0.5 0.1
100-queens 14.7 3.3 2.2 0.6 15.3 2.8 1.8 0.5 12.1 2.0 1.5 0.3
125-queens 19.8 2.9 4.2 1.1 18.3 2.7 4.8 1.1 17.2 2.5 3.1 0.5
150-queens 23.7 3.7 8.1 2.7 22.2 3.2 9.3 2.0 21.3 3.0 5.8 1.0
200-queens 33.3 4.4 26.7 7.2 30.4 4.3 27.1 6.1 26.9 4.8 18.7 4.0
250-queens 43.5 5.6 52.6 12.0 41.6 5.2 56.4 13.1 37.1 4.5 44.8 9.1
300-queens 57.8 5.7 98.6 33.6 50.4 6.5 118.6 28.5 45.9 4.9 77.6 19.7
Instance
8-queens0.0 0.0 0.1 0.1 0.0 0.0 0.1 0.0 0.0 0.0 0.1 0.0
20-queens 1.3 0.6 0.1 0.1 1.1 0.5 0.1 0.1 0.8 0.6 0.1 0.1
50-queens 5.2 1.6 0.2 0.1 4.9 1.2 0.2 0.1 4.2 1.4 0.1 0.1
75-queens 10.0 2.0 0.9 0.1 8.7 1.9 0.8 0.1 7.6 2.3 0.6 0.1
100-queens 12.7 2.7 2.6 0.3 13.4 2.6 2.5 0.6 11.8 2.1 2.1 0.4
125-queens 17.8 2.1 6.3 0.9 15.6 3.1 5.1 1.0 14.4 2.7 4.7 1.0
150-queens 21.2 4.3 8.2 2.7 21.2 2.7 8.6 1.9 19.5 3.3 7.7 1.6
200-queens 30.3 3.5 28.6 3.9 30.5 3.8 25.8 5.3 27.0 4.2 22.9 5.0
250-queens 36.9 3.7 59.1 11.6 36.2 3.0 62.5 10.9 32.1 4.1 52.8 10.0
300-queens 46.7 7.0 93.5 21.9 46.9 4.6 111.3 27.2 42.5 6.6 89.7 16.8