The Scientific World Journal / 2014 / Article / Tab 11

Research Article

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

Table 11

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

BPP
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.

N2C1W1_A 48 53.4 0.7 0.35 0.12 53.7 0.7 0.08 0.03 53.1 0.7 0.02 0.01
N2C1W1_B 49 54.3 0.7 0.29 0.08 54.4 0.8 0.09 0.02 53.3 0.5 0.02 0.01
N3C2W2_A 107 121.4 1.5 1.84 0.33 121.8 1.4 0.47 0.16 120.2 1.3 0.07 0.02
N3C2W2_B 105 117.7 1.8 1.93 0.54 118.2 2.2 0.39 0.20 116.7 1.1 0.06 0.03
N3C3W1_A 66 73.9 0.8 1.48 0.42 73.6 0.8 0.42 0.18 73.2 0.9 0.07 0.03
N3C3W1_B 71 80.4 0.9 1.46 0.37 79.8 0.7 0.46 0.24 79.2 0.9 0.06 0.02
N4C1W1_A 240 277.9 2.4 7.79 2.90 275.4 2.4 5.84 1.85 273.4 1.7 0.37 0.12
N4C1W1_B 262 300.4 3.2 7.48 3.12 298.8 1.4 5.93 2.15 295.8 2.2 0.45 0.21
N4C1W1_C 241 277.9 2.6 7.67 2.69 276.8 2.7 6.15 2.05 273.6 1.6 0.49 0.18
N4C2W1_A 210 245.8 2.9 7.08 2.41 244.8 2.1 6.02 1.99 242.6 1.9 0.51 0.24

Instance

N2C1W1_A 48 53.2 0.9 0.37 0.10 53.4 0.8 0.06 0.02 52.8 0.6 0.01 0.01
N2C1W1_B 49 54.0 0.5 0.25 0.12 54.1 0.7 0.08 0.02 53.5 0.6 0.01 0.01
N3C2W2_A 107 121.0 1.3 1.93 0.41 122.0 1.5 0.51 0.19 120.4 1.5 0.06 0.02
N3C2W2_B 105 117.4 1.5 2.12 0.77 117.9 1.9 0.40 0.22 116.8 1.0 0.05 0.01
N3C3W1_A 66 74.2 1.0 1.82 0.57 73.3 0.5 0.58 0.21 73.0 0.6 0.08 0.02
N3C3W1_B 71 80.1 0.7 1.39 0.28 79.5 1.1 0.49 0.32 78.9 1.0 0.06 0.03
N4C1W1_A 240 276.3 2.7 7.91 2.49 274.3 2.1 6.12 2.09 273.5 1.4 0.43 0.26
N4C1W1_B 262 299.8 3.4 8.27 3.93 299.4 1.8 6.29 2.77 295.3 2.0 0.51 0.28
N4C1W1_C 241 278.2 2.9 8.93 3.00 277.1 2.2 7.00 2.22 272.9 1.9 0.68 0.25
N4C2W1_A 210 245.2 3.1 8.11 2.91 245.1 2.1 5.99 2.42 242.9 2.1 0.89 0.32

Instance

N2C1W1_A 48 52.9 0.8 0.41 0.09 52.7 0.9 0.21 0.12 52.7 0.6 0.02 0.01
N2C1W1_B 49 53.8 0.7 0.31 0.12 53.5 0.7 0.32 0.11 52.8 0.7 0.02 0.01
N3C2W2_A 107 119.2 1.1 1.95 0.77 120.1 1.6 1.84 0.70 118.9 1.1 0.08 0.03
N3C2W2_B 105 117.2 1.9 1.99 0.71 117.4 2.7 1.72 0.81 116.4 1.4 0.09 0.04
N3C3W1_A 66 73.8 0.7 2.11 0.70 72.8 0.9 2.21 1.00 72.8 0.7 0.10 0.03
N3C3W1_B 71 80.1 1.2 2.01 0.54 78.4 1.1 1.87 0.91 78.1 0.5 0.12 0.04
N4C1W1_A 240 278.1 2.8 7.89 2.71 276.0 2.8 6.84 2.08 273.5 1.9 0.47 0.12
N4C1W1_B 262 298.4 3.7 8.21 3.03 297.1 2.1 6.94 2.72 295.1 2.8 0.53 0.32
N4C1W1_C 241 277.1 2.2 9.00 3.09 275.9 2.4 8.95 2.71 273.0 2.1 0.81 0.37
N4C2W1_A 210 242.4 3.1 8.15 3.12 244.1 2.6 7.99 2.40 241.7 1.5 0.97 0.42