Table 8 Results of statistical operators based on 100 independent runs of each algorithm for Problem II
From: Bio-inspired computational heuristics to study Lane–Emden systems arising in astrophysics model
Methods | X | Min | Max | Mean | Median | STD | Variance | MSE |
|---|---|---|---|---|---|---|---|---|
SQP | 0.1 | 0.00E+00 | 1.00E−05 | 0.00E+00 | 0.00E+00 | 2.43E−06 | 5.92E−12 | 1.05E−11 |
0.3 | 0.12E−04 | 0.19E−02 | 0.14E−03 | 0.14E−03 | 9.59E−06 | 9.19E−11 | 1.92E−08 | |
0.5 | 0.99E−03 | 0.10E−02 | 0.10E−02 | 0.10E−02 | 8.71E−06 | 7.59E−11 | 1.05E−06 | |
0.7 | 0.31E−02 | 0.38E−02 | 0.38E−02 | 0.31E−02 | 6.10E−06 | 3.72E−11 | 1.47E−05 | |
0.9 | 0.10E−01 | 0.10E−01 | 0.10E−01 | 0.10E−01 | 5.88E−06 | 3.45E−11 | 1.04E−04 | |
PS | 0.1 | 5.35E−06 | 1.16E−03 | 2.62E−04 | 1.94E−04 | 2.40E−04 | 5.75E−08 | 6.86E−08 |
0.3 | 6.54E−06 | 2.15E−03 | 3.46E−04 | 2.88E−04 | 3.18E−04 | 1.28E−07 | 1.20E−07 | |
0.5 | 8.28E−06 | 1.83E−03 | 8.89E−04 | 9.11E−04 | 4.08E−04 | 1.66E−07 | 7.91E−07 | |
0.7 | 7.19E−06 | 4.63E−03 | 3.67E−03 | 3.73E−03 | 5.62E−04 | 3.16E−07 | 1.34E−05 | |
0.9 | 7.58E−06 | 1.09E−02 | 9.99E−03 | 1.01E−02 | 0.11E−02 | 1.16E−06 | 9.99E−05 | |
PS-SQP | 0.1 | 1.66E−08 | 2.00E−04 | 1.73E−05 | 7.01E−06 | 2.65E−05 | 7.01E−10 | 2.98E−10 |
0.3 | 8.63E−05 | 0.27E−02 | 0.14E−03 | 0.13E−03 | 2.64E−05 | 6.99E−10 | 2.09E−08 | |
0.5 | 0.74E−03 | 0.11E−02 | 0.10E−02 | 0.10E−02 | 3.65E−05 | 1.33E−09 | 1.06E−06 | |
0.7 | 0.37E−02 | 0.39E−02 | 0.38E−02 | 0.38E−02 | 3.38E−05 | 1.14E−09 | 1.48E−05 | |
0.9 | 0.10E−01 | 0.10E−01 | 0.10E−01 | 0.10E−02 | 3.05E−05 | 9.29E−10 | 0.10E−03 | |
GA | 0.1 | 2.04E−07 | 9.47E−01 | 0.18E−01 | 7.54E−05 | 1.18E−02 | 0.14E−01 | 0.34E−03 |
0.3 | 0.71E−05 | 9.17E−02 | 0.18E−01 | 0.22E−03 | 1.16E−02 | 0.13E−01 | 0.33E−03 | |
0.5 | 0.36E−03 | 8.75E−02 | 0.18E−01 | 0.10E−02 | 1.13E−02 | 0.11E−01 | 0.34E−03 | |
0.7 | 0.14E−02 | 8.22E−02 | 0.20E−01 | 0.39E−02 | 1.07E−02 | 0.11E−01 | 0.40E−03 | |
0.9 | 0.5068E−02 | 7.57E−02 | 0.24E−01 | 0.10E−01 | 1.00E−02 | 0.10E−01 | 0.61E−03 | |
GA-SQP | 0.1 | 4.04E−08 | 4.27E−05 | 6.15E−06 | 4.62E−06 | 6.24E−06 | 3.89E−11 | 3.72E−11 |
0.3 | 0.12E−02 | 0.18E−03 | 0.14E−03 | 0.14E−03 | 1.01E−05 | 1.02E−10 | 2.00E−08 | |
0.5 | 0.10E−02 | 0.10E−02 | 0.10E−02 | 0.10E−02 | 8.79E−06 | 7.72E−11 | 1.05E−06 | |
0.7 | 0.38E−02 | 0.38E−02 | 0.38E−02 | 0.38E−02 | 8.27E−06 | 6.84E−11 | 1.48E−05 | |
0.9 | 0.10E−01 | 0.10E−01 | 0.10E−01 | 0.10E−01 | 7.59E−06 | 5.76E−11 | 0.10E−03 |