Table 11 Results of statistics based on 100 independent runs of each algorithm for Problem III
From: Bio-inspired computational heuristics to study Lane–Emden systems arising in astrophysics model
Methods | x | Min | Max | Mean | STD | Variance | MSE |
|---|---|---|---|---|---|---|---|
SQP | 0.1 | 8.691E−08 | 1.020E−03 | 2.640E−05 | 1.030E−04 | 1.070E−08 | 2.640E−05 |
0.3 | 0.132E−03 | 0.723E−03 | 0.333E−03 | 5.730E−05 | 3.290E−09 | 3.330E−04 | |
0.5 | 0.134E−02 | 0.259E−02 | 0.242E−02 | 1.150E−04 | 1.320E−08 | 2.420E−03 | |
0.7 | 0.783E−02 | 0.893E−02 | 0.880E−02 | 1.030E−04 | 1.050E−08 | 8.800E−03 | |
0.9 | 0.218E−01 | 0.224E−01 | 0.223E−01 | 5.940E−05 | 3.530E−09 | 2.240E−02 | |
PS | 0.1 | 3.812E−06 | 5.934E−01 | 0.937E−02 | 0.661E−01 | 0.440E−02 | 0.937E−02 |
0.3 | 5.215E−06 | 4.442E−01 | 0.763E−02 | 0.511E−01 | 0.260E−02 | 0.763E−02 | |
0.5 | 2.342E−05 | 3.891E−01 | 0.828E−02 | 0.436E−01 | 0.220E−02 | 0.828E−02 | |
0.7 | 0.406E−03 | 3.695E−01 | 0.137E−01 | 0.391E−01 | 0.150E−02 | 0.137E−01 | |
0.9 | 0.158E−01 | 3.648E−01 | 0.266E−01 | 0.355E−01 | 0.130E−02 | 0.266E−01 | |
PS-SQP | 0.1 | 3.824E−06 | 5.933E−01 | 0.937E−02 | 0.600E−01 | 0.440E−02 | 0.937E−02 |
0.3 | 5.232E−06 | 4.442E−01 | 0.763E−01 | 0.657E−01 | 0.260E−02 | 0.763E−02 | |
0.5 | 2.341E−05 | 3.891E−01 | 0.828E−02 | 0.699E−01 | 0.190E−02 | 0.828E−02 | |
0.7 | 0.406E−03 | 3.695E−01 | 0.137E−01 | 0.722E−01 | 0.150E−02 | 0.137E−01 | |
0.9 | 0.158E−01 | 3.648E−01 | 0.266E−01 | 0.722E−01 | 0.130E−02 | 0.266E−01 | |
GA | 0.1 | 1.224E−06 | 4.256E−01 | 0.946E−02 | 0.600E−01 | 0.360E−02 | 0.946E−02 |
0.3 | 5.632E−05 | 4.670E−01 | 0.103E−01 | 0.657E−01 | 0.430E−02 | 0.103E−01 | |
0.5 | 4.856E−05 | 4.981E−01 | 0.132E−01 | 0.699E−01 | 0.490E−02 | 0.132E−01 | |
0.7 | 0.634E−01 | 5.172E−01 | 0.201E−01 | 0.722E−01 | 0.520E−02 | 0.201E−01 | |
0.9 | 0.201E−02 | 5.224E−01 | 0.338E−01 | 0.722E−01 | 0.520E−02 | 0.338E−01 | |
GA-SQP | 0.1 | 6.86E−09 | 2.680E−05 | 7.920E−06 | 5.42E−06 | 2.940E−11 | 7.920E−06 |
0.3 | 0.293E−03 | 0.387E−03 | 0.338E−03 | 1.45E−05 | 2.110E−10 | 3.380E−04 | |
0.5 | 0.241E−02 | 0.246E−02 | 0.244E−03 | 8.49E−06 | 7.200E−11 | 2.440E−03 | |
0.7 | 0.879E−02 | 0.883E−02 | 0.881E−02 | 7.79E−06 | 6.060E−11 | 8.820E−03 | |
0.9 | 0.223E−01 | 0.223E−01 | 0.223E−01 | 7.23E−06 | 5.220E−11 | 2.240E−02 |