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Table 5 Results of statistics based on 100 independent runs of each algorithm

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

2.06E−09

1.58E−05

3.35E−06

2.71E−06

2.81E−06

7.92E−12

3.35E−06

0.3

3.54E−07

7.33E−05

1.39E−05

1.10E−05

1.19E−05

1.41E−10

1.39E−05

0.5

3.19E−08

1.03E−04

1.23E−05

8.93E−06

1.32E−05

1.74E−10

1.23E−05

0.7

3.07E−07

8.17E−05

1.06E−05

7.53E−06

1.07E−05

1.15E−10

1.06E−05

0.9

4.25E−07

7.35E−05

1.19E−05

9.49E−06

1.08E−05

1.16E−10

1.19E−05

PS

0.1

8.94E−07

1.24E−03

2.73E−04

2.08E−04

4.82E−05

2.32E−09

2.95E−05

0.3

1.71E−06

1.52E−03

4.66E−04

3.66E−04

1.09E−04

1.20E−08

4.73E−05

0.5

2.67E−06

1.39E−03

4.76E−04

3.61E−04

1.06E−04

1.12E−08

4.74E−05

0.7

3.82E−07

1.56E−03

4.52E−04

3.65E−04

8.49E−05

7.20E−09

4.54E−05

0.9

1.56E−06

1.52E−03

4.65E−04

3.42E−04

1.01E−04

1.01E−08

4.74E−05

PS-SQP

0.1

7.20E−08

3.51E−04

2.95E−05

1.14E−05

2.65E−04

7.02E−08

2.73E−04

0.3

3.38E−07

9.57E−04

4.73E−05

1.72E−05

3.78E−04

1.43E−07

4.65E−04

0.5

3.73E−07

8.88E−04

4.74E−05

1.66E−05

3.87E−04

1.50E−07

4.76E−04

0.7

2.18E−07

6.01E−04

4.54E−05

1.81E−05

3.72E−04

1.39E−07

4.52E−04

0.9

1.37E−07

8.15E−04

4.74E−05

1.70E−05

3.86E−04

1.49E−07

4.65E−04

GA

0.1

1.34E−07

1.55E−03

1.65E−04

7.79E−05

2.54E−04

6.45E−08

1.65E−04

0.3

1.75E−07

2.86E−03

3.20E−04

2.13E−04

3.83E−04

1.47E−07

3.20E−04

0.5

1.79E−07

5.57E−03

4.23E−04

1.66E−04

7.39E−04

5.46E−07

4.23E−04

0.7

1.07E−05

5.82E−03

4.59E−04

1.52E−04

8.02E−04

6.43E−07

4.59E−04

0.9

1.39E−06

4.39E−03

3.85E−04

1.67E−04

6.13E−04

3.76E−07

3.85E−04

GA-SQP

0.1

2.42E−07

3.68E−05

5.58E−06

4.46E−06

2.54E−04

6.45E−08

5.58E−06

0.3

4.71E−08

5.00E−05

1.19E−05

7.77E−06

3.83E−04

1.47E−07

1.18E−05

0.5

1.01E−07

5.00E−05

9.80E−06

7.51E−06

7.39E−04

5.46E−07

9.80E−06

0.7

7.70E−07

5.10E−05

9.94E−06

7.26E−06

8.02E−04

6.43E−07

9.94E−06

0.9

1.20E−07

5.21E−05

1.07E−05

7.77E−06

6.13E−04

3.76E−07

1.07E−05