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Table 12 Comparison of results on the basis of statistical performance indices for truncated 75% independent runs with better fitness

From: Memetic computing through bio-inspired heuristics integration with sequential quadratic programming for nonlinear systems arising in different physical models

Methods

Problem-1

Problem-2

Problem-3

Problem-4

Problem-5

Problem-6

Mean

STD

Mean

STD

Mean

STD

Mean

STD

Mean

STD

Mean

STD

GA-1

3.6E−03

1.6E−03

1.5E−07

9.4E−08

8.5E−04

3.6E−04

5.5E−10

1.2E−09

5.3E−05

3.2E−05

5.6E−05

1.5E−04

GA-2

2.6E−03

1.7E−03

1.9E−07

1.2E−07

5.5E−03

6.1E−03

2.2E−08

7.5E−08

2.8E−05

1.6E−05

2.4E−05

4.0E−05

GA-3

5.4E−03

1.3E−03

7.3E−04

6.1E−04

1.9E−03

1.0E−03

5.7E−07

1.6E−06

1.0E−03

9.0E−04

2.0E−03

3.4E−03

GA-4

5.2E−03

1.7E−03

5.3E−06

3.3E−06

5.5E−03

5.3E−03

3.3E−07

5.6E−07

1.2E−04

6.7E−05

8.6E−04

8.1E−04

GA-5

3.3E−03

1.7E−03

1.2E−07

8.1E−08

8.2E−04

3.9E−04

9.3E−11

2.4E−10

5.4E−05

2.8E−05

4.1E−05

1.2E−04

GA-6

2.8E−03

1.8E−03

1.6E−07

9.6E−08

5.6E−03

6.4E−03

1.6E−09

6.2E−09

3.0E−05

1.6E−05

1.6E−05

2.4E−05

GA-7

5.4E−03

1.5E−03

5.0E−04

4.6E−04

1.7E−03

7.7E−04

3.1E−07

5.8E−07

6.5E−04

5.1E−04

9.5E−04

1.8E−03

GA-8

5.2E−03

1.6E−03

4.9E−06

3.1E−06

7.4E−03

6.8E−03

1.5E−06

3.0E−06

1.1E−04

6.0E−05

1.1E−03

1.2E−03

GA-9

3.5E−03

1.9E−03

7.0E−07

4.1E−07

1.0E−03

4.7E−04

1.1E−09

2.4E−09

8.1E−05

4.5E−05

5.5E−05

8.3E−05

GA-10

3.1E−03

1.9E−03

1.1E−06

5.5E−07

5.7E−03

7.2E−03

1.3E−07

3.8E−07

5.4E−05

3.1E−05

3.6E−04

1.0E−03

GA-11

5.6E−03

1.2E−03

1.4E−03

9.7E−04

2.1E−03

1.0E−03

8.1E−07

1.5E−06

1.1E−03

9.5E−04

5.9E−03

1.4E−02

GA-12

5.3E−03

1.7E−03

2.9E−05

1.8E−05

7.5E−03

6.5E−03

1.2E−06

2.0E−06

2.1E−04

1.3E−04

2.7E−03

4.1E−03

GA-SQP-1

6.9E−17

1.7E−17

1.8E−32

7.0E−33

3.1E−08

5.7E−08

3.9E−22

1.0E−22

1.2E−15

1.3E−15

9.7E−32

6.2E−32

GA-SQP-2

7.0E−17

1.8E−17

1.8E−32

6.8E−33

4.1E−08

6.7E−08

4.9E−22

2.9E−22

7.4E−16

5.9E−16

9.5E−32

6.6E−32

GA-SQP-3

7.0E−17

1.7E−17

1.6E−32

5.8E−33

6.2E−09

1.2E−08

4.0E−22

8.8E−23

2.4E−16

3.2E−16

1.1E−31

8.9E−32

GA-SQP-4

6.5E−17

1.8E−17

1.6E−32

7.2E−33

8.4E−09

1.3E−08

3.4E−22

1.3E−22

2.0E−16

2.5E−16

1.0E−31

6.5E−32

GA-SQP-5

6.6E−17

1.5E−17

2.0E−32

8.6E−33

4.1E−08

7.0E−08

4.0E−22

6.8E−23

6.7E−16

6.6E−16

1.1E−31

7.5E−32

GA-SQP-6

6.9E−17

1.7E−17

1.7E−32

8.0E−33

4.2E−08

7.0E−08

8.0E−22

1.3E−21

1.0E−15

1.1E−15

9.2E−32

5.8E−32

GA-SQP-7

6.7E−17

1.8E−17

1.4E−32

5.4E−33

1.2E−08

3.0E−08

4.0E−22

8.2E−23

2.5E−16

3.6E−16

8.0E−32

5.8E−32

GA-SQP-8

6.9E−17

1.8E−17

1.6E−32

6.0E−33

3.5E−08

6.4E−08

3.6E−22

1.2E−22

2.7E−16

4.3E−16

9.1E−32

6.6E−32

GA-SQP-9

6.9E−17

1.6E−17

1.7E−32

7.4E−33

3.4E−08

6.2E−08

3.9E−22

1.2E−22

8.4E−16

1.0E−15

7.8E−32

5.1E−32

GA-SQP-10

6.7E−17

1.7E−17

1.8E−32

7.5E−33

4.9E−08

7.2E−08

1.3E−21

2.2E−21

5.4E−16

4.4E−16

8.2E−32

5.7E−32

GA-SQP-11

6.8E−17

1.5E−17

1.4E−32

5.6E−33

8.8E−09

1.3E−08

3.9E−22

8.8E−23

4.7E−16

6.5E−16

8.5E−32

6.5E−32

GA-SQP-12

6.7E−17

1.9E−17

1.4E−32

6.0E−33

4.4E−08

6.9E−08

3.6E−22

1.4E−22

3.0E−16

4.2E−16

8.7E−32

7.1E−32