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Table 4 Results obtained by ATMDE and ATMDE1 on 18 benchmark test functions

From: Improved Differential Evolution with Shrinking Space Technique for Constrained Optimization

Function

Method

Best solution

f best

Median solution

f median

Mean solution

μ f

Worst solution

f worst

Standard deviation

σ f

g01

ATMDE

−15.000

−15.000

−15.000

−15.0000

0

 

ATMDE1

−14.999 9

−14.999 9

−14.999 9

−14.999 9

8.98 × 10−7

g02

ATMDE

−0.803 617

−0.803 617

−0.803 617

−0.803 610

1.24 × 10−6

 

ATMDE1

−0.802 125

−0.802 125

−0.802 124

−0.802 092

6.14 × 10−6

g03

ATMDE

−1.005 00

−1.005 00

−1.005 00

−1.005 00

2.08 × 10−9

 

ATMDE1

−1.005 00

−1.005 00

−0.985 8

−0.798 4

4.93 × 10−2

g04

ATMDE

−30 665.53

−30 665.53

−30 665.53

−30 665.5

1.11 × 10−11

 

ATMDE1

−30 665.53

−30 665.53

−30 665.53

−30 665.53

1.85 × 10−11

g05

ATMDE

5126.496 71

5 126.496 71

5126.496 71

5 126.496 71

1.01 × 10−12

 

ATMDE1

5126.496 71

5 126.496 71

5126.496 71

5 126.496 71

2.95 × 10−9

g06

ATMDE

−6961.813

−6961.813

−6961.813

−6961.81

1.85 × 10−12

 

ATMDE1

−6961.813

−6961.813

−6961.813

−6961.81

2.78 × 10−12

g07

ATMDE

24.306 209

24.306 209

24.306 209

24.306 209

2.21 × 10−8

 

ATMDE1

24.3062 497

24.306 2497

24.306 253

24.306 364

2.09 × 10−5

g08

ATMDE

−0.095 825

−0.095 825

−0.095 825

−0.095 825

2.56 × 10−17

 

ATMDE1

−0.095 825

−0.095 825

−0.095 825

−0.095 825

2.82 × 10−17

g09

ATMDE

680.630 05

680.630 05

680.630 05

680.630 05

4.63 × 10−13

 

ATMDE1

680.630 05

680.630 05

680.630 05

680.630 05

4.85 × 10−13

g10

ATMDE

7 049.248 02

7 049.248 02

7 049.248 02

7 049.248 02

8.70 × 10−7

 

ATMDE1

7 049.339 29

7 049.699 7

7 049.800 6

7 051.246 3

4.59 × 10−1

g11

ATMDE

0.749 90

0.749 90

0.749 90

0.749 90

1.01 × 10−7

 

ATMDE1

0.749 90

0.749 90

0.749 90

0.749 90

1.12 × 10−16

g12

ATMDE

−1.000 00

−1.000 00

−1.000 00

−1.000 00

0

 

ATMDE1

−1.000 00

−1.000 00

−1.000 00

−1.000 00

0

g14

ATMDE

−47.764 888

−47.764 888

−47.764 888

−47.764 88

1.95 × 10−10

 

ATMDE1

−47.764 888

−47.764 888

−47.764 888

−47.764 88

1.67 × 10−8

g15

ATMDE

961.715 022

961.715 022

961.715 022

961.715 022

6.94 × 10−13

 

ATMDE1

961.715 022

961.715 022

961.715 022

961.715 022

6.94E × 10−13

g16

ATMDE

−1.905 155

−1.905 155

−1.905 155

−1.905 155

6.78 × 10−16

 

ATMDE1

−1.905 102

−1.905 102

−1.905 102

−1.905 102

6.78 × 10−16

g18

ATMDE

−0.866 025

−0.866 025

−0.866 025

−0.866 025

7.45 × 10−10

 

ATMDE1

−0.866 025

−0.866 025

−0.866 025

−0.866 025

4.49 × 10−6

g19

ATMDE

32.655 63

32.655 86

32.656 00

32.657 25

3.75 × 10−4

 

ATMDE1

32.676 38

32.702 88

32.704 75

32.774 96

2.16 × 10−2

g24

ATMDE

−5.508 013

−5.508 013

−5.508 013

−5.508 013

3.74 × 10−15

 

ATMDE1

−5.508 013

−5.508 013

−5.508 013

−5.508 013

4.52 × 10−15

 

w/t/l

6/12/0

6/12/0

7/11/0

7/11/0

14/3/1