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Table 3 Mean and ranking of the different reflection parameter β

From: Hybrid beluga whale optimization algorithm with multi-strategy for functions and engineering optimization problems

Functions

The mean, rank of the different reflection parameter β

β = 0.5

β = 0.6

β = 0.7

β = 0.8

β = 0.9

β = 1

β = 1.1

β = 1.2

β = 1.3

β = 1.4

β = 1.5

cec01

1

1

1

1

1

1

1

1

1

1

1

1

1

1

11

1

1

1

1

1

1

1

cec02

4.71

4.55

4.66

4.58

4.67

4.56

4.67

4.70

4.59

4.56

4.39

11

2

7

5

9

4

8

10

6

3

1

cec03

2.67

2.30

2.60

2.72

2.64

2.41

2.65

2.66

2.77

2.52

2.47

9

1

5

10

6

2

7

8

11

4

3

cec04

14.27

12.43

14.16

13.39

11.25

10.37

11.21

11.16

12.21

11.79

14.05

11

7

10

8

4

1

3

2

6

5

9

cec05

1.01

1.01

1.01

1.01

1.00

1.00

1.01

1.02

1.01

1.02

1.01

4

7

9

5

2

1

8

10

3

11

6

cec06

1.32

1.19

1.16

1.61

1.24

1.53

1.37

1.24

1.51

1.83

1.65

5

2

1

9

3

8

6

4

7

11

10

cec07

603.55

578.12

595.27

614.05

627.40

535.17

706.69

703.65

620.42

615.88

549.06

5

3

4

6

9

1

11

10

8

7

2

cec08

3.81

3.76

3.75

3.80

3.80

3.75

3.73

3.74

3.83

3.57

3.86

9

6

5

7

8

4

2

3

10

1

11

cec09

1.19

1.22

1.20

1.17

1.19

1.18

1.19

1.18

1.19

1.20

1.18

7

11

9

1

5

4

6

2

8

10

3

cec10

15.12

16.13

17.10

17.07

15.13

15.15

17.30

18.18

14.01

15.30

17.85

2

6

8

7

3

4

9

11

1

5

10

Mean rank

6.4

4.6

5.9

6.9

5

3

6.1

6.1

6.1

5.8

5.6

  1. The bold represents the optimal values of the evaluation indicators