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Table 2 Mean and ranking of the different reflection parameter α

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

Functions

The mean, rank of the different reflection parameter α

α = 0.5

α = 0.6

α = 0.7

α = 0.8

α = 0.9

α = 1

α = 1.1

α = 1.2

α = 1.3

α = 1.4

α = 1.5

cec01

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

11

1

1

1

cec02

4.79

4.57

4.50

4.57

4.53

4.34

4.45

4.71

4.59

4.67

4.53

11

6

3

7

5

1

2

10

8

9

4

cec03

2.86

2.60

2.13

2.44

2.53

2.52

2.66

2.74

3.05

2.71

3.26

9

5

1

2

4

3

6

8

10

7

11

cec04

25.88

19.85

19.39

16.34

14.51

12.94

13.53

14.41

13.55

15.63

15.00

11

10

9

8

5

1

2

4

3

7

6

cec05

1.08

1.06

1.02

1.01

1.01

1.00

1.02

1.04

1.07

1.08

1.12

9

7

5

2

3

1

4

6

8

10

11

cec06

3.12

2.88

1.93

1.51

1.46

1.45

1.22

1.53

2.08

1.93

2.41

11

10

6

4

3

2

1

5

8

7

9

cec07

605.99

601.84

749.69

616.05

597.50

600.80

691.22

632.90

628.68

661.35

668.87

4

3

11

5

1

2

10

7

6

8

9

cec08

4.02

4.17

3.88

3.91

3.93

3.69

3.98

3.96

3.94

4.05

3.84

9

11

3

4

5

1

8

7

6

10

2

cec09

1.24

1.24

1.22

1.22

1.21

1.16

1.18

1.23

1.25

1.23

1.24

10

9

4

5

3

1

2

7

11

6

8

cec10

18.53

17.08

13.38

13.13

11.11

15.03

20.44

20.49

20.25

19.55

21.26

6

5

3

2

1

4

9

10

8

7

11

Mean rank

8.1

6.7

4.6

4

3.1

1.7

4.5

7.5

6.9

7.2

7.2

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