Table 4 Findings on unimodal reference functions (F1 to F7).

From: Improved optimization based on parrot’s chaotic optimizer for solving complex problems in engineering and medical image segmentation

Algorithms

Metric

F1

F2

F3

F4

F5

F6

F7

PO

Mean

−8.7718e−30

7.5698e−32

1.0805e−35

−7.7079e−30

0.99979

−0.5

0.0021875

Std

8.6429e−31

1.1135e−47

6.7961e−51

3.3405e−30

0.00098788

0.0002205

0.0060337

Rank

11

9

10

11

10

1

9

CPO-1

Mean

2.2632e−73

5.1604e−97

−3.918e−126

5.747e−113

0.010512

−0.5

0.0070087

Std

2.8675e−73

2.8143e−97

1.377e−126

3.059e−113

0.0030663

5.9731e−06

0.0066965

Rank

7

2

1

4

1

1

11

CPO-2

Mean

1.4684e−72

2.0807e−69

0

3.8769e−81

0.018519

−0.5

−0.0005080

Std

8.7735e−73

1.2017e−69

0

2.3162e−81

0.038156

4.7803e−06

0.00059386

Rank

8

6

11

10

3

1

4

CPO-3

Mean

−2.0714e−90

1.5357e−89

−2.5865e−64

7.153e−111

0.020987

−0.5

−0.0084807

Std

9.9463e−91

9.8942e−90

1.208e−64

3.098e−111

0.046121

4.5476e−06

0.0030797

Rank

2

4

9

5

5

1

1

CPO-4

Mean

−1.1389e−90

2.477e−112

−7.8564e−88

1.353e−120

0.023922

−0.5

−0.0022564

Std

8.2423e−91

1.616e−111

5.87e−88

8.498e−121

0.057475

1.0384e−05

0.00079279

Rank

3

1

3

2

7

1

3

CPO-5

Mean

3.4877e−77

1.4544e−64

−1.1489e−93

1.413e−111

0.020732

−0.5

0.0017392

Std

1.9899e−77

1.1467e−64

1.7405e−92

9.087e−112

0.04522

2.2503e−05

0.001781

Rank

6

7

2

6

4

1

8

CPO-6

Mean

−3.0811e−86

2.6024e−83

−2.866e−64

−2.7646e−86

0.024874

−0.5

−0.0057192

Std

1.257e−86

1.2487e−83

1.3627e−64

2.2293e−86

0.060637

1.1694e−05

0.00302

Rank

4

5

8

9

8

1

2

CPO-7

Mean

−1.1589e−61

0

−1.1979e−72

−7.749e−118

0.018367

−0.5

0.0062348

Std

9.0444e−62

0

7.8174e−73

4.291e−118

0.032511

9.6396e−05

0.0032556

Rank

10

10

7

3

2

1

10

CPO-8

Mean

5.1029e−81

0

6.0472e−83

−1.399e−100

1

−0.5

0.00069701

Std

1.8927e−80

0

2.811e−83

6.709e−101

2.9175e−05

1.3102e−05

0.004508

Rank

5

10

4

8

11

1

6

CPO9

Mean

−3.2055e−71

1.6997e−95

7.5616e−76

4.754e−106

0.021788

−0.5

0.0010939

Std

1.5977e−71

8.2221e−96

2.946e−76

1.194e−105

0.050635

6.6214e−06

0.0010383

Rank

9

3

6

7

6

1

7

CPO-10

Mean

2.194e−109

3.8305e−57

−1.5437e−81

5.413e−131

0.08719

−0.5

−0.0002437

Std

9.656e−109

2.0528e−56

6.6674e−81

1.383e−129

0.21091

2.4701e−06

0.0050028

Rank

1

8

5

1

9

1

5