Table 6 Outcomes on multimodal benchmark functions with fixed dimensions (F14 to F23).

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

Algorithms

Metric

F14

F15

F16

F17

F18

F19

F20

F21

F22

F23

PO

Mean

−2.878e−06

0.15182

−0.31136

4.5667

−0.5

0.50963

0.48301

1.0001

1.0002

4

Std

0.039299

0.036599

0.56745

10.9012

0.70711

0.36809

0.39528

2.8094e−05

4.1593e−05

0.0006310

Rank

11

4

2

2

1

10

8

1

1

2

CPO-1

Mean

−31.9783

0.1605

0.3114

2.7083

−0.5

0.50946

0.34694

4.0001

4.0001

4.0001

Std

0.0002385

0.037731

0.56746

0.61277

0.70711

0.36833

0.18924

0.0018993

0.0006964

0.0006257

Rank

2

8

4

1

1

9

6

3

2

3

CPO-2

Mean

−31.9783

0.13678

0.31159

4.5667

−0.5

0.50977

0.34494

4.0001

4.0001

4.0001

Std

1.1397e−05

0.040622

0.567

10.9012

0.70711

0.36786

0.19009

3.9159e−05

0.0006292

0.0006306

Rank

3

1

6

2

1

11

5

3

2

3

CPO-3

Mean

−0.027781

0.15227

0.31142

2.7083

−0.5

0.5078

0.48542

3.9974

4.0001

4.0001

Std

1.9254e−05

0.035161

0.56743

0.61277

0.70711

0.37099

0.28411

0.096006

0.0006287

0.0006296

Rank

10

5

5

1

1

5

9

2

2

3

CPO-4

Mean

−31.9784

1.9508

−0.31128

5.9499

−0.5

0.50748

0.34508

4.0002

4.0001

4.0001

Std

0.0011457

1.8121

0.56761

4.9142

0.70711

0.37151

0.19014

0.14338

0.0006289

0.0006306

Rank

1

11

3

3

1

3

4

4

2

3

CPO-5

Mean

−23.9784

0.18232

−0.31141

5.9499

−0.5

0.50881

0.3447

1.0001

4.0001

4.0566

Std

11.3023

0.046545

0.56746

4.9142

0.70711

0.36938

0.19037

1.4364e−05

0.0006428

0.14926

Rank

8

9

1

3

1

7

2

1

2

6

CPO-6

Mean

−31.9783

0.15354

−0.31141

2.7083

−0.5

0.50774

0.50153

1.0001

4.0001

3.9999

Std

1.1409e−06

0.034451

0.56746

0.61277

0.70711

0.37109

0.30168

4.953e−05

0.0006276

0.02663

Rank

4

6

1

1

1

4

10

1

2

1

CPO-7

Mean

−31.9783

0.18419

−0.31141

5.9499

−0.5

0.50933

0.34383

4.0001

4.0001

4.0003

Std

8.1103e−05

0.047206

0.56746

4.9142

0.70711

0.36858

0.19075

5.3883e−05

0.0006334

0.025795

Rank

5

10

1

3

1

8

1

3

2

4

CPO-8

Mean

−0.027789

0.1604

0.3114

2.7083

−0.5

0.50815

0.3448

4.0001

4.0001

4.0009

Std

1.7353e−06

0.036725

0.56747

0.61277

0.70711

0.37043

0.19017

5.5582e−05

0.0006269

0.029768

Rank

9

7

4

1

1

6

3

3

2

5

CPO-9

Mean

−31.9783

0.14465

0.31143

2.7083

−0.5

0.50706

0.44414

1.0001

4.0001

4.0001

Std

2.5676e−06

0.036943

0.56743

0.61277

0.70711

0.37219

0.27642

1.4268e−05

0.00062777

0.00063165

Rank

9

2

6

1

1

2

7

1

2

3

CPO-10

Mean

−31.9783

0.15

−0.31141

5.9499

−0.5

0.49752

0.34508

1.0001

4.0001

4.0001

Std

1.5314e−05

0.034803

0.56745

4.9142

0.70711

0.38771

0.18987

1.122e−05

0.0006807

0.0006313

Rank

7

3

1

3

1

1

4

1

2

3