Table 4 Performance analysis for unimodal variable-dimension benchmark functions.

From: Chameleon swarm algorithm with Morlet wavelet mutation for superior optimization performance

F. No.

F10

F11

F12

Metrics

Median

Mean

Std. dev.

Median

Mean

Std. dev.

Median

Mean

Std. dev.

Proposed

6.19E−06

1.32E−05

2.51E−05

5.52E−21

2.40E−20

4.34E−20

0.00533168

0.00646178

0.0037578

CSA

6.60E−02

0.11517009

0.149641953

1.79E−07

2.47E−07

2.01E−07

48.04349124

50.54523542

17.34103894

ABC

1241.975

1402.788

750.5982

0.000124

0.000247

0.000282

128.8663

134.1316

29.39484

ACO

13.0063

13.7159

5.10303

7.39E−04

1.24E−03

1.16E−03

2.63076

2.70499

4.43E-01

EHO

0.006492

0.00651

0.000444

8.73E−11

1.28E−10

1.16E−10

0.353929

0.354485

0.014399

EWA

2.517293

11.39267

23.56852

8.94E−07

2.18E−06

3.29E−06

7.466396

14.35868

14.94444

GSA

2.07E−17

2.12E−17

6.08E−18

2.13E−18

3.38E−17

9.47E−17

2.17E−08

2.21E−08

3.49E-09

KHA

0.020362

0.026725

0.02001

2.22E−08

6.97E−08

1.50E − 07

0.035143

0.052076

0.061898

MBO

4596.25

14744.9

22191.3

1.71E−13

5.32E−13

8.30E−13

423.6722

455.6837

379.9961

PSO

3.21E−04

1.44E−02

6.22E−02

1.13E−15

1.75E−09

7.52E-09

2.37E-05

7.49E-05

9.73E-05

SCA

2.63E-04

1.13E-01

0.612081

4.96E-14

1.35E-09

6.45E-09

6.59E-06

4.71E-05

7.98E-05

F. No.

F13

F14

F15

Metrics

Median

Mean

Std. dev.

Median

Mean

Std. dev.

Median

Mean

Std. dev.

Proposed

0.18304515

0.22068021

0.1882462

0.00010503

0.00010722

2.36E-05

-155

-155

0

CSA

11.8880527

12.1822205

2.30788966

0.04923997

0.04781611

0.02958289

-145

-144.1

12.8716475

ABC

61.09136

61.24847

3.794662

1102.435

1285.905

580.0211

-132

-131.9

5.510804

ACO

79.6819

80.3156

4.35088

12.7369

13.5783

5.8264

-155

-155

0

EHO

0.02531

0.025286

0.001971

2.904072

2.876425

0.282671

-42

-42.1667

4.000718

EWA

0.985505

1.344147

1.023447

10.87574

29.13764

36.82736

-29.5

-31.1667

9.089909

GSA

3.22E-09

0.00784

0.0316

2.60E-17

2.46E-17

6.72E-18

-118

-118.067

2.58554

KHA

0.672508

0.707143

0.251597

0.018918

0.025874

0.024961

-69.5

-69.7

8.847949

MBO

29.15408

31.31096

25.76838

5374.206

18974.32

25001.76

-155

-141.633

23.68978

PSO

11.62564

15.29934

10.26808

4.251723

4.17188

0.300366

-106.5

-107.033

5.635377

SCA

1.20E + 01

1.27E + 01

8.59E + 00

4.380958

4.339362

4.13E-01

-108

-108.567

3.88E + 00

F. No.

F16

F17

F18

Metrics

Median

Mean

Std. dev.

Median

Mean

Std. dev.

Median

Mean

Std. dev.

Proposed

0.01837619

0.03352073

0.04473552

6.55E-35

1.12E-30

3.20E-30

0.1931209

2.63902853

7.45892528

CSA

285.490459

288.25074

47.4462996

9.06E-06

0.00072376

0.00360032

82.996705

140.372557

155.406148

ABC

194.1793

14811.07

71275.07

553.2635

4650.138

14193.3

193181.6

261336.7

222116.3

ACO

1.79E + 20

2.23E + 22

6.63E + 22

2.45E + 06

3.99E + 06

3.98E + 06

4.14E + 04

4.71E + 04

2.50E + 04

EHO

0.36319

0.357741

0.01336

3.92E-26

4.52E-26

3.18E-26

28.87013

28.86558

0.024155

EWA

16.71175

25.38461

23.04249

5.95E-09

0.013327

0.047334

256.4014

1538.986

3501.003

GSA

54.294

57.2278

38.3186

2.54E-88

4.47E-88

6.25E-88

26.0875

28.2475

11.7991

KHA

593.1884

2.47E + 12

1.28E + 13

1.01E-11

5.78E-11

1.49E-10

33.72902

61.43647

54.47974

MBO

3.94E + 28

1.81E + 38

6.85E + 38

44412.16

4.74E + 08

1.86E + 09

1.59E + 07

3.60E + 07

7.10E + 07

PSO

8.84E-06

1.63E-05

2.13E-05

0.019961

11.86305

37.93097

35.98856

239.1065

554.296

SCA

4.39E-06

5.41E-05

1.11E-04

0.004608

144.4601

548.8833

30.98788

148.2003

4.83E + 02

F. No.

F19

F20

F21

Metrics

Median

Mean

Std. dev.

Median

Mean

Std. dev.

Median

Mean

Std. dev.

Proposed

3.23E-09

3.99E-09

3.20E-09

0.039781

0.12569

0.21624

1.29E-05

2.18E-05

2.66E-05

CSA

0.000290

0.000507

0.000947

3.921985

6.11043

6.445442

9.479590

12.36284

10.195504

ABC

1.835381

1.840576

0.913245

1803.107

2367.89

1856.635

109.4227

120.606

37.40893

ACO

5.26E-03

6.02E-03

2.72E-03

1.85E + 02

2.17E + 02

1.19E + 02

1.79E + 02

2.00E + 02

1.17E + 02

EHO

6.01E-05

5.99E-05

3.21E-06

0.909557

0.906891

0.01413

0.000292

0.000289

4.27E-05

EWA

275.002

280.5366

109.2263

2.663677

13.7822

34.05692

133.3671

128.9955

29.75407

GSA

3.71E-17

3.75E-17

1.28E-17

0.666667

0.667923

0.006882

0.011159

0.017749

0.016491

KHA

5.400354

9.023223

10.98069

0.827851

0.971692

0.43077

0.586635

0.67029

0.408763

MBO

14.16177

347.1522

616.0515

8.73E + 05

7.72E + 05

6.85E + 05

1991.609

3067.511

3226.672

PSO

1.02E-07

3.38E-06

1.38E-05

0.698241

1.295457

1.484248

2.46E-03

1.56E-01

4.76E-01

SCA

1.29E-07

4.98E-06

1.29E-05

0.710611

0.90133

0.499484

0.006219

0.025125

0.041677

F. No.

F22

F23

F24

Metrics

Median

Mean

Std. dev.

Median

Mean

Std. dev.

Median

Mean

Std. dev.

Proposed

-0.9999999

-0.7666655

0.43018239

-0.9999999

-0.76666545

0.43018239

6.20E-07

8.84E-07

9.16E-07

CSA

4.34E-232

4.34E-232

0

4.34E-232

4.34E-232

0

2.13E + 00

3.41E + 00

2.98E + 00

ABC

5.67E-51

2.74E-46

1.29E-45

5.67E-51

2.74E-46

1.29E-45

2.38E + 02

2.32E + 02

8.58E + 01

ACO

6.30E-216

3.00E-206

1.70E-209

6.30E-216

3.00E-206

1.70E-209

8.90E-01

1.00E + 00

4.82E-01

EHO

1.92E-74

7.76E-70

3.53E-69

1.92E-74

7.76E-70

3.53E-69

1.03E-03

9.96E-04

1.06E-04

EWA

7.00E-42

1.69E-37

7.70E-37

7.00E-42

1.69E-37

7.70E-37

3.05E-01

2.87E + 00

6.13E + 00

GSA

7.63E-43

3.27E-37

1.04E-36

7.63E-43

3.27E-37

1.04E-36

1.53E-16

1.81E-16

1.01E-16

KHA

9.10E-228

2.71E-45

1.48E-44

9.10E-228

2.71E-45

1.48E-44

4752.622

4874.505

3272.272

MBO

4.30E-232

1.50E-210

1.80E-222

4.30E-232

1.50E-210

1.80E-222

1.39E-02

3.28E-02

4.96E-02

PSO

7.73E-199

1.77E-191

0

7.73E-199

1.77E-191

0

4.84E-06

3.39E-05

8.33E-05

SCA

6.49E-199

1.87E-193

0

6.49E-199

1.87E-193

0

1.81E-05

3.56E-04

1.06E-03

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