Table 5 The results of the comparative algorithms using 10 problems.

F14

Worst

12.67050581

7.87399298

20.153487

10.7631989

10.76318078

12.6705058

8.84083596

7.87399298

12.6705058

12.67050581

12.6705058

0.99800384

Average

11.22871328

3.46153322

11.6423197

5.91452234

4.430366407

10.0008871

5.91041948

3.95657622

10.2484056

6.357423538

10.2484168

0.99800384

Best

6.903335694

0.99800384

2.98210516

1.04142317

0.998003838

1.9920309

0.99800384

1.9920309

2.98210516

0.998003838

2.98214977

0.99800384

STD

2.883585058

3.05112364

7.05382488

5.59880129

4.398662004

5.33923745

3.49166286

2.77279444

4.84420032

6.237319475

4.84417802

2.2204E−16

p-value

0.739880311

0.05544802

0.75564276

0.28608619

0.12566764

0.94748619

0.19646438

0.06504

0.00876924

0.362494117

0.99999751

NaN

h

0

0

0

0

0

0

0

0

1

0

0

NaN

Rank

11

2

12

6

4

8

5

3

9

7

10

1

F15

Worst

0.137547173

0.02239807

0.01944894

0.00177878

0.012153699

0.00122511

0.0190415

0.02570566

0.00053727

0.020510841

0.00169393

0.00179588

Average

0.038608658

0.00618421

0.0059945

0.00105948

0.007492163

0.00063369

0.00686398

0.00868632

0.00036622

0.010486822

0.00136168

0.00129502

Best

0.000535841

0.00051012

0.00036524

0.00060692

0.002251949

0.00038238

0.00099899

0.00156496

0.00030749

0.000322095

0.0009246

0.00062639

STD

0.06634506

0.01081119

0.00901165

0.00050419

0.004231065

0.00039744

0.00850489

0.01150378

0.00011406

0.011491072

0.00032616

0.00054839

p-value

0.30364893

0.40117229

0.33797078

0.55045645

0.027154943

0.09865452

0.23910628

0.24663593

0.0160758

0.161158633

0.8413999

NaN

h

0

0

0

0

1

0

0

0

1

0

0

NaN

Rank

12

7

6

3

9

2

8

10

1

11

5

4

F16

Worst

−1.0316274

−1.03162845

−1.0316113

−1.0306182

−1.028709671

−1.0316279

−1.03162845

−1.0316285

−1.03162845

−1.02163122

−1.00555441

−1.0316285

Average

−1.03162788

−1.03162845

−1.0316191

−1.031206

−1.030836903

−1.0316281

−1.03162845

−1.0316285

−1.03162845

−1.02437939

−1.02166111

−1.0316285

Best

−1.03162842

−1.03162845

−1.0316274

−1.0316189

−1.031628453

−1.0316284

−1.03162845

−1.0316285

−1.03162845

−1.02642711

−1.02967662

−1.0316285

STD

4.36226E−07

4.527E−14

7.6834E−06

0.00042098

0.001421256

2.0698E−07

0

1.0972E−12

1.2229E−15

3.14018E−16

0.01092679

0.00210927

p-value

0.000467632

0.00046743

0.00047071

0.00071621

0.002270408

0.00046756

0.00046743

0.00046743

0.00046743

0.000467432

0.64251835

NaN

h

1

1

1

1

1

1

1

1

1

1

0

NaN

Rank

7

4

8

9

10

6

1

5

3

11

12

2

F17

Worst

0.526415671

0.39788736

0.41147589

0.42646937

2.705391088

0.41571201

0.4171287

0.39788736

0.39788736

0.397887358

2.7084418

0.39788736

Average

0.482973813

0.39788736

0.40323364

0.41317838

0.976186241

0.40234778

0.40387738

0.39788736

0.39788736

0.397887358

0.97852727

0.39788736

Best

0.446946925

0.39788736

0.39810975

0.39933327

0.398349732

0.39789263

0.3989155

0.39788736

0.39788736

0.397887358

0.39820477

0.39788736

STD

0.032811055

7.3672E−13

0.00602327

0.01127907

1.152804502

0.00890949

0

9.9374E−13

8.1745E−14

5.58341E−11

1.15328659

0.00885603

p-value

0.003486362

0.22488475

0.9082412

0.24221356

0.359111453

0.81571174

0.22488475

0.22488475

0.22488475

0.224884753

0.35747627

NaN

h

1

0

0

0

0

0

0

0

0

0

0

NaN

Rank

10

3

7

9

11

6

8

4

2

5

12

1

F18

Worst

133.2192847

3

3.09374022

3.01364678

88.04332156

3.00141575

3

3

3

3

6.55938074

5.05063346

Average

58.97489119

3

3.03266837

3.00402691

24.2609788

3.00068982

3

3

3

3

4.26636628

3.72964718

Best

3.000000006

3

3.00010867

3.00007263

3.000000213

3.00009702

3

3

3

3

3.1504242

3.05495372

STD

66.33325762

2.4688E−13

0.0433615

0.00646017

42.52156184

0.00057392

3.4111E−15

7.4852E−12

1.4043E−15

2.39659E−12

1.58034074

0.90077889

p-value

0.146858659

0.15635165

0.17313076

0.15829406

0.371593032

0.15668131

0.15635165

0.15635165

0.15635165

0.156351651

0.57664708

NaN

h

0

0

0

0

0

0

0

0

0

0

0

NaN

Rank

12

3

8

7

11

6

2

5

1

4

10

9

F19

Worst

−2.98834265

−3.86133876

−3.6975601

−3.8401859

−3.711626854

−3.8582594

−3.86278215

−3.8625048

−3.48737595

−3.86278181

−3.44732398

−3.8627809

Average

−3.63220834

−3.86209723

−3.8141571

−3.8493715

−3.81469797

−3.8607235

−3.86278215

−3.8627099

−3.66914744

−3.86278206

−3.65762283

−3.8627818

Best

−3.85245084

−3.86278199

−3.8618

−3.8536653

−3.86262932

−3.8627572

−3.86278215

−3.8627821

−3.84637169

−3.86278215

−3.84685809

−3.8627821

STD

0.429287542

0.00079161

0.07863385

0.00618548

0.070912407

0.00185776

4.4409E−16

0.00013686

6.2128E−07

1.68459E−07

0.16436573

0.14838242

p-value

0.876131657

0.04062558

0.13490915

0.05136628

0.127109859

0.04165783

0.04012357

0.04017605

0.04012379

0.040123631

0.92048994

NaN

h

0

1

0

0

0

1

1

1

1

1

0

NaN

Rank

12

5

9

7

8

6

1

4

10

2

11

3

F20

Worst

−2.75474647

−3.17185684

−2.7688127

−1.1472715

−2.836003074

−3.09247

−1.92840801

−3.2001825

−3.20301393

−3.13707717

−2.58543778

−3.3219935

Average

−2.8778129

−3.21843614

−3.0296705

−2.0811773

−3.068273249

−3.1867005

−2.59686222

−3.291542

−3.29224986

−3.24603228

−2.80402094

−3.3219944

Best

−3.10170884

−3.32199517

−3.2343212

−3.1051935

−3.258252624

−3.3218714

−2.9649216

−3.3219952

−3.32199517

−3.32199501

−3.05923775

−3.3219952

STD

0.156493328

0.07020118

0.19497552

1.07152142

0.180382859

0.0976611

9.1835E−07

0.06090632

0.05949062

0.091740964

0.19728207

0.4582083

p-value

0.289934065

0.03645003

0.13282148

0.41021419

0.104040794

0.04541057

0.01943959

0.02383167

0.02370102

0.032065768

0.43804396

NaN

h

0

1

0

0

0

1

1

1

1

1

0

NaN

Rank

9

5

8

12

7

6

11

3

2

4

10

1

F21

Worst

−2.18596912

−5.10077214

−0.8759254

−0.4961999

−2.589564162

−5.0550343

−2.6828604

−2.6828604

−5.05517393

−0.88199088

−9.71138683

−5.0551977

Average

−3.58677362

−8.89009279

−4.4641144

−0.687209

−4.409238943

−7.5982171

−7.01111437

−5.1435295

−8.26917227

−5.28623527

−9.92193825

−8.8786992

Best

−4.81224691

−10.1531997

−8.6719126

−0.8812226

−9.825834623

−10.145149

−10.1531997

−10.1532

−10.1382589

−10.1525611

−10.113395

−10.1532

STD

1.094929468

2.52621377

3.28190227

0.22043117

3.611107272

2.93657959

3.75520938

3.52204404

2.54900097

3.794085536

0.19589341

2.21635324

p-value

0.009091973

0.72442828

0.10302954

0.00049216

0.118291292

0.7278166

0.5849053

0.18372469

0.73054048

0.223389158

0.18792064

NaN

h

1

0

0

1

0

0

0

0

0

0

0

NaN

Rank

11

2

9

12

10

5

6

8

4

7

1

3

F22

Worst

−2.30981772

−1.83759297

−0.9100821

−0.9051754

−1.832669608

−5.0688767

−2.75193356

−2.7658973

−5.08767182

−2.76583636

−4.93777097

−10.370167

Average

−3.17348251

−4.92228356

−3.8750238

−2.3383417

−4.219754845

−5.8573638

−7.17165923

−3.4846996

−7.74530619

−6.82382085

−7.3508181

−10.387623

Best

−3.68809229

−10.4029406

−4.9929731

−4.6593709

−6.359102207

−8.2073083

−10.4029406

−3.7243003

−10.4029406

−10.4029039

−10.1075203

−10.396087

STD

0.605095198

3.76046295

1.97881003

1.67564413

1.950460194

0.01209859

3.8552782

0.47920151

3.06877183

4.15087361

2.74388523

1.56663435

p-value

0.018689878

0.66234071

0.16727114

0.02199515

0.238372091

0.00116889

0.55090379

0.02745879

0.31515858

0.678315047

0.38098354

NaN

h

1

0

0

1

0

1

0

1

0

0

0

NaN

Rank

11

7

9

12

8

6

4

10

2

5

3

1

F23

Worst

−1.59516963

−2.87114271

−1.1884186

−0.5569522

−2.422560173

−5.085234

−2.42173403

−1.6765533

−5.12848079

−3.83525475

−4.94136018

−10.522643

Average

−3.33598532

−8.62009304

−3.2261868

−1.738865

−5.831923294

−6.4555886

−3.12998071

−5.2942177

−7.83244529

−5.83117935

−7.74327225

−10.526756

Best

−4.78624715

−10.5364098

−5.037733

−2.6657177

−8.686879719

−10.495533

−3.8354268

−10.53641

−10.5364098

−10.5256726

−10.5361665

−10.532165

STD

1.552366882

3.83263356

1.67133162

0.87761112

3.213306715

0.00468345

0.81458219

3.77375206

3.12226927

3.188474934

3.2108987

2.69334972

p-value

0.091531795

0.39106445

0.08773292

0.01580344

0.776120642

0.02330328

0.05599628

0.63422345

0.52908397

0.774876896

0.56144338

NaN

h

0

0

0

1

0

1

0

0

0

0

0

NaN

Rank

9

2

10

12

6

5

11

8

3

7

4

1

Mean ranking

1.0400E+01

4.0000E+00

8.6000E+00

8.9000E+00

8.4000E+00

5.6000E+00

5.7000E+00

6.0000E+00

3.7000E+00

6.3000E+00

7.8000E+00

2.6000E+00

Final ranking

12

3

10

11

9

4

5

6

2

7

8

1