Table 3 Results of 28 CEC 2017 test functions.

F1

Ave

16390.36

15274.26

121784.9

2246.506

3521.035

725.3185

1549.699

597.9355

Std

5762.984

4513.54

39413.99

860.0044

1101.601

300.3302

560.3574

179.7286

Best

9776.66

7266.987

71127.09

1119.029

1358.994

120.1386

710.385

337.5552

Worst

41382.59

26914.02

240492.2

4591.444

7102.541

1308.091

2714.528

1104.013

Rank

7

6

8

4

5

2

3

1

F2

Ave

19740.1

13654.87

132117.1

2354.767

3779.673

900.0767

1597.85

665.8007

Std

8388.282

4707.138

36424.05

814.7934

1299.684

412.1841

450.9566

328.0756

Best

11570.83

7290.891

71390.64

1201.961

1900.628

144.7142

897.6605

221.6378

Worst

51519.16

26875.37

236021.9

4876.112

6378.923

1889.331

2650.73

1710.897

Rank

7

6

8

4

5

2

3

1

F3

Ave

38929.01

20056.42

146550.2

2704.729

5340.562

1169.496

1555.42

739.2599

Std

24650.32

5389.834

67450.23

949.0901

1931.974

623.3047

469.3103

292.3168

Best

14098.18

10972.66

63262.78

749.4075

1764.695

197.729

804.5971

137.7921

Worst

126776.8

29844.65

389636.1

4544.796

9293.727

2677.381

3100.082

1343.898

Rank

7

6

8

4

5

2

3

1

F4

Ave

447.0613

359.608

470.6214

194.9837

102.3442

50.0424

51.53558

72.62289

Std

19.30658

26.8081

56.15751

39.30629

20.38368

18.26776

13.43174

26.09159

Best

411.6071

318.576

386.1919

111.8155

51.77435

22.30663

29.60683

26.86387

Worst

485.6216

426.3383

653.7859

274.7184

149.9896

117.2172

75.29625

150.2386

Rank

7

6

8

5

4

1

2

3

F5

Ave

325028.2

99145.45

341037.8

5736.793

3710.559

57.09044

69.14104

43.02481

Std

35620.65

29797.47

76733.67

5598.059

2843.834

29.41261

35.99781

26.41215

Best

242140.5

51601.55

134159.9

739.838

166.7934

25.24266

27.8477

17.8781

Worst

376352.7

149724.3

475135.6

27943.53

11227.84

129.8995

140.1747

90.69399

Rank

7

6

8

5

4

2

3

1

F6

Ave

1261.814

765.9951

1228.713

593.6837

170.7535

89.69491

71.92145

65.48505

Std

112.6612

79.03592

158.3802

131.9519

54.11342

57.86617

15.68964

17.69515

Best

898.2397

615.1741

925.3144

400.7633

80.98091

20.01599

40.34002

38.80459

Worst

1430.226

965.5229

1545.396

944.0388

272.4567

207.4737

103.5988

113.4247

Rank

8

6

7

5

4

3

2

1

F7

Ave

\(-\) 377.159

\(-\) 573.576

\(-\) 416.244

\(-\) 773.327

\(-\) 511.825

\(-\) 573.311

\(-\) 811.15

\(-\) 1.5E+43

Std

63.57724

45.37313

72.63339

112.3316

90.60397

36.33445

70.0443

4.84E+43

Best

\(-\) 553.414

\(-\) 696.159

\(-\) 604.775

\(-\) 985.893

\(-\) 733.83

\(-\) 668.043

\(-\) 969.215

\(-\) 2.6E+44

Worst

\(-\) 280.283

\(-\) 499.187

\(-\) 302.229

\(-\) 547.443

\(-\) 388.028

\(-\) 518.872

\(-\) 682.083

\(-\) 1E+39

Rank

8

4

7

3

6

5

2

1

F8

Ave

5.722125

2.287336

\(-\) 90.3668

8.129464

\(-\) 90.3668

\(-\) 90.3668

\(-\) 82.6567

\(-\) 3E+103

Std

0.232184

2.405491

1.42E-14

3.411346

1.42E-14

7.74E-06

2.009444

1.6E+104

Best

5.348394

\(-\) 2.68583

\(-\) 90.3668

0.729383

\(-\) 90.3668

\(-\) 90.3668

\(-\) 86.2228

\(-\) 9E+104

Worst

6.175079

7.508745

\(-\) 90.3668

14.43854

\(-\) 90.3668

\(-\) 90.3668

\(-\) 79.4028

\(-\) 544.032

Rank

7

6

2

8

2

4

5

1

F9

Ave

7.859585

1.882859

\(-\) 0.60917

4.14192

\(-\) 0.60917

\(-\) 0.60917

\(-\) 0.60917

\(-\) 2E+102

Std

0.505224

0.632881

1.11E-16

1.5106

1.11E-16

1.11E-16

1.11E-16

1.3E+103

Best

6.169975

0.977378

\(-\) 0.60917

0.121161

\(-\) 0.60917

\(-\) 0.60917

\(-\) 0.60917

\(-\) 7E+103

Worst

8.463553

2.922364

\(-\) 0.60917

6.155098

\(-\) 0.60917

\(-\) 0.60917

\(-\) 0.60917

\(-\) 51.1904

Rank

8

6

2

7

2

2

2

1

F10

Ave

27.70813

\(-\) 10.3646

\(-\) 53.5712

9.547615

\(-\) 44.3923

\(-\) 53.5712

\(-\) 53.5712

\(-\) 5E+99

Std

5.205864

6.099629

1.42E-14

7.589109

2.646261

1.42E-14

1.42E-14

2.8E+100

Best

7.581283

\(-\) 21.7079

\(-\) 53.5712

\(-\) 7.75474

\(-\) 53.5712

\(-\) 53.5712

\(-\) 53.5712

\(-\) 2E+101

Worst

31.81643

1.228834

\(-\) 53.5712

25.51546

\(-\) 41.3376

\(-\) 53.5712

\(-\) 53.5712

\(-\) 459.332

Rank

8

6

3

7

5

3

3

1

F11

Ave

\(-\) 928.594

\(-\) 2061.25

\(-\) 2968.71

\(-\) 2968.71

\(-\) 2826.81

\(-\) 2958.64

\(-\) 2965.36

\(-\) 4E+117

Std

135.1363

127.8206

1.36E-12

0.001986

115.6511

1.050908

1.574803

8.5E+117

Best

-1130.98

\(-\) 2332.36

\(-\) 2968.71

\(-\) 2968.71

\(-\) 2965.36

\(-\) 2960.41

\(-\) 2967.63

\(-\) 3E+118

Worst

\(-\) 678.431

\(-\) 1894.43

\(-\) 2968.71

\(-\) 2968.7

\(-\) 2372.87

\(-\) 2956.41

\(-\) 2960.98

\(-\) 3E+113

Rank

8

7

2

3

6

5

4

1

F12

Std

1169.452

875.5764

2322.572

885.7662

420.3523

52.91501

36.63748

22.68553

Best

13119.34

6944.853

10416.99

879.7966

112.6125

43.16138

79.50999

39.80919

Worst

18537.69

10575.31

20397.19

4759.118

1756.88

243.1293

278.5379

148.2482

Rank

8

6

7

5

4

3

2

1

F13

Ave

1.17E+09

4.71E+08

1.64E+09

23658801

19866940

1276.159

1849.588

186.0049

Std

1.22E+08

1.36E+08

5.79E+08

35086261

21345735

2107.314

1921.987

215.8787

Best

8.57E+08

2.34E+08

8.13E+08

98540.02

278881.7

81.90974

197.8234

15.02459

Worst

1.37E+09

8.6E+08

3.04E+09

1.17E+08

74504145

11339.16

8011.013

861.1705

Rank

7

6

8

5

4

2

3

1

F14

Ave

20.55451

21.0767

21.22937

20.34958

21.01813

21.00969

20.86115

20.57452

Std

0.091166

0.050263

0.078061

2.738795

0.064285

0.043008

0.135245

0.377544

Best

20.31387

20.9888

21.01737

9.221197

20.8551

20.92349

20.53308

20.00103

Worst

20.72167

21.187

21.36783

21.24764

21.11189

21.10998

21.02578

21.07211

Rank

2

7

8

1

6

5

4

3

F15

Ave

31.08557

35.9302

82.70136

32.93115

11.9522

2.066781

7.163248

3.01162

Std

0.261735

5.59808

10.38579

3.177097

2.975002

1.006947

1.232726

0.996155

Best

30.54141

28.74334

62.78564

27.18412

3.361548

0.684767

4.865848

1.084125

Worst

31.67137

56.91089

98.38665

39.42577

16.02069

3.383453

9.412996

5.242846

Rank

5

7

8

6

4

1

3

2

F16

Ave

594.9008

385.4391

558.463

69.89105

52.95416

2.597163

0.503066

0.000235

Std

33.44309

33.32432

58.24028

32.45081

24.83393

0.845638

0.228482

0.000227

Best

515.6976

323.6651

452.5787

34.24972

5.400209

1.494102

0.13408

3.87E-05

Worst

638.7122

446.4413

721.0028

168.5943

105.4668

4.56431

1.030278

0.001034

Rank

8

6

7

5

4

3

2

1

F17

Ave

4.839954

3.048085

4.822181

1.034259

1.178009

0.102787

0.032653

0.014416

Std

0.405947

0.244332

0.526547

0.306854

0.153559

0.068759

0.025853

0.016457

Best

3.196709

2.475471

3.457002

0.421228

0.783047

0.023076

0.003302

1.24E-09

Worst

5.325538

3.500722

6.060877

1.682323

1.684028

0.282841

0.121787

0.053899

Rank

8

6

7

4

5

3

2

1

F18

Ave

16731.67

8137.728

16285.51

3382.595

930.7571

157.8395

136.2912

95.89401

Std

765.5193

1150.65

2043.941

1493.962

563.0715

43.31238

22.44457

27.37024

Best

14870.77

5712

12074.25

733.25

274.6916

49.30984

92.17999

49.62664

Worst

18174.5

10159.25

20614.5

6939.25

2538.502

233.2719

181.7811

158.3148

Rank

8

6

7

5

4

3

2

1

F19

Ave

98.04325

79.1096

105.9417

59.95555

46.73388

17.66944

31.89367

36.72545

Std

5.28926

5.53246

8.256637

7.265089

7.078254

5.824603

10.94815

10.86692

Best

89.58958

66.90288

89.95235

45.21141

33.90327

8.606595

14.89938

18.79102

Worst

109.2924

92.11404

125.5473

75.36737

59.03599

37.94426

57.98126

57.87767

Rank

7

6

8

5

4

1

2

3

F20

Ave

4.982317

8.283657

9.288992

9.129113

8.057498

7.928323

6.871566

4.441001

Std

0.727351

0.468564

0.679801

0.350126

0.527314

0.39647

0.946003

2.056662

Best

3.397255

6.835538

7.883686

8.424282

6.617262

7.269141

3.546776

1.786408

Worst

6.423946

9.070479

10.31134

9.709902

9.281343

8.751545

8.139509

8.747879

Rank

2

6

8

7

5

4

3

1

F21

Ave

67445.7

30033.12

66871.83

5944.941

3619.129

251.1147

329.3822

229.3483

Std

9016.148

3605.984

10075.86

2103.804

1926.571

42.43206

52.90613

58.73787

Best

45867.26

23309.62

41791.64

2311.301

717.0305

133.1851

212.5481

117.4258

Worst

88192.66

36253.71

88355.96

10829.64

8884.589

340.8627

417.5176

342.3145

Rank

8

6

7

5

4

2

3

1

F22

Ave

3.93E+10

7.79E+09

4.43E+10

1.16E+08

1.34E+08

207788

372423.9

67120.56

Std

1.17E+10

3.4E+09

2.22E+10

1.36E+08

1.24E+08

347682.1

786556.2

182228.8

Best

1.94E+10

2.27E+09

1.27E+10

11651577

6147306

1540.225

1199.08

37.20334

Worst

6E+10

1.73E+10

1.2E+11

7.4E+08

5.03E+08

1406803

4118863

964448.2

Rank

7

6

8

4

5

2

3

1

F23

Ave

21.06779

21.03788

21.20693

21.19242

21.02427

21.0348

21.02531

21.02971

Std

0.044029

0.057323

0.080397

0.038082

0.076971

0.054319

0.06183

0.071168

Best

20.96282

20.89373

21.01334

21.09161

20.89776

20.89389

20.91385

20.85072

Worst

21.14187

21.15155

21.36726

21.26513

21.13628

21.11738

21.17033

21.12169

Rank

6

5

8

7

1

4

2

3

F24

Ave

91.43276

68.88141

115.6148

36.01533

27.02552

8.152929

11.77475

13.8755

Std

10.33423

8.068163

20.65332

6.887154

4.793997

3.895589

3.722382

4.415046

Best

74.41131

55.22059

81.01546

19.93047

16.64385

1.808132

5.640359

3.277399

Worst

113.2778

86.29732

167.9191

51.14618

36.57314

16.52161

18.10662

22.74272

Rank

7

6

8

5

4

1

2

3

F25

Ave

1073.615

775.1709

1094.399

350.25

271.7935

36.98215

44.17926

53.14991

Std

91.06728

77.13654

138.0716

69.61146

65.10425

21.79589

19.47186

44.56591

Best

931.4218

643.2293

749.7917

231.1964

129.4514

9.415654

19.18936

5.178364

Worst

1268.655

1009.39

1342.32

486.7187

367.6462

93.87166

97.67148

179.1858

Rank

7

6

8

5

4

1

2

3

F26

Ave

17.48915

8.274159

17.02248

1.759184

1.990522

0.424011

0.432566

0.023887

Std

2.34074

1.278369

3.964884

0.412131

0.478537

0.194148

0.181923

0.012649

Best

11.20961

5.656325

9.22956

1.265472

1.117279

0.131875

0.117404

0.002944

Worst

22.00205

11.79399

25.55075

3.089761

2.943767

0.937747

0.878427

0.05999

Rank

8

6

7

4

5

2

3

1

F27

Ave

67070.72

28757.71

67645.61

7754.825

3806.555

246.7407

352.9514

293.3594

Std

9902.239

4618.194

15099.48

3327.85

1875.217

70.43844

76.38448

56.98996

Best

44844.25

19707.94

32415.99

3490.25

523.3656

83.92798

242.1166

165.327

Worst

84548.25

37635.75

94855.42

18620.52

8312.75

556.6591

501.3527

412.2416

Rank

7

6

8

5

4

1

3

2

F28

Ave

130.6911

114.9146

151.3742

95.85742

69.2167

48.9047

58.60287

69.34061

Std

9.947596

9.512374

11.99604

14.74497

8.970095

8.386626

11.46358

10.90694

Best

110.4925

96.15783

124.8565

71.22044

58.24728

32.10655

40.69642

47.29991

Worst

145.5178

131.5152

171.95

128.8579

88.85181

65.27887

100.5927

86.75665

Rank

7

6

8

5

3

1

2

4