Table 10 Optimization results of CEC 2011 test suite.

C11-F1

Mean

5.920103

6.183228

6.738518

7.663933

6.039163

7.299507

13.57783

15.02735

11.12614

20.03647

23.68149

19.48093

25.589

Best

2E-10

0.059473

0.981494

2.086606

0.026815

1.917445

8.453028

11.70977

1.171431

17.66003

22.05158

11.75673

24.27333

Worst

12.30606

12.36437

12.7852

13.42714

12.33324

12.89891

17.51285

18.02634

18.2779

22.43279

24.77817

25.79976

27.26328

Std

7.476538

7.198024

7.106069

6.833248

7.348851

6.659064

4.489697

2.968292

7.876573

2.230811

1.454978

7.575792

1.390322

Median

5.687176

6.154532

6.593691

7.570993

5.898301

7.190838

14.17272

15.18664

12.52762

20.02652

23.9481

20.18362

25.40969

Rank

1

3

4

6

2

5

8

9

7

11

12

10

13

C11-F2

Mean

−26.3179

−26.118

−25.712

−24.7491

−26.2297

−24.7205

−18.4083

−6.80337

−22.4843

−9.13516

−14.3114

−22.2721

−11.4007

Best

−27.0676

−26.8407

−26.4316

−25.4532

−26.9672

−25.1705

−21.957

−9.02685

−24.6968

−10.3883

−19.8679

−23.7385

−14.0856

Worst

−25.4328

−25.3903

−25.0044

−23.972

−25.4155

−24.3606

−14.3388

−5.11857

−18.7559

−8.05643

−9.79705

−19.5489

−9.44663

Std

0.767703

0.724938

0.671114

0.691313

0.744805

0.383093

4.234766

1.834314

2.856253

1.056973

5.031236

2.029882

2.352976

Median

−26.3856

−26.1205

−25.706

−24.7856

−26.268

 − 24.6755

−18.6688

−6.53403

−23.2422

−9.04796

−13.7903

−22.9005

−11.0353

Rank

1

3

4

5

2

6

9

13

7

12

10

8

11

C11-F3

Mean

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

Best

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

Worst

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

Std

2.08E–19

2.02E–16

2.65E–10

5.21E–12

9.1E–17

2.43E–15

1.02E–16

1.14E–12

3.98E–15

8.96E–14

2.3E–19

6.59E–20

3.16E–18

Median

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

1.15E–05

Rank

3

1

13

11

2

8

7

12

9

10

5

4

6

C11-F4

Mean

0

0

0

0

0

0

0

0

0

0

0

0

0

Best

0

0

0

0

0

0

0

0

0

0

0

0

0

Worst

0

0

0

0

0

0

0

0

0

0

0

0

0

Std

0

0

0

0

0

0

0

0

0

0

0

0

0

Median

0

0

0

0

0

0

0

0

0

0

0

0

0

Rank

1

1

1

1

1

1

1

1

1

1

1

1

1

C11-F5

Mean

−34.1274

−33s.9869

−33.4735

−32.6509

−34.0665

−33.375

−27.5271

−26.2509

−31.4941

−8.28938

−26.6454

−5.892

−6.84436

Best

−34.7494

−34.6029

−34.1393

−33.4062

−34.6859

−33.5294

−27.7046

−31.484

−34.1989

−10.7244

−31.2638

−9.82996

−8.43368

Worst

−33.3862

−33.4208

−32.8248

−31.8708

−33.4042

−33.2165

−27.2122

−23.6131

−27.3312

−6.42043

−23.2282

−3.93246

−4.93201

Std

0.612958

0.546605

0.591415

0.735292

0.577418

0.14038

0.23884

4.037264

3.202875

1.998215

3.849145

3.023656

1.676274

Median

−34.1871

−33.962

−33.465

−32.6633

−34.088

−33.3771

−27.5958

−24.9532

−32.2231

−8.00632

−26.0448

−4.90278

−7.00588

Rank

1

3

4

6

2

5

8

10

7

11

9

13

12

C11-F6

Mean

−24.1119

−23.8724

−23.516

−22.9111

−24.0056

−22.3573

−19.8144

−7.9834

−19.4891

0

−21.6613

−0.95891

−1.96296

Best

−27.4298

−27.1611

−26.6314

−25.8646

−27.3106

−25.0833

−22.9152

−16.8457

−22.2461

0

−26.9874

−3.83566

−7.85186

Worst

−23.0059

−22.7382

−22.3718

−21.8038

−22.8869

−21.0226

−12.7528

0

−17.8223

0

−16.7906

0

0

Std

2.415463

2.394967

2.27064

2.152354

2.406217

2.08112

5.248052

10.09718

2.315651

0

4.76581

2.094307

4.287194

Median

−23.0059

−22.7951

−22.5303

−21.9881

−22.9125

−21.6616

−21.7947

−7.54395

−18.944

0

−21.4335

0

0

Rank

1

3

4

5

2

6

8

10

9

13

7

12

11

C11-F7

Mean

0.860699

0.871324

0.907054

0.970842

0.865551

0.908844

1.750956

0.883102

1.073368

1.804349

1.101417

1.149726

1.82829

Best

0.582266

0.609562

0.650113

0.730509

0.594615

0.646949

1.64062

0.800399

0.808639

1.580978

0.914546

0.816436

1.426014

Worst

1.025027

1.013836

1.059499

1.129486

1.020055

1.059054

1.913631

0.966353

1.306208

1.94451

1.323653

1.428968

2.040515

Std

0.219737

0.203006

0.20541

0.190162

0.212148

0.208132

0.127446

0.098176

0.224655

0.174751

0.206477

0.349056

0.302915

Median

0.91775

0.930948

0.959302

1.011686

0.923767

0.964686

1.724787

0.882827

1.089312

1.845955

1.083734

1.176751

1.923316

Rank

1

3

5

7

2

6

11

4

8

12

9

10

13

C11-F8

Mean

220

220.3405

222.1997

230.7489

220.1693

223.8941

266.5276

224.5

227.5731

224.5

249.0859

495.4306

222.75

Best

220

219.956

220.6414

226.762

219.996

220

245.4229

220

220

220

220

251

220

Worst

220

220.725

224.0346

235.1052

220.3427

233.822

313.0551

238

235.1462

238

301

606.3905

231

Std

0

0.484819

1.604077

3.75

0.218589

7.283881

34.14759

9.828182

9.549379

9.828182

41.94558

183.6816

6.006111

Median

220

220.3405

222.0615

230.5642

220.1693

220.8771

253.8161

220

227.5731

220

237.6718

562.166

220

Rank

1

3

4

9

2

6

11

7

8

7

10

12

5

C11-F9

Mean

8789.286

10,582.77

46,680.33

115,573.8

9598.543

15,223.47

378,067.3

146,438.6

44,149.83

450,581.2

908,719.2

1,195,008

2,145,417

Best

5457.674

7894.025

39,942.32

83,096.81

7106.216

11,013.91

209,009

82,594.58

18,796.43

372,659.4

776,984.3

959,191.4

2,055,477

Worst

14,042.29

15,642.6

51,101.42

131,782.7

14,764.83

20,468.25

639,683.2

221,696.4

77,480.91

577,846.5

978,482.7

1,463,389

2,271,153

Std

4040.59

3772.539

5184.928

24,089.06

3856.725

4542.441

214,422.1

62,641.89

27,082.33

98,531.16

97,986.7

294,523.9

115,752.2

Median

7828.591

9397.229

47,838.78

123,707.9

8261.564

14,705.85

331,788.6

140,731.8

40,160.98

425,909.4

939,704.9

1,178,726

2,127,520

Rank

1

3

6

7

2

4

9

8

5

10

11

12

13

C11-F10

Mean

−21.4889

−21.0979

−20.8902

−20.4228

−21.3142

−20.6354

−12.6331

−14.0006

−13.871

−10.232

−12.2919

−10.3421

−10.016

Best

−21.8299

−21.4464

−21.2161

−20.7713

−21.6586

−21.1909

−13.3341

−21.1288

−14.3623

−10.3156

−12.8412

−10.3763

−10.0336

Worst

−20.7878

−20.4449

−20.2387

−19.7949

−20.6347

−19.9709

−12.1541

−10.4071

−12.6687

−10.1842

−11.4186

−10.2991

−10.0025

Std

0.518028

0.490697

0.484134

0.470434

0.505223

0.548418

0.544438

5.27389

0.883739

0.064444

0.74327

0.038528

0.017366

Median

−21.669

−21.2501

−21.053

−20.5626

−21.4817

−20.6899

−12.5221

−12.2332

−14.2264

−10.2142

−12.454

−10.3466

−10.0139

Rank

1

3

4

6

2

5

9

7

8

12

10

11

13

C11-F11

Mean

571,712.3

742,421.9

675,338.1

1,467,342

648,720.9

1,173,966

1,304,182

1,384,293

3,936,396

5,689,705

1,497,804

5,701,929

6,697,096

Best

260,837.9

466,634.7

386,344.9

1,170,537

353,643.8

894,529.2

1,190,534

603,550.3

3,739,692

5,689,705

1,344,136

5,689,705

6,654,808

Worst

828,560.9

980,059.1

917,618.6

1,710,560

896,926.1

1,411,503

1,456,040

2,963,819

4,315,401

5,689,705

1,679,064

5,714,152

6,784,052

Std

271,080

246,881.2

254,206.4

256,302

260,140

287,705.3

120,975.1

1,167,134

282,438.7

0

152,222.7

15,413.55

64,409.66

Median

598,725.2

761,497

698,694.5

1,494,135

672,156.8

1,194,916

1,285,077

984,901.8

3,845,245

5,689,705

1,484,009

5,701,929

6,674,762

Rank

1

4

3

8

2

5

6

7

10

11

9

12

13

C11-F12

Mean

1,199,805

1,211,309

1,422,984

2,415,324

1,205,078

1,589,444

5,845,383

1,340,623

1,431,117

15,685,253

6,263,817

2,428,911

15,862,796

Best

1,155,937

1,169,359

1,373,887

2,289,705

1,162,072

1,563,793

5,424,799

1,170,807

1,262,817

14,751,661

5,942,068

2,236,087

15,726,437

Worst

1,249,353

1,265,507

1,476,057

2,544,926

1,256,726

1,612,360

6,051,865

1,504,078

1,572,455

16,408,417

6,496,367

2,663,553

16,005,029

Std

48,993.46

52,223.07

52,541.69

117,800

50,406.9

26,873.37

316,690.3

148,633.4

140,192.2

759,437.6

261,428

192,429.7

124,270.4

Median

1,196,965

1,205,184

1,420,995

2,413,333

1,200,757

1,590,812

5,952,435

1,343,803

1,444,597

15,790,467

6,308,418

2,408,001

15,859,858

Rank

1

3

5

8

2

7

10

4

6

12

11

9

13

C11-F13

Mean

15,444.2

15,444.09

15,445.65

15,532.49

15,445.26

15,449.9

15,537.51

15,514.52

15,502.94

15,984.05

140,082

15,495.68

31,517.17

Best

15,444.19

15,443.73

15,445.55

15,490.5

15,445.1

15,448.78

15,493.87

15,492.18

15,495.79

15,646.58

100,822.9

15,476.66

15,462.15

Worst

15,444.21

15,444.72

15,445.85

15,636.83

15,445.54

15,451.17

15,596.65

15,557.03

15,515.31

16,605.73

193,331

15,536

79,293.98

Std

0.009445

0.478391

0.145075

76.58996

0.215158

1.194419

52.32485

32.82946

9.444644

474.0736

45,481.82

29.66999

34,782.32

Median

15,444.2

15,443.96

15,445.61

15,501.32

15,445.2

15,449.83

15,529.76

15,504.44

15,500.33

15,841.94

133,087

15,485.03

15,656.28

Rank

2

1

4

9

3

5

10

8

7

11

13

6

12

C11-F14

Mean

18,295.35

18,340.82

18,335.58

39,546.26

18,317.17

18,437.51

19,256.06

19,536.54

19,263.05

341,308.2

19,175.82

19,211.78

19,197.69

Best

18,241.58

18,282.19

18,280.3

33,471.35

18,261.2

18,373.24

19,098.84

19,430.12

19,113.29

31,488.89

18,855.78

19,030.02

18,882.71

Worst

18,388.08

18,430.95

18,427.97

49,676.34

18,408.73

18,504.76

19,382.88

19,630.9

19,455.49

660,566.8

19,413.1

19,363.98

19,532.85

Std

74.38679

71.57923

75.54823

7936.489

73.00297

60.7239

141.7149

91.07887

164.8416

329,799.5

261.0218

150.1261

290.1312

Median

18,275.87

18,325.07

18,317.03

37,518.68

18,299.37

18,436.02

19,271.26

19,542.58

19,241.71

336,588.6

19,217.2

19,226.55

19,187.6

Rank

1

4

3

12

2

5

9

11

10

13

6

8

7

C11-F15

Mean

32,883.58

32,887.2

40,442.45

222,574.1

32,887.58

35,071.35

219,895.5

33,122.71

33,084.29

17,036,307

327,796.7

33,330.48

8,766,184

Best

32,782.17

32,789.41

33,989.56

110,195.9

32,787.79

32,840

33,017.83

33,039.96

33,047.44

3,566,969

289,724.9

33,319.18

3,988,196

Worst

32,956.46

32,959.66

47,742.85

533,443.4

32,960.27

41,562.65

314,838.5

33,187.07

33,149.24

25,406,717

353,867.8

33,338.43

15,026,014

Std

79.94256

77.67837

8120.385

226,670.8

78.92186

4726.113

138,936.3

71.03783

50.84676

10,844,349

32,583.82

9.361516

5,526,697

Median

32,897.86

32,899.86

40,018.7

123,328.5

32,901.13

32,941.36

265,862.9

33,131.91

33,070.24

19,585,771

333,797

33,332.16

8,025,262

Rank

1

2

8

10

3

7

9

5

4

13

11

6

12

C11-F16

Mean

133,550

134,169.5

133,946.4

316,794.7

133,838.9

134,949.1

142,544.9

142,673.9

146,279

98,220,886

20,674,185

87,910,864

84,408,504

Best

131,374.2

132,008.7

131,841.4

168,845.8

131,669.7

132,724.9

136,575.8

133,079.6

143,646

95,713,439

10,493,845

72,716,866

68,217,489

Worst

136,310.8

137,075.2

136,516.6

611,139.3

136,665.3

137,375.5

147,961.5

152,615.5

151,904

1.01E + 08

37,415,902

1.05E + 08

1.08E + 08

Std

2485.329

2515.941

2309.548

217,959.4

2498.282

2282.485

5188.973

8996.661

4151.659

2,442,036

12,712,449

15,220,715

18,439,517

Median

133,257.5

133,797.1

133,713.8

243,596.9

133,510.4

134,848

142,821.2

142,500.2

144,783

98,060,477

17,393,496

86,936,590

80,723,913

Rank

1

4

3

9

2

5

6

7

8

13

10

12

11

C11-F17

Mean

1,926,615

1,983,558

2.35E + 08

1.57E + 09

1,952,428

1.31E + 08

9.76E + 09

3,236,561

3,055,798

2.47E + 10

1.24E + 10

2.3E + 10

2.42E + 10

Best

1,916,953

1,922,926

2.14E + 08

1.13E + 09

1,919,784

1.08E + 08

6.96E + 09

2,333,961

2,042,163

2.37E + 10

1.09E + 10

2.03E + 10

2.26E + 10

Worst

1,942,685

2,075,218

2.57E + 08

1.91E + 09

1,990,296

1.49E + 08

1.3E + 10

3,933,469

4,978,873

2.57E + 10

1.31E + 10

2.66E + 10

2.73E + 10

Std

12,470.83

72,807.99

20,877,833

3.69E + 08

33,768.09

23,145,715

2.76E + 09

806,246.3

1,444,811

9.08E + 08

1.1E + 09

3.1E + 09

2.33E + 09

Median

1,923,412

1,968,045

2.35E + 08

1.61E + 09

1,949,815

1.33E + 08

9.55E + 09

3,339,406

2,601,077

2.46E + 10

1.28E + 10

2.26E + 10

2.34E + 10

Rank

1

3

7

8

2

6

9

5

4

13

10

11

12

C11-F18

Mean

942,057.5

946,540.9

1,509,543

12,785,127

944,146.7

1,055,430

9,641,866

992,950.7

1,034,076

34,159,342

12,198,065

1.49E + 08

1.26E + 08

Best

938,416.2

940,015.9

1,245,098

9,086,579

939,204.9

1,028,519

4,144,222

965,927.8

967,816.8

27,054,473

9,077,664

1.25E + 08

1.22E + 08

Worst

944,706.9

957,937.7

1,987,616

14,482,383

950,740.2

1,085,666

16,934,301

1,005,714

1,209,033

36,959,114

15,413,362

1.65E + 08

1.31E + 08

Std

2882.138

8582.375

378,440.5

2,754,779

5262.437

28,895.02

5,897,910

19,955.69

127,634.6

5,193,739

3,091,078

19,727,839

4,154,662

Median

942,553.5

944,104.9

1,402,730

13,785,774

943,320.8

1,053,767

8,744,471

1,000,080

979,727.2

36,311,890

12,150,617

1.53E + 08

1.26E + 08

Rank

1

3

7

10

2

6

8

4

5

11

9

13

12

C11-F19

Mean

1,025,341

1,042,836

1,599,321

12,616,413

1,033,303

1,176,661

10,291,018

1,524,075

1,373,985

39,223,360

6,818,060

1.91E + 08

1.27E + 08

Best

967,927.7

986,740.3

1,496,947

10,986,585

976,479.3

1,115,159

2,076,737

1,145,008

1,240,381

27,439,684

2,515,303

1.73E + 08

1.24E + 08

Worst

1,167,142

1,186,697

1,701,410

15,579,735

1,176,043

1,291,762

18,641,683

2,062,414

1,556,914

48,957,518

8,991,630

2.2E + 08

1.31E + 08

Std

103,555.5

104,922.3

110,315.2

2,297,524

104,166.9

87,598.01

8,515,809

421,168.3

144,637.7

10,180,470

3,211,288

22,502,803

3,102,132

Median

983,146.6

998,953.7

1,599,462

11,949,667

990,344.2

1,149,861

10,222,827

1,444,439

1,349,322

40,248,119

7,882,654

1.85E + 08

1.27E + 08

Rank

1

3

7

10

2

4

9

6

5

11

8

13

12

C11-F20

Mean

941,250.4

944,067.1

1,441,411

13,471,341

942,588.1

1,031,567

7,326,695

976,129.4

1,000,440

38,105,472

15,671,493

1.76E + 08

1.27E + 08

Best

936,143.2

940,087.2

1,366,949

11,896,204

937,988.7

1,011,525

6,903,007

964,906.8

978,541.6

37,267,078

10,376,829

1.61E + 08

1.21E + 08

Worst

946,866.6

948,285.3

1,514,452

15,865,552

947,574.4

1,066,940

7,892,426

988,890.8

1,017,515

39,011,796

24,312,978

1.91E + 08

1.32E + 08

Std

5208.733

4026.358

66,988.52

1,843,844

4675.262

27,750.41

462,083.5

11,664.05

18,346.54

792,412.9

6,650,888

18,415,907

4,991,383

Median

940,995.9

943,948

1,442,122

13,061,803

942,394.6

1,023,902

7,255,674

975,360

1,002,851

38,071,507

13,998,083

1.76E + 08

1.28E + 08

Rank

1

3

7

9

2

6

8

4

5

11

10

13

12

C11-F21

Mean

12.71443

13.21891

13.79709

19.32464

12.9428

14.62207

39.23486

29.10064

22.70134

109.9653

43.65333

115.531

112.0717

Best

9.974206

10.56784

11.22903

18.86382

10.24258

12.34717

35.89634

25.53524

20.87773

51.93913

38.02115

99.51578

63.46985

Worst

14.97499

15.4836

16.01574

19.82398

15.20538

16.70867

43.43102

32.44838

25.05194

162.7197

46.73021

128.9644

137.425

Std

2.506594

2.464445

2.376962

0.43465

2.487614

2.288612

3.637903

4.087745

1.999736

49.54801

4.310747

15.66338

37.53049

Median

12.95425

13.41211

13.9718

19.30539

13.16162

14.71622

38.80603

29.20946

22.43784

112.6011

44.93097

116.8218

123.6959

Rank

1

3

4

6

2

5

9

8

7

11

10

13

12

C11-F22

Mean

16.12513

16.58732

17.43416

21.06867

16.33467

17.90737

46.79181

34.00153

25.2922

111.7436

49.91934

116.2026

100.6545

Best

11.50133

12.23683

12.84301

17.27831

11.83377

13.43906

40.60225

25.89615

24.07836

71.91816

41.07087

97.62745

99.72026

Worst

19.55286

19.81785

20.8036

24.87509

19.67374

21.17591

51.45752

39.30212

26.20769

132.3202

60.00375

128.152

102.0605

Std

4.36122

4.089225

4.36193

3.566982

4.238879

4.068777

5.337981

6.715222

1.102373

29.69358

8.479631

15.15482

1.127333

Median

16.72317

17.14729

18.04502

21.06064

16.91559

18.50726

47.55373

35.40392

25.44138

121.368

49.30137

119.5155

100.4187

Rank

1

3

4

6

2

5

9

8

7

12

10

13

11

Sum rank

25

62

111

168

45

118

183

158

147

241

201

222

237

Mean rank

1.136364

2.818182

5.045455

7.636364

2.045455

5.363636

8.318182

7.181818

6.681818

10.95455

9.136364

10.09091

10.77273

Total rank

1

3

4

8

2

5

9

7

6

13

10

11

12

Wilcoxon: p-value

1.68E–15

8.56E–15

1.50E–15

6.22E–15

3.21E–15

1.58E–15

9.00E–15

1.58E–15

6.54E–15

3.37E–15

1.58E–15

3.68E–12