Table 7 Analysis and comparative performance of HGMRFO and eight competitive algorithms on IEEE CEC2011 real-world optimization problems (continue).

F1

17.47391973

5.470206253

\(+\)

14.49837455

8.171808684

\(+\)

18.39017045

4.832461831

\(+\)

15.36003099

5.171082772

\(+\)

11.87523968

5.524929846

\(+\)

F2

− 26.3244037

1.656718405

–

− 26.88276512

0.99276452

–

− 16.18868877

4.294438424

\(+\)

− 25.94040242

2.455154294

–

− 26.62955583

0.749051232

–

F3

1.15149E−05

5.42962E−19

\(+\)

1.15149E−05

2.25642E−13

\(\approx\)

1.15149E−05

3.15322E−16

\(+\)

1.15149E−05

1.66472E−12

\(+\)

-0.00016673

0.001272924

–

F4

14.63862887

1.455780439

–

16.40534169

2.437398369

\(+\)

19.6290455

3.270347476

\(+\)

16.36766023

2.308586321

\(+\)

14.9065653

1.800079766

–

F5

− 33.09055389

1.913171334

–

− 33.23537396

2.298288735

–

− 32.8725704

2.805451308

–

− 33.47936543

1.744126034

–

-34.38493325

1.869106511

–

F6

− 21.75572359

2.998252639

\(\approx\)

-25.80920512

2.896806136

–

− 13.71199977

1.259428287

\(+\)

− 21.5756295

2.988086601

\(+\)

− 24.63935566

3.217541092

–

F7

0.902931326

0.16389891

–

1.363284765

0.203944019

–

0.902780281

0.297667563

–

0.679256235

0.140544396

–

0.862423633

0.137602163

–

F8

222.2352941

6.932786555

\(+\)

220

0

\(\approx\)

226.1960784

9.325276635

\(+\)

220.1960784

1.400280084

\(\approx\)

222.5598923

18.28128751

\(\approx\)

F9

1589904.934

159370.1404

\(+\)

2135.206489

993.4579601

\(+\)

168422.6584

52202.81824

\(+\)

1283.549936

840.0984967

–

19127.71596

20848.31813

\(+\)

F10

− 18.12383684

1.624224768

\(+\)

− 15.49218405

2.975753264

\(+\)

− 15.83479707

5.102266813

\(+\)

-21.43541163

0.068391611

–

− 20.60571549

1.872118363

\(+\)

F11

52058.8457

501.9985769

–

52529.47876

505.5468325

\(+\)

52610.30649

605.8632139

\(+\)

52119.66365

585.5883124

–

52418.09374

612.1166024

\(\approx\)

F12

25182957.66

459011.4329

\(+\)

17440882.59

56153.82026

\(\approx\)

23000560.47

494246.0606

\(+\)

23783090.49

1097011.939

\(+\)

20710781.14

312942.3379

\(+\)

F13

15486.55437

25.32639738

\(+\)

15468.22705

19.4346151

\(+\)

15478.33871

18.48017631

\(+\)

20987.3529

10339.77788

\(+\)

15467.65744

16.77429917

\(+\)

F14

19204.57794

176.424332

–

18932.32268

234.841745

–

19293.25358

197.0702334

–

19148.02808

147.896134

–

19169.49537

145.1695674

–

F15

34815.04219

9335.104487

\(+\)

33098.41705

88.44948903

\(+\)

33139.7153

71.13062863

\(+\)

33209.61569

36.76770821

\(+\)

33077.44101

78.75436034

\(+\)

F16

140010.8218

1792.983414

\(+\)

141479.4314

5022.125221

\(+\)

140007.4902

3321.066885

\(+\)

139806.732

1628.401082

\(+\)

138409.456

3958.554788

\(\approx\)

F17

1942026.469

6446.837188

–

2871549.196

1311885.532

\(+\)

2011168.457

105698.1168

\(+\)

2367006.454

486255.7322

\(+\)

1977864.331

56206.98396

\(\approx\)

F18

1110518.393

503000.1294

–

1258159.344

420559.2879

\(+\)

951569.1447

31903.50043

–

944986.0217

2523.787517

–

4474834.607

645974.5764

\(+\)

F19

1784687.323

659327.8104

\(+\)

1820408.143

347330.8087

\(+\)

1116859.444

125359.5343

–

1125227.721

107804.1035

–

4995847.583

565237.9004

\(+\)

F20

1312959.317

1299154.349

\(\approx\)

1198325.572

351096.6118

\(+\)

947681.2809

2995.376903

–

945006.8768

2615.209042

–

4607782.125

749556.5714

\(+\)

F21

18.39059825

3.209004489

\(+\)

19.94380741

4.515853198

\(+\)

18.50395419

3.316156684

\(+\)

15.65184742

1.738959283

\(+\)

15.31140339

2.333974974

\(+\)

F22

30.88547681

5.371732874

\(+\)

23.97320647

4.397468261

\(+\)

22.62070558

2.348901878

\(+\)

23.64428422

1.889889231

\(+\)

21.46801535

2.180518032

\(+\)

W/T/L

12/2/8

14/3/5

16/0/6

11/1/10

11/4/7