Table 5 Comparative results of different algorithm benchmark functions (50 dimension).

From: An Adaptive Cultural Algorithm with Improved Quantum-behaved Particle Swarm Optimization for Sonar Image Detection

Fun

Eva

ACA-IQPSO

CA-IQPSO

CPSO

IQSO

QPSO

PSO

F1

min

0.079e-15

5.993

3.022

5.687

10.155

50.737

max

6.226e-15

72.933

92.352

102.872

65.798

120.925

mean

2.789e-15

33.574

29.618

32.045

31.107

83.588

Std

1.763e-15

18.837

25.664

25.771

16.246

18.127

F2

min

0.003e-10

11.413

9.414

18.179

19.553

155.707

max

1.255e-10

239.987

292.441

238.381

352.719

392.073

mean

0.263e-10

143.819

102.649

96.500

130.760

276.319

Std

0.344e-10

66.769

74.853

67.903

94.867

57.905

F3

min

0.007

60.837

76.891

38.798

56.907

108.870

max

0.022

126.338

117.621

117.436

126.870

147.691

mean

0.011

93.902

94.424

91.066

84.466

125.894

Std

0.004

18.486

12.151

20.197

19.590

10.936

F4

min

0.011e-11

274.721

287.470

230.325

269.614

512.951

max

1.199e-11

493.853

586.535

447.801

513.792

625.668

mean

0.344e-11

381.700

361.106

359.192

388.933

558.881

Std

0.332e-11

61.096

74.189

60.012

76.402

32.732

F5

min

1.081

5.610

2.703

21.911

0.062e + 3

812.024

max

26.163

22.874

22.951

967.887

1.110e + 3

4.904e + 3

mean

15.445

11.520

10.221

289.082

0.375e + 3

2.286e + 3

Std

8.625

4.924

5.120

252.810

0.365e + 3

1.230e + 3

F6

min

0.001e-29

0.013

0.025

0.115

0.899

2.226

max

0.540e-28

5.436

17.217

25.656

24.134

71.606

mean

0.053e-28

1.916

3.834

4.258

5.964

30.829

Std

0.121e-28

1.826

4.326

5.827

6.581

18.573

F7

min

0.161e-6

21.388

48.744

25.611

30.336

101.733

max

1.009e-6

403.579

1.868e + 6

262.016

154.344

2.214e + 9

mean

0.429e-6

114.307

8.917e + 4

86.307

80.571

2.212e + 8

Std

0.211e-6

102.428

4.176e + 5

57.587

43.984

5.443e + 8

F8

min

12.171

20.174

15.978

102.736

90.465

8.113

max

67.160

75.547

58.729

126.795

127.968

19.749

mean

38.540

43.109

36.572

111.762

114.639

14.570

Std

14.330

12.646

11.917

7.749

7.380

3.224

F9

min

1.167e-14

1.277e + 3

2.456e + 3

2.320

3.478

278.003

max

1.252e-10

3.376e + 4

3.185e + 4

188.456

636.117

1.140e + 3

mean

1.643e-11

1.253e + 4

1.316e + 4

47.756

113.181

530.507

Std

3.053e-11

9.087e + 3

7.354e + 3

51.224

141.091

212.928

F10

min

1.548e-5

288.425

99.606

1.441

3.799

27.471

max

26.913

927.776

465.631

22.398

33.833

157.421

mean

1.492

552.816

297.274

11.694

17.970

83.039

Std

5.977

168.856

110.946

6.713

7.287

42.022

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