Table 5 Optimization result of pressure vessel design compared with other methods.

From: An intelligent hybrid grey wolf-particle swarm optimizer for optimization in complex engineering design problem

Algorithm

Statistical results

Optimum variable

f (x1,x2,x3,x4)

Best value

Worst value

Mean value

SD value

Rank

Ts

Th

R

L

HGWPSO

5.9864E+03

7.9068E+03

7.0940E+03

993.5137

1

1.2680

0.6227

64.8953

11.6436

73880.69240

HMFOPSO

1.8084E+04

7.9770E+08

2.6593E+08

4.6053E+08

11

4.6893

1.1194

108.3815

10

74527.49710

HPSOALO

1.6454E+04

3.3631E+04

2.7705E+04

7.7484E+03

8

2.6400

0.8120

65.2256

10

16454.04480

HGWOWOA

7.8948E+03

1.1057E+04

9.6865E+03

1.6225E+03

5

1.0802

0.5461

52.3730

103.3057

78940.83850

HGWOSCA

1.0577E+04

1.6015E+04

1.3662E+04

2.7771E+03

7

1.1171

0.9953

51.0125

119.4567

105760.95130

GWO

1.0115E+05

1.0688E+05

1.0403E+05

2.8617E+03

13

6.1875

6.1875

65.7073

10

101152.8429

PSO

3.4289E+04

8.7371E+04

6.0703E+04

2.6542E+04

12

2.29953

1.3102

75.6737

104.0264

342890.19320

MFO

1.7667E+04

1.077E+05

5.7454E+04

4.6053E+08

10

5.0038

3.4700

77.8128

98.7630

107774.34880

WOA

1.0276E+04

1.156E+04

1.3257E+04

2.9406E+03

6

1.3994

0.9046

57.2007

49.8198

10276.18410

SCA

7.4672E+03

1.5170E+04

1.1005E+04

3.9277E+03

3

1.4531

0.7145

68.8923

22.6484

10479.00390

ALO

7.8707E+03

9.7807E+03

8.7942E+03

956.5815

4

1.1998

0.5058

52.7850

87.7040

78700.65220

COA

1.5200E+04

5.8623E+07

1.9552E+07

3.3836E+07

9

0.9264

3.9620

43.56829

161.3903

18607.67190

GJO

6.2578E+03

7.7917E+03

6.9028E+03

795.5170

2

0.91011

0.5599

46.8555

126.9746

66580.81270

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