Table 6 Optimization result of string/compression spring 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)

Best value

Worst value

Mean value

SD value

Rank

W

D

N

HGWPSO

0.0132

0.0138

0.0134

3.3074E-04

1

0.0592

0.5664

4.9299

0.013069

HMFOPSO

1.6915E+09

1.7682E+09

1.7257E+09

3.9028E+07

13

1.7809

0.7952

8.5056

1.718e+09

HPSOALO

9.3035E+08

9.3035E+08

9.3035E+08

0

11

0.05001

0.2500

2

9.303e+08

HGWOWOA

0.0209

0.0264

0.0233

0.0028

5

0.0643

0.52914

10.0854

0.026408

HGWOSCA

0.0145

0.0168

0.0157

0.0011

3

0.0666

0.8328

2.5335

0.016768

GWO

0.0343

5.3568E+07

1.7856E+07

3.0928E+07

9

0.1173

1.0773

15

5.357e+07

PSO

9.9971E+08

1.1786E+09

1.0594E+09

1.0324E+08

12

0.4189

0.3425

10.711

9.998e+08

MFO

9.3175E+08

1.1156E+09

1.0157E+09

9.2934E+07

10

0.8394

0.8339

4.8842

1.116e+09

WOA

0.0185

9.3035E+08

4.6932E+08

4.6523E+08

6

0.05000

0.2500

2

9.303e+08

SCA

0.0234

0.0326

0.0294

0.052

7

0.0782

1.3001

2.0356

0.032058

ALO

0.0168

0.0181

0.0175

6.8278E-04

4

0.06832

0.8722

2.4497

0.018109

COA

8.1084E+08

8.4566E+08

8.2572E+08

1.7958E+07

8

0.05059

0.3282

2.3873

8.207e+08

GJO

0.0134

0.0136

0.0135

1.1603E-04

2

0.05001

0.3147

15

0.013976

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