Table 8 Optimization result of gear train 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

y1

y2

y3

y4

HGWPSO

1.0847E−10

0.73226

0.24409

0.42277

1

5

5

15

11.5525

1.0847e−10

HMFOPSO

0.049028

8.2495

3.5085

4.2478

13

5.0789

8.2401

13.6159

8.40500

0.049028

HPSOALO

0.035741

0.73226

0.50009

0.40213

9

14.5583

15

15

14.5583

0.73226

HGWOWOA

2.6635E−06

4.7091E−05

2.0276E−05

2.36E−05

7

5

5.7210

14.2062

14.11567

2.6635e−06

HGWOSCA

1.088E−06

5.1218E−06

2.8835E−06

2.0531E−06

4

5.1167

5.1513

13.1050

13.7247

5.1218e−06

GWO

1.2187E−06

0.003919

0.0013073

0.0022619

6

5

6.5422

15

15

1.2187e−06

PSO

0.026329

3.1529

1.2036

1.7002

10

14.4685

13.3570

12.45651

8.08086

3.1529

MFO

0.14432

0.61196

0.30851

0.26309

11

6.25445

13.3518

14.6642

10.8641

0.14432

WOA

0.035741

0.73226

0.50009

0.40213

9

5

5

5

5

0.73226

SCA

1.1618E−06

2.1518E−05

8.9877E−06

1.0963E−05

5

5

5

15

11.6386

1.1618e−06

ALO

9.1606E−08

2.0076E−06

9.3967E−07

9.767E−07

3

5

6.4789

15

15

9.1606e−08

COA

9.9406E−06

0.14285

0.048325

0.081858

12

5.0316

5

7.0761

6.8081

0.14285

GJO

5.1967E−09

7.8778E−08

3.3584E−08

3.9565E−08

2

5.0757

5

12.4581

14.1066

1.6777e−08

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