Table 5 The rHV values obtained by the competitive algorithms.

From: An improved multi-objective particle swarm optimization algorithm for the design of foundation pit of rail transit upper cover project

ID

 

MOGWO

MOMVO

MOSSA

MOSMA

MOPSO

MOIPSO

TP1

Mean

1.1570E + 00

1.1528E + 00

1.1852E + 00

1.1699E + 00

1.1527E + 00

1.1456E + 00

 

Std

4.2081E−03

1.4500E−03

5.9764E−03

1.3939E−02

1.8185E−03

1.8757E−04

TP2

Mean

1.1602E + 00

1.1787E + 00

1.1959E + 00

1.1685E + 00

1.2803E + 00

1.1663E + 00

 

Std

8.3879E−03

4.4029E−02

2.3095E−02

8.2137E−03

3.5125E−02

8.4971E−03

TP3

Mean

1.8680E + 00

1.9003E + 00

1.9881E + 00

1.8588E + 00

1.8851E + 00

1.8529E + 00

 

Std

7.1853E−03

8.5067E−03

6.4983E−02

8.3678E−04

4.4464E−02

5.6354E−04

TP4

Mean

1.1545E + 00

1.1518E + 00

1.1846E + 00

1.1897E + 00

1.1525E + 00

1.1454E + 00

 

Std

3.8022E−03

1.8115E−03

6.6763E−03

2.2729E−02

2.4537E−03

1.5926E−04

TP5

Mean

1.1578E + 00

1.1612E + 00

1.1757E + 00

1.1551E + 00

1.1508E + 00

1.1454E + 00

 

Std

5.8143E−03

1.9751E−03

4.0478E−03

7.4899E−03

4.2216E−03

1.0910E−04

TP6

Mean

2.3868E + 00

2.4601E + 00

2.9926E + 00

2.4230E + 00

2.4344E + 00

2.3739E + 00

 

Std

7.3031E−03

2.4587E−01

1.8237E + 00

6.8788E−02

2.6480E−02

1.5502E−03

TP7

Mean

7.7826E−02

8.2614E−02

8.3504E−02

8.3998E−02

9.5610E−02

7.9041E−02

 

Std

1.4243E−04

2.6569E−03

1.3806E−03

7.1764E−04

2.4528E−02

2.9242E−03

TP8

Mean

6.8968E−02

6.9152E−02

6.9330E−02

6.9861E−02

7.7308E−02

6.8879E−02

 

Std

3.9694E−05

4.9654E−05

8.2215E−05

5.2233E−04

2.1392E−02

1.7268E−05

TP9

Mean

6.3888E−01

6.5197E−01

6.4724E−01

8.7813E−01

6.3846E−01

6.3558E−01

 

Std

3.3641E−03

5.4462E−02

7.6354E−03

1.4489E−01

2.8035E−03

1.2665E−04

TP10

Mean

5.4336E−02

5.4495E−02

5.4640E−02

5.4549E−02

5.5037E−02

5.4247E−02

 

Std

3.6199E−05

4.0563E−05

6.9886E−05

4.1626E−04

1.5270E−03

7.2067E−06

TP11

Mean

4.1292E−01

3.6776E−01

3.6411E−01

3.2889E−01

3.9861E−01

3.5143E−01

 

Std

3.0093E−02

3.5211E−02

3.6077E−02

3.3862E−02

4.9353E−02

9.8215E−03

TP12

Mean

2.7049E−01

2.5046E−01

2.5118E−01

2.2766E−01

2.7181E−01

2.3924E−01

 

Std

1.4374E−02

1.9206E−02

2.1430E−02

2.7284E−02

3.9512E−02

4.2977E−03

TP13

Mean

1.1655E + 00

1.1501E + 00

1.2183E + 00

-7.2895E−02

4.4915E−01

1.1519E + 00

 

Std

2.7001E−02

7.8964E−04

1.0608E−01

4.0785E−02

4.5621E + 00

1.4503E−02

TP14

Mean

3.7261E−01

3.5471E−01

3.5378E−01

3.3909E−01

3.8481E−01

3.4739E−01

 

Std

2.8360E−02

3.2546E−02

3.0049E−02

2.6671E−02

8.0526E−02

1.2268E−02

TP15

Mean

2.5106E−01

2.4897E−01

2.4229E−01

2.2181E−01

2.4829E−01

2.3403E−01

 

Std

9.1150E−03

1.4895E−02

1.9800E−02

2.5702E−02

2.3067E−02

4.6928E−03

TP16

Mean

7.7788E−02

8.3715E−02

8.3578E−02

8.3793E−02

1.2745E−01

7.7721E−02

 

Std

2.0296E−05

2.7118E−03

2.2878E−03

6.3767E−04

1.2644E−01

1.3618E−05

TP17

Mean

6.8965E−02

6.9178E−02

6.9369E−02

6.9787E−02

8.5111E−02

6.8883E−02

 

Std

3.3408E−05

6.8952E−05

1.0279E−04

3.1088E−04

3.5404E−02

1.4803E−05

TP18

Mean

6.3956E−01

6.3957E−01

6.5233E−01

9.2448E−01

6.3918E−01

6.3559E−01

 

Std

3.0895E−03

3.2479E−03

8.0959E−03

1.4951E−01

5.1054E−03

1.0329E−04

TP19

Mean

5.4328E−02

5.4508E−02

5.4649E−02

5.4578E−02

5.4584E−02

5.4248E−02

 

Std

2.0207E−05

4.1924E−05

8.5727E−05

5.1561E−04

4.7495E−04

1.2092E−05

TP20

Mean

2.6596E−01

2.4536E−01

2.4589E−01

2.2288E−01

2.6805E−01

2.3916E−01

 

Std

1.1087E−02

1.9432E−02

1.6988E−02

2.1727E−02

3.0021E−02

4.3317E−03

TP21

Mean

2.4994E−01

2.4721E−01

2.3935E−01

2.3285E−01

2.5103E−01

2.3549E−01

 

Std

1.0471E−02

2.1624E−02

1.4942E−02

2.4451E−02

1.5094E−02

5.1365E−03

TP22

Mean

2.6269E−01

2.4000E−01

2.4497E−01

2.2303E−01

2.5204E−01

2.3496E−01

 

Std

1.4045E−02

1.6589E−02

1.4528E−02

2.8151E−02

1.5695E−02

3.3715E−03

TP23

Mean

2.6644E−01

2.5416E−01

2.4113E−01

2.2017E−01

2.7758E−01

2.3498E−01

 

Std

1.3370E−02

1.5939E−02

1.0315E−02

2.0365E−02

3.4474E−02

4.1594E−03

TP24

Mean

2.5805E−01

2.4337E−01

2.3938E−01

2.2101E−01

2.5665E−01

2.3590E−01

 

Std

1.1050E−02

1.2546E−02

1.5220E−02

2.5725E−02

3.1715E−02

3.9984E−03

  1. Significant values are in bold