Table 7 The IGDF 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

8.5468E−03

6.5198E−03

2.2995E−02

8.1294E−03

5.9222E−03

2.5257E−03

 

Std

2.1846E−03

8.7371E−04

1.9206E−03

1.6857E−03

7.1728E−04

1.0467E−04

TP2

Mean

9.5515E−03

2.7285E−02

2.6095E−02

1.5083E−02

6.3341E−02

1.4024E−02

 

Std

5.3821E−03

4.0687E−02

6.4527E−03

4.7220E−03

2.1218E−02

6.1126E−03

TP3

Mean

5.2788E−03

1.2015E−02

2.3158E−02

3.8380E−03

6.7240E−03

2.3493E−03

 

Std

1.0048E−03

1.7366E−03

3.7457E−03

3.4025E−04

3.8293E−03

1.0988E−04

TP4

Mean

6.8661E−03

5.9506E−03

1.9459E−02

8.1946E−03

5.5405E−03

2.4257E−03

 

Std

1.6371E−03

1.0731E−03

1.7409E−03

1.7700E−03

9.9526E−04

9.1353E−05

TP5

Mean

9.6554E−03

1.1415E−02

1.9608E−02

5.7720E−03

5.2897E−03

2.4703E−03

 

Std

3.6857E−03

1.0814E−03

2.2468E−03

2.3748E−03

2.1804E−03

6.5773E−05

TP6

Mean

3.9180E−03

7.1973E−03

1.8353E−02

5.6569E−03

1.0443E−02

2.6470E−03

 

Std

2.9480E−04

9.1862E−04

3.6170E−03

2.8656E−03

4.0691E−03

1.2958E−04

TP7

Mean

2.0317E−02

2.6278E−01

1.8574E−01

1.2595E−01

3.0559E−01

5.8823E−02

 

Std

2.2433E−02

9.8250E−02

4.0910E−02

4.9416E−02

2.5900E−01

1.0787E−01

TP8

Mean

2.1159E−02

3.7910E−02

5.4262E−02

3.0324E−02

2.2897E−01

1.1606E−02

 

Std

2.9810E−03

4.4885E−03

7.3646E−03

7.9532E−03

3.3599E−01

1.6913E−03

TP9

Mean

5.6436E−03

1.0715E−02

1.8578E−02

1.5423E−02

7.3809E−03

2.1252E−03

 

Std

2.1447E−03

1.4405E−02

3.2678E−03

8.2066E−03

4.9186E−03

1.3988E−04

TP10

Mean

2.7850E−02

5.2242E−02

6.8782E−02

2.5594E−02

9.8962E−02

1.3106E−02

 

Std

4.5880E−03

5.9846E−03

1.0115E−02

1.2280E−02

1.5347E−01

1.1319E−03

TP11

Mean

2.1591E−01

1.3991E−01

1.5700E−01

1.2130E−01

2.1808E−01

9.1685E−02

 

Std

6.6061E−02

1.9874E−02

1.6267E−02

1.9979E−02

9.6049E−02

3.6316E−03

TP12

Mean

2.2511E−01

1.3157E−01

1.8893E−01

1.5000E−01

4.1425E−01

9.2759E−02

 

Std

5.6969E−02

2.1701E−02

2.9966E−02

1.8690E−02

1.6347E−01

3.5739E−03

TP13

Mean

8.1370E−03

4.7153E−03

1.8535E−02

5.6284E−02

3.5475E−02

3.1957E−03

 

Std

3.1754E−03

2.8659E−04

3.0599E−03

1.6803E−02

2.8777E−02

2.6221E−04

TP14

Mean

1.3649E−01

1.4035E−01

1.7659E−01

1.6332E−01

2.3852E−01

9.8903E−02

 

Std

1.7283E−02

1.3265E−02

1.5188E−02

1.6619E−02

1.7749E−01

7.4769E−03

TP15

Mean

1.2513E−01

1.4636E−01

1.8341E−01

1.4710E−01

1.9297E−01

1.0291E−01

 

Std

9.8741E−03

1.5911E−02

1.6693E−02

1.6311E−02

8.4177E−02

1.2630E−02

TP16

Mean

1.9877E−01

2.4343E−01

2.6583E−01

1.4885E−01

6.1912E−01

1.9415E−01

 

Std

1.1636E−03

4.8728E−02

3.9451E−02

4.4732E−02

4.2749E−01

4.2011E−04

TP17

Mean

1.0328E−01

1.1700E−01

1.3641E−01

7.6933E−02

4.6011E−01

9.5413E−02

 

Std

2.6676E−03

5.6220E−03

8.7409E−03

7.4139E−03

5.1952E−01

1.7723E−03

TP18

Mean

9.1022E−02

8.6010E−02

9.6766E−02

6.8602E−02

8.6905E−02

8.3046E−02

 

Std

4.4171E−03

1.5945E−03

4.6806E−03

4.5128E−03

2.5132E−03

1.7015E−04

TP19

Mean

1.6210E−01

1.7599E−01

2.0472E−01

1.4492E−01

2.0303E−01

1.4756E−01

 

Std

6.4253E−03

1.2161E−02

1.6993E−02

9.0120E−03

9.1653E−02

1.5241E−03

TP20

Mean

3.0629E−01

2.4575E−01

2.7787E−01

2.1402E−01

4.0929E−01

2.0256E−01

 

Std

3.8097E−02

1.7685E−02

2.8653E−02

1.2033E−02

1.3565E−01

5.7944E−03

TP21

Mean

2.0525E−01

2.3107E−01

2.6502E−01

2.3167E−01

2.5890E−01

1.9284E−01

 

Std

1.7583E−02

1.2726E−02

1.1410E−02

1.0414E−02

7.1277E−02

5.4464E−03

TP22

Mean

2.5635E−01

2.0709E−01

2.1965E−01

1.9569E−01

2.4508E−01

1.6687E−01

 

Std

5.7817E−02

1.5214E−02

9.0920E−03

1.4996E−02

5.3930E−02

2.9362E−03

TP23

Mean

3.5603E−01

3.0741E−01

3.1226E−01

2.5393E−01

5.1035E−01

2.5171E−01

 

Std

5.1100E−02

3.7120E−02

1.3942E−02

1.0111E−02

1.7163E−01

5.0916E−03

TP24

Mean

2.7442E−01

2.4468E−01

2.5727E−01

2.2052E−01

3.1200E−01

2.0833E−01

 

Std

5.0324E−02

1.1122E−02

1.2080E−02

1.5772E−02

9.8288E−02

4.8848E−03