Table 6 HV values for 5 MOPSO and ASDMOPSO.

From: Multi-objective particle swarm algorithm based on angular segmentation archive and dynamic update tactics

Problem

M

D

 

CMOPSO

NMPSO

MOPSOCD

MOPSO

MPSOD

ASDMOPSO

ZDT1

2

30

Mean

Std

7.1997e−1

(5.99e−4)−

6.8912e−1

(1.27e−2)−

7.2098e−1

(1.21e−3)≈

0.0000e + 0

(0.00e + 0)−

5.9247e−1 (4.19e−2)−

7.2129e−01

(6.03e−05)

ZDT2

2

30

Mean

Std

4.4443e−1

(1.05e−3)−

4.3373e−1

(1.34e−2)−

3.5891e−1

(1.42e−1)−

0.0000e + 0

(0.00e + 0)−

2.8091e−1 (8.73e−2)−

4.4657e−01

(2.05e−05)

ZDT3

2

30

Mean

Std

5.9994e−1

(1.39e−3)−

5.7102e−1

(7.16e−3)−

5.8591e−1

(2.77e−2)−

6.5564e−4

(1.75e−3)−

4.6280e−1 (4.59e−2)−

6.0005e−01

(1.37e−04)

ZDT4

2

10

Mean

Std

0.0000e + 0

(0.00e + 0)−

 

0.0000e + 0

(0.00e + 0)−

0.0000e + 0

(0.00e + 0)−

0.0000e + 0 (0.00e + 0)−

6.9846e−01

(1.33e−01)

ZDT6

2

10

Mean

Std

3.9035e−1

(4.98e−5) + 

3.8978e−1

(2.06e−4)−

3.8905e−1

(1.22e−3)−

0.0000e + 0

(0.00e + 0)−

3.7749e−1 (8.73e−3)−

3.9015e−01

(1.31e−05)

UF1

2

30

Mean

Std

5.7482e−1

(1.77e−2) + 

5.3366e−1

(2.34e−2)−

9.2488e−2

(9.05e−2)−

1.7961e−1

(5.35e−2)−

3.6349e−1 (5.50e−2)−

4.9805e−01

(1.61e−02)

UF2

2

30

Mean

Std

6.4681e−1

(7.49e−3) + 

6.1819e−1

(6.27e−3)−

5.3943e−1

(2.07e−2)−

6.1132e−1

(8.75e−3)−

5.7994e−1 (1.11e−2)−

6.4061e−01

(4.58e−03)

UF3

2

30

Mean

Std

2.6683e−1

(3.81e−2)−

2.8723e−1

(4.79e−2)−

2.2645e−1

(7.63e−2)−

1.7937e−1

(2.64e−2)−

1.7360e−1 (1.69e−2)−

3.4111e−01

(3.21e−02)

UF4

2

30

Mean

Std

2.8868e−1

(1.20e−2)

3.6166e−1

(1.28e−2) + 

3.3391e−1

(1.08e−2)−

2.1306e−1

(4.15e−3)−

3.0658e−1 (4.40e−3)−

1.2726e−01

(3.36e−03)

UF5

2

30

Mean

Std

9.4110e−3

(2.20e−2) + 

0.0000e + 0

(0.00e + 0)≈

0.0000e + 0

(0.00e + 0)≈

0.0000e + 0

(0.00e + 0)≈

0.0000e + 0 (0.00e + 0)≈

0.0000e + 00

(0.00e + 0)

UF6

2

30

Mean

Std

1.5727e−1

(5.15e−2) + 

2.2070e−2

(3.27e−2)≈

0.0000e + 0

(0.00e + 0)−

0.0000e + 0

(0.00e + 0)−

0.0000e + 00(0.00e + 0)−

7.1557e−03

(6.25e−02)

UF7

2

30

Mean

Std

4.5126e−1

(7.87e−2) + 

3.9036e−1

(9.47e−2)≈

2.6253e−2

(3.79e−2)−

3.8297e−2

(2.33e−2)−

2.7589e−1 (5.15e−2)−

4.1627e−01

(1.26e−02)

UF8

3

30

Mean

Std

1.8293e−2

(1.78e−2)−

2.7633e−1

(6.28e−2)−

1.0132e−2

(1.28e−2)−

2.5649e−1

(3.32e−2)−

5.7408e−2 (1.93e−2)−

3.4690e−01

(2.89e−02)

UF9

3

30

Mean

Std

1.8081e−2

(2.69e−2)−

3.1197e−1

(5.18e−2) + 

3.0344e−2

(3.39e−2)

2.5578e−1

(2.39e−2)−

1.1504e−1 (2.81e−2)−

2.8639e−01

(2.11e−02)

UF10

3

30

Mean

Std

0.0000e + 0

( 0.00e + 0)−

0.0000e + 0

(0.00e + 0)−

0.0000e + 0

(0.00e + 0)−

0.0000e + 0

(0.00e + 0)−

0.0000e + 0 (0.00e + 0)−

2.7421e−01

(3.86e−02)

DTLZ1

3

7

Mean

Std

0.0000e + 0

(0.00e + 0)−

0.0000e + 0

(0.00e + 0)−

0.0000e + 0

(0.00e + 0)−

0.0000e + 0

(0.00e + 0)−

0.0000e + 0 (0.00e + 0)−

5.9780e−04

(6.98e + 00)

DTLZ2

3

12

Mean

Std

5.5924e−1

(1.11e−3)−

5.6875e−1

(9.49e−4) + 

4.7859e−1

(1.87e−2)−

5.4019e−1

(7.15e−3)−

5.4961e−1 (2.17e−3)−

4.1042e−02

(8.54e−03)

DTLZ3

3

12

Mean

Std

0.0000e + 0

(0.00e + 0)−

0.0000e + 0

(0.00e + 0)−

0.0000e + 0

(0.00e + 0)−

0.0000e + 0

(0.00e + 0)−

0.0000e + 0 (0.00e + 0)−

4.1886e−03

(2.53e + 01)

DTLZ4

3

12

Mean

Std

5.4030e−1

(8.49e−2)−

5.5358e−1

(5.63e−2) + 

2.8241e−1

(5.10e−2)−

4.6129e−1

(6.25e−2)−

4.2632e−1 (4.24e−2)−

3.7090e−01

(8.65e−01)

DTLZ5

3

12

Mean

Std

1.9895e−1

(2.56e−4) + 

1.9818e−1

(3.83e−4)−

1.7164e−1

(9.56e−3)−

1.9858e−1

(9.37e−4)−

1.4248e−1 (7.36e−3)−

2.4535e−02

(1.29e + 00)

DTLZ6

3

12

Mean

Std

1.6476e−1

(7.55e−2)−

1.9804e−1

(6.40e−4) + 

1.7311e−1

(5.43e−2)−

0.0000e + 0

(0.00e + 0)−

5.8464e−3 (1.80e−2)−

1.3678e−02

(1.99e−04)

DTLZ7

3

22

Mean

Std

2.6967e−1

(1.30e−2)−

2.8095e−1

(6.92e−4) + 

2.6843e−1

(7.06e−3)−

0.0000e + 0

(0.00e + 0)−

7.1984e−2 (4.17e−2)−

1.6227e−01

(2.03e−02)

Best/all

   

7/22

6/22

0/22

0/22

0/22

9/22

 ± /≈

   

7/15/0

6/13/3

0/20/2

0/21/1

0/21/1

–

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