Table 7 HV values for 5 MOEA and ASDMOPSO.

ZDT1

2

30

Mean

Std

8.5274e−3 (1.83e−2)−

6.0276e−1 (2.12e−2)−

4.8568e−1 (3.46e−2)−

6.1393e−1 (1.69e−2)−

1.4767e−1 (5.05e−2)−

7.2129e−01

(6.03e−05)

ZDT2

2

30

Mean

Std

2.1144e−2 (7.07e−2)−

3.0344e−1 (2.33e−2)−

7.0276e−2 (6.03e−2)−

2.5351e−1 (3.78e−2)−

0.0000e + 0 (0.00e + 0)−

4.4657e−01

(2.05e−05)

ZDT3

2

30

Mean

Std

3.2427e−2 (6.18e−2)−

4.9551e−1 (3.21e−2)−

5.0081e−1 (1.28e−2)−

5.5474e−1 (8.86e−3)−

3.8083e−1 (2.14e−2)−

6.0005e−01

(1.37e−04)

ZDT4

2

10

Mean

Std

2.0966e−3 (1.15e−2)−

8.6915e−2 (8.59e−2)−

4.2997e−3 (1.66e−2)−

0.0000e + 0 (0.00e + 0)−

0.0000e + 0 (0.00e + 0)−

6.9846e−01

(1.33e−01)

ZDT6

2

10

Mean

Std

3.6287e−1 (8.54e−2)≈

6.8634e−2 (4.79e−2)−

0.0000e + 0 (0.00e + 0)−

0.0000e + 0 (0.00e + 0)−

0.0000e + 0 (0.00e + 0)−

3.9015e−01

(1.31e−05)

UF1

2

30

Mean

Std

8.6414e−2 (6.86e−2)−

5.3896e−1 (2.61e−2)−

5.1022e−1 (3.30e−2)≈

5.4146e−1 (3.51e−2) + 

2.2314e−1 (6.73e−2)−

4.9805e−01

(1.61e−02)

UF2

2

30

Mean

Std

5.1284e−1 (2.83e−2)−

6.3799e−1 (6.69e−3)≈

6.3009e−1 (6.94e−3)−

6.2399e−1 (7.30e−3)−

5.1343e−1 (1.79e−2)−

6.4061e−01

(4.58e−03)

UF3

2

30

Mean

Std

1.2226e−1 (2.17e−2)−

2.0905e−1 (1.14e−2)−

2.2358e−1 (1.13e−2)−

1.9518e−1 (1.09e−2)−

9.2357e−2 (1.40e−2)−

3.4111e−01

(3.21e−02)

UF4

2

30

Mean

Std

2.8234e−1 (8.99e−3)−

3.2372e−1 (4.38e−3)−

3.2442e−1 (2.79e−3) + 

3.2202e−1 (4.20e−3)−

2.9545e−1 (4.01e−3)−

1.2726e−01

(3.36e−03)

UF5

2

30

Mean

Std

0.0000e + 0 (0.00e + 0)≈

2.4987e−4 (1.26e−3)≈

4.2485e−4 (2.33e−3)≈

2.2105e−3 (8.42e−3) + 

0.0000e + 0 (0.00e + 0)≈

0.0000e + 00

(1.75e−01)

UF6

2

30

Mean

Std

0.0000e + 0 (0.00e + 0)−

1.4259e−2 (1.73e−2)−

1.1077e−2 (1.56e−2)≈

3.0877e−2 (2.33e−2) + 

0.0000e + 0 (0.00e + 0)−

7.1557e−03

(6.25e−02)

UF7

2

30

Mean

Std

2.4430e−2 (4.02e−2)−

3.8790e−1 (5.65e−2)−

3.3758e−1 (5.89e−2)−

3.5981e−1 (7.82e−2)−

1.1043e−1 (5.18e−2)−

4.1627e−01

(1.26e−02)

UF8

3

30

Mean

Std

2.6973e−2 (2.99e−2)−

1.9908e−1 (3.07e−2)−

1.8468e−1 (3.08e−2)−

2.7020e−1 (3.45e−2)−

1.6876e−1 (4.45e−2)−

3.4690e−01

(2.89e−02)

UF9

3

30

Mean

Std

7.4309e−2 (4.44e−2)−

2.5124e−1 (5.40e−2)−

2.5440e−1 (5.25e−2)−

2.6808e−1 (3.87e−2)≈

2.0061e−1 (4.37e−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)−

7.6458e−3 (3.38e−2)≈

5.3905e−3 (2.44e−2)≈

3.6769e−2 (1.03e−1) + 

0.0000e + 0 (0.00e + 0)−

5.9780e−04

(6.98e + 00)

DTLZ2

3

12

Mean

Std

4.1543e−1 (3.16e−2)−

5.6361e−1 (1.31e−3) + 

5.5634e−1 (2.54e−3)−

5.6283e−1 (1.08e−3)−

5.5285e−1 (3.94e−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

1.9152e−1 (8.47e−2)−

5.6283e−1 (2.15e−3) + 

5.5450e−1 (2.80e−3)−

5.5407e−1 (3.98e−2)−

4.9093e−1 (9.90e−2)−

3.7090e−01

(8.65e−01)

DTLZ5

3

12

Mean

Std

1.4603e−1 (2.00e−2)−

1.8308e−1 (2.45e−3)−

1.8616e−1 (1.68e−3)−

1.9679e−1 (6.86e−4) + 

1.9198e−1 (1.88e−3)−

2.4535e−02

(1.29e + 00)

DTLZ6

3

12

Mean

Std

9.8346e−3 (3.90e−2)−

1.1168e−1 (4.23e−2)−

1.0343e−1 (4.56e−2)−

1.8121e−1 (2.29e−2) + 

9.5555e−3 (2.92e−2)−

1.3678e−02

(1.99e−04)

DTLZ7

3

22

Mean

Std

7.6737e−3 (3.15e−2)−

2.1788e−1 (2.06e−2)−

1.9161e−1 (1.47e−2)−

2.2360e−1 (9.16e−3) + 

7.6151e−2 (2.70e−2)−

1.6227e−01

(2.03e−02)

Best/all

0/22

2/22

1/22

7/22

0/22

12/22

 ± /≈

0/20/2

2/17/3

1/17/4

7/14/1

0/21/1

–