Table 4 IGD values for 5 MOPSO and ASDMOPSO.

ZDT1

2

30

Mean

Std

3.1089e−3

(3.79e−4)≈

2.9713e−2

(1.01e−2)−

2.8044e−3

(8.52e−4) + 

1.5425e + 0

(5.67e−2)−

8.8460e−2

(2.98e−2)−

2.9181e−03

(6.03e−05)

ZDT2

2

30

Mean

Std

3.0877e−3

(6.27e−4)−

2.0089e−2

(1.03e−2)−

1.0202e−1

(1.79e−1)−

3.0114e + 0

(1.84e−1)−

1.3859e−1

(8.68e−2)−

2.3039e−03

(2.05e−05)

ZDT3

2

30

Mean

Std

3.7884e−3

(7.54e−4)≈

9.1301e−2

(1.89e−2)−

2.8715e−2

(3.99e−2)−

1.2212e + 0

(1.10e−1)−

1.8753e−1

(3.85e−2)−

3.7016e−03

(1.37e−04)

ZDT4

2

10

Mean

Std

2.0718e + 1

(5.36e + 0)−

1.4735e + 1

(7.79e + 0)−

1.8067e + 1

(8.15e + 0)−

9.8898e + 0

(3.30e + 0)−

3.8296e + 1

(7.60e + 0)−

3.1751e−02

(1.33e−01)

ZDT6

2

10

Mean

Std

1.5714e−3

(4.24e−5) + 

2.2838e−3

(2.39e−4)−

2.9631e−3

(1.33e−3)−

5.6080e + 0

(3.18e−1)−

1.5002e−2

(9.49e−3)−

1.7889e−03

(1.31e−05)

UF1

2

30

Mean

Std

1.0143e−1

(2.73e−2) + 

1.2262e−1

(1.31e−2)−

6.2357e−1

(1.60e−1)−

4.7901e−1

(7.66e−2)−

2.6641e−1

(4.59e−2)−

1.4380e−01

(1.61e−02)

UF2

2

30

Mean

Std

6.0232e−2

(6.91e−3) + 

8.4490e−2

(6.24e−3)−

1.4311e−1

(1.65e−2)−

1.0066e−1

(1.18e−2)−

1.1255e−1

(1.02e−2)−

7.0211e−02

(4.58e−03)

UF3

2

30

Mean

Std

3.8866e−1

(4.86e−2)−

3.4596e−1

(5.37e−2)−

4.1694e−1

(9.99e−2)−

4.5968e−1

(3.40e−2)−

4.9970e−1

(1.82e−2)−

3.1007e−01

(3.21e−02)

UF4

2

30

Mean

Std

1.1209e−1

(9.54e−3)−

6.2087e−2

(8.79e−3)≈

7.8401e−2

(8.73e−3)−

1.8122e−1

(3.83e−3)−

1.0005e−1

(3.57e−3)−

5.8775e−02

(3.36e−03)

UF5

2

30

Mean

Std

8.8676e−1

(2.11e−1) + 

1.5447e + 0

(4.54e−1)≈

3.9357e + 0

(4.16e−1)−

2.5596e + 0

(3.21e−1)−

2.8064e + 0

(3.18e−1)−

1.5923e + 00

(1.75e−01)

UF6

2

30

Mean

Std

3.9056e−1

(6.53e−2) + 

6.8682e−1

(1.76e−1)≈

2.9698e + 0

(5.68e−1)−

2.0660e + 0

(3.36e−1)−

1.3633e + 0

(2.47e−1)−

6.6584e−01

(6.25e−02)

UF7

2

30

Mean

Std

1.1609e−1

(1.03e−1)≈

1.7469e−1

(1.24e−1)≈

6.0732e−1

(1.15e−1)−

6.1993e−1

(6.54e−2)−

2.3329e−1

(5.11e−2)−

1.1257e−01

(1.26e−02)

UF8

3

30

Mean

Std

5.9413e−1

(1.32e−1)−

4.9245e−1

(8.12e−2)−

7.5427e−1

(1.81e−1)−

4.3059e−1

(3.11e−2)−

5.5204e−1

(4.69e−2)−

2.4590e−01

(2.89e−02)

UF9

3

30

Mean

Std

9.1534e−1

(1.37e−1)−

4.6979e−1

(5.75e−2)−

8.9333e−1

(1.68e−1)−

5.3776e−1

(2.92e−2)−

6.5354e−1

(4.00e−2)−

1.5482e−01

(2.11e−02)

UF10

3

30

Mean

Std

4.4683e + 0

(5.30e−1)−

1.6161e + 0

(3.72e−1)−

5.1165e + 0

(5.49e−1)−

1.4839e + 0

(3.59e−1)−

4.1545e + 0

(3.44e−1)−

3.2131e−01

(3.86e−02)

DTLZ1

3

7

Mean

Std

1.4173e + 1

(4.26e + 0)≈

5.8179e + 0

(2.83e + 0)−

1.9600e + 1

(5.26e + 0)−

5.8118e + 0

(2.87e + 0) + 

1.0877e + 1

(3.01e + 0)−

1.5262e + 01

(6.98e + 00)

DTLZ2

3

12

Mean

Std

4.1399e−2

(6.71e−4) + 

5.7068e−2

(1.59e−3)−

9.2590e−2

(1.05e−2)−

4.9033e−2

(2.49e−3)−

4.5533e−2

(1.43e−3)−

7.3637e−02

(8.54e−03)

DTLZ3

3

12

Mean

Std

1.9638e + 2

(3.74e + 1)−

1.1605e + 2

(2.05e + 1)−

1.1974e + 2

(3.77e + 1)−

1.7206e + 2

(4.11e + 1)−

1.4398e + 2

(1.83e + 1)−

2.5642e + 01

(2.53e + 01)

DTLZ4

3

12

Mean

Std

7.3589e−2

(1.65e−1) + 

9.1581e−2

(1.22e−1)−

3.1887e−1

(3.79e−2)−

2.1203e−1

(1.43e−1)−

1.3780e−1

(3.42e−2)−

8.0242e + 00

(8.65e−01)

DTLZ5

3

12

Mean

Std

4.5516e−3

(2.87e−4) + 

7.0440e−3

(7.61e−4)−

3.5864e−2

(1.03e−2)−

4.9848e−3

(6.11e−4)−

5.3948e−2

(5.34e−3)≈

2.8583e−01

(1.29e + 00)

DTLZ6

3

12

Mean

Std

1.7537e−1

(3.73e−1)≈

1.2465e−2

(2.41e−3)−

1.2781e−1

(2.87e−1)−

7.3051e + 0

(2.73e−1)−

1.0651e + 0

(3.75e−1)−

2.5578e−03

(1.99e−04)

DTLZ7

3

22

Mean

Std

7.5017e−2

(1.36e−1)−

4.8544e−2

(3.36e−3)−

7.5281e−2

(1.78e−2)≈

6.5050e + 0

(5.79e−1)−

5.1902e−1

(1.14e−1)−

7.1473e−02

(2.03e−02)

Best/all

8/22

0/22

1/22

1/22

0/22

12/22

 ± /≈

8/9/5

0/20/2

1/20/1

1/21/0

0/21/1

–