Table 5 IGD values for 5 MOEA and ASDMOPSO.

ZDT1

2

30

Mean

Std

1.0842e + 0

(2.21e−1)−

8.7077e−2

(1.67e−2)−

1.8438e−1

(3.16e−2)−

8.2307e−2

(1.36e−2)−

5.4011e−1

(8.15e−2)−

2.9181e−03

(6.03e−05)

ZDT2

2

30

Mean

Std

9.8906e−1

(3.88e−1)−

1.0235e−1

(1.94e−2)−

4.3195e−1

(1.68e−1)−

1.5379e−1

(4.29e−2)−

1.9246e + 0

(2.35e−1)−

2.3039e−03

(2.05e−05)

ZDT3

2

30

Mean

Std

1.0114e + 0

(2.20e−1)−

1.5117e−1

(1.80e−2)−

1.4885e−1

(1.27e−2)−

6.9465e−2

(1.20e−2)−

3.1860e−1

(3.22e−2)−

3.7016e−03

(1.37e−04)

ZDT4

2

10

Mean

Std

8.4460e + 0

(4.44e + 0)−

6.9756e−1

(2.50e−1)−

1.9388e + 0

(7.69e−1)−

2.1530e + 0

(6.74e−1)−

2.7790e + 1

(7.09e + 0)−

3.1751e−02

(1.33e−01)

ZDT6

2

10

Mean

Std

1.6022e−1

(7.26e−1)≈

3.9215e−1

(1.27e−1)−

1.0976e + 0

(2.23e−1)−

1.1969e + 0

(1.99e−1)−

4.4460e + 0

(4.39e−1)−

1.7889e−03

(1.31e−05)

UF1

2

30

Mean

Std

6.4792e−1

(1.28e−1)−

1.1770e−1

(2.02e−2) + 

1.4116e−1

(2.59e−2)≈

1.1835e−1

(2.74e−2)−

4.0368e−1

(7.43e−2)−

1.4380e−01

(1.61e−02)

UF2

2

30

Mean

Std

1.7112e−1

(2.32e−2)−

6.2838e−2

(5.88e−3) + 

6.9790e−2

(5.80e−3)−

7.7772e−2

(6.98e−3)≈

1.5360e−1

(1.38e−2)−

7.0211e−02

(4.58e−03)

UF3

2

30

Mean

Std

5.6721e−1

(3.76e−2)−

4.5587e−1

(1.37e−2)−

4.3483e−1

(1.35e−2)−

4.6318e−1

(1.21e−2)−

6.1786e−1

(2.39e−2)−

3.1007e−01

(3.21e−02)

UF4

2

30

Mean

Std

1.1824e−1

(7.56e−3)−

8.6432e−2

(3.37e−3)−

8.5602e−2

(2.04e−3)−

8.9131e−2

(3.39e−3)−

1.0718e−1

(3.14e−3)−

5.8775e−02

(3.36e−03)

UF5

2

30

Mean

Std

2.8031e + 0

(6.42e−1)−

1.0649e + 0

(2.00e−1) + 

1.1123e + 0

(1.97e−1)−

1.1803e + 0

(3.47e−1)−

3.0224e + 0

(2.75e−1)−

1.5923e + 00

(1.75e−01)

UF6

2

30

Mean

Std

2.5990e + 0

(6.96e−1)−

7.0132e−1

(1.15e−1)≈

6.9655e−1

(1.08e−1)≈

5.7947e−1

(6.43e−2) + 

1.9405e + 0

(2.62e−1)−

6.6584e−01

(6.25e−02)

UF7

2

30

Mean

Std

7.1659e−1

(1.31e−1)−

1.4212e−1

(5.81e−2)−

1.9484e−1

(7.00e−2)−

1.8376e−1

(8.48e−2)−

4.3041e−1

(8.34e−2)−

1.1257e−01

(1.26e−02)

UF8

3

30

Mean

Std

7.2454e−1

(1.53e−1)−

3.0655e−1

(2.03e−2)−

3.2194e−1

(1.68e−2)−

3.7281e−1

(4.24e−2)−

3.5726e−1

(2.76e−2)−

2.4590e−01

(2.89e−02)

UF9

3

30

Mean

Std

7.4669e−1

(8.52e−2)−

4.9090e−1

(5.82e−2)−

4.9059e−1

(5.67e−2)−

4.9817e−1

(4.73e−2)−

5.5467e−1

(5.51e−2)−

1.5482e−01

(2.11e−02)

UF10

3

30

Mean

Std

4.6115e + 0

(1.00e + 0)−

2.8969e + 0

(5.38e−1)−

1.8644e + 0

(3.32e−1)−

1.7284e + 0

(4.07e−1)−

2.9772e + 0

(4.29e−1)−

3.2131e−01

(3.86e−02)

DTLZ1

3

7

Mean

Std

1.5007e + 1

(7.98e + 0)≈

1.0584e + 0

(4.55e−1)−

8.8053e−1

(2.88e−1)−

6.5586e−1

(3.16e−1) + 

2.9042e + 0

(1.04e + 0)−

1.5262e + 01

(6.98e + 00)

DTLZ2

3

12

Mean

Std

1.2238e−1

( 2.13e−2)−

3.8989e−2

(3.67e−4) + 

4.3114e−2

(1.54e−3)−

3.9449e−2

(4.53e−4)−

4.4050e−2

(2.31e−3)−

7.3637e−02

(8.54e−03)

DTLZ3

3

12

Mean

Std

1.0913e + 2

(6.10e + 1)−

3.6663e + 1

(8.93e + 0)−

3.4213e + 1

(9.13e + 0)≈

2.5259e + 1

(7.78e + 0) + 

7.7192e + 1

(1.51e + 1)−

2.5642e + 01

(2.53e + 01)

DTLZ4

3

12

Mean

Std

4.4636e−1

(1.25e−1)−

3.9475e−2

(7.54e−4) + 

4.3707e−2

(1.43e−3)−

5.7169e−2

(9.15e−2)−

1.7920e−1

(2.24e−1)−

8.0242e + 00

(8.65e−01)

DTLZ5

3

12

Mean

Std

5.9821e−2

(1.57e−2)−

2.4362e−2

(2.28e−3)−

2.2186e−2

(1.97e−3)−

6.9854e−3

(6.42e−4) + 

1.2404e−2

(4.16e−3)−

2.8583e−01

(1.29e + 00)

DTLZ6

3

12

Mean

Std

2.3702e + 0

(9.42e−1)−

1.3716e−1

(1.84e−1)−

1.3706e−1

(8.23e−2)−

2.8604e−2

(3.46e−2)−

8.1269e−1

(4.02e−1)−

2.5578e−03

(1.99e−04)

DTLZ7

3

22

Mean

Std

4.0798e + 0

(1.56e + 0)−

3.4649e−1

(2.73e−1)−

2.2071e−1

(4.36e−2)−

1.3447e−1

(2.33e−2)−

6.8312e−1 (1.62e−1)−

7.147e−02

(2.03e−02)

Best/all

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 ± /≈

0/20/2

5/16/1

0/19/3

4/17/1

0/22/0

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