Table 4 The IGD + values of each algorithm under DTLZ test function set.

DTLZ1

210

5

9

50,000

5.4003e-2 + 

1.5947e-1 + 

2.0774e + 0 -

5.3152e-2 + 

1.0647e-1 + 

3.7108e + 0 -

2.9905e-1 = 

1.8933e-1

120

8

12

80,000

1.3737e-1 + 

5.9272e-1 -

4.1711e-1 -

1.1954e-1 + 

3.1664e-1 = 

1.0387e + 1 -

6.8535e-1 -

2.8542e-1

220

10

14

100,000

1.4769e-1 + 

7.2469e + 0 -

8.8517e-1 -

1.3048e-1 + 

8.3924e-1 -

1.5156e + 1 -

2.7614e-1 = 

2.5172e-1

120

15

19

150,000

2.2349e-1 + 

9.4258e + 0 -

2.8365e-1 + 

1.3790e-1 + 

5.0260e-1 -

1.3875e + 1 -

6.5422e-1 -

3.5965e-1

210

20

24

200,000

2.2481e-1 + 

9.3309e + 0 -

4.5746e-1 -

1.6666e-1 + 

8.0636e-1 -

1.5591e + 1 -

3.6458e-1 -

3.5095e-1

DTLZ2

210

5

14

50,000

1.6527e-1 = 

1.7821e-1 -

1.6540e-1 = 

1.9109e-1 -

2.0750e-1 -

4.9499e-1 -

1.7034e-1 -

1.6521e-1

120

8

17

80,000

3.8065e-1 -

4.0698e-1 -

3.8560e-1 -

3.6903e-1 -

4.3033e-1 -

7.9209e-1 -

4.0195e-1 -

3.6720e-1

220

10

19

100,000

4.7420e-1 -

4.5148e-1 -

4.5110e-1 -

4.6004e-1 -

4.6881e-1 -

1.0473e + 0 -

4.6671e-1 -

4.4616e-1

120

15

24

150,000

6.4867e-1 -

6.2585e-1 -

6.2973e-1 -

6.3264e-1 -

6.6750e-1 -

1.0550e + 0 -

8.9269e-1 -

6.2218e-1

210

20

29

200,000

6.5148e-1 -

6.1969e-1 -

6.1879e-1 -

6.2318e-1 -

6.4903e-1 -

1.2107e + 0 -

9.9909e-1 -

6.1322e-1

DTLZ3

210

5

14

50,000

1.1698e + 0 = 

5.1725e-1 + 

7.1807e + 1 -

1.0987e + 0 = 

6.4495e-1 = 

1.1581e + 1 -

1.0539e + 1 -

5.9449e-1

120

8

17

80,000

2.5655e + 0 -

8.4418e + 1 -

4.0228e + 1 -

8.1182e-1 = 

1.8472e + 1 -

2.8202e + 2 -

9.1431e + 0 -

6.8794e-1

220

10

19

100,000

3.2004e + 0 -

3.1999e + 2 -

5.1333e + 1 -

8.6527e-1 = 

2.7983e + 1 -

2.6209e + 2 -

7.2165e + 0 -

7.2040e-1

120

15

24

150,000

2.1328e + 0 -

3.3395e + 2 -

2.5591e + 1 -

1.0815e + 0 -

1.6209e + 1 -

3.2994e + 2 -

6.1555e + 0 -

9.5758e-1

210

20

29

200,000

2.5213e + 0 = 

4.3459e + 2 -

3.0349e + 1 -

9.5225e-1 = 

1.7519e + 1 -

2.6283e + 2 -

3.3351e + 0 -

9.0277e-1

DTLZ4

210

5

14

50,000

1.6529e-1 = 

1.7664e-1 -

1.7405e-1 -

5.2939e-1 -

2.1035e-1 -

8.1621e-1 -

1.8138e-1 -

1.6511e-1

120

8

17

80,000

4.0282e-1 -

3.9595e-1 -

4.2069e-1 -

5.6005e-1 -

4.1932e-1 -

1.1092e + 0 -

4.3026e-1 -

3.6871e-1

220

10

19

100,000

4.8134e-1 -

4.5501e-1 -

4.5717e-1 -

6.0607e-1 -

5.7120e-1 -

1.2416e + 0 -

4.7395e-1 -

4.4366e-1

120

15

24

150,000

6.5020e-1 -

6.2531e-1 = 

6.3164e-1 = 

7.2987e-1 -

1.1275e + 0 -

1.3703e + 0 -

6.6058e-1 -

6.3211e-1

210

20

29

200,000

6.5026e-1 -

6.1635e-1 = 

6.2298e-1 -

7.1755e-1 -

8.2321e-1 -

1.1596e + 0 -

6.3198e-1 -

6.1575e-1

DTLZ5

210

5

14

50,000

9.6402e-2 -

2.1288e-1 -

7.6419e-2 -

2.2706e-2 + 

8.9792e-2 -

2.6274e-1 -

4.7844e-1 -

5.1597e-2

120

8

17

80,000

2.6238e-1 -

2.9420e-1 -

1.7051e-1 -

6.8646e-2 + 

1.9624e-1 -

5.4800e-1 -

4.1579e-1 -

1.1191e-1

220

10

19

100,000

3.2831e-1 -

3.3781e-1 -

1.7234e-1 -

6.6163e-2 + 

3.1319e-1 -

3.5538e-1 -

3.5697e-1 -

1.0527e-1

120

15

24

150,000

3.4743e-1 -

5.8173e-1 -

2.8348e-1 = 

1.4050e-1 + 

4.1625e-1 -

6.8191e-1 -

3.5844e-1 -

2.8180e-1

210

20

29

200,000

2.9862e-1 -

9.3667e-1 -

2.8745e-1 -

1.4048e-1 + 

4.0044e-1 -

3.8062e-1 -

3.1290e-1 = 

2.3796e-1

DTLZ6

210

5

14

50,000

1.4586e-1 -

4.3300e-1 -

7.3172e-2 = 

2.2479e-2 + 

7.0134e-1 -

8.4996e + 0 -

6.1138e-1 -

7.3573e-2

120

8

17

80,000

4.9878e-1 = 

7.3612e-1 -

1.3526e-1 + 

6.8613e-2 + 

7.0673e-1 -

8.3398e + 0 -

8.6361e-1 -

2.8757e-1

220

10

19

100,000

4.4525e-1 -

1.8789e + 0 -

1.3517e-1 + 

6.6174e-2 + 

6.5643e-1 -

8.2579e + 0 -

5.0839e-1 -

3.0680e-1

120

15

24

150,000

4.0594e-1 = 

1.3273e + 0 -

2.7741e-1 + 

1.5784e-1 + 

7.1029e-1 -

8.3792e + 0 -

5.6217e-1 -

3.8476e-1

210

20

29

200,000

3.7936e-1 = 

2.0407e + 0 -

2.2879e-1 + 

1.4048e-1 + 

7.0974e-1 -

8.5613e + 0 -

4.1838e-1 -

3.3691e-1

DTLZ7

210

5

24

50,000

2.8435e-1 + 

2.4034e-1 + 

5.6321e-1 -

5.5786e-1 -

3.8631e-1 -

2.5644e + 0 -

7.0401e-1 -

2.8693e-1

120

8

27

80,000

8.3652e-1 = 

7.1349e-1 + 

1.9469e + 0 -

3.1542e + 0 -

2.0880e + 0 -

2.5099e + 1 -

1.2987e + 0 -

9.2514e-1

220

10

29

100,000

1.1666e + 0 -

8.9342e-1 + 

2.4581e + 0 -

3.8701e + 0 -

3.1548e + 0 -

3.6530e + 1 -

1.6777e + 0 -

9.7142e-1

120

15

34

150,000

8.1169e + 0 -

3.0008e + 0 = 

3.1411e + 0 = 

4.5074e + 0 -

1.0915e + 1 -

6.3729e + 1 -

5.7671e + 0 -

2.8809e + 0

210

20

39

200,000

1.2549e + 1 -

4.5136e + 0 -

7.0299e + 0 -

5.4853e + 0 -

1.5302e + 1 -

6.7502e + 1 -

3.7298e + 0 = 

3.4861e + 0

 + /-/ = 

6/21/8

5/27/3

5/25/5

15/16/4

1/32/2

0/35/0

0/31/4