IEEE Computational Intelligence Magazine - August 2022 - 45

AUGUST 2022 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 45
TABLE IV IGD values obtained by 11 MOEAs on SMOP1-SMOP8 with 100 to 5000 decision variables.
PROBLEM (D)
NSGA-II
SMOP1 (100)
SMOP2 (100)
SMOP3 (100)
SMOP4 (100)
SMOP5 (100)
SMOP6 (100)
SMOP7 (100)
SMOP8 (100)
SMOP1 (500)
SMOP2 (500)
SMOP3 (500)
SMOP4 (500)
SMOP5 (500)
SMOP6 (500)
SMOP7 (500)
SMOP8 (500)
SMOP1 (1000)
SMOP2 (1000)
SMOP3 (1000)
SMOP4 (1000)
SMOP5 (1000)
SMOP6 (1000)
SMOP7 (1000)
SMOP8 (1000)
SMOP1 (5000)
SMOP2 (5000)
SMOP3 (5000)
SMOP4 (5000)
SMOP5 (5000)
SMOP6 (5000)
SMOP7 (5000)
SMOP8 (5000)
Average ranking
1.3881e-1
5.9326e-1
8.9196e-1
1.8464e-1
3.7593e-1
5.1558e-2
3.7936e-1
1.6116e+0
1.9086e-1
8.1616e-1
1.0870e+0
3.4758e-1
3.7684e-1
5.4521e-2
4.0898e-1
1.7140e+0
2.3802e-1
9.5843e-1
1.2041e+0
4.2098e-1
3.8407e-1
6.4852e-2
4.7519e-1
1.9015e+0
4.1609e-1
1.2129e+0
1.6060e+0
5.8178e-1
4.2033e-1
1.2156e-1
7.5066e-1
2.3367e+0
5.8125
MOEA/D-DE MOEA/DVA LMEA
4.9338e-1
1.6633e+0
1.5554e+0
8.2157e-1
4.2447e-1
1.7537e-1
4.8911e-1
2.6267e+0
5.9608e-1
1.8533e+0
1.6620e+0
9.1579e-1
4.3490e-1
2.0103e-1
5.3185e-1
2.6506e+0
6.0626e-1
1.8104e+0
1.6637e+0
9.4218e-1
4.4126e-1
2.0711e-1
5.4254e-1
2.7501e+0
5.6506e-1
1.7842e+0
1.6850e+0
9.1493e-1
4.5025e-1
2.1264e-1
5.7751e-1
2.7799e+0
8.5625
1.1699e+0
1.9698e+0
2.3901e+0
1.0420e+0
8.2484e-1
3.7933e-1
1.9933e+0
3.3817e+0
1.3679e+0
2.0746e+0
2.4751e+0
1.0823e+0
9.5036e-1
4.1971e-1
2.3711e+0
3.5499e+0
1.4011e+0
2.1029e+0
2.4833e+0
1.0962e+0
9.5534e-1
4.2930e-1
2.4557e+0
3.5972e+0
1.4404e+0
2.1319e+0
2.5065e+0
1.1102e+0
9.7775e-1
4.4097e-1
2.5780e+0
3.6356e+0
11.0000
7.5073e-1
1.6498e+0
1.9913e+0
8.0055e-1
5.6683e-1
2.2736e-1
1.5488e+0
3.2100e+0
5.8926e-1
1.4881e+0
1.7723e+0
7.0549e-1
5.0357e-1
1.8076e-1
1.1668e+0
3.0276e+0
6.3298e-1
1.4979e+0
1.8615e+0
7.0554e-1
5.0427e-1
1.9409e-1
1.1352e+0
2.8570e+0
9.4475e-1
1.7309e+0
2.1669e+0
8.1680e-1
6.3210e-1
2.7834e-1
1.5629e+0
3.0393e+0
9.2813
WOF-SMPSO
2.7445e-1
9.4523e-1
7.2635e-1
5.2006e-1
3.7125e-1
8.3967e-2
1.7419e-1
8.1791e-1
2.6890e-1
3.1368e-1
7.0546e-1
8.9249e-2
3.5916e-1
7.9325e-2
9.3594e-2
5.6815e-1
2.5378e-1
4.4390e-1
7.0493e-1
5.2047e-2
3.5629e-1
8.2004e-2
9.3192e-2
5.6434e-1
1.8574e-1
1.7927e-1
7.0202e-1
9.6085e-3
3.4951e-1
2.7805e-2
8.4597e-2
5.3245e-1
4.8125
LSMOF-NSGA-II
5.4056e-2
1.4431e-1
7.1078e-1
6.4901e-3
3.6417e-1
8.2906e-3
2.2770e-1
7.0334e-1
5.1330e-2
1.2903e-1
6.8492e-1
4.8261e-3
3.7463e-1
6.3450e-3
1.7344e-1
7.1543e-1
5.8896e-2
1.3484e-1
6.8275e-1
4.8741e-3
3.6945e-1
6.1533e-3
1.8547e-1
7.1966e-1
1.0086e-1
2.0046e-1
7.0319e-1
1.3846e-2
3.5416e-1
1.8836e-2
1.7858e-1
5.6989e-1
4.1563
IM-MOEA
3.7859e-1
1.2576e+0
2.1896e+0
4.7911e-1
4.2339e-1
1.4209e-1
7.6863e-1
2.6644e+0
4.4007e-1
1.1803e+0
2.3002e+0
6.1920e-1
4.4195e-1
1.6410e-1
8.3552e-1
2.8422e+0
4.3913e-1
1.2829e+0
2.3367e+0
6.2804e-1
4.4841e-1
1.6891e-1
8.2090e-1
2.6160e+0
4.4519e-1
1.3522e+0
2.3627e+0
6.8302e-1
4.5318e-1
1.7937e-1
8.4136e-1
2.7928e+0
8.0313
LMOCSO
4.5991e-1
1.6623e+0
1.6021e+0
8.0353e-1
4.1629e-1
1.5128e-1
5.4583e-1
2.4326e+0
5.3002e-1
1.7608e+0
1.6474e+0
8.5216e-1
4.2999e-1
1.8067e-1
6.2655e-1
2.3489e+0
5.5384e-1
1.8253e+0
1.6860e+0
8.8435e-1
4.3506e-1
1.8522e-1
6.1863e-1
2.3568e+0
5.9038e-1
1.7897e+0
1.7051e+0
9.0018e-1
4.4112e-1
1.9077e-1
6.1830e-1
2.4849e+0
8.0313
SparseEA MOEA/PSL
7.5149e-3
1.8031e-2
1.2013e-2
4.6541e-3
6.7538e-3
8.0869e-3
2.8884e-2
1.5041e-1
1.1723e-2
2.3902e-2
1.1323e-2
4.6319e-3
7.1022e-3
7.0130e-3
4.3760e-2
1.8299e-1
1.5394e-2
4.1015e-2
1.4260e-2
4.6623e-3
7.2164e-3
7.2044e-3
5.2677e-2
1.7740e-1
1.8127e-2
5.5943e-2
1.3926e-2
4.7285e-3
7.0693e-3
7.8950e-3
7.6508e-2
2.0764e-1
1.5625
9.6493e-3
3.7669e-2
1.6880e-2
5.0302e-3
6.0333e-3
8.3891e-3
3.7442e-2
1.6878e-1
1.9205e-2
5.9364e-2
2.2764e-2
5.0911e-3
6.1487e-3
7.6552e-3
6.4013e-2
2.3051e-1
2.5844e-2
7.1310e-2
2.8652e-2
4.9091e-3
5.7937e-3
7.5569e-3
8.2947e-2
2.5142e-1
3.8444e-2
9.8401e-2
4.5589e-2
4.9284e-3
5.7860e-3
8.1920e-3
1.2622e-1
3.2451e-1
2.9375
PM-MOEA
1.0619e-2
2.4476e-2
1.3663e-2
4.1171e-3
5.8328e-3
9.3224e-3
4.2378e-2
1.7536e-1
1.6715e-2
3.6876e-2
2.0308e-2
4.0797e-3
5.2572e-3
5.0900e-3
5.8032e-2
1.7838e-1
2.1628e-2
5.2607e-2
2.4684e-2
4.1184e-3
4.7038e-3
4.9861e-3
7.3822e-2
1.8902e-1
3.4955e-2
8.7136e-2
3.2480e-2
4.0531e-3
4.8330e-3
5.3264e-3
1.1568e-1
2.9041e-1
1.8125
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