IEEE Computational Intelligence Magazine - August 2022 - 44

44 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | AUGUST 2022
TABLE III CSD 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
1.9337e-1
3.0427e-1
2.9980e-1
1.6997e-1
1.4063e-1
1.3167e-1
7.6009e-1
1.0803e+0
2.0078e-1
2.2361e-1
2.1226e-1
2.9639e-1
1.5555e-1
1.3524e-1
2.9905e-1
3.6262e-1
1.5571e-1
2.5495e-1
2.5065e-1
2.9679e-1
1.8111e-1
1.3829e-1
3.0360e-1
3.6972e-1
3.0581e-1
2.3548e-1
2.0494e-1
2.9513e-1
1.8998e-1
2.1177e-1
3.7257e-1
2.7640e-1
5.7500
MOEA/D-DE
4.3614e-1
6.8635e-1
3.3553e-1
6.4059e-1
3.7059e-1
4.6350e-1
8.7693e-1
1.3295e+0
4.7565e-1
5.3837e-1
2.2364e-1
7.4486e-1
3.6846e-1
4.9684e-1
3.5295e-1
5.0656e-1
3.5225e-1
5.2097e-1
2.5065e-1
7.9097e-1
3.9310e-1
4.9495e-1
3.5633e-1
5.6807e-1
4.3757e-1
3.9400e-1
2.0494e-1
6.3529e-1
3.9632e-1
4.6564e-1
2.9600e-1
4.3124e-1
8.3125
MOEA/DVA
7.8851e-1
8.1987e-1
6.9653e-1
7.5967e-1
6.1990e-1
7.2521e-1
1.6762e+0
1.8521e+0
6.5680e-1
6.2014e-1
4.5775e-1
8.4093e-1
6.8601e-1
5.8008e-1
9.4878e-1
9.3498e-1
5.2676e-1
5.9670e-1
4.6366e-1
8.7980e-1
5.8350e-1
5.5872e-1
9.0563e-1
9.0280e-1
7.1662e-1
4.1265e-1
4.0782e-1
7.4225e-1
4.8896e-1
5.0253e-1
1.0383e+0
1.0415e+0
10.6875
LMEA
5.9369e-1
6.7602e-1
4.9054e-1
5.4760e-1
4.6552e-1
6.0050e-1
1.3955e+0
1.6576e+0
5.2181e-1
4.9237e-1
3.1473e-1
5.4238e-1
5.8986e-1
4.4997e-1
7.4620e-1
7.8791e-1
4.3443e-1
4.9781e-1
3.4697e-1
5.8962e-1
5.9136e-1
5.1353e-1
7.2155e-1
7.3794e-1
6.5268e-1
5.3216e-1
3.3496e-1
6.3870e-1
6.4584e-1
7.2834e-1
9.1123e-1
9.3653e-1
9.4688
WOF-SMPSO
2.3918e-1
3.7089e-1
2.5190e-1
3.3175e-1
1.4168e-1
1.7961e-1
4.1530e-1
7.8605e-1
2.5840e-1
1.7649e-1
1.6350e-1
2.4601e-1
1.0433e-1
1.8761e-1
1.6603e-1
1.8598e-1
1.9660e-1
2.0615e-1
1.9917e-1
2.4536e-1
1.2368e-1
1.9575e-1
1.7128e-1
1.7119e-1
2.5393e-1
1.3689e-1
1.5823e-1
2.0108e-1
1.3207e-1
1.4962e-1
1.5326e-1
1.7614e-1
4.8438
LSMOF-NSGA-II
1.4151e-1
2.4525e-1
2.0252e-1
1.1802e-1
9.6309e-2
8.8620e-2
6.1877e-1
8.5502e-1
1.4826e-1
1.3007e-1
1.1170e-1
1.9151e-1
1.5748e-1
8.2919e-2
2.4426e-1
3.0491e-1
1.0731e-1
1.5315e-1
1.4570e-1
1.9047e-1
1.4881e-1
8.9246e-2
2.4907e-1
3.0418e-1
2.0094e-1
1.8393e-1
1.6087e-1
2.4033e-1
1.3989e-1
1.2542e-1
2.3453e-1
2.2673e-1
4.4688
IM-MOEA
3.7767e-1
5.4250e-1
5.7921e-1
3.4479e-1
3.0165e-1
2.7609e-1
1.1281e+0
1.4568e+0
3.8710e-1
4.0178e-1
3.8878e-1
4.1929e-1
4.2196e-1
2.7406e-1
5.9310e-1
6.5754e-1
3.1717e-1
4.0175e-1
4.0951e-1
4.0549e-1
4.1826e-1
2.7406e-1
5.8356e-1
7.2364e-1
4.3473e-1
3.8831e-1
3.9645e-1
3.9630e-1
4.4364e-1
2.8417e-1
5.0184e-1
5.5521e-1
7.9375
LMOCSO
4.1068e-1
6.5158e-1
3.5256e-1
5.2913e-1
2.4447e-1
3.4374e-1
9.0127e-1
1.2191e+0
4.1421e-1
5.1778e-1
2.2364e-1
6.3857e-1
2.7542e-1
3.5664e-1
4.1848e-1
4.3061e-1
3.3554e-1
5.3552e-1
2.5065e-1
6.9149e-1
2.8160e-1
3.5636e-1
4.1170e-1
4.2391e-1
4.3757e-1
3.9517e-1
2.0494e-1
5.7324e-1
2.8988e-1
3.6945e-1
3.1529e-1
3.2799e-1
7.7500
SparseEA MOEA/PSL
4.8689e-2
5.5829e-2
7.0560e-2
4.9980e-2
4.4203e-2
4.7910e-2
1.0306e-1
1.5662e-1
6.8524e-2
4.6055e-2
5.0797e-2
6.0793e-2
5.6343e-2
4.7825e-2
5.2182e-2
7.5297e-2
5.3307e-2
7.0190e-2
6.2881e-2
5.3168e-2
7.0232e-2
5.0686e-2
6.6191e-2
5.5697e-2
8.4255e-2
5.1404e-2
4.6221e-2
7.9108e-2
8.3544e-2
6.5937e-2
7.0545e-2
7.5387e-2
1.5313
6.9883e-2
1.3044e-1
8.6080e-2
6.5248e-2
4.6993e-2
4.4372e-2
2.1786e-1
3.2522e-1
7.7962e-2
6.1991e-2
5.4376e-2
9.1078e-2
4.7540e-2
5.9739e-2
8.1813e-2
1.0165e-1
4.8398e-2
9.2543e-2
7.5598e-2
1.0773e-1
4.8329e-2
5.7827e-2
6.9131e-2
8.5294e-2
1.1666e-1
6.6315e-2
8.5894e-2
8.9054e-2
4.8379e-2
6.1343e-2
1.1192e-1
1.1516e-1
2.4375
PM-MOEA
9.4315e-2
9.0096e-2
1.0548e-1
5.6740e-2
3.7296e-2
4.8082e-2
2.4001e-1
2.9235e-1
7.4613e-2
7.5849e-2
5.1477e-2
1.3729e-1
4.0170e-2
3.3376e-2
1.0454e-1
8.8172e-2
5.3906e-2
4.0488e-2
5.5213e-2
1.4350e-1
3.6738e-2
3.5731e-2
1.1651e-1
7.7375e-2
7.2000e-2
6.6043e-2
6.6826e-2
1.4608e-1
4.6288e-2
3.5237e-2
1.1669e-1
4.4007e-2
2.0313
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