IEEE Computational Intelligence Magazine - August 2022 - 49

AUGUST 2022 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 49
TABLE VI HV values obtained by 11 MOEAs on seven applications with 100 to 6241 decision variables.
PROBLEM (D)
NSGA-II
NN1 (301)
NN2 (521)
NN3 (1241)
NN4 (6241)
FS1 (100)
FS2 (500)
FS3 (800)
FS4 (4434)
PM1 (100)
PM2 (500)
PM3 (1000)
PM4 (5000)
CD1 (105)
CD2 (453)
CD3 (1133)
CD4 (4039)
CN1 (102)
CN2 (500)
CN3 (1000)
CN4 (5000)
PO1 (100)
PO2 (500)
PO3 (1000)
PO4 (5000)
KP1 (100)
KP2 (500)
KP3 (1000)
KP4 (5000)
Average ranking
4.0033e-1
3.0025e-1
3.4234e-1
3.5159e-1
7.5146e-1
6.9445e-1
9.9902e-1
9.9960e-1
2.8312e-1
1.7204e-1
1.2228e-1
8.7578e-2
6.6456e-1
7.1968e-1
6.6584e-1
6.1449e-1
9.0513e-1
8.6220e-1
8.4360e-1
8.3380e-1
9.8922e-2
9.3142e-2
9.2252e-2
9.1318e-2
7.4078e-2
8.2443e-2
7.1668e-2
8.1896e-2
5.3571
MOEA/D-DE MOEA/DVA LMEA
3.9943e-1
3.0287e-1
3.4782e-1
3.4005e-1
5.7736e-1
5.5587e-1
4.8129e-1
6.8766e-1
8.1623e-2
1.3025e-1
1.0926e-1
9.5478e-2
5.5241e-1
5.5582e-1
4.7085e-1
4.5724e-1
7.7200e-1
7.2559e-1
7.0641e-1
7.0253e-1
1.0477e-1
9.5953e-2
9.4490e-2
9.1970e-2
0.0000e+0
0.0000e+0
0.0000e+0
0.0000e+0
7.5714
8.2934e-2
5.9979e-2
6.8343e-2
6.7343e-2
5.9490e-2
5.4355e-2
3.5813e-2
4.1322e-2
8.2645e-3
8.2645e-3
8.2645e-3
8.2645e-3
4.2328e-1
4.0857e-1
3.4262e-1
3.2446e-1
6.3961e-1
5.9812e-1
5.7786e-1
5.6215e-1
9.3647e-2
9.1493e-2
9.1168e-2
9.0988e-2
0.0000e+0
3.8694e-2
3.6040e-2
5.1387e-2
10.3929
4.1292e-1
3.0456e-1
3.4964e-1
3.4481e-1
5.8842e-1
5.6351e-1
3.2751e-1
3.6185e-1
5.7655e-2
9.0380e-2
7.8952e-2
6.6640e-2
5.4283e-1
5.7754e-1
4.8436e-1
4.4330e-1
7.5409e-1
7.2889e-1
7.1164e-1
6.8867e-1
9.6665e-2
9.2746e-2
9.2043e-2
9.1280e-2
0.0000e+0
0.0000e+0
0.0000e+0
0.0000e+0
8.1429
WOF-SMPSO
3.9293e-1
3.0817e-1
3.6260e-1
3.3685e-1
7.2928e-1
9.1048e-1
9.9907e-1
9.6340e-1
2.1942e-1
1.2756e-1
1.0825e-1
9.6512e-2
6.8954e-1
7.4032e-1
7.1771e-1
6.9845e-1
9.0973e-1
9.7602e-1
9.9777e-1
9.9900e-1
9.9460e-2
9.3684e-2
9.2646e-2
9.1418e-2
4.7146e-2
6.2569e-2
5.6379e-2
6.2676e-2
5.0357
LSMOF-NSGA-II
3.9402e-1
3.0323e-1
3.4953e-1
3.4354e-1
7.1699e-1
9.0097e-1
9.9914e-1
9.9974e-1
2.1178e-1
1.2305e-1
1.0755e-1
9.5333e-2
6.7560e-1
7.4826e-1
6.5668e-1
6.5275e-1
8.7807e-1
9.5645e-1
9.9625e-1
9.9844e-1
9.6591e-2
9.2428e-2
9.1741e-2
9.1259e-2
5.5309e-2
6.0454e-2
3.1971e-2
3.6947e-2
6.1786
IM-MOEA
3.9730e-1
3.0944e-1
3.5777e-1
3.5219e-1
4.7300e-1
4.3429e-1
2.3090e-1
2.5494e-1
1.5057e-1
1.4990e-1
4.7697e-2
1.2200e-1
6.4754e-1
6.8097e-1
6.0266e-1
5.9581e-1
8.7795e-1
9.2119e-1
9.5660e-1
9.6591e-1
1.1899e-1
1.1460e-1
1.1031e-1
1.0221e-1
6.3722e-3
0.0000e+0
0.0000e+0
0.0000e+0
6.3214
LMOCSO
3.9862e-1
2.9797e-1
3.5647e-1
3.6199e-1
4.7016e-1
4.2526e-1
2.3153e-1
2.5595e-1
9.5224e-2
9.7368e-2
4.5595e-2
6.2657e-2
5.1358e-1
5.0673e-1
4.1732e-1
3.9536e-1
7.5954e-1
7.1210e-1
7.4710e-1
7.1954e-1
1.1665e-1
1.0973e-1
1.0622e-1
9.7699e-2
4.3875e-2
4.6692e-2
4.1131e-2
4.6799e-2
7.8929
SparseEA MOEA/PSL
9.9425e-1
8.0317e-1
8.6952e-1
9.3084e-1
7.4621e-1
9.1924e-1
9.9905e-1
9.9969e-1
3.0572e-1
1.6867e-1
1.3407e-1
1.0248e-1
5.9453e-1
6.0493e-1
6.2029e-1
5.7544e-1
9.2745e-1
9.8335e-1
9.9818e-1
9.9939e-1
1.2433e-1
1.2464e-1
1.2413e-1
1.2457e-1
9.0874e-2
8.2996e-2
7.9945e-2
8.4221e-2
2.6429
9.9175e-1
7.9986e-1
8.9675e-1
9.2786e-1
7.3136e-1
9.2304e-1
9.9914e-1
9.9976e-1
3.3445e-1
1.9429e-1
1.4634e-1
1.1165e-1
6.2768e-1
5.3080e-1
4.4462e-1
4.0449e-1
9.2518e-1
9.8208e-1
9.9833e-1
9.9937e-1
1.2382e-1
1.2374e-1
1.2378e-1
1.2494e-1
8.8037e-2
8.1820e-2
7.6705e-2
7.8732e-2
3.1429
PM-MOEA
9.7726e-1
7.7881e-1
8.6733e-1
9.3878e-1
7.5187e-1
9.1365e-1
9.9914e-1
9.9976e-1
3.5000e-1
1.8008e-1
2.0506e-1
1.8328e-1
7.2724e-1
7.5426e-1
7.5505e-1
7.6296e-1
9.2792e-1
9.5224e-1
9.9860e-1
9.9946e-1
1.2458e-1
1.1747e-1
1.2456e-1
1.2387e-1
8.8215e-2
7.8282e-2
7.6881e-2
8.1078e-2
1.8571
IEEE Computational Intelligence Magazine - August 2022

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