IEEE Computational Intelligence Magazine - August 2022 - 47

AUGUST 2022 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 47
TABLE V CSD 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
3.0048e+0
2.7123e+0
2.7509e+0
2.8317e+0
1.0310e+0
1.9188e+0
7.4050e-1
9.6118e-1
7.6220e-1
4.6142e-1
5.7829e-1
1.3943e+0
5.3290e-1
9.0566e-1
7.2943e-1
8.4893e-1
3.0989e-1
4.2488e-1
8.4086e-1
9.4161e-1
2.1728e+0
1.8878e+0
2.1851e+0
2.2480e+0
2.3645e+0
1.5385e+0
1.5456e+0
1.8292e+0
4.0357
MOEA/D-DE MOEA/DVA
4.8785e+0
5.1884e+0
4.9408e+0
5.0684e+0
4.2886e+0
5.1181e+0
5.6488e+0
5.6669e+0
5.0103e+0
4.5193e+0
5.2072e+0
5.3115e+0
2.6848e+0
3.8227e+0
3.5010e+0
3.6898e+0
2.6261e+0
3.2954e+0
3.7315e+0
4.3802e+0
6.1017e+0
5.4235e+0
5.1581e+0
4.9446e+0
8.1903e+0
5.6739e+0
5.7187e+0
4.8805e+0
10.7143
LMEA
2.2764e+0
2.6272e+0
2.3780e+0
2.3007e+0
1.8985e+0
2.5088e+0
1.5696e+0
1.6380e+0
3.6105e+0
2.3554e+0
3.2521e+0
3.6887e+0
1.8945e+0
2.8390e+0
2.3132e+0
2.7008e+0
1.7920e+0
2.2900e+0
3.0956e+0
3.5873e+0
4.4328e+0
4.1223e+0
4.0712e+0
4.3841e+0
6.9903e+0
7.0932e+0
6.9999e+0
5.8212e+0
8.3214
1.7258e+0
3.0637e+0
3.2701e+0
3.3388e+0
2.0280e+0
2.6017e+0
2.8488e+0
2.8669e+0
1.1951e+0
8.6373e-1
9.7103e-1
9.9924e-1
1.0816e+0
1.5851e+0
1.4050e+0
1.7421e+0
1.0605e+0
1.4615e+0
1.8393e+0
2.2234e+0
4.5555e+0
3.2365e+0
3.3181e+0
3.4730e+0
3.7214e+0
4.6544e+0
4.1731e+0
3.7548e+0
6.1786
WOF-SMPSO
3.7028e+0
3.9284e+0
3.5023e+0
3.0731e+0
1.2903e+0
1.3877e+0
4.2424e-1
5.0166e-1
3.4305e+0
3.4327e+0
3.8133e+0
3.7022e+0
1.2997e+0
2.1970e+0
1.3378e+0
1.5173e+0
1.0771e+0
1.0587e+0
1.5798e+0
1.6530e+0
3.4440e+0
2.6118e+0
2.3105e+0
2.4696e+0
4.5562e+0
3.0759e+0
2.6701e+0
2.6734e+0
6.3571
LSMOF-NSGA-II
3.2312e+0
3.9938e+0
3.5899e+0
3.8022e+0
1.0999e+0
7.6036e-1
3.2308e-1
2.7824e-1
3.1172e+0
3.0287e+0
3.6349e+0
3.7936e+0
1.3088e+0
2.0061e+0
1.5063e+0
1.7041e+0
1.3401e+0
1.9627e+0
2.3397e+0
2.5253e+0
4.8379e+0
4.0805e+0
4.0289e+0
3.3497e+0
3.5374e+0
2.6566e+0
4.8160e+0
5.3619e+0
7.1429
IM-MOEA
2.2574e+0
2.7048e+0
1.7052e+0
2.2865e+0
3.1714e+0
3.9152e+0
4.4488e+0
4.4669e+0
2.7137e+0
1.9572e+0
2.5700e+0
2.6837e+0
1.1181e+0
1.9279e+0
1.7765e+0
2.0949e+0
1.1292e+0
1.6843e+0
2.3631e+0
2.8313e+0
4.5704e+0
4.4928e+0
4.0696e+0
3.8710e+0
6.4506e+0
6.3339e+0
7.0592e+0
6.7026e+0
7.8571
LMOCSO
1.5509e+0
1.8528e+0
1.7826e+0
1.9593e+0
2.9045e+0
3.7789e+0
4.0488e+0
4.0669e+0
3.2038e+0
2.7711e+0
3.3428e+0
2.2026e+0
2.0159e+0
2.8943e+0
2.7489e+0
2.8086e+0
1.9874e+0
2.3819e+0
2.8499e+0
3.5155e+0
4.2169e+0
4.1498e+0
3.7363e+0
4.1257e+0
5.2506e+0
3.7750e+0
3.7728e+0
4.1176e+0
7.8214
SparseEA
5.3702e-1
6.8162e-1
2.8771e-1
2.1026e-1
6.6861e-1
5.4259e-1
3.2308e-1
3.8634e-1
6.3366e-1
7.0696e-1
1.6347e+0
2.0138e+0
5.5563e-1
5.6652e-1
3.6724e-1
3.8743e-1
6.3345e-1
6.7480e-1
8.6170e-1
7.6144e-1
1.8698e+0
1.3542e+0
7.4388e-1
8.9096e-1
1.5292e+0
9.7928e-1
1.1240e+0
9.8494e-1
2.2857
MOEA/PSL
4.1100e-1
6.2156e-1
7.6494e-1
9.7486e-1
5.7484e-1
5.5087e-1
4.3138e-1
6.8423e-1
1.5542e+0
1.6241e+0
1.7843e+0
1.1828e+0
3.1490e-1
4.1858e-1
5.2786e-1
9.5351e-1
3.9408e-1
2.4352e-1
6.2590e-1
9.0327e-1
6.5916e-1
7.4433e-1
1.0596e+0
1.4762e+0
8.3318e-1
9.7818e-1
7.0271e-1
7.0353e-1
2.2857
PM-MOEA
7.1119e-1
8.1119e-1
8.1605e-1
8.5385e-1
6.2380e-1
8.3448e-1
6.4616e-1
7.7268e-1
1.1475e+0
1.2144e+0
5.4839e-1
6.0856e-1
2.1683e-1
8.0706e-1
3.5349e-1
2.9303e-1
1.7191e-1
1.0404e+0
3.8083e-1
6.6124e-1
1.6701e+0
2.8456e+0
1.3492e+0
1.6541e+0
1.2534e+0
1.8173e+0
1.9674e+0
1.6885e+0
2.6429
IEEE Computational Intelligence Magazine - August 2022

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