# Research on Multi-Objective Evolutionary Algorithms Based on Large-Scale Decision Variable Analysis
## 4 Experiment
### Comparison of Algorithm Experimental Results and Analysis on Different Test Problems
** & **NSGA-II** & **MOEA/D** & **NSGA-III** & **LMEA** & **DVA-TPCEA** \\ \hline \multirow{8}{*}{DTLZ4} & \multirow{8}{*}{5} & 100 & 2.5538e-1 & 5.6546e-1 & 3.1385e-1 & 2.6412e-1 & 4.1015e-1 \\  & & & (4.89e-3) & (4.05e-1) & (1.39e-1) & (1.55e-2) & (8.64e-2) \\  & & 500 & 2.6381e-1 & 6.1212e-1 & 9.4811e-1 & 2.7223e-1 & 2.7139e-1 \\  & & & (1.81e-2) & (5.82e+0) & (1.01e+0) & (2.46e-2) & (6.74e+0) \\  & & 1000 & 3.5101e+1 & 8.4722e+1 & 4.1660e+1 & 7.7894e-1 & \\  & & & (2.82e+0) & (1.12e+1) & (4.96e+0) & (8.20e-1) & (1.51e+0) \\ \cline{2-7}  & & 100 & 9.7936e+0 & 6.8012e-1 & 5.6919e-1 & 5.0832e-1 & 4.7680e-1 \\  & & & (1.20e+0) & (5.36e-2) & (6.38e-2) & (2.47e-2) & (3.40e-2) \\ \cline{2-7}  & & 500 & 4.3077e+1 & 4.8038e-1 & 4.5494e-1 & 5.2723e-1 & 8.9858e+0 \\  & & & (2.20e+1) & (1.42e-1) & (1.89e-2) & (3.98e-3) & (4.51e+0) \\  & & 1000 & 1.0845e+2 & 7.8128e+1 & 1.2198e+0 & 8.6922e-1 & 2.0190e+1 \\  & & & (7.62e+0) & (4.39e-1) & (8.62e-1) & (1.24e-1) & (1.64e+1) \\ \hline \multirow{8}{*}{DTLZ5} & \multirow{8}{*}{5} & 100 & 2.8140e+0 & 3.0149e-2 & 2.1886e-1 & 5.0632e-2 & 4.9923e-2 \\  & & & (4.24e-1) & (4.28e-4) & (6.00e-2) & (7.52e-5) & (2.42e-2) \\ \cline{1-1}  & & 500 & 3.1322e+1 & 3.7270e+1 & 9.6500e+0 & 5.1713e-2 & 3.0129e+0 \\ \cline{1-1}  & & (1.23e+0) & (8.84e-1) & (9.55e-1) & (8.51e-6) & (1.09e+1) \\ \cline{1-1}  & & 1000 & 7.2015e+1 & 7.7672e+1 & 3.4050e-1 & 5.7896e-3 & 7.8018e-1 \\ \cline{1-1}  & & & (1.25e+0) & (8.10e-1) & (2.55e-1) & (1.25e-1) & (3.97e-1) \\ \cline{1-1} \cline{2-7}  & & 100 & 4.2740e+0 & 7.3749e-2 & 3.5658e-1 & 2.3923e-3 & 8.1336e-2 \\  & & & (4.60e-1) & (2.20e-5) & (4.77e-1) & (6.95e-5) & (1.06e-2) \\ \cline{1-1}  & & 500 & 3.3645e+1 & 3.7202e+1 & 1.7521e+1 & 2.2732e-3 & 9.4864e-2 \\  & & & (8.32e+0) & (7.03e-1) & (4.12e-1) & (4.47e-5) & (7.58e+0) \\ \cline{1-1}  & & 1000 & 7.7702e+1 & 9.4516e-2 & 1.9678e+1 & 7.7362e-3 & 6.1010e+0 \\  & & & (1.82e+0) & (7.77e-3) & (4.91e+0) & (4.58e-1) & (3.89e+0) \\ \hline \multirow{8}{*}{DTLZ6} & \multirow{8}{*}{5} & 100 & 7.1490e+1 & 1.2735e+1 & 7.7892e+0 & 5.0732e-2 & 3.2933e-2 \\  & & & (2.75e+0) & (2.50e+1) & (5.79e+0) & (1.601e-4) & (6.52e-3) \\ \cline{1-1}  & & 500 & 4.2925e+2 & 3.8203e+2 & 3.9452e+2 & 5.4921e-2 & 3.4546e-2 \\ \cline{1-1}  & & (2.47e+0) & (5.03e+0) & (4.37e+0) & (4.450e-3) & (3.96e-3) \\ \cline{1-1}  & & 1000 & 8.7913e+2 & 6.8319e+2 & 6.0349e+2 & 8.9785e+1 & 5.9962e+2 \\ \cline{1-1}  & & & (3.48e+0) & (1.01e+1) & (4.16e+0) & (1.35e+0) & (7.71e-1) \\ \hline \multirow{8}{*}{DTLZ6} & \multirow{8}{*}{10} & 100 & 7.5160e+1 & 1.3776e-1 & 2.3937e-1 & 6.9326e-2 & 6.3895e-2 \\  & & & (1.71e+0) & (2.52e-2) & (1.32e+1) & (2.425e-3) & (4.73e-3) \\ \cline{1-1}  & & 500 & 4.2938e+2 & 1.3036e+2 & 3.4694e+2 & 8.3834e-3 & 8.1608e-3 \\ \cline{1-1}  & & (1.18e+1) & (7.25e+1) & (3.33e+1) & (7.313e-4) & (4.93e-3) \\ \cline{1-1}  & & 1000 & 8.8177e+2 & 5.6228e+2 & 7.2006e+2 & 8.9494e+2 & 7.6215e-1 \\ \cline{1-1}  & & & (3.90e+1) & (1.53e+1) & (1.58e+1) & (1.87e+0) & (6.23e-1) \\ \hline \multirow{8}{*}{DTLZ7} & \multirow{8}{*}{5} & 100 & 3.9399e-1 & 1.1448e+0 & 4.0068e-1 & 3.3182e-1 & 3.0111e-1 \\  & & & (1.65e-2) & (1.01e-2) & (1.16e-2) & (9.26e-3) & (7.99e-2) \\ \cline{1-1}  & & 500 & 5.0010e-1 & 8.7343e+0 & 5.2885e-0 & 1.9951e+1 & 5.4803e-1 \\ \cline{1-1}  & & (1.51e-2) & (6.60e-1) & (4.08e-1) & (1.97e-1) & (6.96e-2) \\ \cline{1-1}  & & 1000 & 7.0548e+0 & 8.9161e-1 & 2.7150e+0 & 1.9339e+1 & 1.9717e+1 \\ \cline{1-1}  & & & (5.72e-1) & (7.43e-2) & (1.14e-1) & (6.66e-1) & (5.14e-1) \\ \cline{1-1} \cline{2-7}  & & 100 & 2.5078e+0 & 2.2422e+0 & 1.5533e+0 & 1.0388e+0 & 2.8114e+0 \\ \cline{1-1}  & & (4.49e-1) & (4.77e-1) & (2.89e-1) & (2.01e-2) & (4.31e-1) \\ \cline{1-1} \cline{2-7}  & & 500 & 2.1319e+1 & 2.2126e+0 & 1.7238e+0 & 4.0394e-1 & 3.6949e+0 \\ \cline{1-1}  & & (1.12e+1) & (3.45 Table 5 presents the statistical results of the IGD values obtained from 20 independent runs of seven algorithms on the LSMOP1-LSMOP5 problems with five objectives and  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Prob. ** & **Obj. ** & **Des.