# Research on Multi-Objective Evolutionary Algorithms Based on Large-Scale Decision Variable Analysis
## 4 Experiment
### Analysis and Comparison of Algorithm Effects  
From the experimental results presented above, the DVA-TPCEA algorithm demonstrates exceptional overall performance and stability, showcasing its unique advantages. However, in some cases, the IGD value may not fully reflect the quality of the solution set. Therefore, to visually demonstrate the effectiveness of the proposed framework, we present the actual performance of the DVA-TPCEA algorithm compared to various algorithms on the 10-objective DTLZ and WFG test instances. Figure 2 presents the parallel coordinate \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Prob.** & **Obj. Des.** & **NSGA-II** & **MOEA/D** & **NSGA-III** & **LMEA** & **S3 CMAES** & **FDV** & **DVA-TPCEA** \\ \hline \multirow{4}{*}{LSMOP1} & & 100 & 5.4328e-1 & 2.4476e-1 & 3.4853e-1 & 1.2051e+0 & 1.8968e+0 & 4.6402e-1 & 3.1966e-1 \\  & & (9.84e-2) & (4.54e-2) & (1.45e-1) & (1.45e+0) & (9.36e-1) & (3.57e-2) & (5.67e-2) \\ \cline{2-10}  & & 500 & 1.0055e+0 & 2.1723e+0 & 1.0185e+1 & 5.8259e+0 & 4.6981e+1 & 1.1189e+0 & 2.4694e+0 \\  & & (8.98e-1) & (2.90e-1) & (6.99e-1) & (4.58e+0) & (2.60e+1) & (1.75e-1) & (7.51e-1) \\ \cline{2-10}  & & 1000 & 8.9591e+0 & 2.5585e+0 & 3.2853e+0 & 1.0973e+1 & 2.9408e+1 & 1.2205e+0 & 2.0533e+0 \\  & & (4.75e-1) & (6.53e-1) & (3.77e-1) & (4.17e-1) & (2.98e+1) & (2.96e-1) & (6.50e-1) \\ \hline \multirow{4}{*}{LSMOP2} & & 100 & 3.2877e-1 & 2.5318e-1 & 2.3706e-1 & 2.2908e-1 & 3.2142e-1 & 2.8929e-1 & 3.1354e-1 \\  & & (1.93e-2) & (1.67e-2) & (1.52e-2) & (9.43e-2) & (1.70e-2) & (1.05e-2) & (1.37e-2) \\ \cline{1-1}  & & 500 & 2.0638e-1 & 1.7359e-1 & 1.7242e-1 & 2.4805e-1 & 5.1896e-1 & 1.6626e-1 & 1.1482e-1 \\ \cline{1-1}  & & (8.78e-3) & (6.10e-4) & (6.81e-4) & (1.80e-2) & (7.53e-2) & (1.41e-3) & (9.81e-3) \\ \cline{1-1}  & & 1000 & 1.9435e-1 & 1.5301e-1 & 1.5269e-1 & 2.0084e-1 & 5.0604e-1 & 1.4884e-1 & 1.1566e-1 \\ \cline{1-1}  & & (3.42e-3) & (6.87e-5) & (1.78e-4) & (1.77e-2) & (6.73e-2) & (9.55e-4) & (2.06e-2) \\ \hline \multirow{4}{*}{LSMOP3} & & 100 & 1.4837e+0 & 3.3315e-1 & 7.5363e-1 & 5.0776e-1 & 2.6812e+0 & 1.3632e+0 & 6.3663e-1 \\  & & (7.58e-1) & (5.36e-0) & (1.65e-1) & (2.56e-1) & (1.08e+0) & (8.06e-1) & (1.63e-2) \\ \cline{1-1}  & & 500 & 1.7681e+1 & 2.0509e+3 & 7.9487e+0 & 7.4396e-1 & 3.6018e+4 & 3.9530e+0 & 9.5883e-1 \\ \cline{1-1}  & & (2.54e+0) & (1.61e+3) & (1.49e+1) & (1.49e-1) & (2.99e+4) & 2.86e+0 & (0.00e+0) \\ \cline{1-1}  & & 1000 & 2.1924e+1 & 1.4478e+0 & 1.1001e+1 & 3.0022e+3 & 3.0187e+4 & 3.9600e+0 & 1.4310e+0 \\ \cline{1-1}  & & (2.33e+0) & (6.47e-1) & (9.20e-1) & (4.21e+3) & (1.55e+4) & (3.53e+0) & (8.68e+2) \\ \hline \multirow{4}{*}{LSMOP4} & & 100 & 5.0522e-1 & 3.9637e-1 & 2.8159e-1 & 2.3732e-1 & 4.9438e-1 & 5.0644e-1 & 3.3174e-1 \\  & & (4.80e-2) & (5.71e-2) & (2.15e-2) & (7.49e-2) & (1.75e-2) & (1.05e-2) & (8.03e-3) \\ \cline{1-1}  & & 500 & 3.6244e-1 & 2.8316e-1 & 2.7324e-1 & 4.2991e-1 & 8.7969e-1 & 2.7351e-1 & 2.7431e-1 \\ \cline{1-1}  & & (2.28e-2) & (8.06e-3) & (4.76e-3) & (3.50e-2) & (2.53e-1) & (4.22e-3) & (2.00e-2) \\ \cline{1-1}  & & 1000 & 2.8964e-1 & 2.1752e-1 & 2.0870e-1 & 2.8460e-1 & 5.7982e-1 & 2.0708e-1 & 3.0586e-1 \\ \cline{1-1}  & & (1.81e-2) & (8.37e-4) & (7.64e-4) & (3.32e-2) & (1.68e-1) & (1.98e-3) & (1.99e-2) \\ \hline \multirow{4}{*}{LSMOP5} & & 100 & 6.9343e+0 & 1.5185e+0 & 6.0402e-1 & 8.7284e-1 & 1.1959e+0 & 9.4981e-1 & 1.0314e+0 \\ \cline{1-1}  & & (8.82e+0) & (2.39e+0) & (2.97e-1) & (1.59e-1) & (5.53e-2) & (7.64e-2) & (3.70e-2) \\ \cline{1-1}  & & 500 & 1.9804e+1 & 9.9662e-1 & 5.3844e+0 & 1.6316e+1 & 9.4261e+1 & 1.1245e+0 & 9.6925e-1 \\ \cline{1-1}  & & (1.72e+0) & (1.65e-1) & (9.35e-1) & (1.36e+0) & (7.40e+1) & (5.15e-2) & (6.26e-2) \\ \cline{1-1}  & & 1000 & 2.2542e+1 & 1.6878e+1 & 7.2829e+0 & 1.2738e+0 & 4.4433e+1 & 1.2060e+0 & 4.0762e+0 \\ \cline{1-1}  & & (2.66e+0) & (7.29e-1) & (4.37e-1) & (2.63e-1) & (3.44e+1) & (5.56e-2) & (6.82e+0) \\ \hline \multicolumn{4}{c}{+/\(-/=\)} & 2/8/5 & 6/3/6 & 2/8/5 & 7/5/3 & 0/15/0 & 6/8/1 & - \\ \hline \end{tabular}
\end{table}