# A Dynamic Parameter Tuning Strategy for Decomposition-Based Multi-Objective Evolutionary Algorithms
## 4 Discussion
### Experimental Results and Analysis
#### 4.3.2 Analysis of IGD Performance Index Results
As can be seen from Figure 7, the MOEA/D-DPA algorithm significantly improves the HV metrics over the original MOEA/D-PBI algorithm on the four ZDT test problems, especially on the ZDT2 and ZDT4 test problems, where the HV metrics obtained by the MOEA/D-DPA algorithm are optimal. In general, both IGD metrics and HV metrics combine to demonstrate the convergence and diversity of the algorithms, i.e., the dynamic parameterization strategy exhibits better performance metrics than the original PBI decomposition strategy on the ZDT test problem, but on the ZDT3 test problem, the IGD metrics of the MOEA/D-DPA algorithm are slightly worse than those of the MOEA/D-PBI algorithm, but the HV metrics are better than those of the MOEA/D-PBI algorithm. This is due to the fact that although both IGD and HV metrics combine to show the performance of the algorithms, the HV metrics are more inclined to reflect the population diversity of the algorithms. Therefore, it is proven that the MOEA/D-DPA algorithm improves population diversity in discontinuous bi-objective optimization problems. In the test problems, except for ZDT4, the metrics solved by the MOEA/D-DPA algorithm have better stability. Therefore, it is concluded that the DPA strategy improves the solution performance of the algorithm to a greater extent, which is consistent with the previous conclusion. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **MOEA/D-DPA** & **MOEA/D-SPS** & **MOEA/D-PBI** & **MOEA/D-AGG** & **MOEA/D-TCHE** & **MOEA/D-2 PBI** \\ \hline ZDT1 & 6.03E-1 (5.2E-3) & 5.28E-1 (4.4E-2) & 3.43E-1 (2.7E-1) & **6.34E-1 (3.1E-2)** & 5.42E-1 (7.6E-2) & 1.85E-1 (1.2E-1) \\ ZDT2 & **3.09E-1 (1.2E-2)** & 1.85E-1 (9.7E-2) & 8.15E-2 (1.6E-1) & 3.21E-4 (5.9E-3) & 2.37E-1 (6.7E-2) & 0.00E+0 (4.3E-3) \\ ZDT3 & 3.52E-1 (5.0E-3) & 2.06E-2 (9.6E-2) & 1.96E-1 (1.2E-1) & **3.75E-1 (1.1E-1)** & 3.02E-1 (4.0E-2) & 1.55E-1 (3.4E-2) \\ ZDT4 & **3.68E-1 (2.9E-1)** & 6.82E-5 (1.0E-1) & 6.94E-5 (2.3E-1) & 3.25E-2 (6.1E-2) & 9.39E-3 (1.9E-2) & 0.00E+0 (0.00E+0) \\ DTL2/ & **7.92E-1 (1.1E-3)** & 7.70E-1 (3.6E-3) & 7.62E-1 (1.1E-2) & 3.33E-14 (4.0E-1) & 1.41E- (4.2E-1) & 7.51E-1 (8.5E-3) \\ DTL2 & **4.10E-1 (3.2E-3)** & 3.84E-1 (1.6E-3) & 3.56E-1 (8.1E-3) & 8.43E-8 (6.2E-7) & 3.64E-1 (3.4E-3) & 2.94E-1 (1.7E-2) \\ DTL2/ & **4.03E-1 (1.1E-2)** & 3.67E-1 (2.7E-1) & 1.37E-1 (2.6E-1) & 8.63E-6 (3.2E-9) & 1.53E-1 (1.6E-1) & 2.75E-1 (1.8E-1) \\ DTL2/ & **3.39E-1 (6.0E-3)** & 3.67E-1 (1.0E-2) & 3.40E-1 (1.8E-2) & 4.42E-8 (6.2E-5) & 3.47E-1 (7.0E-2) & 2.82E-1 (2.8E-2) \\ DTL2/ & **8.93E-2 (8.8E-5)** & 8.87E-2 (4.9E-4) & 8.64E-2 (3.9E-4) & 3.43E-9 (2.2E-7) & 8.84E-2 (4.0E-4) & 8.75E-2 (1.7E-3) \\ DTL2/ & 9.02E-2 (9.9E-6) & 8.98E-2 (3.0E-4) & 8.76E-2 (3.2E-4) & 2.43E-4 (5.2E-9) & 9.14E-2 (4.5E-4) & **9.36E-2 (1.5E-3)** \\ DTL2/ & 7.25E-4 (9.1E-3) & 9.09E-4 (9.9E-3) & 4.68E-2 (1.9E-2) & **1.12E-1 (8.7E-2)** & 7.27E-4 (2.2E-3) & 1.01E-2 (1.6E-2) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: HIV median and quartile of algorithms. Figure 7: _Cont._  
As can be seen from the HV boxplots of the five algorithms on the DTLZ test problem in Figure 8, the MOEA/D-DPA algorithm achieves higher performance and is more stable than the MOEA/D-SPS algorithm on the triple-objective problem in most cases. However, both the MOEA/D-DPA algorithm and the MOEA/D-SPS algorithm yielded poor HV performance metrics on the DTLZ7 test problem. Overall, it is concluded that the MOEA/D-DPA algorithm has some solution quality improvement over the MOEA/D-PBI algorithm on the triple-objective problem, but there is still some room for improvement. Figure 8: _Cont_. Figure 7: Box plots of HV of algorithms on ZDT test suites.