# 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
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & **MOEA/D-DPA** & **MOEA/D-SPS** & **MOEA/D-PBI** & **MOEA/D-AGG** & **MOEA/D-TCHE** & **MOEA/D-2 PBI** \\ \hline ZDT1 & 4.30E-3 (1.5E-4) & 4.30E-3 (6.7E-4) & 7.70E-3 (3.6E-3) & **1.12E-3 (6.4E-4)** & 2.78E-3 (1.1E-3) & 1.23E-2 (3.1E-3) \\ ZDT2 & **5.77E-4 (3.7E-4)** & 4.71E-3 (1.8E-3) & 1.14E-2 (6.2E-3) & 1.32E-2 (3.2E-3) & 3.06E-3 (1.4E-3) & 2.21E-2 (4.6E-3) \\ ZDT3 & 8.98E-3 (1.7E-3) & 1.57E-2 (2.7E-3) & 1.42E-2 (1.1E-3) & **4.15E-3 (1.8E-3)** & 6.84E-3 (7.9E-4) & 9.85E-3 (1.0E-3) \\ ZDT4 & **8.43E-3 (4.8E-3)** & 3.69E-2 (3.1E-2) & 9.35E-2 (5.9E-2) & 3.86E-2 (1.9E-2) & 4.79E-2 (3.0E-2) & 5.48E-1 (1.6E-1) \\ DTLZ1 & 8.99E-4 (2.3E-5) & 9.87E-4 (1.6E-4) & 6.60E-4 (3.0E-4) & 4.90E-3 (3.21E-5) & 2.12E-2 (2.6E-2) & 3.47E-2 (3.4E-2) \\ DTLZ2 & **3.55E-4 (1.3E-6)** & 6.29E-4 (1.4E-5) & 7.61E-4 (2.0E-5) & 5.35E-3 (1.5E-6) & 7.74E-4 (1.1E-5) & 1.08E-3 (6.5E-5) \\ DTLZ3 & **3.07E-3 (1.2E-2)** & 2.11E-2 (4.6E-2) & 6.10E-2 (1.2E-1) & 2.00E-2 (2.3E-2) & 2.28E-1 (2.5E-1) & 3.11E-1 (4.0E-1) \\ DTLZ4 & **1.03E-3 (8.7E-4)** & 1.42E-3 (9.5E-4) & 1.24E-3 (2.1E-4) & 5.88E-3 (1.0E-11) & 1.32E-3 (2.7E-4) & 1.69E-3 (2.7E-4) \\ DTLZ5 & 1.03E-3 (9.8E-6) & 1.06E-3 (4.6E-5) & 1.44E-3 (2.6E-5) & 3.09E-2 (5.5E-10) & **9.92E-4 (3.0E-5)** & 1.01E-3 (1.7E-4) \\ DTLZ6 & **1.56E-3 (2.7E-5)** & 1.78E-3 (7.5E-5) & 1.78E-3 (7.5E-5) & 4.65E-2 (1.9E-2) & 4.25E-3 (9.4E-3) & 7.42E-3 (2.1E-2) \\ DTLZ7 & 3.75E-2 (5.1E-3) & 3.66E-2 (5.2E-3) & **9.96E-3 (4.3E-4)** & 1.54E-2 (3.8E-3) & 2.91E-3 (4.2E-3) & 2.74E-2 (3.9E-3) \\ \hline \end{tabular}
\end{table} 
Table 3: IGD mean and standard deviation of algorithms. strategy has some performance enhancement effect on the PBI decomposition strategy on the three-objective problem and is better than similar improved algorithms. As can be seen from the boxplots in Figure 5, the DPA strategy achieves better IGD metrics on the ZDT1, ZDT2, and ZDT4 problems, thus proving that its derived solution sets are closer to the ideal Pareto distance. It can also be seen that the IGD metrics obtained by the DPA strategy on all four test problems are more stable than those obtained by the original PBI decomposition strategy. On the ZDT3 problem, the IGD metrics obtained by both the DPA strategy and the SPS strategy are unsatisfactory. As demonstrated by the box plots presented in Figure 6, the MOEA/D-DPA algorithm achieves better IGD metrics than the MOEA/D-PBI algorithm on the test problems except DTZL7 and is more stable. The MOEA/D-DPA and MOEA/D-SPS algorithms do not perform well on the DTLZ7 test problem, which shows that on the triple-objective problem, the DPA decomposition strategy has some solution quality improvement over the original PBI decomposition strategy, but there is still room for improvement. Figure 5: Box plots of IGD of algorithms on ZDT test suites. Figure 6: _Cont_. Combining the HV performance metrics of the algorithms in Tables 5 and 6, it can be seen that the MOEA/D-DPA algorithm has better HV metrics than the original MOEA/D-PBI algorithm and outperforms the similar improved MOEA/D-SPS and MOEA/D-2 PBI algorithms on all four test problems of ZDT. And the MOEA/D-DPA algorithm finds the optimal HV metric value on ZDT2 and ZDT4 problems. Therefore, it is believed that the MOEA-DPA algorithm solution improves the convergence and diversity of the solution to the bi-objective problem. On the three-objective problem, the improved MOEA/D-DPA algorithm performs better than the original PBI strategy on all the test problems except DTLZ7 and achieves the optimal value of the five decomposition strategies. However, it performs poorly on the DTLZ7 test problem. In summary, it is concluded that the MOEA/D-DPA algorithm enhances population diversity and improves solution quality to some extent, which is consistent with the previous conclusions.