# 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
Table 3 presents the statistical results of the IGD metrics for five comparison algorithms obtained from 20 independent runs on the DTLZ4 to DTLZ7 problems with 100, 500, and 1000 decision variables. The optimal results for each test instance are highlighted with a dark gray background, while the suboptimal results are marked with a light gray background. The Wilcoxon rank-sum test was employed with a significance level of 0.05, where the symbols \"+\", \"-\", and \(\approx\) indicate results that are significantly better than, significantly worse than, and statistically similar to the proposed DVA-TPCEA algorithm, respectively. From Table 3, it can be observed that the algorithms NSGA-II, MOEA/D, NSGA-III, LMEA, and DVA-TPCEA achieve optimal or suboptimal results in 4, 6, 5, 16, and 17 instances, respectively. Notably, the performances of LMEA and DVA-TPCEA significantly surpass those of the other algorithms, with DVA-TPCEA slightly outperforming LMEA. Although the comparative results of individual algorithms indicate that the performance of LMEA is slightly superior to that of DVA-TPCEA, the overall results show that DVA-TPCEA demonstrates better diversity and stability in optimization outcomes when compared to all other algorithms. As the number of decision variables increases from 100 to 1000, the performance of LMEA and DVA-TPCEA consistently maintains a good level across all test problems, indicating that both algorithms exhibit good scalability in addressing the challenges posed by high-dimensional decision spaces, particularly in solving the DTLZ4 problem. LMEA shows more significant advantages in the DTLZ4 and DTLZ5 problems, while the proposed algorithm achieves most of the suboptimal IGD values in these instances, demonstrating its effectiveness in handling such problems. In the five-objective and ten-objective DTLZ6 problems, as the number of decision variables increases from 100 to 1000, the proposed algorithm attains the best IGD values, indicating that the directional search mechanism in the dual-population evolutionary algorithm, combined with decision variable analysis, facilitates the population's convergence. Moreover, the information exchange between populations helps avoid local optima and aids in finding the global optimum. Table 4 presents the statistical results of the IGD values for five algorithms on the WFG6 to WFG9 problems. The algorithms NSGA-II, MOEA/D, NSGA-III, LMEA, and DVA-TPCEA exhibit the number of optimal or suboptimal performances across 48 test instances as follows: 5, 2, 13, 13, and 15, respectively. Notably, the DVA-TPCEA algorithm stands out with the best performance, ranking first, followed by NSGA-III and LMEA. While LMEA performs better than DVA-TPCEA with 100 to 500 decision variables, DVA-TPCEA shows a clear advantage in test instances with 1000 decision variables. This indicates that the DVA-TPCEA algorithm is more effective and flexible when dealing with larger-scale decision variable problems. Additionally, NSGA-III also achieves good IGD values compared to the first two algorithms, attributed to its successful guidance of offspring generation toward the ideal regions of the objective space through the sampling of ideal points. This strategy allows NSGA-III to more accurately locate areas close to the true Pareto front during the search process, thereby increasing the likelihood of finding high-quality solutions. Overall, DVA-TPCEA demonstrates a superior performance across multiple test instances, showcasing its comprehensive advantages in solving complex problems. \begin{table}
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**Prob. ** & **Obj. ** & **Des.