## 5 Experimental Results and Analysis  
By simulating the Pareto approximation frontiers in the three-dimensional space obtained by MaOISSA and the four comparison algorithms in the test function SMOP3, Figure 2 shows that the Pareto approximation frontiers of NSGA-III and MaOISSA are basically the same, Tables 3 and 4 regarding for 4-objective and 5-objective problems, show that MaOISSA's overall index is better than NSGA-III, indicating that MaOISSA has some advantage in high-dimensional and multi-dimensional goals as the number of dimensions increases. Compared with SPEAE/R and CMOPSO, MaOISSA has better diversity and convergence, while SMPSO has poorer convergence and diversity in the Pareto approximate frontier in three-dimensional space. In Table 5, in terms of IGD values of the five algorithms on the test function SMOP3 when the target dimension was three, five, eight, and thirteen, it can be seen that, when the target dimension was three, the NSGA-III algorithm performs better, but MaOISSA has similar results to NSGA-III. With the increase of objective dimension, the MaOISSA algorithm has better convergence than other algorithms, which indicates that Maoissa algorithm has better convergence and diversity in high-dimensional multi-objective optimization. Tables 3 and 4 show the statistical results of IGD and HV of MaOISSA, CMOPSO, SPEAE/R, NSGA-III and SMPSO3 in 12 test functions. The non-parametric statistical Wilcoxon rank sum test with a significance threshold of 5% is used to compare the five algorithms. \"\(\approx\)\" in the table means that the two algorithms are identical, \"+\" means that the algorithm is better than MaOISSA and \"\(-\)\" means that the algorithm is worse than the MaOISSA. M is the target space dimension of a test function in the table, and D is the decision variable dimension of a test function. Each method is run 30 times for each test function to compute the mean value and standard deviation of the results, with the ideal result for each test function indicated in bold. As can be seen from Table 3, the algorithm in this paper obtains optimal IGD values in 9 of the 12 test functions. In comparison to NSGA-III and SPEA/R, both of which are high-dimensional multi-objective optimization problems, MaOISSA has better convergence and diversity on DTL5, MaF2, MaF4, MaF7, and SMOP3, showing that the algorithm can deal with multi-modal problems well. For the high-dimensional multi-objective particle swarm optimization algorithm, the IGD values of CMPSO and SMPSO are much different from those of MaOISSA, so it cannot show the advantage of convergence speed. MaOISSA does not obtain better results for DTLZ4, DTLZ6, and MaF5. However, this algorithm is not much different than the best results, indicating that the algorithm has better robustness for different types of problems. As can be seen from Table 4, HV of MaOISSA obtains the optimal average value on 8 of the 12 test functions with the best performance on DTLZ1-3, DTLZ5, MaF2, MaF3, MaF7, and SMOP3. it is approximate to SPEA/R result on DTLZ4. NSGAIII receives better results on DTLZ6 test function, SMPSO is better than other algorithms on MaF4 test function, SPEA/R is better than other algorithms on MaF5 test function. The above results show that MaOISSA has better overall performance in most cases. Figure 3 depicts box plots of the IGD metrics for the populations of the five algorithms throughout 30 different tests on the 12 chosen issues. The horizontal point is the name of the comparison algorithm, while the vertical coordinate represents the IGD metric scale. The outer top and bottom lines of each column of the box plot reflect the sample's maximum and lowest values, the inner top and bottom lines represent the upper and lower quartiles, and the \"+\" represents discrete values.