# Transfer Learning Based on Clustering Difference for Dynamic Multi-Objective Optimization
## 4 Experiments
### Performance Comparison with Other Algorithms  
In this section, performance comparison experiments are performed. The above indicators MIGD and MS are used, and some algorithms are compared with the algorithm proposed in this paper. Firstly, the MIGD values of six algorithms are compared, proving the proposed algorithm's effectiveness. These six algorithms include a dynamic multi-objective optimization algorithm (TCD-DMOEA) that combines clustering difference and transfer learning, a dynamic multi-objective optimization algorithm (Tr-DMOEA) that combines only transfer learning methods [28], a dynamic NSGA-II algorithm (DNSGA-II-A, DNSGA-II-B) [49], PPS [42], and MOEA based on [PERSON]'s predictions (KF-DMOEA) [50]. A comparison of TCD-DMOEA and Tr-DMOEA was conducted to prove the performance of our proposed strategy. According to the difference in performance index and running time, it could be determined that the clustering difference strategy proposed in this paper can not only maintain good convergence and diversity, but also effectively reduce the possibility of negative transfer.  
Figure 5 plots the IGD values obtained by different algorithms after each change. These curves show that under 20 different test functions, the curve obtained by the method was basically at the bottom, and the curve of the method fluctuated less, which meant that the method is not only better performing, but also more stable.  
The statistical results of MIGD and MS values that were run 20 times are shown in Tables 2 and 3, respectively. Table 2 shows the MIGD values for six algorithms in three different configurations. Bold words in the table indicate that the algorithm had the best diversity on this benchmark, and the last column represents the \"winner\" in this comparison. It can be seen from Table 2 that TCD-DMOEA obtained 44 of the 60 best results, accounting for 73.3%. KF-DMOEA achieved five best results, PPS achieved three best results, and DNSGA-II-A and DNSGA-II-B achieved six and two best results, respectively. Specifically, TCD-DMOEA performed well at most test functions in all dynamic test setups, and DNSGA-II-A achieved better convergence than TCD-DMOEA on DF9 and DF12. The value of PPS was obviously superior to that of other algorithms on DF11.  
Table 3 shows the MS values for six comparison algorithms, and it is clear that TCD-DMOEA obtained 38 out of 60 best results, KF-DMOEA obtained only one best result, PPS obtained five best results, and Tr-DMOEA obtained nine best results. DNSGA-II-A and DNSGA-II-B achieved four and three best results, respectively. Specifically, TCD  
DMOEA performed well at most test functions in all dynamic test setups, with Tr-DMOEA performing better on F8 and DNSGA-II-B performing better on DF10.  
The above experimental results show that TCD-DMOEA could obtain a set of solutions with good convergence and diversity for most test problems. However, it did not perform well enough on some reference functions, such as DF9, DF11, and DF12. TCD-DMOEA also had some shortcomings, which may have been due to the large variation in the POS of these problems, so it was difficult to accurately predict in the target domain processing stage, and the final output of the population quality was poor.  
At the same time, it can be found from Table 2 that except for F8, F9 and F10, TCD-DMOEA achieved good performance on the F test function set in most cases. These three test functions were characterized by POS jumps from one region to another, and the geometry of the two consecutive POFs was completely different. This resulted in a low degree of similarity between the source domain and the target domain, which ultimately increased the likelihood of negative transfer.