# Transfer Learning Based on Clustering Difference for Dynamic Multi-Objective Optimization
## 5 Conclusions  
In recent years, transfer learning has been proven to be one of the effective means to solve dynamic multi-objective optimization problems. However, the efficiency of transfer learning (also known as negative transfer) decreases significantly when the target domain is poorly similar to the source domain, or when the transfer learning method is incorrect. Negative transfer forces a search for solutions in the wrong direction, wasting a lot of computing resources. As a result, the running speed becomes slower and the convergence becomes worse. In this article, a transfer learning method based on a cluster difference dynamic multi-objective optimization algorithm, TCD-DMOEA, was proposed. The TCD-DMOEA applies a clustering difference strategy to increase the similarity between the target domain and the source domain to reduce the likelihood of negative transfer, and the TradaBoost algorithm to classify good-quality populations. Therefore, when the environment changes drastically, the proposed method can improve the quality of the population in the drastically changing \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Functions** & **DNSGA-II-A** & **DNSGA-II-B** & **TCD-DMOEA** & **PPS** & **Tr-DMOEA** & **KF-DMOEA** \\ \hline DF1 & 23.0258 & 27.0289 & 10.0028 & 30.1587 & 461.5591 & 30.4620 \\ DF2 & 29.8561 & 28.4196 & 9.8974 & 29.7459 & 363.2698 & 29.4512 \\ DF3 & 39.274 & 30.4785 & 10.0525 & 18.4148 & 459.2658 & 27.1253 \\ DF4 & 48.1478 & 30.0753 & 9.7598 & 17.4654 & 165.5802 & 23.3695 \\ DF5 & 29.4796 & 31.7592 & 8.8895 & 30.6544 & 399.0036 & 32.4890 \\ DF6 & 31.1548 & 29.2971 & 8.9536 & 24.8569 & 524.2016 & 21.0256 \\ DF7 & 43.4574 & 28.1490 & 9.2587 & 25.2584 & 378.0154 & 23.1016 \\ DF8 & 30.4765 & 29.0253 & 8.1258 & 28.5298 & 425.0455 & 27.4694 \\ DF9 & 30.4654 & 36.4695 & 8.5891 & 20.1489 & 484.0154 & 25.9726 \\ DF10 & 24.8989 & 24.6497 & 8.1856 & 89.2103 & 866.5962 & 97.6546 \\ DF11 & 21.4890 & 25.0245 & 9.9782 & 81.0365 & 890.4168 & 91.6469 \\ DF12 & 26.5982 & 21.4694 & 10.0159 & 49.2016 & 970.1460 & 47.4102 \\ DF13 & 19.0023 & 21.7592 & 7.9987 & 85.4160 & 1093.0001 & 98.7912 \\ DF14 & 18.8898 & 19.1654 & 12.0238 & 85.0489 & 908.4590 & 96.4694 \\ F5 & 132.0001 & 32.0795 & 13.0173 & 48.2203 & 513.4169 & 59.8591 \\ F6 & 63.8994 & 31.5911 & 13.5924 & 50.1605 & 545.2416 & 60.4991 \\ F7 & 54.6565 & 57.2259 & 12.3654 & 59.2056 & 571.1560 & 61.1697 \\ F8 & 32.7879 & 56.7411 & 13.2485 & 76.8569 & 1269.2036 & 86.7952 \\ F9 & 58.9891 & 39.2899 & 12.2498 & 52.5892 & 970.2596 & 63.7961 \\ F10 & 57.4590 & 29.0595 & 11.1475 & 49.0412 & 597.5269 & 52.5610 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The average running time (seconds) of the six algorithms under the S2 configuration. Figure 6: Average running time (s) obtained by comparing algorithms under the configuration of \(n_{t}=5\), \(\tau_{t}=10\). environment, thereby improving the convergence and diversity of the dynamic multi-objective algorithm, and at the same time improve the running speed of the algorithm. The above experimental results fully demonstrate that the algorithm significantly improves the performance of dynamic optimization. Compared with existing transfer learning-based algorithms, the proposed algorithms are tens or even hundreds of times faster at finding POS. Although the proposed TCD-DMOEA can generate a high-quality initial population, the reliability of the acquired individuals becomes very poor. When the environmental changes are more complex, the accuracy of the cluster-based difference strategy will decrease, and due to the added classifier, the computational complexity of the algorithm will increase. Therefore, in future research work, we will explore the following promising directions. First, it would be beneficial for our static evolution process to try to combine multiple response mechanisms to cope with environmental changes, rather than employing a single strategy. Second, we can try to use classifiers with lower complexity to speed up the optimization process.