# Transfer Learning Based on Clustering Difference for Dynamic Multi-Objective Optimization
## 1 Introduction
Experimental results show that this method can accelerate population convergence and accurately track the optimal solution in the new environment. [PERSON] et al. [29] proposed a fast dynamic multi-objective evolutionary algorithm based on manifold learning. This method combines the memory mechanism with the learning characteristics of manifold transfer to predict the optimal individual in new instances in the process of evolution. The process is shown in Figure 1d. [PERSON] et al. [30] recently proposed the combination of PPS method and transfer learning to improve population prediction. [PERSON] et al. [31] proposed a method based on individual transfer learning to solve DMOPs. Unlike the existing method, this method uses a pre-search strategy to filter out some high-quality individuals with good diversity, avoiding negative migration caused by individual agglomeration. [PERSON] et al. [32] also applied transfer learning to solve DMOPs with a large amount of computing, and used alternative auxiliary evolution algorithms, especially MOEA/DEGO, as the baseline to evolve and optimize under limited functional assessment. In addition, transfer learning is used to map the previously archived training data to the current environment to quickly start the proxy model building process, so that the dynamic multi-objective evolutionary algorithm can better adapt to the new environment. Combining the above transfer learning strategies, the transfer learning strategy has good performance in solving dynamic multi-objective optimization test problems that contain periodic changes and have a large degree of change. However, the application of transfer learning to DMOP solving is still in its infancy. Multiple studies have shown that hybrid change response methods generally perform better than single methods because hybrid methods can handle more diverse dynamic features than single methods. This is demonstrated by the increasing use of mixed strategies in recent work [33]. However, the existing transfer learning methods often need a long training time, which is the main obstacle of some DMOPs. One of the reasons for the slow running speed is that the existing transfer learning methods often realize knowledge reuse by searching the potential space, which will require more parameter settings and consume more computing resources, resulting in a large amount of computing resources wasted on searching low-quality individuals, which greatly increases the possibility of negative transfer [34; 35]. If the knowledge possessed by these high-quality individuals can be transferred (from the perspective of convergence and diversity), then more effective and accurate prediction models can be built for the application of DMOPs in various real complex environments. At the same time, existing dynamic multi-objective optimization algorithms based on forecasting strategies usually use a single forecasting strategy. On the one hand, a single prediction strategy cannot quickly and effectively respond to complex environmental changes; on the other hand, the group diversity generated by a single prediction strategy is poor, and it cannot quickly and effectively track the Pareto front, resulting in the algorithm not being able to quickly converge. Based on the above analysis, in order to reduce the occurrence of negative transfer and improve the running speed, this paper proposes a new environment response mechanism that combines the cluster difference strategy and the transfer learning strategy. In this paper, the similarity between the source domain and the target domain is improved by adding a clustering difference strategy to predict individuals before transfer learning, thereby reducing the possibility of negative transfer. Then, the transfer learning method TadaBoost [36] is used to build the prediction model. A higher quality initial population is generated through this model, followed by subsequent multi-objective optimization.