Dynamic multi-objective optimization problems (DMOPs) are challenging as they require capturing the Pareto optimal front (POF) and Pareto optimal set (POS) during the optimization process. In recent years, transfer learning (TL) has emerged the empirical knowledge and is an effective approach to solve DMOPs. However, negative transfer can occur when the transfer method is not suitable for the transfer task. It may deviate the search path and seriously reduce the efficiency, so how to reduce the occurrence of negative transfer to save the running time of dynamic multi-objective evolutionary algorithm (DMOEA) is an important issue to be addressed. A division-selection transfer learning evolutionary algorithm for dynamic multi-objective optimization (DST-DMOEA) is designed towards this aim. Specifically, individuals with high Spearman correlation are relatively stable in different environments, selecting them to train the Support Vector Regression (SVR) model ensures a more accurate capture of solution features, predicting the objective values of historical solutions based on the model, and thus divide historical solutions into elite and non-elite solutions. Subsequently, for the elite solutions, individual TL that incorporates local information for optimization and transfer is used, while the non-elite solutions are handled with manifold TL method to obtain the overall data distribution and understand the internal structure. Then, merge the predicted individuals generated by two parts of TL will constitute as the initial population in the optimization process. Compared with other algorithms, the initial solution of DST-DMOEA is closer to the real POF, effectively reducing negative transfer. In addition, in 51 test instances, DST-DMOEA has shown superior performance in over 30 instances.

动态多目标优化问题 （DMOP） 具有挑战性，因为它们需要在优化过程中捕获帕累托最优前沿 （POF） 和帕累托最优集 （POS）。近年来，迁移学习 （TL） 已成为实证知识的兴起，是解决 DMOP 的有效方法。但是，当传输方法不适合传输任务时，可能会发生负传输。它可能偏离搜索路径，严重降低效率，因此如何减少负迁移的发生以节省动态多目标进化算法 （DMOEA） 的运行时间是一个亟待解决的重要问题。为此，设计了一种用于动态多目标优化的除法选择迁移学习进化算法 （DST-DMOEA）。具体来说，Spearman 相关性高的个体在不同环境中相对稳定，选择他们来训练支持向量回归 （SVR） 模型可以更准确地捕捉解特征，根据模型预测历史解的客观值，从而将历史解分为 elite 和非 elite 解。随后，对于精英解决方案，使用包含本地信息进行优化和传输的单个 TL，而非精英解决方案则使用多种 TL 方法处理，以获得整体数据分布并了解内部结构。然后，合并由 TL 的两个部分生成的预测个体将构成优化过程中的初始种群。与其他算法相比，DST-DMOEA 的初始解更接近真实 POF，有效减少了负转移。 此外，在 51 个测试实例中，DST-DMOEA 在 30 多个实例中表现出卓越的性能。