Many dynamic multi-objective optimization problems have been widely developed to track the changing optima quickly and effectively in dynamic environments. Prediction-based methods can be used to predict future changes by learning past experience. This paper employed a new prediction strategy combining Takagi-Sugeno fuzzy nonlinear regression prediction and multi-step prediction named TSMP to estimate the new initial Pareto solutions whenever the environment changes. In TSMP, when environmental changes occur, the next initial center of Pareto solutions (PS) is predicted by a Takagi-Sugeno fuzzy nonlinear regression prediction model and then one trail population is generated by combining the predicted center and an approximate manifold of PS. Moreover, the other trail population is generated by a linear multi-step prediction model. Furthermore, the next initial PS is reinitialized by a random hybridization of these two trail populations. The proposed TSMP strategy is systematically compared with re-initialization strategy (RIS), feed-forward prediction strategy (FPS) and population prediction strategy (FPS) under different multi-objective optimizers on benchmark test problems with different features. Experimental results and performance comparisons with other state-of-the-art algorithms indicate that TSMP is effective and promising for solving dynamic multi-objective optimization problems.

已经广泛开发了许多动态多目标优化问题，以在动态环境中快速有效地跟踪变化的最佳情况。基于预测的方法可以通过学习过去的经验来预测未来的变化。本文采用了一种新的预测策略，将Takagi-Sugeno模糊非线性回归预测和名为TSMP的多步预测相结合，以在环境变化时估计新的初始Pareto解。在TSMP中，当环境发生变化时，通过Takagi-Sugeno模糊非线性回归预测模型预测Pareto解（PS）的下一个初始中心，然后通过组合预测的中心和PS的近似流形生成一个尾迹种群。此外，其他线索人口是通过线性多步预测模型生成的。此外，接下来的初始PS通过这两个尾迹种群的随机杂交而重新初始化。针对不同特征的基准测试问题，在不同的多目标优化器下，将拟议的TSMP策略与重新初始化策略（RIS），前馈预测策略（FPS）和种群预测策略（FPS）进行了比较。实验结果和与其他最新算法的性能比较表明，TSMP对于解决动态多目标优化问题是有效且有前途的。在具有不同功能的基准测试问题上，不同的多目标优化程序下的前馈预测策略（FPS）和总体预测策略（FPS）。实验结果和与其他最新算法的性能比较表明，TSMP对于解决动态多目标优化问题是有效且有前途的。在具有不同功能的基准测试问题下，不同的多目标优化程序下的前馈预测策略（FPS）和总体预测策略（FPS）。实验结果和与其他最新算法的性能比较表明，TSMP对于解决动态多目标优化问题是有效且有前途的。