Dynamic multiobjective optimization problems (DMOPs) usually involve multiple conflicting objectives that change over time. A good evolutionary algorithm should be able to quickly track the moving Pareto optimal front (POF) and Pareto optimal set (POS) over time. To solve DMOPs, a predictive method is proposed herein based on grey prediction model, which is composed of three essential ingredients. The first one is that the population is divided into multiple clusters, which can help the population to preserve diversity throughout the evolutionary process. The second one is that the individuals used to detect environmental changes are taken from different clusters, which in turn help the proposed algorithm to detect environmental changes more promptly and accurately. The third one is to build the grey prediction model by using the centroid point of each cluster when detecting the environmental change, and then generate the initial population. Empirical results show that the proposed algorithm can deal with dynamic environments and track the varying POS and POF effectively and efficiently, and achieve better performances on most test problems than several selected state-of-the-art algorithms.

动态多目标优化问题（DMOP）通常涉及随时间变化的多个冲突目标。一个好的进化算法应该能够随时间快速跟踪运动的帕累托最优前沿（POF）和帕累托最优集合（POS）。为了解决DMOP问题，本文提出了一种基于灰色预测模型的预测方法，该模型由三个基本要素组成。第一个是将种群分为多个集群，这可以帮助种群在整个进化过程中保持多样性。第二个是用于检测环境变化的个体来自不同的群集，这反过来又有助于所提出的算法更迅速，准确地检测环境变化。第三是在检测环境变化时利用每个簇的质心点建立灰色预测模型，然后生成初始种群。实验结果表明，与几种先进的算法相比，该算法能够有效应对动态环境，有效地跟踪变化的POS和POF，并且在大多数测试问题上具有更好的性能。