## 6 Related Works  
The basic idea of a DMOEA is predicting the change patterns of DMOP environments (\(PS\) and \(PF\)) and generating new individuals for population re-initialization to adapt to the new environment when it is changed. Therefore, there are several related works aiming at designing accurate prediction methods for DMOEAs.  
[PERSON] et al. [20] first divided the population into several sub-populations, and calculated the accelerations of the center points for these sub-populations. Then, they calculated the velocity for each sub-population based on its center point's acceleration, and re-initialized a population by adding the velocity and each individual for every sub-population. [PERSON] et al. [21] first detected the intensity of the environmental change based on the difference between the objective function values of a small proportion of the population in two consecutive environments. Then, based on the detection result, they predicted new individuals by a multi-objective particle swarm optimization algorithm [22] with adapted particle velocity updates and the strength Pareto evolutionary algorithm [23]. Different from most works that employed the first-order difference strategy, where the trajectory of moving solutions is decreased by the centroid of \(PS\), [PERSON] et al. [24] proposed to use the second-order difference method that considered both \(PF\) and \(PS\). The new \(PS\) center is decided by the joint trajectories of \(PF\) and \(PS\) by mapping them into a new two-dimensional space.  
To overcome the limitation of most DMOEAs that only rely on predictions from adjacent environments, resulting in a new population adapting to the new environment not well, [PERSON] et al. [25] used the Fuzzy C-Means clustering algorithm to cluster all historical PSs, and then divided the clusters into high-quality and low-quality sets based on their center points. With the cluster result, a Support Vector Machine (SVM) classifier was trained to predict whether a new solution is high quality. The re-initialized population consists of randomly generated individuals that are predicted to be high quality by the SVM classifier and Gaussian-mutated initial individuals. [PERSON] et al. [26] employed correlation alignment and a probabilistic annotation classifier to get high-quality solutions from the current population and randomly generated individuals in the new environment. Based on the dynamic change pattern of elite individuals, which is learned by correlation analysis and a denoising autoencoder, this work identified the parents of current elite solutions, and then used a denoising autoencoder to transfer the change pattern to new environments. This step predicted a set of individuals based on current elitist solutions and the last \(PS\). Individuals predicted by these two steps form the re-initialized population for the new environment.  
In this paper, to make better predictions by capturing different moving styles of \(PF\) for the DMOP, we try to establish a relation model of different points on \(PF\). This is the first attempt to introduce the inter-correlations between the movement of different points into the DMOEA, to our best knowledge.