## 1 Introduction  
Dynamic Multi-objective Optimization Problems (DMOPs) have attracted the attention of scientists and developers for decades due to their common appearances in various fields, e.g., logistics [1], disaster management [2], nuclear physics [3], and chemical reaction equipment management [4]. Solving DMOPs is challenging work due to the uncertain change of the actual environmental chaos. The Dynamic Multi-Objective Evolutionary Algorithm (DMOEA) is one of the most efficient ways to overcome this challenge. A DMOEA employs a global search strategy of an evolutionary algorithm (EA) that is inspired by a natural or social law to solve DMOP instances (multi-objective optimization problems) in every steady environmental state (i.e., static multi-objective problems), and tunes searching directions to adapt to changed environments by some reaction/prediction approaches. It is challenging to design a DMOEA for solving DMOPs. This is mainly because the real world can bring rapid changes to DMOPs, which requires the DMOEA to not only capture the change fast and accurately but also respond to the change in a reasonable way [5]. Therefore, several works have studied responsive approaches for DMOEA to upgrade the search area (the population) based on the predicted movement of the optimal solution set (PS) or the Pareto optimal front (PF) when the environment (the current DMOP instance) is changed. But there are still some issues that existing related works have ignored or not addressed. First, the majority of DMOEAs assume the PS/PF is moving linearly, which falls short of reality. Second, most DMOEAs predict PS/PF movements by only mining the relationship for every single independent variable. These methods infer the new value of a variable from its historical values, and thus do not consider correlations between different variables, even though the phenomenon is common in the real world. Last but not least, to our best knowledge, no existing DMOEA considers the moving interconnectedness of different solutions of PS. Due to the above issues, the current related works can result in inaccurate predicted results, which may lead to bad population updates for the DMOP and degrade the performance of the solution solving. To overcome the above issues, in this paper, we design a prediction approach based on linear regression (LR) technology to capture correlations between variables and between optimal solutions to accurately learn the movement pattern of PS/PF. To be specific, for the DMOP, by using historical values of all variables jointly, we establish an LR model where the variables in the current environment are the regressand and the variables in the last environment are the regressors. With the LR-based prediction model, we can calculate the variable values in the next environment by the current ones and update the current population based on the predicted variable values to adapt to the new environment. In brief, the contributions of this paper include the following three aspects:  
* We propose a PS/PF movement prediction model based on LR to learn correlations between variables and between optimal solutions, which predicts key points of PS in the new environment based on ones of the current PS. * We design a DMOEA based on the above LR-based prediction model, which updates the population based on the predicted key points of PS when the environment is changed and employs the Non-dominated Sorting Genetic Algorithm II (NSGA-II) to evolve the population when the environment is stable. * We conduct experiments based on CEC 2018 benchmark DMOPs. The results show that our DMOEA has the best overall performance in solving DMOP, compared with six other up-to-date DMOEAs. The following contents are organized as follows. The second section illustrates the terminologies that are related to the DMOP and helpful for understanding this paper. The third section presents our proposed DMOEA based on the LR-based prediction model.