## 4 Experiment Environment  
For evaluating the effectiveness and efficiency of our proposed DMOEA, we conducted extensive experiments to compare the performance with six other DMOEAs on the CEC 2018 benchmark test suite [9]. The six benchmark DMOEAs are as follows:  
1. FL (Forward-Looking) [10] is one of the simplest and most widely used methods for the environmental response of DMOPs. FL assumes that \(PF\) moves with a uniform velocity and predicts that the new \(PF\) is moving from the current \(PF\) with the same step as the last movement (from the last \(PF\) to the current \(PF\)). For the \(PF\) center point and every dimension, the moving velocity is \(v_{k}^{(t)}=x_{k}^{(t)}-x_{k}^{(t-1)}\), and the new position of each \(PF\) point is \(x_{k}^{(t+1)}=x_{k}^{(t)}+v_{k}^{(t)}\). 2. FLV (Velocity Forward-Looking) assumes that \(PF\) moves with changeable velocity and the velocity is changed with a constant acceleration. Thus, the new position of a key point in a dimension is \(x_{k}^{(t+1)}=x_{k}^{(t)}+v_{k}^{(t)}+\frac{1}{2}\cdot(a_{k}^{(t)})^{2}\). \(v_{k}^{(t)}\) is the last moving velocity of the center point. \(a_{k}^{(t)}\) represents the last moving acceleration of the center point, which is calculated by \(a_{k}^{(t)}=v_{k}^{(t)}-v_{k}^{(t-1)}\). 3. KF (Kalman Filtering-based DMOEA) [11; 12] employs the Kalman filtering technology to model the movement of the \(PF\) center point. 4. SVR (Support Vector Regression-based DMOEA) [13; 14] learns a regression model by support vector regression for the \(PF\) center point in every dimension based on its historical locations, and predicts the new location by the learned regression model. 5. XGB (eXtreme Gradient Boosting-based DMOEA) [15] is similar to SVR except that the regression model is learned by XGB, which is a classical and widely used ensemble learning with boosting technologies. 6. RF (Random Forest Regression-based DMOEA) is similar to the above two methods except that the regression model is learned by RF, which is an ensemble learning exploiting the bagging technology. Due to our focus on the prediction method to adapt to the environmental changes for DMOPs, all of the above DMOEAs exploit NSGA-II as the evolutionary strategy when the environment is stable. The CEC 2018 benchmark test suite includes 14 DMOPs with varied _PS_ and _PF_ movement patterns. The details of these 14 DMOPs are shown in Tables 1-3. In our experiment, we set the environment change to severe by setting the frequency of change and the severity of change to 10 for each DMOP. The number of changes was 30. The number of variables was 10. All of these parameters of DMOPs were set referring to the report that proposes the CEC 2018 test suite [9]. The performance metrics used for evaluating DMOEAs include Mean Inverted Generational Distance (MIGD) [16; 17]. Mean Hypervolume Difference (MHVD) [18], and Mean Average Crowding Distance (MACD). MIGD is the average of Inverted Generational Distance (IGD) in all environment cases for solving DMOPs. The calculation of IGD is conducted first by uniformly sampling points from the ideal _PF_ (_PF_\({}^{*}\)). Then, for each point on the _PF_\({}^{*}\), it identifies the closest point on the solved _PF_ (obtained by the algorithm), sums all these minimum distances, and then computes their average. A smaller IGD value reflects better alignment between the algorithm's results and _PF_\({}^{*}\). In summary, MIGD can be calculated by Equations (18) and (19). \[IGD_{t} =\frac{\sum_{p\in PF_{t}^{*}}\min_{p\in PF_{t}}||p^{*}-p||}{|PF_{t }^{*}|} \tag{18}\] \[MIGD =\frac{1}{T}\cdot\sum_{t\leq T}IGD_{t} \tag{19}\]  
Due to the common unknown ideal _PF_ for real DMOPs, some works use MHVD as a quality metric to quantify the performance of DMOEAs. MHVD is the average value of HVD between _PF_\({}^{*}\) and solved _PF_ for all environments. HVD is the difference between the hypervolumes of _PF_\({}^{*}\) and the solved _PF_. The hypervolume is the Lebesgue measure of the volume dominated by a set of points with respect to a reference point.