## 2 Knowledge and Tools of Model Preparation
The parameters of BP and MOEA/D are shown in Tables 9 and 10, respectively. #### 5.2.2 Convergence Testing of Optimization Algorithms

To discuss the performance of MOEA/D algorithm, different population size numbers are selected to test ability under four test functions, and two multi-objective optimization algorithms, Multi-objective Grey Wolf Optimization (MOGWO) and Multi-objective Dragonfly Algorithm (MODA), are selected as the compared model. Table 11 shows the details of the four test functions. Through the comparison of different optimization methods, it is proved that the prediction ability of MOEA/D is better than that of other multi-objective algorithms. A total of 20 experiments are carried out in each case and the average value is obtained. The calculation results of each index are shown in Table 12. \begin{table}
\begin{tabular}{c c} \hline \hline
**Experimental Parameters** & **Value Setting** \\ \hline iterations & 100 \\ Population size & 100 \\ Optimizing parameter dimension & 4 \\ Neighbor size & 26 \\ Crossover rate & 2 \\ Simulated binary crossover parameter & 2 \\ Polynomial variation parameter & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Default settings of Multi-objective Evolutionary Algorithm based on Decomposition (MOEA/D). \begin{table}
\begin{tabular}{c c} \hline \hline
**Experimental Parameters** & **Value Setting** \\ \hline Training function & TRAINLM \\ Adapt learning function & LEARNGDM \\ Performance function & MSE \\ Number layers & 3 \\ Inputs layer nodes number (layer 1) & 4 \\ Hidden layer nodes number (layer 2) & 5 \\ Output layer nodes number (layer 3) & 1 \\ Activation function hidden layer & TANSIG \\ Activation function output layer & PURELIN \\ Epochs & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Default settings of Back Propagation (BP). We choose two performance indexes of optimization algorithm as the criteria to evaluate the performance of optimization algorithm, which are Inverted Generational Distance (IGD) index and Spread index. In addition, the running time of different algorithms is compared. In particular, IGD is an indicator of the convergence condition of the algorithm, and its result can be used to judge the robustness and stability of the algorithm. If the IGD value is smaller, the ability of the algorithm is better. In Pareto set, Spread is usually used to evaluate the distribution of solutions. If SP is equal to 0, all non-dominant solutions are equidistant. The final simulated results are shown in Table 12. Considering all the algorithms, when the population size is 100, 200, 300 and 500, respectively, the larger the population size has the better the convergence effect. For MOGWO, too large of a population leads to over fitting of data, which makes the algorithm worse. Compared with different algorithms, MOEA/D has the best performance for ZDT1, ZDT2, ZDT3 and ZDT4. The IDG of MOEA/D algorithm is far less than that of other algorithms, which shows the MOEA/D algorithm has the best convergence performance, and MODA is the second best optimal algorithm. The convergence effect of MOGWO algorithm is much worse than other algorithms. For Spread, MOEA/D has the best allocation performance. The elapsed time of MOEA/D algorithm is significantly lower than the other two algorithms, which shows that MOEA/D is undoubtedly the fastest and best algorithm in terms of working efficiency. ### Combination Mechanism of Combined Model

For the sake of verifying the effectiveness of the designed nonlinear combination mechanism MOEA/D-BP, a simple average strategy and a linear combination mechanism are selected as the comparison in this study. Among them, the simple average strategy computes the mean value of the prediction results of each model, while the linear combination mechanism uses the multi-objective algorithm MOEA/D as the weight determination method to get the final prediction results. The compared consequences between the developed model and the other two methods are represented in Table 13.