## 5 Conclusions  
1. This paper proposed to conduct optimization design for vehicle-side crash safety using the ARBF-MLPA method combined with NSGA-II optimization algorithm; compared to traditional static metamodels, this method improves the solution-finding efficiency significantly.
2. It analyzed and discussed the point-adding strategy of ARBF-MLPA method, model updating and optimizing process. Then, it validated the effectiveness and fast convergence speed of the algorithm using the mathematical examples of different optimal fronts edge.
3. It conducted optimization design for vehicle-side crash using ARBF-MLPA, selected peak collision force and the amount of chest intrusion as optimization targets, reduce peak collision force and the amount of chest intrusion while ensuring lightweight of vehicles. After 6 iterations solved the model convergence, results showed that, the model after optimization has higher accuracy than finite element solution and has better crashworthiness too, while also realizing the lightweight characteristic of the vehicles.
4. The ARBF-MLPA, combined with the NSGA-II optimization method described in this paper, achieved good effects in vehicle-side crashworthiness optimization analysis. In order to verify the universality of this method, it is necessary to apply this method widely to solution-finding methods of various multi-objective problems.  
Conceptualization: D.G. and B.Y.; Methodology, D.G.; Software, G.C.; Validation, B.Y., G.C. and Q.L.; Formal Analysis, Q.L.; Investigation, B.Y.; Resources, D.G.; Data Curation, B.Y.; Writing--Original Draft Preparation, G.C.; Writing--Review & Editing, B.Y.; Visualization, L.; Supervision, D.G.; Project Administration, D.G.; Funding Acquisition, D.G. All authors have read and agreed to the published version of the manuscript.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{1}{c}{**Parameters**} & **EFM** & **ARBF-MLPA** & **EFM after Optimization** & **Optimal Ratio** \\ \hline \multirow{6}{*}{Designed variables} & t\({}_{1}\) (mm) & 1.5 & 1.76 & 1.76 & \multirow{6}{*}{} \\  & t\({}_{2}\) (mm) & 1.2 & 0.93 & 0.93 & \\ \cline{1-1}  & t\({}_{3}\) (mm) & 1.5 & 1.12 & 1.12 & \\ \cline{1-1}  & t\({}_{4}\) (mm) & 0.75 & 0.86 & 0.86 & \\ \cline{1-1}  & t\({}_{5}\) (mm) & 1.5 & 1.20 & 1.20 & \\ \hline \multirow{6}{*}{Response value} & \(d\) (mm) & 161.45 & 154.48 & \multirow{6}{*}{} & 152.12 & \(-\)4.32\% \\  & Error & \(\backslash\) & & 1.53\% & \\ \cline{1-1}  & \(F\) (KN) & 161.50 & 158.10 & \multirow{6}{*}{} & 152.12 & \(-\)2.11\% \\ \cline{1-1}  & Error & \(\backslash\) & & 3.78\% & \\ \cline{1-1}  & \(m\) (Kg) & 11.67 & 10.03 & & 10.03 & \(-\)14.05\% \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparison of whole-vehicle crash worthiness before and after optimization.  
**Funding:** This work is supported by the research fund of National Natural Science Foundation of China (Grant Nos. 52175239) and by the Shanghai Automotive Industry Technology Development Foundation (Grant No.1744).  
**Data Availability Statement:** The data used to support the findings of this study are available from the corresponding author upon request.  
**Conflicts of Interest:** The authors declare that they have no conflict of interest.