## 5 Energy Absorption Effect Optimization
### Parameter Optimization  
A multi-island genetic algorithm is employed to optimize the parameters affecting the specific energy absorption and the maximum initial peak force of the anti-climb energy-absorbing device. With the specific energy absorption \(SEA\) and the peak force \(F\) as the optimization objectives, the honeycomb aluminum yield strength \(c\), connecting diaphragm thickness \(t_{1}\), thin-walled outer tube thickness \(t_{2}\), and thin-walled inner tube thickness \(t_{3}\) are considered as design variables. The optimization problem regarding the anti-climb energy-absorbing device's influencing parameters is defined as follows:  
\[\left\{ \begin{array}{l}Maximize:SEA\\ Minimize:F\\ Subject:X^{L}\leq X\leq X^{M}\end{array} \right. \tag{10}\]  
In the formula, \(X=[c,t_{1},t_{2},t_{3}]\) represents the design variables of the optimization model (mm), \(X^{L}=[x_{1}^{l},x_{2}^{l},x_{3}^{l},x_{4}^{l}]\) represents the lower bounds, and \(X^{M}=[x_{1}^{m},x_{2}^{m},x_{3}^{m},x_{4}^{m}]\) represents the upper bounds for the four design variables. The constraint boundary conditions are \(t_{1}\in[2,6]\), \(t_{2}\in[2,6]\), \(t_{3}\in[2,5]\), \(c\in[90,110]\). The optimization results for the specific energy absorption and maximum peak force of the anti-climb energy-absorbing device, obtained using the multi-island genetic algorithm, are presented in Table 4. The predicted results from the surrogate model established by the response surface method are compared with the actual values in Table 5.  
From Table 4, it can be seen that the maximum relative errors between the predicted values and the actual values for the specific energy absorption and the maximum peak force of the anti-climb energy-absorbing device, as established by the response surface method, are 2.5% and 9.9%, respectively. These error values are both less than 10%, indicating that the established surrogate model meets the computational requirements and possesses a \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Parameter**} & \multicolumn{3}{c}{**Crashworthiness**} \\ \cline{2-7}  & \(c\) **(MPa)** & \(t_{1}\) **(mm)** & \(t_{2}\) **(mm)** & \(t_{3}\) **(mm)** & \(SEA\) (kJ/kg)** & \(F\) **(kN)** & \(Q\) **(kJ)** \\ \hline Initial parameter & 100 & 4 & 4 & 2 & 14.5 & 880 & 238 \\ Optimized result & 104 & 2.5 & 4.5 & 5 & 16.5 & 939 & 303 \\ Effect after optimization & / & & / & / & +13.8\% & 6.7\% & 27.3\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of optimization results. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Evaluation Index** & \(SEA\) & \(F\) & **Acceptance Level** \\ \hline _ARE_ & 0.058 & 0.038 & \textless{}0.2 \\ _MRE_ & 0.169 & 0.122 & \textless{}0.3 \\ _R_\({}^{2}\) & 0.923 & 0.977 & \textgreater{}0.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Error analysis of the response surface model. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Comparison** & \(c\) **(MPa)** & \(t_{1}\) **(mm)** & \(t_{2}\) **(mm)** & \(t_{3}\) **(mm)** & \(SEA\) (kJ/kg)** & \(F\) **(kN)** & \(RE\) **(SEA)** & \(RE\) **(F)** \\ \hline True value & 104 & 2.5 & 4.5 & 5 & 16.5 & 939 & 2.5\% \\ Predicted value & 104 & 2.5 & 4.5 & 5 & 16.9125 & 846 & 2.5\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Verification of prediction results. satisfactory predictive capability. Using the surrogate model in conjunction with a multi-island genetic algorithm to optimize the initial structure of the anti-climb energy-absorbing device, the optimized parameters obtained, such as the connecting diaphragm thickness, thin-walled outer tube thickness, thin-walled inner tube thickness, and the yield strength of the aluminum honeycomb, result in an energy absorption of 303 kJ and a maximum peak force of 939 kN. This represents an increase of 27.3% in energy absorption and 13.8% in specific energy absorption, with only a 6.7% increase in the maximum peak force, achieving the goal of absorbing more energy while keeping the initial peak force as low as possible.