## 4 Conclusions  
The design and multi-objective optimization of four types of auxetic sandwich panels (ASPs), including re-entrant honeycomb (REH), double-arrow honeycomb (DAH), star honeycomb (SH), and tetra-chiral honeycomb (CH), under air-blast loading were successfully conducted using a machine learning approach. The blastworthiness performance of ASPs was evaluated using the finite element method. The optimization objectives were to reduce permanent displacement (\(\delta_{p}\)) and increase specific energy absorption (SEA). The nondominated sorting genetic algorithm II (NSGA-II) was employed for optimization, utilizing an artificial neural network (ANN) metamodel. The results of the optimization process are summarized as follows:  
* The ANN metamodel that was formed was proven to be accurate in predicting the blastworthiness performance of ASPs. The optimization process using NSGA-II produces optimal designs efficiently. The optimization results shows that the permanent displacement conflicts with the SEA. * Global sensitivity analysis using the SHapley Additive exPlanations (SHAP) method indicates that cell thickness in ASPs is the primary factor influencing blastworthiness performance, significantly affecting stiffness and plastic-bending moments within auxetic cells. Meanwhile, the corner angle and node radius in the CH model are identified as the least influential variables. * The configuration of auxetic structures enables effective energy absorption, enhancing the blast resistance of sandwich structures, as the material flows toward the impact zone. The occurrence of global negative Poisson's ratio (NPR) behavior in ASPs under air-blast loading is influenced by rapid and high-velocity blast impulses, leading to localized unit cell collapse near the blast source. Generally, the REH and CH models exhibit more dominant NPR behavior at lower relative densities. Figure 23: Comparison of (**a**) energy absorption (EA) and (**b**) SEA for each part of the AFV subsystem for different structure types. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Single Plate (20 mm)** & **Optimized AFSP** & **Optimized ASP DAH** \\ \hline Max. displ. (mm) & 156.56 & 110.40 & 67.34 (56.99\% */39.00\% **) \\ \hline SEA (J/g) & 0.60 & 1.76 & 2.61 (335.00\% */48.30\% **) \\ \hline Max. acc. (1000G) & 118.01 & 99.20 & 55.99 (52.55\% */43.56\% **) \\ \hline \hline \end{tabular}  
* Improvement of optimized ASP DAH with respect to single plate. ** Improvement of optimized ASP DAH with respect to optimized AFSP.  
\end{table} 
Table 9: Blastworthiness parameters of the AFV subsystem without and with various types of protective structures. * Multi-objective optimization substantially enhances blastworthiness performance. Compared to baseline models, optimization achieves SEA improvements ranging from 26.21% to 83.68% for equivalent permanent displacements and reduces permanent displacement by 12.55% to 35.60% for equivalent SEA. The balanced REH and DAH models outperform baseline models in SEA only by 98.06% and 47.84%, respectively, while SH and CH models exhibit improvements in both permanent displacement (4.63-11.86%) and SEA (13.14-49.37%). Furthermore, the optimized ASP outperforms the optimized aluminum foam sandwich panel (AFSP) in SEA by 133.33-156.86%. However, only optimized DAH and SH produce better permanent displacement reduction by 36.71% and 6.49%, respectively. Among the four auxetic configurations, the DAH structure offers the best blastworthiness performance. * ASPs demonstrate promising results in armored fighting vehicle (AFV) applications, meeting structural integrity requirements effectively. In dynamic response scenarios, optimized ASP DAH significantly reduce maximum displacement and acceleration of occupant floors by 39.00-56.99% and 43.56-52.55%, respectively, compared to other structures. The AFV subsystem incorporating optimized ASP DAH achieves a 48.30% increase in SEA over optimized AFSP and a remarkable 335.00% increase over single plates.