## 1 Introduction
This opposite deformation behavior of auxetic materials leads to enhanced mechanical properties, such as more resistance to indentation [20; 21], increased shear modulus [22; 23], improvement in fracture toughness [24; 25; 26], and high energy absorption [20; 27]. Auxetic materials also outperform conventional materials in other aspects, such as high energy harvesting efficiency for vortex-induced vibration problems [28] and improved acoustic performance [29]. Due to these superior properties, auxetic materials have found applications in diverse fields such as medicine, biomedicine, sports, and engineering (for more details, see reference [30]). Although auxetic materials have superior mechanical properties, the application of ASVs in ASVs remains relatively uncommon and under-researched. Several studies have investigated auxetic sandwich panels (ASPs) under air-blast loading. For instance, [PERSON] et al. [31] and [PERSON] et al. [32] studied the responses of ASVs and hexagonal HSPs to blast loading numerically and experimentally, respectively. Both studies demonstrated that ASVs exhibit higher blast resistance than conventional HSPs due to increased compressive stiffness as the impact zone of the ASP shrinks inward. [PERSON] et al. [33] examined the dynamic response of cylindrical ASVs, conventional HSPs, and AFSPs subjected to blast loading. The results showed that cylindrical ASVs outperformed both conventional HSPs and AFSPs across all design parameter combinations. [PERSON] et al. [34] conducted experiments on close-in blast loading on ASVs. The results showed that the introduction of the ASP effectively prevented damage to the concrete base under close-in blast loading. [PERSON] et al. [35; 36] conducted experimental studies on the blast response of ASVs with re-entrant and double-arrow structures as the core under paper tube-guided air-blast loading. The results showed that the double-arrow structure had 10.9-20.5% less permanent displacement than re-entrant structures. [PERSON] et al. [37] conducted blast experiments on 3D-printed auxetic honeycomb sandwich beams (AHSBs). The results showed that AHSBs possess better blast performance than regular honeycomb. Overall, most research on ASVs under blast loading indicates that the ASP offers superior blastworthiness compared to previous structures. The primary objective of blastworthiness performance is to protect occupants within a structure. One quantifiable metric is the displacement or acceleration experienced by occupants. Additionally, blastworthy structures must achieve sufficient lightweight construction to facilitate the mobility of ASVs. Given the complex and nonlinear relationships between the geometric parameters of auxetic structures and their blastworthiness performance, machine learning (ML) methods have emerged as valuable tools for modeling these intricate interactions. By utilizing surrogate models or metamodels, researchers can better predict outcomes based on various input variables. Furthermore, ML has been applied to predict specific properties of metamaterials, particularly auxetic structures, such as stiffness [38; 39], sound absorption [40], Poisson's ratio [39; 41; 42; 43], and energy absorption capacity [38; 44]. Accurately modeling these properties enhances the design and performance of the blastworthy structures. As previously mentioned, the objectives of minimizing structural displacement often conflicts with the effort of weight reduction. Multi-objective optimization has been demonstrated as effective in addressing this challenge. Numerous studies have focused on multi-objective optimization of blastworthiness performance; for instance, [PERSON] et al. [10] optimized the design of multi-V hulls for light AFVs using artificial neural networks (ANNs) and the nondominated sorting genetic algorithm II (NSGA-II). They optimized for lower tibia force and hull mass, achieving a 33-42% improvement in blastworthiness and a 43% reduction in mass compared to the baseline design. [PERSON] et al. [45] and [PERSON] et al.