# Multi-Objective Optimization of Square Corrugation Multilayer Nested Structures
## 1 Introduction  
Rail vehicle safety is a continuous and crucial problem that concerns people with the development of railway technology. For the protection of rail vehicle safety, scientists currently focus on two main aspects, namely active safety protection and passive safety protection, to conduct research [1; 2; 3]. For the aspect of active safety protection, track life prediction and fault diagnosis can effectively and timely maintain railways, thereby preventing railway accidents [4; 5]. In the study of [PERSON] et al., the prediction model was established by Artificial Neural Networks (ANNs) to estimate the buckling temperature of complex tracks [6]. A risk analysis method based on fault tree analysis (FTA) was developed by [PERSON] et al., and this model provides an idea for predicting the risk of railway derailment [7]. In addition, measures such as brake control and warning systems can also improve the active safety protection performance of trains [8; 9; 10]. However, it is necessary to investigate passive safety protection, which can mitigate collision force and damage suffered during secondary accidents. For the aspect of passive safety protection, installing guardrails [11], anti-climbing devices [12], couplers [13], and energy-absorbing devices [14; 15] can effectively enhancethe crashworthiness of the train. Thin-walled energy absorption tubes as energy-absorbing devices are extensively applied to the transportation industry due to extraordinary crashworthiness characteristics [16; 17; 18]. The thin-walled tubes which are equipped in the front impact zone will first suffer crushing; the reasonable structural design of thin-walled structures can make the crushing process more stable and controllable, thereby protecting the safety of passengers in the survival space. The corrugation configuration was proposed, and researchers confirmed that corrugation tubes have good potential for crashworthiness [19]. Experimental studies have shown that the maximum plastic moment at the corrugation groove can first guide the occurrence of collapse to diminish the peak force [20; 21], and corrugation tubes with appropriate amplitude possess ordered progressive mode which contributes to more uniform load fluctuations [22]. Adding rib plates into thin-walled tubes can generate a stable folding pattern and increase the number of corner elements [23; 24]. [PERSON] et al. found that the interaction between the foam blocks and the reinforced rib can ameliorate the crash resistance performance [25]. In addition, rib plates can affect significantly the energy absorption capacity and deformation mode [23; 26]. Another method is to set up multi-layer structures or subunits within thin-walled tubes [27; 28]. The deformation mode usually develops toward a better mode due to the mutual constraints between the inner and outer layers [29; 30]. [PERSON] et al. found that the number of nested layers should not be excessive; otherwise, the comprehensive crushing performance will decrease [31]. [PERSON] et al. indicated that the deformation mode is more controllable due to the resistance effect of the outer tube [32]. The research of [PERSON] et al. showed that the increase in ripple and number of layers will form a more stable and plastic hinge [33]. In addition, optimizing structural parameters based on structural design to obtain the most reasonable parameter scheme is crucial for improving vehicle crashworthiness. For the aspect of structural parameter optimization, non-dominated sorting genetic algorithm II (NSGA-II) became one of the frequently used optimization methods in various fields due to its convenience and adaptability [21; 33; 34]. However, as the number of optimization objectives increases, low-dimensional multi-objective optimization algorithms similar to NSGA-II will lose effectiveness, and the NSGA-III algorithm used to solve high-dimensional problems can be applied [3].