## 1 Introduction  
Weight reduction of rail vehicles has gained considerable importance with the development of rail transportation [1; 2]. In order to meet the basic requirements of rail vehicles while reducing their weight, producing innovative panel structures has gained considerable importance [3; 4]. In recent years, sandwich structures have played a significant role in innovative practical applications due to their low density and high structural performance. Research on the optimization of these sandwich structures for various industrial applications is receiving increasing attention [5; 6]. A sandwich composite structure (Figure 1) consists of two thin, highly rigid face sheets that are separated by a lightweight core. The core material usually has low mechanical properties, but its greater thickness results in high structural stiffness and strength [7; 8; 9]. A review of the literature has shown that research on sandwich structures has been approached from different perspectives. [PERSON] and [PERSON] studied the bending, buckling, and free vibration of sandwich structures using different analytical models [10]. [PERSON] et al. studied the crash behavior of sandwich structures consisting of aluminum honeycomb cores filled with expanded polypropylene foam (EPP) under both in-plane and out-of-plane compressive loads [11]. [PERSON] et al. investigated the optimization of the interface between the epoxy foam core and the Carbon Fiber-Reinforced Plastic (CFRP) face sheets in a sandwich structure to improve the compressive and impact properties of the final sandwich structure [12]. In another study, [PERSON] et al. achieved the optimization of the bottom panel of a heavy truck, which focused on a composite sandwich structure under distributed out-of-plane loads. Their results showed that replacing the face sheet of the sandwich structure with CFRP material resulted in a significant weight reduction [13]. [PERSON] et al. proposed a framework for the optimization of laminated sandwich panels by addressing a multi-objective optimization problem considering cost, dynamic behavior, and carrying load. The authors presented Pareto-optimal solutions and identified the design points that provide the best trade-off [14]. In the railway field, many investigations have been carried out from different points of view. [PERSON] and [PERSON] performed shear and bending tests on composite sandwich structures for rail sleeper applications. They concluded that the composite sandwich structures could potentially replace conventional railway sleepers [15]. In another study, [PERSON] et al. investigated the weight optimization of a car body for a transit train based on material selection and size optimization procedures for the components of the car body, such as the roof, side walls, and subframe. The study found that the use of sandwich structures resulted in a significant weight reduction of up to 29% [16]. [PERSON] et al. proposed a multiscale design approach for sandwich composite structures on rail vehicle roofs. Experimental, theoretical, and numerical analyses were used to optimize the structural design in terms of cost efficiency [17]. In another study, [PERSON] et al. used Glass Fiber-Reinforced Plastic (GFRP) sandwich composites to fabricate railcar ceiling panels and walls and demonstrated an overall weight reduction of 20% compared to conventional stainless steel ceiling panels and sidewalls [18]. [PERSON] et al. developed a lightweight construction approach to improve the sound insulation of floating floors in rail vehicles. The authors optimized several variables, reduced the mass by 15.2%, and significantly increased the sound insulation [19]. [PERSON] and [PERSON] proposed a multifunctional optimization for the body of high-speed trains. They achieved a weight reduction of up to 17% by using composite sandwic, while also meeting the thermal, fire protection, and acoustic requirements [20]. [PERSON] et al.