## 7 Conclusions  
Optimization of weight and cost is considered a crucial factor in designing high-speed trains. Advanced composite sandwich structures have been studied as a viable solution to achieve a lighter train floor in order to reduce the energy consumption of the vehicle. Although studies on optimizing weight and cost for high-speed train floors are still limited, it is evident that many researchers have implemented weight-saving techniques in the railcar industry through the use of composite structures. For instance, a weight reduction of 40% was achieved in [20], while a reduction of 29% was achieved in [16]. These results highlight the strong motivation to discover innovative design techniques in this field. The purpose of our study was to develop a multi-objective weight and cost optimization method for high-speed train floors. The sandwich floor structure to be optimized consists of laminated face sheets and a hexagonal honeycomb core. During the optimization different variations of Fiber Metal Laminates (FMLs) as face sheet constructions with aluminum honeycomb cores were examined. The aim of the structural optimization was to construct the optimal sandwich structure in order to provide the minimal weight and minimal cost of the structure. In the optimization, the elaborated weight and cost objective functions, as well as five design constraints, were applied. The Neighborhood Cultivation Genetic (NCGA) algorithm was used to solve the optimization task. Using the NCGA optimization algorithm resulted in obtaining approximately 16,600 feasible designs that satisfied the design constraints; of these, 13 were characterized as Pareto optimal solutions. A comprehensive analysis of the Pareto optimal solutions was conducted to investigate the correlation between weight and cost objectives. The main findings of this study can be summarized as follows:  
* The analysis showed that, at the expense of cost, using CFRP as a face sheet provided a maximum weight reduction of about 62% in this study, compared to the aluminum face sheet as a basic structure. * Furthermore, a knee point was identified that strikes a balance between weight and cost, resulting in a weight reduction of approximately 32% by using FML materials. This provides valuable insights for designers who must consider both weight savings and cost-effectiveness when designing high-speed train floors. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Design Points**} & \multicolumn{4}{c}{**Maximal Deflection**} & \multirow{2}{*}{**Remarks**} \\  & & **(mm)** & & & **Maximal Stress in the Face Sheet (MPa)** & \\ \cline{2-6}  & **Optimization** & **FEM** & **Result** & **Difference (\%)** & **Speculation Result** & **Difference (\%)** & \\ \hline Minimal weight & 0.9957 & 1.004 & 0.83 & 13.655 & 13.11 & 3.99 & single weight \\ Minimal cost & 1 & 1.062 & 6.20 & 8.695 & 9.49 & 9.14 & optimization \\ Knee point & 0.9999 & 0.883 & 11.69 & 11.3333 & 10.26 & 9.47 & and cost \\  & & & & & & & optimization \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparisons of optimization and FE solutions. * The present study conducted an optimization process and subsequently validated its outcomes through Finite Element (FE) simulations. The results of the analysis indicated that there was an acceptable level of agreement between the optimization process and the FE simulations with a maximum difference value of about 11%. This provides a reasonable level of confidence in the obtained results. To conclude, the proposed multi-objective optimization method utilizing the TCGA algorithm with diverse constituent materials and structural components presents a novel contribution in the context of weight reduction and cost-effectiveness, which has not been previously explored. The results of this research suggested that sandwich configurations using composite materials are a promising approach to realize lightweight and cost-effective train floors.