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The lightweight design of electric heavy quadricycle (L7e) vehicles has contributed to energy savings and sustainable mobility. This study proposes an optimization methodology to design a monocoque sandwich structure under operating conditions for an L7e using a finite element model via HyperWorks. Woven fiberglass fabrics and high-density PVC foam are assigned as the face and core to construct the sandwich structure, respectively. Free-size optimization based on weight minimization is applied to obtain the suitable initial thickness of face and core structures in all components. Multi-objective size optimization is then performed by minimizing both mass and material cost to determine the optimal thickness of each layer. Finally, shuffle optimization is used to modify the stacking sequence for each component to maximize structural stiffness. The results indicate that the core thickness in the passenger compartment is sufficient to maintain stiffness while maintaining the structure's lightweight. However, shuffle optimization is insignificant for the current monocoque model, as the structural stiffness is only marginally improved after the process. Additionally, this study examines the optimized models for structural stiffness and discusses suitable procedures for designing a lightweight and safe electric vehicle. [ABSTRACT FROM AUTHOR]