The optimisation of electric vehicle battery boxes while preserving their structural performance presents a formidable challenge. Many studies typically involve fewer than 10 design variables in their optimisation processes, a deviation from the reality of battery box design scenarios. The present study, for the first time, attempts to use sensitivity analysis to screen the design variables and achieve an efficient optimisation design with a large number of original design variables. Specifically, the sensitivity analysis method was proposed to screen a certain number of optimisation variables, reducing the computational complexity while ensuring the efficiency of the optimisation process. A combination of the Generalised Regression Neural Network (GRNN) and the Non-Dominated Sorting Genetic Algorithm II (NSGA-II) was employed to construct surrogate models and solve the optimisation problem. The optimisation model integrates these techniques to balance structural performance and weight reduction. The optimisation results demonstrate a significant reduction in battery box weight while maintaining structural integrity. Therefore, the proposed approach in this study provides important insights for achieving high-efficiency multi-objective optimisation of battery box structures.