Electric screw propeller vehicles represent an innovative solution for traversing difficult environments such as peat soil, particularly for fresh fruit bunch (FFB) transportation in the palm oil industry. However, the unique propulsion mechanism and demanding operational conditions impose significant structural challenges on the vehicle chassis, requiring a design that is both robust and lightweight to support electric vehicle efficiency. This study focuses on the design and optimization of a chassis for an electric screw-propelled vehicle for FFB transport operating on peat soil terrain. Advanced computational intelligence techniques, namely a Back Propagation Neural Network (BPNN) and a Genetic Algorithm (GA), are employed. The BPNN predicts key structural responses, including equivalent stress, fatigue life, safety factor, and weight, with high accuracy based on variations in material type and beam thickness. Furthermore, the GA utilizes these predictions to optimize the design. The optimized results show excellent agreement with finite element simulations, with deviations of only 3.47% in stress, 2.31% in fatigue life, 1.19% in safety factor, and 0.31% in weight, confirming the high predictive accuracy of the hybrid BPNN–GA model. The optimized chassis achieves a balanced trade-off between structural strength and light weight efficiency while remaining within allowable design limits. To the authors’ knowledge, this study represents the first application of a hybrid BPNN–GA approach for optimizing a screw-propeller vehicle chassis operating on peat soil terrain, offering a novel computational strategy for lightweight and reliable electric vehicle design in soft-terrain environments.