<p>The detonation of landmines poses a significant threat to armored vehicles and their crews on battlefield. To enhance the resistance of vehicles to shallow-buried explosives, sandwich structures are commonly employed. This paper employs an uncertain design approach with the optimization objective of rear panel displacement to conduct reliability optimization of sandwich anti-explosion structures and perform parameter sensitivity analysis. In order to improve the computational efficiency and the robustness of the algorithm, the single-objective optimization problem of minimizing the weight of the structure under the reliability constraints is transformed into a bi-objective optimization problem in terms of the structural areal density and the probability of failure, and is solved using the NSGA-II optimization algorithm. In local sensitivity analysis, the thickness of the front and rear panels, as well as the core thickness, exhibits a substantial influence on rear panel displacement. Regarding global reliability sensitivity analysis, the displacement of the front and rear panels exerts a more significant impact on the failure probability of rear panel displacement. The reliability optimization method proposed in this paper holds considerable engineering significance for optimizing sandwich panels under explosive loads. This offers a valuable framework for researchers and engineers involved in the design of sandwich structures for efficient energy absorption in the context of shallow-buried landmine scenarios.</p>