A combined weighting-based multi-objective topology optimization framework: Methodology and application to a hovercraft gearbox

To address the limitations of single weighting schemes and static-dynamic performance trade-offs in gearbox topology optimization, this paper proposes a universal multi-objective framework integrating game-theory combined weighting (AHP-entropy method) and compromise programming. Applied to a hovercraft reducer housing, the method establishes a joint weight allocation model coupling compliance and the first four natural frequencies. Topology optimization via the SIMP variable density method and secondary CAD reconstruction demonstrate superior convergence robustness compared to single weighting strategies. The optimized housing achieves a 4.2% mass reduction and a 60.0% decrease in maximum stress, while raising the 4th-order natural frequency to successfully avoid the 200 Hz excitation band. This generalized methodology provides standard guidance for multi-performance collaborative optimization of transmission housings.