Two stage multiobjective topology optimization method via SwinUnet with enhanced generalization

Topology optimization is a critical tool for modern structural design, yet existing methods often prioritize single objectives (e.g., compliance minimization) and suffer from prohibitive computational costs, especially in multi-objective scenarios. To address these limitations, this paper introduces a novel two-stage multi-objective topology optimization (MOTO) method that uniquely integrates data-driven learning with physics-informed refinement, and both stages are implemented within nearly identical network frameworks, ensuring simplicity and consistency in execution. Firstly, a MOTO mathematical model based on the constraint programming method that considers competing objectives of compliance, stress distribution, and material usage was constructed. Secondly, a novel neural network that incorporates shifted windows attention mechanism and lightweight modules was developed to enhance feature extraction while maintaining computational efficiency. Finally, the proposed model was trained in two stages: In Stage-1, utilizing adaptive input tensors, the network predicts near-optimal geometries across variable design domains (including rectangular and L-shaped configurations) and diverse boundary conditions in real time, requiring only 1,650 samples per condition. In Stage-2, the near-optimal structures from Stage-1 were physically optimized to achieve optimal performance. Experimental results demonstrate that the method's capability to generate high-accuracy, computationally efficient solutions with robust generalization capabilities. It effectively tackles challenges associated with multi-scale design domains and non-convex geometries, various and even untrained boundary conditions while significantly reducing data dependency, a critical advancement for data-driven topology optimization. The novel approach offers new insights for multi-objective structural design and promotes advancements in structural design practices.