Xiang Cheng, Chen Airong, Li Hua, Wang Dalei, Ge Baixue, Chang Haocheng
College of Civil Engineering, Fuzhou University, Fuzhou, 350116, China.
Department of Bridge Engineering, Tongji University, Shanghai, 200092, China.
Sci Rep. 2025 Mar 18;15(1):9350. doi: 10.1038/s41598-025-92793-0.
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.
拓扑优化是现代结构设计的关键工具，但现有方法往往优先考虑单一目标（例如，最小化柔度），并且存在计算成本过高的问题，尤其是在多目标场景中。为了解决这些局限性，本文介绍了一种新颖的两阶段多目标拓扑优化（MOTO）方法，该方法独特地将数据驱动学习与物理信息细化相结合，并且两个阶段都在几乎相同的网络框架内实现，确保了执行的简单性和一致性。首先，基于约束规划方法构建了一个考虑柔度、应力分布和材料使用等相互竞争目标的MOTO数学模型。其次，开发了一种结合移位窗口注意力机制和轻量级模块的新型神经网络，以在保持计算效率的同时增强特征提取。最后，所提出的模型分两个阶段进行训练：在第一阶段，利用自适应输入张量，网络实时预测跨可变设计域（包括矩形和L形配置）以及各种边界条件的近最优几何形状，每个条件仅需1650个样本。在第二阶段，对第一阶段的近最优结构进行物理优化以实现最优性能。实验结果表明，该方法能够生成具有强大泛化能力的高精度、计算高效的解决方案。它有效地应对了与多尺度设计域和非凸几何形状、各种甚至未训练的边界条件相关的挑战，同时显著降低了数据依赖性，这是数据驱动拓扑优化的一项关键进展。这种新颖的方法为多目标结构设计提供了新的见解，并推动了结构设计实践中的进步。
