Enhanced data-driven topology design with multilevelmesh and correlation-based mutation for stress-related multi-objective optimization

Abstract Topology optimization (TO) serves as a widely applied structural design approach to tackle various engineering problems. Nevertheless, sensitivity-based TO methods usually struggle with solving strongly nonlinear optimization problems. By leveraging high capacity of deep generative model, which is an influential machine learning technique, the sensitivity-free data-driven topology design (DDTD) methodology is regarded as an effective means of overcoming these issues. The DDTD methodology depends on initial dataset with a certain regularity, making its results highly sensitive to initial dataset quality. This limits its effectiveness and generalizability, especially for optimization problems without priori information. In this research, we proposed a multi-level mesh DDTD-based method with correlation-based mutation module to escape from the limitation of the quality of the initial dataset on the results and enhance computational efficiency. The core is to employ a correlation-based mutation module to assign new geometric features with physical meaning to the generated data, while utilizing a multi-level mesh strategy to progressively enhance the refinement of the structural representation, thus avoiding the maintenance of a high degree-of-freedom (DOF) representation throughout the iterative process. The proposed multi-level mesh DDTD-based method can be driven by a low-quality initial dataset without the need for time-consuming construction of a specific dataset, thus significantly increasing generality and reducing application difficulty, while further lowering computational cost of DDTD methodology. Various comparison experiments with the traditional sensitivity-based TO methods on stress-related strongly nonlinear problems demonstrate the generality and effectiveness of the proposed method.