Meta-Initialized Hierarchical Surrogate Optimization for Computationally Efficient Topology Optimization

Abstract Topology optimization enables lightweight, high-stiffness designs, but practical deployment is limited by repeated finite element method (FEM) cost and sensitivity to numerical regularization such as density-filter radius tuning. We propose Meta-Initialized Hierarchical Surrogate Optimization (MH-SO), a compute-budgeted acceleration framework for task families across benchmark types, mesh resolutions, and volume fractions. MH-SO integrates first-order model-agnostic meta-learning (FO-MAML), hierarchical reinforcement learning (HRL) using proximal policy optimization (PPO) and asynchronous advantage actor-critic (A3C), an interface-aware update map, and a graph neural network (GNN) surrogate for rapid response evaluation. Periodic full-FEM guarding bounds surrogate drift, and all objectives are recomputed by full-FEM evaluation. On canonical two-dimensional (2D) linear-elastic compliance benchmarks, MH-SO improves normalized compliance over a soft-kill bi-directional evolutionary structural optimization (Soft-BESO) baseline by up to 3.04% and reduces wall-clock time by 3.4 to 3.5 times under compute parity with matched stopping criteria for all compared methods. Transferring the same pipeline to linearized eigenvalue buckling load factor (BLF) maximization achieves a 12.91% BLF increase and up to 7.2 times wall-clock speedup relative to a solid isotropic material with penalization (SIMP) baseline. Held-out mean absolute percentage error (MAPE) is 1.9% to 2.6% for compliance surrogates and 4.38% to 4.71% for the buckling surrogate. MH-SO is a complementary acceleration layer for early-stage screening, not a replacement for full-FEM-based analysis workflows.